JP2012073031A - Input physical quantity estimation method, estimation device and estimation program - Google Patents

Abstract

The input to the system can be estimated on the basis of the output from the system when both the input to the system and the output from the system are multivariable (multiple / multidimensional physical quantities). To do.
Processing for calculating a first approximation coefficient, processing for calculating an estimated input physical quantity, processing for determining the validity of the estimated input physical quantity, processing for determining the estimated input physical quantity, and calculating an estimated output physical quantity A process for calculating the residual, a process for comparing the residual with the increase / decrease table, a process for determining the next estimated input physical quantity component, and a process for performing the censoring determination.
[Selection] Figure 1

Description

  The present invention relates to an input physical quantity estimation method, an estimation device, and an estimation program. More specifically, the present invention relates to a technique for estimating an input to the system based on an output from the system caused by an input to the system.

  As a conventional technique for estimating the input to the system based on the output from the system resulting from the input to the system, for example, there is a method of estimating the displacement based on the acceleration of the measurement object (Patent Document 1). ). This displacement estimation method measures the acceleration of the measurement object, calculates the displacement equivalent parameter by integrating the measured acceleration twice, and the drift component included in the displacement equivalent parameter increases or decreases monotonously. The drift component included in the displacement equivalent parameter is estimated from the calculation result of the displacement equivalent parameter based on the calculation result, and the displacement signal of the measurement object is calculated by removing the drift component estimated from the displacement equivalent parameter. .

JP2003-130629

  However, in the displacement estimation method of Patent Document 1, when estimating the drift component included in the displacement equivalent parameter for estimating the displacement of the measurement object, it is assumed that the drift component monotonously increases or decreases. Specifically, focusing on the fact that the displacement signal obtained by integrating the acceleration signal twice increases or decreases almost monotonically from zero, the drift component is estimated by linear approximation. In a system where both input and output are one variable (in other words, a one-dimensional physical quantity) and a linear relationship is established between them, the input to the system can be estimated based on the output. The input to the system cannot be estimated when both the input and the output are multivariables (in other words, multi-dimensional and multi-dimensional physical quantities). For this reason, it is difficult to say that the versatility of the estimation method is high.

  Therefore, the present invention can estimate the input to the system based on the output from the system when both the input to the system and the output from the system are multivariable (multiple / multidimensional physical quantities). An object of the present invention is to provide an input physical quantity estimation method, an estimation device, and an estimation program.

In order to achieve this object, the input physical quantity estimation method according to claim 1 is the case where 16 output physical quantity types are output from the system due to the input to the system represented by the four input physical quantity components. When four input physical quantity components are estimated based on the 16 types of output physical quantity types, for each of the four input physical quantity components, four input physical quantity components V _VN (provided by subscript VN: Input physical quantity component identification number (integer from 1 to 4)) and 16 output physical quantity C _{S, EC by} output physical quantity type (subscript EC: identification number of output physical quantity type (integer from 1 to 16)) And the fourth approximation coefficient D _{m1, m2, m3, m4, EC} (where subscripts m1, m2, m3, m4: coefficient identification numbers ( A process of calculating an integer from 1 to 5)) The input physical quantity component was estimated target, first with fourth approximation coefficient _{D m1, m2, m3, m4} , EC and estimated input physical quantity component V _{E, VN} and from equation 2-1 to equation 2-3 sequentially a first approximation coefficient calculation processing to calculate the approximate coefficients a _{m1, EC,} 16 pieces by substituting a first approximation coefficient a _{m1, EC} and output physical quantity C _M obtained from the _{system, EC} in equation 2-4 process for the selection and processing of calculating the estimated input physical quantity V _{E, 1, EC} four each per output physical quantity type, one for each output physical quantity type four by the estimated input physical quantity V _{E, 1, EC} Then, the average V _{E, av} of the estimated input physical quantity selected for each output physical quantity type is calculated, and the average V _{E, av} is used as the estimation input physical quantity V _{E, VN} for the input physical quantity component to be estimated. calculating a process, a first approximation coefficient a _m1 in equation _{3, EC} and estimated input physical quantity average V _E, by substituting _av estimated output physical quantity C _E, the _EC Comprising: a process that, the estimated output physical quantity C _E in Equation _{4, EC} and obtained from the system output physical quantity C _M, the residual C _R by substituting the _EC, and a process of calculating the _EC, 16 pieces of outputs When a predetermined number of output physical quantity types among physical quantity types has an absolute value of the residual CR _{, EC} equal to or less than a predetermined censoring determination threshold value, and the end condition is not satisfied. The input physical quantity component to be estimated is newly determined and the process returns to the first approximation coefficient calculation process. When the end condition is satisfied, the estimation process is terminated.
(Equation 1-1)
C _{S, EC} = A ′ _{1, EC} · (V ₁ ) ⁴ + A ′ _{2, EC} · (V ₁ ) ³ + A ′ _{3, EC} · (V ₁ ) ² + A ′ _{4, EC} · (V ₁ )
+ A ' _{5, EC}
(Equation 1-2)
A ′ _{m1, EC} = B ′ _{m1,1, EC} · (V ₂ ) ⁴ + B ′ _{m1,2, EC} · (V ₂ ) ³ + B ′ _{m1,3, EC} · (V ₂ ) ²
+ B ' _{m1,4, EC}・ (V ₂ ) + B' _{m1,5, EC}
(Equation 1-3)
B ′ _{m1, m2, EC} = C ′ _{m1, m2,1, EC} · (V ₃ ) ⁴ + C ′ _{m1, m2,2, EC} · (V ₃ ) ³
_{+ C 'm1, m2,3, EC} · (V 3) 2 + C' m1, m2,4, EC · (V 3) + C 'm1, m2,5, EC
(Equation 1-4)
C ′ _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V ₄ ) ⁴ + D _{m1, m2, m3,2, EC} · (V ₄ ) ³
+ D _{m1, m2, m3,3, EC}・ (V ₄ ) ² + D _{m1, m2, m3,4, EC}・ (V ₄ )
+ D _{m1, m2, m3,5, EC}
(Equation 2-1)
C _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V _{E, 4} ) ⁴ + D _{m1, m2, m3,2, EC} · (V _{E, 4} ) ³
+ D _{m1, m2, m3,3, EC}・ (V _{E, 4} ) ² + D _{m1, m2, m3,4, EC}・ (V _{E, 4} )
+ D _{m1, m2, m3,5, EC}
(Equation 2-2)
B _{m1, m2, EC} = C _{m1, m2,1, EC} · (V _{E, 3} ) ⁴ + C _{m1, m2,2, EC} · (V _{E, 3} ) ³
+ C _{m1, m2,3, EC}・ (V _{E, 3} ) ² + C _{m1, m2,4, EC}・ (V _{E, 3} ) + C _{m1, m2,5, EC}
(Equation 2-3)
A _{m1, EC} = B _{m1,1, EC} · (V _{E, 2} ) ⁴ + B _{m1,2, EC} · (V _{E, 2} ) ³ + B _{m1,3, EC} · (V _{E, 2} ) ²
+ B _{m1,4, EC}・ (V _{E, 2} ) + B _{m1,5, EC}
(Equation 2-4)
0 = A _{1, EC}・ (V _{E, 1, EC} ) ⁴ + A _{2, EC}・ (V _{E, 1, EC} ) ³ + A _{3, EC}・ (V _{E, 1, EC} ) ²
+ A _{4, EC}・ (V _{E, 1, EC} ) + A _{5, EC} −CM _{, EC}
(Equation 3)
C _{E, EC} = A _{1, EC} · (V _{E, av} ) ⁴ + A _{2, EC} · (V _{E, av} ) ³ + A _{3, EC} · (V _{E, av} ) ²
+ A _{4, EC}・ (V _{E, av} ) + A _{5, EC}
(Equation 4)
C _{R, EC} = C _{M, EC} −C _{E, EC}

The input physical quantity estimation apparatus according to claim 2 is a memory in which data of 16 types of output physical quantities output from the system due to inputs to the system represented by four input physical quantity components are stored. Each of the four input physical quantity components, in order to estimate the four input physical quantity components based on the 16 output physical quantity types, Input physical quantity V _{VN for} each of four input physical quantity components acquired as a sample in advance (subscript VN: input physical quantity component identification number (integer of 1 to 4)) and 16 output physical quantities for each type of output physical quantity C _S, The fourth approximation coefficient D _{m1, m2} using the combination data with _EC (subscript EC: identification number of output physical quantity type (integer number from 1 to 16)) and Formula 1-1 to Formula 1-4 in order _{. m3, m4, EC} (was And, the subscript m1, m2, m3, m4: means for calculating an identification number of the coefficients (each an integer from 1 to 5)), the input physical quantity component was estimated target fourth approximation coefficient D _{m1, m @ 2, m3,} First approximation coefficient calculation means for calculating the first approximation coefficient A _{m1, EC} using _{m4, EC} and the estimated input physical quantity component V _{E, VN and} Expressions 2-1 to 2-3 in order; Substituting the first approximation coefficient A _{m1, EC} and the output physical quantity C _{M, EC} obtained from the system into 4 gives four estimated input physical quantities V _{E, 1, EC} for every 16 output physical quantity types. Means for calculating, means for selecting one for each output physical quantity type from four estimated input physical quantities V _{E, 1, EC} , and average V _E, for the estimated input physical quantity selected for each output physical quantity type means for calculating _{av and} setting the average V _{E, av} as an estimated input physical quantity V _{E, VN} for the input physical quantity component; Means for calculating the estimated output physical quantity C _{E, EC} by substituting the approximation coefficient A _{m1, EC} and the average V _{E, av} of the estimated input physical quantity, and the estimated output physical quantity C _{E, EC} and the above-mentioned system obtained from Equation 4 output physical quantity C _M, by substituting _EC residual C _R, and means for calculating the _EC, 16 pieces of the residual C _R at the output a physical quantity different predetermined number of output physical quantity _type, absolute _EC The end condition is that the magnitude of the value is equal to or less than a predetermined cutoff determination threshold value. If the end condition is not satisfied, a new input physical quantity component to be estimated is newly determined and the first approximation coefficient calculation process is performed. Returning, when the termination condition is satisfied, the estimation process is terminated.

According to a third aspect of the present invention, there is provided an input physical quantity estimation program in which data of 16 types of output physical quantities output from the system due to inputs to the system represented by four input physical quantity components is stored. When estimating four input physical quantity components based on 16 types of output physical quantity, a computer connected to a storage device having a storage unit or storing the data is sampled in advance for each of the four input physical quantity components. The input physical quantity V _{VN for} each of the four input physical quantity components (subscript VN: input physical quantity component identification number (integer of 1 to 4)) and 16 output physical quantities for each type of output physical quantity C _{S, EC} ( However, the fourth approximation coefficient D _{m1, m2, m3,} using the combination data with the subscript EC: output physical quantity type identification number (an integer of 1 to 16) and the formulas 1-1 to 1-4 in order _{. m4, E C} (however, subscripts m1, m2, m3, m4: coefficient identification numbers (each an integer of 1 to 5)), the fourth approximate coefficient D _{m1, m2, m3} for the input physical quantity component to be estimated _{, m4, EC} and the estimated input physical quantity component V _{E, VN and} Formulas 2-1 to 2-3 in order, the first approximation coefficient calculation means for calculating the first approximation coefficient A _{m1, EC} , Formula 2- Substituting the first approximation coefficient A _{m1, EC} and the output physical quantity C _{M, EC} obtained from the system into 4 gives four estimated input physical quantities V _{E, 1, EC} for every 16 output physical quantity types. Means for calculating, means for selecting one for each output physical quantity type from four estimated input physical quantities _{VE, 1, EC} , and calculating the average _{VE, av} for the estimated input physical quantity selected for each output physical quantity type Means for calculating and calculating an estimated input physical quantity V _{E, VN} for the input physical quantity component for which the average V _{E, av is} to be estimated, first approximation to Equation 3 Means for calculating the estimated output physical quantity C _{E, EC} by substituting the coefficient A _{m1, EC} and the average V _{E, av} of the estimated input physical quantity, Equation 4 shows the estimated output physical quantity C _{E, EC} and the output physical quantity obtained from the system C _M, the residual by substituting _EC C _R, together to function as means for calculating the _EC, 16 pieces of the residual C _R at the output a physical quantity different predetermined number of output physical quantity _type, the absolute value of the _EC When the end condition is that the size is equal to or less than a predetermined cutoff determination threshold value, and when the end condition is not satisfied, the input physical quantity component to be estimated is newly determined and the process returns to the first approximation coefficient calculation process, When the termination condition is satisfied, the estimation process is terminated.

  According to these input physical quantity estimation methods, estimation devices, and estimation programs, the relationship between the input to the system and the output from the system is expressed by an approximate expression, and the approximation coefficient of the approximate expression is expressed using the approximate expression. By calculating, the input to the system is estimated based on the output from the system, even if both the input to the system and the output from the system are multivariable (multiple / multidimensional physical quantities). The

  According to the input physical quantity estimation method, the estimation apparatus, and the estimation program of the present invention, when both the input to the system and the output from the system are multivariables (multi-dimensional / multi-dimensional physical quantities), based on the output from the system. Thus, it is possible to estimate the input to the system, so that it is possible to improve versatility as an estimation method.

It is a flowchart explaining an example of embodiment of the input physical-quantity estimation method and input physical-quantity estimation program of this invention. It is a functional block diagram of an input physical quantity estimation device realized by a computer by executing the input physical quantity estimation program of the embodiment. It is a figure which shows the structure of the sensor quoted as an example of the system of this invention. It is a figure explaining the input to the sensor shown in FIG. 3, and the output from a sensor. (A) is a figure explaining the displacement as an input. (B) is a figure explaining the combination of the electrode which measures the electrostatic capacitance as an output. It is a figure explaining the flow of the input physical-quantity estimation method of this invention. It is a figure explaining the outline | summary of the input physical-quantity estimation method of this invention. (A) is a figure explaining the outline | summary of estimation. (B) is a figure explaining the outline | summary of determination. It is a figure explaining the relationship of an approximation coefficient.

  Hereinafter, the configuration of the present invention will be described in detail based on an example of an embodiment shown in the drawings.

  1 to 7 show an example of embodiments of an input physical quantity estimation method, an estimation device, and an estimation program according to the present invention. In the present embodiment, when 16 physical quantities are output from the system due to inputs to the system represented by four physical quantities, the four physical quantities representing the inputs are calculated based on the 16 physical quantities. Take the case of estimation as an example. In addition, it can be said that the input which this embodiment makes object is a physical quantity having 4 degrees of freedom. The physical quantities related to input and output targeted by the present invention are represented by real numbers and can be increased or decreased.

  As a case where 16 physical quantities are output from the system due to input to the system represented by four physical quantities, specifically, as shown in FIG. Four electrodes A, B, C, and D are provided on one surface 1b of a pair of opposing surfaces of a rectangular parallelepiped base material 1a having dynamic elasticity, and the other surface 1b ′ of the pair of surfaces is also provided with the four electrodes. A sensor 1 having four electrodes A ′, B ′, C ′, D ′ at positions facing each of the electrodes A, B, C, D is used as a system, and a force is applied to the sensor 1 to deform (in other words, In this case, when the displacement of each electrode) is given as an input, the capacitance between the electrodes is output from the sensor 1.

  As shown in FIG. 4A, the deformation (displacement) as an input to the sensor 1 as a system is as follows: horizontal X direction displacement (X), horizontal Y direction displacement (Y), vertical Z direction It is expressed by four displacements (in other words, a displacement component with four degrees of freedom), ie, a compression displacement (Z) and a rotational displacement (Θ) around the vertical Z direction axis.

  Further, the sensor 1 includes one of the electrodes A, B, C, and D on one surface 1b of the pair of opposing surfaces of the substrate 1a and the electrode A ′ on the other surface 1b ′ of the pair of surfaces. By combining one of B ′, C ′, and D ′, 16 electrode combinations can be made (see FIG. 4B).

  In the sensor 1 described above, the surface 1b and the surface 1b ′ are opposed to each other with the base material 1a having mechanical elasticity interposed therebetween. Therefore, when force is applied to the sensor 1, the base material 1a is deformed. The relative positional relationship between the electrodes changes, and the capacitance between the 16 sets of electrodes changes. For this reason, the sensor 1 is used as a system, and the deformation (displacement) of the sensor 1 due to the applied force can be regarded as an input, and the change in capacitance between the electrodes due to the deformation can be regarded as an output. It can be said that 16 physical quantities (namely, capacitance between electrodes) are output from the system due to the input to the system represented by four physical quantities (namely, displacement).

In the present embodiment, four physical quantities representing inputs to the system are represented by V _VN (however, subscripts VN = 1, 2, 3, 4; and other subscripts are appropriately added to identify the contents of V). And 16 physical quantities output from the system are represented by C _EC (however, subscript EC = 1, 2, 3,..., 16; other subscripts are appropriately added to identify the contents of C. ). Here, in the following, a physical quantity related to the input to the system is also referred to as an input physical quantity, and a physical quantity related to the output from the system is also referred to as an output physical quantity. Each of the four physical quantities representing the input is also referred to as a component or an input physical quantity component. Further, these four components / input physical quantity components are also expressed as an X component, a Y component, a Z component, and a Θ component. Each of the 16 physical quantities that are output is also referred to as a type or an output physical quantity type.

  First, the principle of input physical quantity estimation based on the output physical quantity in the input physical quantity estimation method of the present invention will be described. In the present invention, an actually acquired output physical quantity (hereinafter also referred to as an acquired output physical quantity or an acquired output physical quantity type) is input, and an estimated input physical quantity (hereinafter also referred to as an estimated input physical quantity or an estimated input physical quantity component) is input. It can be said that it is what outputs.

  In the present invention, the input physical quantity to the system is estimated based on the output physical quantity from the system using an approximate expression representing the relationship between the output physical quantity and the input physical quantity. In this embodiment, a quartic polynomial is used as an approximate expression. As the output physical quantity and the input physical quantity, values as physical quantities may be used as they are, or for example, a difference value from a reference state (in other words, a change amount) may be used.

  The input physical quantity estimation method of the present invention includes estimation and determination, and repeatedly performs estimation and determination to obtain an input physical quantity that will be close to the actual input. Further, in the present invention, the estimation is performed by relating the output physical quantity type and the input physical quantity component by the approximate expression. Then, as shown in FIG. 5, the input physical quantity is estimated for one of the four input physical quantity components (Z component in FIG. 5) in one estimation, and the input physical quantity component to be estimated next is determined in the determination. And estimation processing abortion determination, and the estimation and determination are repeated.

An outline of the input physical quantity estimation method is shown in FIG. FIG. 6 shows the relationship between one specific output physical quantity _{CM, EC} among the 16 output physical quantity types and the input physical quantity zM _{, EC} which is the Z component of the four input physical quantity components. . The subscript M indicates that it is actual or actually acquired by measurement or the like. The subscript E indicates that it is related to estimation.

FIG. 6A shows an outline of estimation. Sixteen output physical quantity types C _{M, EC} (subscript EC = 1 to 16) are acquired (specifically, for example, measured) for a certain input physical quantity. In the input physical quantity estimation method of the present invention, four input physical quantity components representing the certain input physical quantity from the 16 acquired output physical quantity types C _{M, EC} (in this embodiment, X component, Y component, Z component, Θ component) Are independently estimated (Z component in FIG. 6). The estimated input physical quantity component V _{E, 1, (n, VE1 = n ′)} (subscript 1 indicates that it is a component to be estimated _{) at} n estimation times is obtained using 16 acquired output physical quantity types. The approximate expression of 16 elements is solved, and the average value of 16 V _{E, 1, (n, VE1 = n ′), EC} (subscript EC = ₁ to 16) obtained as a solution is obtained. Here, n represents the estimation number of the entire estimation, and n ′ represents the estimation number for each input physical quantity component V _{E, VN} (subscript VN = 1 to 4). Therefore, the subscript (n, VE1 = n ′) represents that the total number of estimations is n and the number of estimations of the component V _{E, 1} is n ′.

For the estimation, an approximate expression f _{E, (n, VE1 = n ′), EC} (which is a fourth-order polynomial as described above ₎ representing the relationship between the output physical quantity and the input physical quantity is used. By substituting the acquired output physical quantity C _{M, EC} into the approximate expression f _{E, (n, VE1 = n ′), EC} , the estimated input physical quantity V _{E, 1, (n, VE1 = n ′), EC} is obtained. . The approximate expression f _{E, (n, VE1 = n ′), EC} has different approximation coefficients A _{m1, (n, VE1 = n ′), EC} for each input physical quantity component and each output physical quantity type. The subscript m1 of the approximate coefficient A is an identification number of the coefficient in the approximate expression. Since there are 5 coefficients per approximate expression in the fourth-order polynomial approximation, the subscript m1 takes values 1, 2,. The approximation coefficient is calculated on the assumption that the entire relationship between the output physical quantity and the input physical quantity can be comprehensively covered, in other words, continuously interpolated. By doing so, it is possible to estimate the input physical quantity from the acquired output physical quantity _{CM, EC} .

The approximate expression represents the relationship between one input physical quantity component. In order to make the approximation coefficient A correspond to the four input physical quantity components, the other three estimated input physical quantity components V _{E, 2, (n} excluding the input physical quantity component V _{E, 1, (n, VE1 = n ′)} to be estimated _{, VE2 = n2)} (Subscript 2 is an identifier of a component, n2 represents the estimated number of the component _{), VE , 3, (n, VE3 = n3)} (Subscript 3 is an identifier of a component, and n3 is ), V _{E, 4, (n, VE4 = n4)} (subscript 4 is an identifier of the component, and n4 represents the estimated number of the component) to determine the approximation coefficient A Do. For the other input physical quantity components V _{E, 2} , V _{E, 3} , V _{E, 4} that are not the input physical quantity components V _{E, 1, (n, VE1 = n ′)} to be estimated, the total estimated number (n− 1) Use the estimated input physical quantity up to the number of times.

In the present invention, the approximate expression is also used to determine the approximate coefficient A. Specifically, the input physical quantity component V _{E, 1, (n, VE1 = n ′) to be} estimated _, the approximate expression f _{E, (n, VE1 = n ′) of EC} , and the approximate coefficient A _{m1, (n of EC , VE1 = n ′), EC} is determined by the second approximate expression using the estimated input physical quantity component V _{E, 2} and the approximate coefficient B, and the approximate coefficient B is determined by the estimated input physical quantity component V _{E, 3} and the approximate coefficient C. The approximate coefficient C is determined by a fourth approximate expression using the estimated input physical quantity component V _{E, 4} and the approximate coefficient D. The approximate expression representing the relationship between the output physical quantity and the input physical quantity component to be estimated is the first approximate expression. The approximation coefficient D is calculated in advance, and the approximation coefficient A used in each estimation is calculated. The relationship between the four types of approximate expressions is shown in FIG.

The estimated input physical quantity V _{E, VN} is identified by the subscript VN. By using the first approximation coefficient A that is updated at each estimation time, the approximate expression can be calculated as f _{E, (n, Z = 1), EC at} an estimated number n ′ = 1 of a specific input physical quantity component (for example, Z component). , F _{E, (n + a, Z = 2), EC} at estimated number n ′ = 2, f _{E, (n + b, Z = 3), EC at} estimated number n ′ = 3 (a and b are The number for representing the number of estimations of the entire estimation), the estimated point approaches the acquisition point. This operation is repeated to obtain a probable estimated point. When the estimated point reaches the allowable range centered on the acquired point, the input physical quantity estimation process ends (see FIG. 6B).

Then, in order to estimate the input physical quantity from the output physical quantity based on the above-described principle, the input physical quantity estimation method of the present invention has 16 output physical quantity types resulting from the input to the system represented by the four input physical quantity components. When the four input physical quantity components are estimated based on the 16 types of output physical quantity when the system is output from the system, the input for each of the four input physical quantity components acquired as a sample in advance for each of the four input physical quantity components Physical quantity V _VN (subscript VN: input physical quantity component identification number (specifically an integer of 1 to 4)) and 16 output physical quantities C _{S, EC} by output physical quantity type (subscript EC: output physical quantity The fourth approximation coefficient D _{m1, m2, m3, m4, EC} (however, subscript) using the combination data with the type identification number (specifically an integer of 1 to 16) and the formulas 6 to 9 in order m1, m2, m3, m4: Identification of coefficients And number processing to calculate the) (specifically, each integer of 1 to 5.) (S1-1), the processing of the entire estimated number n times, the input physical quantity component was estimated target fourth approximation coefficient D _{m1, m1 , m3, m4, EC,} estimated input physical quantity component V _{E, VN and} Equation 5-1 to Equation 5-3 are used in order to obtain the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} first approximation coefficient calculation processing for calculating the (S1-2), first approximation coefficient a _m1 in equation _{5-4, (n, VE1 = n} '), EC and output physical quantity C _M obtained from the _{system, EC} And four estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} calculation processing (S2) for every 16 output physical quantity types, and four estimated inputs. Processing for selecting one for each output physical quantity type from physical quantity V _{E, 1, (n, VE1 = n '), EC} (S3), and average V _{E of} estimated input physical quantities selected for each output physical quantity type _{, 1, (n, VE1 = n ′)} and calculate the average _{VE , 1, (n , VE1 = n ′)} as the estimated input physical quantity V _{E, VN} for the input physical quantity component to be estimated (S4), and the first approximation coefficient A _{m1, (n, VE1 = n ′),} A process (S5) for calculating the estimated output physical quantity _{CE, (n, VE1 = n '), EC} by substituting the average _{VE, 1, (n, VE1 = n')} of _EC and the estimated input physical quantity, 11 the estimated output physical quantity _{C E, (n, VE1 =} n '), EC and output physical quantity C _M obtained from the _system, residual C _R by substituting _{EC, (n, VE1 = n} '), EC (S6), and the absolute value of C _{R, (n, VE1 = n ′), EC} is predetermined in the predetermined number of output physical quantity types among the 16 output physical quantity types. An end condition is that the threshold value is equal to or less than the predetermined threshold value (S9). If the end condition is not satisfied (S9: No), the input physical quantity component to be estimated is newly determined and the first approximation coefficient is calculated. Returning to the process, if the end condition is satisfied (S9) So that ends the estimation process is yes).

The input physical quantity estimation method is realized as the input physical quantity estimation apparatus of the present invention. This input physical quantity estimation device has a storage unit that stores data of 16 types of output physical quantities output from the system due to inputs to the system represented by four input physical quantity components, or the data 4 is obtained in advance as a sample for each of the four input physical quantity components in order to estimate the four input physical quantity components based on the 16 output physical quantity types. Input physical quantity V _VN (subscript VN: input physical quantity component identification number (specifically an integer of 1 to 4)) and 16 output physical quantities C _{S, EC} ( However, the fourth approximation coefficient D _{m1, m2, m3,} using the combination data with the subscript EC: output physical quantity type identification number (specifically, an integer of 1 to 16) and Equation 6 to Equation 9 in order _{. m4, EC} (except Subscripts m1, m2, m3, m4: means for calculating coefficient identification numbers (specifically, integers of 1 to 5)), and input physical quantity components to be estimated as a process of n estimation times Using the fourth approximation coefficient D _{m1, m2, m3, m4, EC, the} estimated input physical quantity component V _{E, VN} , and the equations 5-1 to 5-3 in order, the first approximation coefficient A _{m1, (n, VE1 = n '),} a means for performing a first approximation coefficient calculation process for calculating _EC , a first approximation coefficient A _{m1, (n, VE1 = n'), EC} and an output obtained from the system in Equation 5-4 Substituting the physical quantities C _{M, EC} and calculating four estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} for each of the 16 output physical quantity types, and four each Estimated input physical quantity V _{E, 1, (n, VE1 = n '),} means to select one for each output physical quantity type from _EC , and average V _E, estimated input physical quantity selected for each output physical quantity type _{1, (n, VE1 = n ′)} is calculated and the average _{VE, 1, (n, VE 1 = n ′)} as an estimated input physical quantity component for the estimated physical quantity component V _{E, VN} , the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} and the estimated input the average of the physical quantity _{V E, 1, (n,} VE1 = n ') estimated output physical quantity C _E by _{substituting, (n, VE1 = n'} ), and means for calculating the _EC, the estimated output physical quantity C _E in equation 11 _{, (n, VE1 = n ′), EC} and output physical quantity C _{M, EC} obtained from the system are substituted to calculate residual C _{R, (n, VE1 = n ′), EC.} In the predetermined number of output physical quantity types among the 16 output physical quantity types, the magnitude of the absolute value of _{CR, (n, VE1 = n ′), EC} is less than or equal to a predetermined cutoff judgment threshold. As an end condition, if the end condition is not satisfied, the input physical quantity component to be estimated is newly determined and the process returns to the first approximation coefficient calculation process. If the end condition is satisfied, the estimation process is ended. I have to.

  The above-described input physical quantity estimation method and input physical quantity estimation apparatus are also realized by executing the input physical quantity estimation program of the present invention on a computer. In the present embodiment, a case where the input physical quantity estimation program is executed on a computer will be described as an example.

  FIG. 2 shows the overall configuration of the computer 10 (that is, the input physical quantity estimation device 10) for executing the input physical quantity estimation program 17. The input physical quantity estimation device 10 includes a control unit 11, a storage unit 12, an input unit 13, a display unit 14, and a memory 15, and is connected to each other by a signal line such as a bus. A data server 16 is connected to the input physical quantity estimation device 10 through a signal line such as a bus, and signals such as data and control commands are transmitted / received (ie, input / output) to / from each other via the signal line.

  In the present embodiment, the fourth approximation coefficient calculation sample data is used as the fourth approximation coefficient calculation database 18, and the output physical quantity output and acquired from the system is acquired as the acquired output physical quantity database 19. The input physical quantity thus obtained is stored in the data server 16 as the estimated input physical quantity database 20.

  The control unit 11 performs operations related to the control of the entire input physical quantity estimation device 10 and the estimation of the input physical quantity based on the output physical quantity by the input physical quantity estimation program 17 stored in the storage unit 12. Processing device).

  The storage unit 12 is a device that can store at least data and programs, and is, for example, a hard disk.

  The memory 15 serves as a memory space that is a work area when the control unit 11 executes various controls and calculations, and is, for example, a RAM (abbreviation of random access memory).

  The input unit 13 is an interface for giving at least an operator's command to the control unit 11, and is, for example, a keyboard.

  The display unit 14 performs drawing / display of characters, graphics, and the like under the control of the control unit 11 and is, for example, a display.

A computer accessible to the data server 16 as a storage device in which data of 16 types of output physical quantities output from the system due to inputs to the system represented by the four input physical quantity components are stored In order to estimate the four input physical quantity components based on the 16 output physical quantity types by executing the input physical quantity estimation program 17, the control unit 11 of the input physical quantity estimation apparatus 10 is four input physical quantity components. For each input physical quantity component V _VN (however, subscript VN: input physical quantity component identification number (specifically an integer of 1 to 4)) and 16 output physical quantity types acquired as samples in advance. another output physical quantity C _{S, EC} (where subscripts EC: output physical quantity type of identification number (specifically 1 to 16 integer)) from the combination data and equation 6 with With up to Formula 9 in the order fourth approximation coefficient _{D m1, m2, m3, m4} , EC ( where the subscript m1, m2, m3, m4: identification number of coefficients (integer of specifically from 1 to 5) ), The fourth approximation coefficient calculation unit 11a as a means for calculating the total number of estimations, the fourth approximation coefficient _{Dm1, m2, m3, m4, EC} and the estimated input for the input physical quantity component to be estimated A first approximation coefficient calculation process for calculating the first approximation coefficient _{Am1, (n, VE1 = n '), EC} is performed using the physical quantity components V _{E, VN and} Equations 5-1 to 5-3 in order. Substituting the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} and the output physical quantity C _{M, EC} obtained from the system into the first approximation coefficient calculation unit 11b as a means and Formula 5-4 4 estimated input physical quantities V _{E, 1, (n, VE1 = n ′),} an estimated input physical quantity calculating unit 11c as a means for calculating _EC for every 16 output physical quantity types, and four estimated inputs. Physical quantity _{E, 1, (n, VE1} = n '), the validity determination section 11d as a means for selecting one of each output physical quantity type from _EC, the output physical quantity for each kind in one selected putative input physical quantity average V _{E , 1, (n, VE1 =} n ') is calculated the average _{V E, 1, (n,} VE1 = n') the estimated input physical quantity V _E of the input physical variable component and estimation _target, means to _VN As the estimated input physical quantity determination unit 11e, the first approximation coefficient _{Am1, (n, VE1 = n '), EC} and the average of the estimated input physical quantity _{VE, 1, (n, VE1 = n')} are substituted into Equation 10 The estimated output physical quantity C _{E, (n, VE1 = n ′), EC} as a means for calculating the estimated output physical quantity C _{E, (n, VE1 = n ′), EC} In addition, a residual calculation unit 11g is configured as means for calculating the residual C _{R, (n, VE1 = n ′), EC} by substituting the output physical quantities C _{M, EC} acquired from the system.

In executing the input physical quantity estimation method of the present embodiment, first, estimation processing (S1 to S4) is performed. First, to calculate the first approximation coefficient A _{m1, EC} to produce each output physical quantity type C _M, a first approximate expression in _EC (S1).

As described above, the calculation of the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} is performed as described above. The input physical quantity component V _{E, 1, (n, VE1 = n ′ to be} estimated is n times. _The other three estimated input physical quantity components V _{E, 2, (n, VE2 = n2)} , V _{E, 3, (n, VE3 = n3)} , V _{E, 4, (n, VE4 = n4)} The approximate expression used is used (see FIG. 7). These three estimated input physical quantity components V _{E, 2, (n, VE2 = n2)} , V _{E, 3, (n, VE3 = n3)} , V _{E, 4, (n, VE4 = n4)} are estimated overall. A value obtained by estimation up to (n-1) times is used. However, the unestimated input physical quantity component is V _{E, VN} = 0.

As shown in Table 1, combinations of estimated input physical quantity components represented by the input physical quantities V _{E and VN} vary depending on the types of components as the input physical quantity components V _{E, 1, (n, VE1 = n ′) to be} estimated.

Then, the first approximation coefficient _{Am1, (n, VE1 = n '), EC} is calculated through the three approximation formulas 5-1, 5-2, and 5-3. The subscripts m1, m2, and m3 all take values of 1, 2,.
(Equation 5)
(Equation 5-1): Fourth approximate expression C _{m1, m2, m3, (n, VE1 = n ′), EC} = D _{m1, m2, m3,1, (n, VE1 = n ′), EC} · ( V _{E, 4, (n, VE1 = n ')} ) ⁴
+ D _{m1, m2, m3,2, (n, VE1 = n '), EC} · (V _{E, 4, (n, VE1 = n')} ) ³
+ D _{m1, m2, m3,3, (n, VE1 = n '), EC} · ( _{VE , 4, (n, VE1 = n')} ) ²
+ D _{m1, m2, m3,4, (n, VE1 = n '), EC}・ ( _{VE , 4, (n, VE1 = n')} )
+ D _{m1, m2, m3,5, (n, VE1 = n '), EC}
(Equation 5-2): Third approximate expression B _{m1, m2, (n, VE1 = n ′), EC} = C _{m1, m2,1, (n, VE1 = n ′), EC} · (V _{E, 3 , (n, VE1 = n ')} ) ⁴
+ C _{m1, m2,2, (n, VE1 = n '), EC} · (V _{E, 3, (n, VE1 = n')} ) ³
+ C _{m1, m2,3, (n, VE1 = n '), EC} · (V _{E, 3, (n, VE1 = n')} ) ²
+ C _{m1, m2,4, (n, VE1 = n '), EC}・ ( _{VE, 3, (n, VE1 = n')} )
+ C _{m1, m2,5, (n, VE1 = n '), EC}
(Equation 5-3): Second approximate expression A _{m1, (n, VE1 = n ′), EC} = B _{m1,1, (n, VE1 = n ′), EC} · (V _{E, 2, (n, VE1 = n ')} ) ⁴
+ B _{m1,2, (n, VE1 = n '), EC}・ ( _{VE, 2, (n, VE1 = n')} ) ³
+ B _{m1,3, (n, VE1 = n '), EC} · ( _{VE, 2, (n, VE1 = n')} ) ²
+ B _{m1,4, (n, VE1 = n '), EC}・ ( _{VE, 2, (n, VE1 = n')} )
+ B _{m1,5, (n, VE1 = n '), EC}
(Equation 5-4): First approximate expression 0 = A _{1, (n, VE1 = n ′), EC} · (V _{E, 1, (n, VE1 = n ′), EC} ) ⁴
+ A _{2, (n, VE1 = n ′), EC} · (V _{E, 1, (n, VE1 = n ′), EC} ) ³
+ A _{3, (n, VE1 = n '), EC} · ( _{VE, 1, (n, VE1 = n'), EC} ) ²
+ A _{4, (n, VE1 = n '), EC}・ ( _{VE, 1, (n, VE1 = n'), EC} )
+ A _{5, (n, VE1 = n '), EC} -CM _{, EC}

First approximation equation (Equation 5-4) is the relation between one component of the output obtained physical quantity C _{M, EC} and the estimated input physical quantity V _E. The estimated input physical quantity V _{E of} the first approximate expression becomes the input physical quantity component V _{E, 1, (n, VE1 = n ′), EC} to be estimated at the total estimation number n times. A total of four types of approximate expressions are used to associate the first approximate expression with the other three input physical quantity components that are not the input physical quantity components to be estimated.

The other three input physical quantity components V _{E, 2, (n, VE2 = n2)} , V _{E, 3, (n, VE3 = n3)} , V _{E, 4, (n, VE4 )} that are not the input physical quantity components to be estimated _{= n4)} are the second approximation formula (Formula 5-3), the third approximation formula (Formula 5-2), and the fourth approximation formula (Formula 5-1), respectively. V _{E, 2, (n, VE2 = n2)} (In Equation 5-3, expressed as V _{E, 2, (n, VE1 = n ′)} ; when the estimation target component V _{E, 1} is estimated n ′ times ₍ Meaning the value of the component V _{E, 2} ), V _{E, 3, (n, VE3 = n3)} (in Equation 5-2, expressed as V _{E, 3, (n, VE1 = n ′)} ; estimation target component V _{E , 1} means the value of the component V _{E, 3} when the number of estimations is n ′), V _{E, 4, (n, VE4 = n4)} (V _{E, 4, (n, VE1 = n ′)} ; the estimated input physical quantity up to the total number of estimation times (n−1) times for each of the estimation target component V _{E, 1} is the value of the component V _{E, 4} when the estimation frequency is n ′ times) By substituting, the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} (however, the subscript m1 = 1 to 5) is updated (see FIG. 7). The unestimated input physical quantity components V _{E, 2} , V _{E, 3} and V _{E, 4} are set to zero.

  The update is performed by approximation equations (Equation 5-1 to Equation 5-3) of three input physical quantity components at each estimation time, and estimation is performed by a four-stage approximation equation. The fourth approximate expression calculates the third approximate coefficient C, the third approximate expression calculates the second approximate coefficient B, and the second approximate expression calculates the first approximate coefficient A. If only the first approximate expression is used, the estimation method takes into account four input physical quantity components when one input physical quantity component is used, up to the second approximate expression, two input physical quantity components, and up to the fourth approximate expression.

In this embodiment, a quartic polynomial is used as each approximate expression, and therefore there are 5 coefficients per approximate expression. The identification number of the coefficient is m, and m1 to m4 (each takes values of 1, 2,..., 5) for each of the first to fourth approximation expressions. Then, the approximate coefficients necessary for one estimation in one output physical quantity type _{CM, EC} are the fourth approximate coefficients _{Dm1, m2, m3, m4, (n, VE1 = n '), and EC} is m1 × m2. × m3 × m4 = 5 × 5 × 5 × 5 = 625, third approximation coefficient C _{m1, m2, m3, (n, VE1 = n ′), EC} is m1 × m2 × m3 = 5 × 5 × 5 = 125, second approximation coefficient B _{m1, m2, (n, VE1 = n ′), EC} is m1 × m2 = 5 × 5 = 25, first approximation coefficient A _{m1, (n, VE1 = n ′), EC} becomes m1 = 5.

Among the approximation coefficients, the first to third approximation coefficients A, B, and C are calculated every estimation time. On the other hand, the fourth approximation coefficient D _{m1, m2, m3, m4, (n, VE1 = n ′), EC} is calculated in advance by the following method (S1-1).

  The meaning of the first approximate expression is interpolation of characteristics (in other words, system characteristics) between the output physical quantity and the input physical quantity. If it is possible to estimate the output physical quantity when the four input physical quantity components are in an arbitrary state by the four-stage approximation, the input physical quantity can be mapped from the output physical quantity. For this reason, the first approximate expression has a role of continuously interpolating the entire relationship between the input physical quantity and the output physical quantity acquired in advance by discrete sampling for calculating the fourth approximation coefficient.

  Here, the combination data of the input physical quantity and the output physical quantity acquired in advance for calculating the fourth approximation coefficient is referred to as sample data. Specifically, the sample data is combination data of a certain input physical quantity (four components) and an output physical quantity (16 types) from the system acquired when the input physical quantity is given to the system.

  Since the approximate expression needs to be able to represent the entire relationship between the input physical quantity and the output physical quantity, the sample data (set) needs to be able to interpolate the whole system state. It is desirable that the entire range assumed or allowed as an input physical quantity to the system is covered without any deviation. Specifically, for example, the upper limit value and lower limit value of the range of physical quantities assumed or allowed for each input physical quantity component (hereinafter referred to as “assumed / allowable range”), and the upper limit value and lower limit value are divided into four equal parts. It is conceivable that a total of five values (that is, three) to be used are sample points, and all combinations constituted by one of the five sample points of each of these four components are input physical quantities of sample data.

  A range narrower than the assumed / allowable range may be used as the upper limit value and the lower limit value of the input physical quantity of the sample data. Further, when a certain input physical quantity component changes to a positive range (or negative range), the range of the physical quantity is limited for an input physical quantity component that changes only in a specific range, either positive or negative. The assumed / allowable range may be individually adjusted (specifically limited) to a range that can be considered when a combination of change ranges of each input physical quantity component is specifically assumed. In addition, the equivalent fraction of the assumed / allowable range (or narrower range) is not limited to four, but may be smaller or larger than four in consideration of the desired estimation accuracy and calculation time. Also good. However, as the total number of sample data, the number of unknown coefficients obtained using Equations 6 to 9 is considered.

Specifically, the fourth approximation coefficient D is calculated from the calculation of the first approximation coefficient A ′ for calculating the fourth approximation coefficient, contrary to the estimation of the input physical quantity. The first approximation coefficient A ′ for calculating the fourth approximation coefficient is the relationship between the acquired output physical quantity C _{S, EC of} the fourth approximation coefficient calculation sample data and one component V ₁ of the input physical quantity components (formula 6: First approximation formula of approximation coefficient) Specifically, for each output physical quantity type (EC), the combination data of the input physical quantity component V ₁ and the output physical quantity C _{S, EC of} the fourth approximate coefficient calculation sample data is substituted into Equation 6, for example, the least square method Is used to find the first approximation coefficients A ′ _{1, EC to} A ′ _{5, EC} for calculating the fourth approximation coefficient.
(Equation 6)
C _{S, EC} = A ′ _{1, EC} · (V ₁ ) ⁴ + A ′ _{2, EC} · (V ₁ ) ³ + A ′ _{3, EC} · (V ₁ ) ² + A ′ _{4, EC} · (V ₁ )
+ A ' _{5, EC}

Next, the second approximation coefficient B ′ for calculating the fourth approximation coefficient is represented by the change of the first approximation coefficient A ′ for calculating the fourth approximation coefficient due to the _second input physical quantity component V ₂ (formula 7: Second approximation formula of approximation coefficient). Then, for each output physical quantity type (EC) and coefficient number (m1), the combination data of the input physical quantity component V _{2 of} the fourth approximate coefficient calculation sample data and the first approximate coefficient A ′ _{m1, EC} is expressed by Equation 7. Substitution is performed, and second approximation coefficients B ′ _{m1,1, EC to} B ′ _{m1,5, EC} for calculating the fourth approximation coefficient are obtained by using, for example, the least square method.
(Equation 7)
A ′ _{m1, EC} = B ′ _{m1,1, EC} · (V ₂ ) ⁴ + B ′ _{m1,2, EC} · (V ₂ ) ³ + B ′ _{m1,3, EC} · (V ₂ ) ²
+ B ' _{m1,4, EC}・ (V ₂ ) + B' _{m1,5, EC}

Similarly, the third approximation coefficient C ′ for calculating the fourth approximation coefficient is the one representing the change due to the _third input physical quantity component V ₃ of the second approximation coefficient B ′ for calculating the fourth approximation coefficient (formula 8: Third approximation formula of approximation coefficient), and the fourth approximation coefficient D is a representation of the change due to the _fourth input physical quantity component V ₄ of the third approximation coefficient C ′ for calculating the fourth approximation coefficient (formula 9: Fourth approximation formula of approximation coefficients). For each output physical quantity type (EC) and coefficient number (m1, m2), the combination data of the input physical quantity component V _{3 of} the fourth approximate coefficient calculation sample data and the second approximate coefficient B ′ _{m1, m2, EC Is} substituted into Formula 8, for example, the third approximation coefficient C ′ _{m1, m2,1, EC to} C ′ _{m1, m2,5, EC} for calculating the fourth approximation coefficient is obtained using the least square method, and the output For each physical quantity type (EC) and coefficient number (m1, m2, m3), a combination of the input physical quantity component V _{4 of} the fourth approximate coefficient calculation sample data and the third approximate coefficient C ′ _{m1, m2, m3, EC} By substituting the data into Equation 9, for example, the fourth approximation coefficient D _{m1, m2, m3,1, EC to} D _{m1, m2, m3,5, EC} is obtained using the least square method.
(Equation 8)
B ′ _{m1, m2, EC} = C ′ _{m1, m2,1, EC} · (V ₃ ) ⁴ + C ′ _{m1, m2,2, EC} · (V ₃ ) ³
_{+ C 'm1, m2,3, EC} · (V 3) 2 + C' m1, m2,4, EC · (V 3) + C 'm1, m2,5, EC
(Equation 9)
C ′ _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V ₄ ) ⁴ + D _{m1, m2, m3,2, EC} · (V ₄ ) ³
+ D _{m1, m2, m3,3, EC}・ (V ₄ ) ² + D _{m1, m2, m3,4, EC}・ (V ₄ )
+ D _{m1, m2, m3,5, EC}

The fourth approximation coefficients D _{m1, m2, m3, m4, EC} are calculated by the above-described processing using Formula 6 to Formula 9 in order.

Here, the characteristics between the output physical quantity and the input physical quantity, which are system characteristics, may have different characteristics for each type of output physical quantity. Therefore, the approximation coefficient can be a different value depending on each type (EC) of the output physical quantity. Further, as shown in Table 1, which of the four input physical quantity components is to be estimated in the total estimation number n times (in other words, the input physical quantity component V _{E, 1, ( n, VE1 = n ′), EC} is) _), the estimated input physical quantity component V _E to be used as V _{E, 2} , V _{E, 3} , V _{E, 4 in} Equations 5-1, 5-2, 5-3 _{, VN} changes.

This indicates that the approximation coefficient differs depending not only on the type of output physical quantity but also on the type (component) of the input physical quantity component V _{E, 1 to be} estimated. Accordingly, the fourth approximate coefficient group D includes V _{E, 1} = group corresponding to Z component, V _{E, 1} = group corresponding to X component, V _{E, 1} = group corresponding to Y component, V _{E, 1} = Divided into groups corresponding to Θ components.

  In the present embodiment, the fourth approximation coefficient D is calculated by the fourth approximation coefficient calculation unit 11a of the control unit 11 performing the above-described processing. In the present embodiment, the combination data of the input physical quantity and the output physical quantity as the fourth approximation coefficient calculation sample data is stored in the fourth approximation coefficient calculation database 18 in the data server 16, and the fourth approximation coefficient is calculated. The calculation unit 11a reads the sample data from the database 18 and calculates the fourth approximation coefficient D for each type (component) of the input physical quantity component by performing the above-described processing using the expressions 6 to 9 in order. Equations 6 to 9 are defined in advance in the input physical quantity estimation program 17.

Then, the fourth approximate coefficient calculation unit 11a calculates the fourth approximate coefficients _{Dm1, m2, m3, m4, EC} calculated for each type of input physical quantity component (Z component, X component, Y component, Θ component) Subscripts m1, m2, m3, m4 = 1, 2,..., 5; subscript EC = 1, 2,.

Subsequently, using the fourth approximation coefficient D calculated by the process of S1-1, the first approximation coefficient A _{m1, (n, VE1 = n '), EC} is calculated (S1-2).

  It should be noted that the input physical quantity component to be estimated in the overall estimation count of 1 may be arbitrarily selected, may be specified in advance in the input physical quantity estimation program 17, or the overall estimation count of 1 It may be specified via the input unit 13 at the stage of the processing of S1-2.

In the present embodiment, the first approximation coefficient calculation unit 11b of the control unit 11 performs fourth approximation coefficients D _{m1, m2, m3, m4, for} each type of input physical quantity component stored in the memory 15 in the process of S1-1 _{. The} values of the fourth approximation coefficients D _{m1, m2, m3, m4, EC} corresponding to the input physical quantity component to be estimated in _{the EC} are read from the memory 15, and the above-described equations 5-1 to 5-3 are used in order. Thus, the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} is calculated. In the present embodiment, the estimated input physical quantities V _{E and VN} are stored in the estimated input physical quantity database 20 in the data server 16, and the first approximate coefficient calculation unit 11 b estimates the entire input physical quantity component from the database 20. The values of the estimated input physical quantities V _{E and VN} up to the number (n−1) times are read and the above-described processing is performed. Further, Expressions 5-1 to 5-3 are defined in advance in the input physical quantity estimation program 17.

Then, the first approximation coefficient calculation unit 11b stores the calculated values of the first approximation coefficient _{Am1, (n, VE1 = n '), EC in} the memory 15.

  Next, an estimated input physical quantity is calculated using an approximate expression (S2).

Specifically, the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} calculated by the process of S1-2 is obtained output physical quantity _{CM , EC} and estimated input physical quantity V _{E, 1, (n , VE1 = n ′), EC} , the first approximation coefficient A _{m1, (n, VE1 = n ′), EC} and the acquired output physical quantity C _{M, EC} And the estimated input physical quantity V _{E, 1, (n, VE1 = n ′), EC} is calculated.

The approximate expression holds for each type of output physical quantity (EC). Furthermore, since it is a solution of a fourth-order polynomial, four estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} are obtained from the first approximate expression. Therefore, the calculated number of estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} is 64 in total for the 16 types of output physical quantities.

In the present embodiment, the estimated input physical quantity calculation unit 11c of the control unit 11 stores the values of the first approximation coefficients _{Am1, (n, VE1 = n '), EC} stored in the memory 15 in the process of S1-2. 15 and the estimated input physical quantity V _{E, 1, (n, VE1 = n ′), EC} is calculated using Equation 5-4. In the present embodiment, the acquired output physical quantity C _{M, EC} is stored in the acquired output physical quantity database 19 in the data server 16, and the estimated input physical quantity calculation unit 11 c obtains the acquired output physical quantity C _{M, EC} from the database 19. Read and perform the above processing. Formula 5-4 is defined in advance in the input physical quantity estimation program 17.

Then, the estimated input physical quantity calculation unit 11c stores in the memory 15 the values of the estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} calculated for each of the 16 types of acquired output physical quantities.

  Next, the validity of the estimated input physical quantity is determined (S3).

By the process of S2, four estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} are calculated for every 16 types of output physical quantities. In the processing of S3, the estimated input physical quantity is selected by performing validity determination of these estimated input physical quantities.

The conditions for determining validity are shown below.
1) Real solution 2) Estimated direction indication and V _{E, 1, (n, VE1 = n ′),} in the next estimation input physical quantity component determination (S5 to S8) in the total estimation number (n−1) times _, It is within the effective range considering the result of the estimated input physical quantity in the _EC input physical quantity component

In the determination of the next estimated input physical quantity component (S5 to S8), the input physical quantity component to be estimated is determined in the next overall estimation. At this time, the estimated direction physical quantity V _{E, 1, (n, VE1 = n ′), EC} is also instructed to indicate whether to increase or decrease _EC . Therefore, the validity determination condition is that the estimation result at the total estimation number n matches the estimation direction instruction at the total estimation number (n−1). The effective range is set to consider past estimation results for V _{E, 1, (n, VE1 = n ′) and EC} input physical quantity components at the total estimation number n.

That is, in the determination of the process of S3, first, on the condition that it is a real number solution, the estimated input physical quantity V _E that matches the previous increase / decrease direction instruction of the overall estimation and is within the assumed / tolerable range. _{, 1, (n, VE1 = n '),} only _EC is selected. In addition, since there is no direction of increase / decrease in the previous total estimation at the total estimation count of one, it is not taken into account.

  The estimated input physical quantity that passed the determination is validated and used for the subsequent estimation. Here, when it is determined that a plurality of estimated input physical quantities are valid for one type of output physical quantity, a value close to the average of the estimated input physical quantities of other output physical quantity types is validated. In this way, one estimated input physical quantity is selected for one type of output physical quantity.

In the present embodiment, the validity determination unit 11d of the control unit 11 reads the values of the estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} stored in the memory 15 in the process of S2 from the memory 15. In accordance with the above concept _{, one} estimated input physical quantity V _{E, 1, (n, VE1 = n ′), EC} is selected for every 16 types of output physical quantities.

Then, the validity determination unit 11d stores in the memory 15 the estimated input physical quantity V _{E, 1, (n, VE1 = n ′), EC} selected for every 16 types of output physical quantities.

  Next, the estimated input physical quantity is determined (S4).

Through the processing up to S3, a total of 16 estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} are obtained _, one for every 16 types of output physical quantities. The average of these 16 values is assumed to be the estimated input physical quantity V _{E, 1, (n, VE1 = n ′)} of the input physical quantity component that is the estimation target for the total estimation number n.

In the present embodiment, the estimated input physical quantity determination unit 11e of the control unit 11 uses the values of the 16 estimated input physical quantities V _{E, 1, (n, VE1 = n ′), EC} stored in the memory 15 in the process of S3. Is read from the memory 15 and the average of these 16 values (V _{E, 1, (n, VE1 = n ′)} ) is calculated.

Then, the estimated input physical quantity determination unit 11e stores the calculated average value (V _{E, 1, (n, VE1 = n ′)} ) in the memory 15 and the total estimated number of times of the input physical quantity component that is the estimation target. The estimated input physical quantity V _{E, 1, (n, VE1 = n ′)} up to n times is stored in the estimated input physical quantity database 20 in the data server 16.

  Subsequently, determination processing (S5 to S9) is performed. Of the determination processes, the processes of S5 to S8 are operations for determining the next estimated input physical quantity component, and the process of S9 is an operation for aborting determination.

As the next estimated input physical quantity component determination process, first, an estimated output physical quantity _CE is calculated (S5).

When Formula 5-4 is transformed, Formula 10 is obtained.
(Equation 10)
C _{E, (n, VE1 = n ′), EC} = A _{1, (n, VE1 = n ′), EC} · (V _{E, 1, (n, VE1 = n ′)} ) ⁴
+ A _{2, (n, VE1 = n ′), EC} · (V _{E, 1, (n, VE1 = n ′)} ) ³
+ A _{3, (n, VE1 = n '), EC} · (V _{E, 1, (n, VE1 = n')} ) ²
+ A _{4, (n, VE1 = n '), EC}・ ( _{VE, 1, (n, VE1 = n')} )
+ A _{5, (n, VE1 = n '), EC}

First approximate coefficient A _{m1, (n, VE1 = n ′)} calculated by the process of S1-2, estimated input physical quantity V _{E, 1, (n, VE1 = n ′)} calculated by the process of _EC and S4 Are substituted into Equation 10 to calculate the estimated output physical quantity _{CE, (n, VE1 = n ′), EC} for each output physical quantity type (EC).

In the present embodiment, the estimated output physical quantity calculation unit 11f of the control unit 11 performs the first approximation coefficient _{Am1, (n, VE1 = n '), EC} value stored in the memory 15 in the process of S1-2, and S4. In this process, the estimated input physical quantity V _{E, 1, (n, VE1 = n ′)} stored in the memory 15 is read from the memory 15 and the estimated output physical quantity _{CE, (n, VE1 = n '), EC} is calculated.

Then, the estimated output physical quantity calculation unit 11 f stores the calculated estimated output physical quantity _{CE, (n, VE1 = n ′), EC in} the memory 15.

Then, to calculate the residual C _R (S6).

Specifically, with respect to the estimated output physical quantity C _{E, (n, VE1 = n ′), EC} calculated by the process of S5, the residual C _{R, (n, VE1} is calculated by Expression 11 for each output physical quantity type (EC). _{= n '), EC} is calculated.
( _Equation 11) Residual C _{R, (n, VE1 = n ′), EC} = acquired output physical quantity C _{M, EC} −estimated output physical quantity C _{E, (n, VE1 = n ′), EC}

Further, the value of the residual _{CR, (n, VE1 = n ′), EC} is binarized into positive and negative by the equation 12.
(Equation 12)
If C _{R, (n, VE1 = n ′), EC} <0, then C _{BR, (n, VE1 = n ′), EC} = 0
If C _{R, (n, VE1 = n ′), EC} > 0, then C _{BR, (n, VE1 = n ′), EC} = 1

In the present embodiment, the residual calculation unit 11g of the control unit 11 reads the acquired output physical quantity _{CM, EC} from the acquired output physical quantity database 19 in the data server 16, and is stored in the memory 15 in the process of S5. _{C E, (n, VE1 =} n '), the value of _EC read from the memory 15, the residual C _R by equation _{11, (n, VE1 = n} '), the residual by equation 12 to calculate the _EC C _{R , (n, VE1 = n ′), EC} values are binarized to determine C _{BR, (n, VE1 = n ′), EC} values.

Then, the residual calculation unit 11g sets the calculated residual _{CR, (n, VE1 = n '), EC} value and residual binarization _{CBR, (n, VE1 = n'), EC} value. It is stored in the memory 15.

Next, the residual binarization C _BR is compared with the increase / decrease table V _B (S7).

The increase / decrease table V _B is a table in which the tendency of the change of each output physical quantity type (change from the state where all input physical quantity components are zero) when the input physical quantity changes from zero is binarized by increase / decrease. . The increase / decrease table V _B is a total of eight component directions (specifically, Z (+), Z (−), X () in two directions (increase (+), decrease (−)) of each of the four components of the input physical quantity. (+), X (-), Y (+), Y (-), Θ (+), Θ (-) (8 component directions) (16 patterns in total; hereinafter referred to as component direction patterns) are created in advance, for example, by actually measuring or organizing them as theoretically considered. In addition, it can respond to the change of 4 degrees of freedom by combining four components. Each increase / decrease table V _B corresponding to each component direction pattern is composed of 16 increase / decrease table elements v _{B, EC for} each output physical quantity type (EC). As the value of the increase / decrease table element v _{B, EC} , “1” is given when the change tendency of the output physical quantity type is increasing, and “0” is given when it is decreasing.

Then, by comparing the residual binarization _{CBR, (n, VE1 = n ′), EC} obtained by the processing of S6 and the increase / decrease table V _B , the estimated input physical quantity at the time of the total estimation number n times. Check which ingredients are missing.

The comparison is performed with 16 types of output physical quantities as one set. As shown in Equation 13, residual binarization C _{BR, (n, VE1 = n ′), EC} and increase / decrease table elements v _{B, EC} are _equal. “1” is given as the comparison result value R _{n, EC} to the corresponding output physical quantity type, and “0” is given as the comparison result value R _{n, EC} to the mismatched output physical quantity type.
(Equation 13)
If C _{BR, (n, VE1 = n '), EC} ≠ v _{B, EC,} then R _{n, EC} = 0
If C _{BR, (n, VE1 = n ′), EC} = v _{B, EC} R _{n, EC} = 1

  Then, the total number of “1” s for each component direction pattern is set as the pattern score. The number of pattern points is the number of points in each component direction in all 16 component direction patterns. Then, the total number of pattern points for each of the eight component directions in the four component two directions is obtained. Specifically, for example, the total score for Z (+) in the eight component directions is calculated as the sum of the pattern scores of eight patterns including Z (+) in the sixteen component direction patterns.

In the present embodiment, the comparison unit 11h of the control unit 11 reads the values of the residual binarization C _{BR, (n, VE1 = n ′), EC} stored in the memory 15 in the process of S6 from the memory 15, For each component direction pattern, the comparison result value R _{n, EC} is determined for each output physical quantity type by Equation 13 and the number of pattern points is calculated. Note that the increase / decrease table V _B (specifically, the value of the increase / decrease table element v _{B, EC} for each output physical quantity type (EC)) may be defined in advance in the input physical quantity estimation program 17, for example. Then, it may be stored in the storage unit 12 as an increase / decrease table data file that can be referred to by the control unit 11.

  Then, the comparison unit 11 h calculates the total number of pattern points for each of the eight component directions using the number of pattern points for each component direction pattern, and stores the total number of points in the memory 15.

  Next, the next estimated input physical quantity component is determined (S8).

Specifically, the next estimated input physical quantity component is determined based on the score in the 8-component direction of the 4-component 2-direction described above. The following three points are used for the decision.
1) Number of residual points 2) Number of component estimation times 3) Number of prohibited points

  First, as the residual score, the total score of the pattern scores for each of the eight component directions calculated by the process of S7 is used.

Further, the component estimation frequency score is a score for alleviating that only a certain input physical quantity component is estimated, and is given by Equation 14 for four input physical quantity components (not considering the direction of increase / decrease). Note that n ′ _max in Expression 14 is the maximum value of the estimated number of times for each input physical quantity component, and is not limited to a specific value, and is appropriately set to a value of about 10, for example.
(Equation 14) (Number of component estimation times) = n ′ _max − (Estimation number of each input physical quantity component)

The reason for treating it as four components is that the same input physical quantity component cannot be used as the estimated input physical quantity V _{E, 1} in the total estimation times n, n + 1, n + 2,. This is because if the estimated input physical quantities V _{E, 2} , V _{E, 3} , and V _{E, 4} used in Equations 5-1, 5-2, and 5-3 do not change from the mechanism of updating the approximate coefficient, the approximate coefficient This is because does not change.

Further, the prohibition score is a score for preventing the same input physical quantity component from continuously becoming the estimated input physical quantity V _{E, 1} in the total estimation times n, n + 1, n + 2,. As the number of prohibited points, “−1” is given to the input physical quantity component that has become the estimated input physical quantity V _{E, 1, (n, VE1 = n ′)} in the total estimation number n times (that is, the estimation target). Otherwise, “0” is given. In addition, it is a score with respect to four input physical quantity components (the direction of increase / decrease is not considered) similarly to the component estimation frequency score.

The next estimated input physical quantity component is determined based on the above three points. In the residual component score, the component having the largest score in the 8-component direction is the first dominant input physical quantity component group, and the second largest component is the second dominant input physical quantity component group. The score is given by Equation 15 only for the components included in the first and second dominant input physical quantity component groups.
(Expression 15) (Residual score) + (Component estimation frequency score) + (Prohibited score)

  The larger the score calculated by Expression 15, the more the component is deficient in the estimated input physical quantity at the time of the total estimation number n. Since the dominant one is determined from the eight component directions, the estimated direction is determined together with the next estimated input physical quantity component in the processing.

  In the present embodiment, the next estimated component determination unit 11i of the control unit 11 specifies the first dominant input physical quantity component group and the second dominant input physical quantity component group, and the components included in these components are scored by Expression 15. Is calculated. Further, the next estimated component determination unit 11i specifies the input physical quantity component having the largest calculated score as the component to be estimated next.

  Then, the next estimated component determination unit 11i stores the direction component of the specified input physical quantity in the memory 15 as the next estimated input physical quantity component and the estimated direction instruction.

  Next, an abort determination is made (S9).

The censoring determination is performed based on the residual value _{CR, (n, VE1 = n ′) for} each output physical quantity type calculated by Expression 16 _{, and} the absolute value of _EC .
( _Expression 16) | C _{R, (n, VE1 = n ′), EC} | = | C _{M, (n, VE1 = n ′), EC} −C _{E, (n, VE1 = n ′), EC} |

When the absolute value of the residual C _{R, (n, VE1 = n ′), EC} is equal to or smaller than a predetermined cutoff judgment threshold, the type of the output physical quantity is set to “pass (1)”. The truncation determination threshold value is not limited to a specific value, and is appropriately set in consideration of the size of the output physical quantity in the estimation target system, desired estimation accuracy, and the like. Specifically, for example, it may be set to 1% or several percent of the amount of change for each type of output physical quantity when a certain component of the input physical quantity to the estimation target system is changed from the lower limit to the upper limit.

Then, the input physical quantity estimation processing is terminated when K of the 16 output physical quantity types becomes “pass”. Note that the value of K is not limited to a specific value, and is appropriately set in consideration of a desired estimation accuracy and the like. Specifically, for example, setting to about 13 or 14 is conceivable. As described above, the absolute value of the residual _{CR, (n, VE1 = n ′), EC in} the K output physical quantity types out of the 16 output physical quantity types is equal to or less than the predetermined cutoff determination threshold value. Is the end condition of the estimation process.

In the present embodiment, the abort determination unit 11j of the control unit 11 performs the abort determination based on the residual C _{R, (n, VE1 = n ′), EC} calculated by Expression 16. Note that the abort determination threshold is defined in the input physical quantity estimation program 17 in this embodiment.

  If the termination condition is not satisfied and the continuation of the estimation process is determined (S9: No), the control unit 11 returns the input physical quantity estimation process to the process of S1-2, and sets the total estimation count n to 1. And repeat the process up to S9.

On the other hand, when the termination condition is satisfied and the termination is determined (S9: Yes), the termination determination unit 11j inputs the input physical quantity component (VN) accumulated in the estimated input physical quantity database 20 in the data server 16 at the time. The estimated input physical quantities V _{E and VN up} to n times for each total estimation (in other words, the latest) are displayed on the display unit 14 as final estimation results or recorded in the storage unit 12 as estimation result files. . And the control part 11 complete | finishes the estimation process of an input physical quantity (END).

  According to the input physical quantity estimation method, the estimation apparatus, and the estimation program of the present invention configured as described above, when the input to the system and the output from the system are both multivariables (multiple / multidimensional physical quantities) In addition, since the input to the system can be estimated based on the output from the system, it is possible to improve versatility as an estimation method.

In addition, although the above-mentioned form is an example of the suitable form of this invention, it is not limited to this, A various deformation | transformation implementation is possible in the range which does not deviate from the summary of this invention. For example, in the above-described embodiment, when 16 physical quantities are output from the system due to input to the system represented by four physical quantities, the input is represented based on the 16 physical quantities. The case where one physical quantity is estimated is given as an example, but the number of components of the input physical quantity and the number of types of output physical quantities are not limited to these. Note that, depending on the number of components of the input physical quantity, in the above-described embodiment, the number of approximation formulas expressed as Formula 5-1 to Formula 5-4 and the number of approximation formulas for calculating approximate coefficients expressed as Formula 6 to Formula 9 are as follows. change. Specifically, for example, when the number of components of the input physical quantity is three, approximate expressions of Formula 5-2 to Formula 5-4 are used, and the third approximate formula of Formula 5-2 is the third. The value of the approximate coefficient C is calculated in advance using the approximate expressions for calculating the approximate coefficient from Formula 6 to Formula 8. Alternatively, in the case where the number of components of the input physical quantity is five, in addition to Equations 5-1 to 5-4, the fifth approximation expressed as Equation 17 is also used, and the fifth approximation of the fifth approximation The value of the approximation coefficient E is calculated in advance using Expression 18 in addition to Expression 6 to Expression 9. On the other hand, when changing the number of types of output physical quantities, the range of possible values of the subscript EC of each variable may be adjusted.
(Equation 17)
D _{m1, m2, m3, m4, (n, VE1 = n '), EC}
= E _{m1, m2, m3, m4,1, (n, VE1 = n '), EC}・ ( _{VE , 5, (n, VE1 = n')} ) ⁴
+ E _{m1, m2, m3, m4,2, (n, VE1 = n '), EC}・ ( _{VE , 5, (n, VE1 = n')} ) ³
+ E _{m1, m2, m3, m4,3, (n, VE1 = n '), EC}・ ( _{VE , 5, (n, VE1 = n')} ) ²
+ E _{m1, m2, m3, m4,4, (n, VE1 = n '), EC}・ ( _{VE , 5, (n, VE1 = n')} )
+ E _{m1, m2, m3, m4,5, (n, VE1 = n '), EC}
(Equation 18)
D _{m1, m2, m3, m4, EC} = E _{m1, m2, m3, m4,1, EC} · (V ₅ ) ⁴ + E _{m1, m2, m3, m4,2, EC} · (V ₅ ) ³
+ E _{m1, m2, m3, m4,3, EC}・ (V ₅ ) ² + E _{m1, m2, m3, m4,4, EC}・ (V ₅ )
+ E _{m1, m2, m3, m4,5, EC}

  In the above-described embodiment, a fourth-order polynomial is used as the approximate expression represented by Expressions 5-1 to 5-4. However, the order of these approximate expressions is not limited to the fourth order. The order may be less than the fourth order or may be greater than the fourth order.

  In the above-described embodiment, the data server 16 is used as the storage means for storing the fourth approximate coefficient calculation database 18, the acquired output physical quantity database 19, and the estimated input physical quantity database 20. However, various databases are stored. The storage means is not limited to the data server, and other storage means such as the storage unit 12 and various storage media may be used.

In the above-described embodiment, the combinations of the estimated input physical quantity components represented by the input physical quantities V _{E and VN} are shown in Table 1, but the combinations are not limited to those shown in Table 1, and If all the components in one combination are different, they may be set arbitrarily.

  In the above-described embodiment, the processes of S7 and S8 are performed as the operation of determining the next estimated input physical quantity component. However, the determination process of S7 and S8 is not performed, and the input physical quantity component is determined in advance. The input physical quantity component to be estimated may be used according to the order. That is, the processes of S7 and S8 are preferable operations in that the estimation process can be efficiently performed to shorten the processing time, but are not essential operations in the present invention. Therefore, in the example of the above-described embodiment, for example, the order of the input physical quantity components to be estimated is Z component → X component → Y component → Θ component → Z component → X component → (and so on). After the process of S6, the process of S9 is performed, and when the estimation process is continued (S9: No), the input physical quantity component to be estimated is newly determined according to the above order, and the process returns to the process of S1-2. You may do it. Note that when the processes of S7 and S8 are not performed, the estimated direction instruction is not considered in the process of S3.

10 Input physical quantity estimation device 17 Input physical quantity estimation program

Claims (3)

When 16 output physical quantity types are output from the system due to input to the system represented by the four input physical quantity components, the four input physical quantity components are estimated based on the 16 output physical quantity types. When doing
For each of the four input physical quantity components, the input physical quantity V _VN for each of the four input physical quantity components acquired as a sample in advance (subscript VN: input physical quantity component identification number (integer of 1 to 4)) and the 16 Output physical quantity C _{S, EC for each} output physical quantity type (however, subscript EC: identification number of output physical quantity type (integer number from 1 to 16)) and numerical formulas 1-1 to 1-4 in order Processing to calculate the fourth approximate coefficient D _{m1, m2, m3, m4, EC} (subscript m1, m2, m3, m4: coefficient identification numbers (each is an integer of 1 to 5)),
For the input physical quantity component to be estimated, the fourth approximation coefficient D _{m1, m2, m3, m4, EC, the} estimated input physical quantity component _{VE, VN} , and Equations 2-1 to 2-3 are used in order. by substituting a first approximation coefficient calculating process of calculating an approximate coefficient a _{m1, EC,} the output physical quantity C _M obtained from the first approximation coefficient a _{m1, EC} and the system in equation _2-4, and _EC A process of calculating four estimated input physical quantities V _{E, 1, EC} for each of the 16 output physical quantity types, and one for each output physical quantity type from the four estimated input physical quantities V _{E, 1, EC.} The process of selecting the unit and the average V _{E, av} of the estimated input physical quantity selected for each output physical quantity type and calculating the estimation of the input physical quantity component with the average V _{E, av} as the estimation target The process of setting the input physical quantity V _{E, VN} and the first approximation coefficient A _{m1, EC} and the average V of the estimated input physical quantity in Equation 3 _E, the estimated output physical quantity by substituting _av C _E, the process of calculating the _EC, the estimated output physical quantity C _E, the output obtained from _EC and the system physical quantity C _M, the residual by substituting _EC in equation 4 Processing to calculate _{CR, EC} ,
An end condition is that the magnitude of the absolute value of the residual CR _{, EC} is equal to or less than a predetermined truncation determination threshold in a predetermined number of output physical quantity types among the 16 output physical quantity types. The input physical quantity component to be estimated is newly determined when the condition is not satisfied, and the process returns to the first approximation coefficient calculation process. When the end condition is satisfied, the estimation process is terminated. Physical quantity estimation method.
(Equation 1-1)
C _{S, EC} = A ′ _{1, EC} · (V ₁ ) ⁴ + A ′ _{2, EC} · (V ₁ ) ³ + A ′ _{3, EC} · (V ₁ ) ² + A ′ _{4, EC} · (V ₁ )
+ A ' _{5, EC}
(Equation 1-2)
A ′ _{m1, EC} = B ′ _{m1,1, EC} · (V ₂ ) ⁴ + B ′ _{m1,2, EC} · (V ₂ ) ³ + B ′ _{m1,3, EC} · (V ₂ ) ²
+ B ' _{m1,4, EC}・ (V ₂ ) + B' _{m1,5, EC}
(Equation 1-3)
B ′ _{m1, m2, EC} = C ′ _{m1, m2,1, EC} · (V ₃ ) ⁴ + C ′ _{m1, m2,2, EC} · (V ₃ ) ³
_{+ C 'm1, m2,3, EC} · (V 3) 2 + C' m1, m2,4, EC · (V 3) + C 'm1, m2,5, EC
(Equation 1-4)
C ′ _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V ₄ ) ⁴ + D _{m1, m2, m3,2, EC} · (V ₄ ) ³
+ D _{m1, m2, m3,3, EC}・ (V ₄ ) ² + D _{m1, m2, m3,4, EC}・ (V ₄ )
+ D _{m1, m2, m3,5, EC}
(Equation 2-1)
C _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V _{E, 4} ) ⁴ + D _{m1, m2, m3,2, EC} · (V _{E, 4} ) ³
+ D _{m1, m2, m3,3, EC}・ (V _{E, 4} ) ² + D _{m1, m2, m3,4, EC}・ (V _{E, 4} )
+ D _{m1, m2, m3,5, EC}
(Equation 2-2)
B _{m1, m2, EC} = C _{m1, m2,1, EC} · (V _{E, 3} ) ⁴ + C _{m1, m2,2, EC} · (V _{E, 3} ) ³
+ C _{m1, m2,3, EC}・ (V _{E, 3} ) ² + C _{m1, m2,4, EC}・ (V _{E, 3} ) + C _{m1, m2,5, EC}
(Equation 2-3)
A _{m1, EC} = B _{m1,1, EC} · (V _{E, 2} ) ⁴ + B _{m1,2, EC} · (V _{E, 2} ) ³ + B _{m1,3, EC} · (V _{E, 2} ) ²
+ B _{m1,4, EC}・ (V _{E, 2} ) + B _{m1,5, EC}
(Equation 2-4)
0 = A _{1, EC}・ (V _{E, 1, EC} ) ⁴ + A _{2, EC}・ (V _{E, 1, EC} ) ³ + A _{3, EC}・ (V _{E, 1, EC} ) ²
+ A _{4, EC}・ (V _{E, 1, EC} ) + A _{5, EC} −CM _{, EC}
(Equation 3)
C _{E, EC} = A _{1, EC} · (V _{E, av} ) ⁴ + A _{2, EC} · (V _{E, av} ) ³ + A _{3, EC} · (V _{E, av} ) ²
+ A _{4, EC}・ (V _{E, av} ) + A _{5, EC}
(Equation 4)
C _{R, EC} = C _{M, EC} −C _{E, EC} A storage unit storing data of 16 types of output physical quantities output from the system due to input to the system represented by four input physical quantity components, or a storage device storing the data In order to estimate the four input physical quantity components based on the 16 types of output physical quantity,
For each of the four input physical quantity components, the input physical quantity V _VN for each of the four input physical quantity components acquired as a sample in advance (subscript VN: input physical quantity component identification number (integer of 1 to 4)) and the 16 Output physical quantity C _{S, EC for each} output physical quantity type (however, subscript EC: identification number of output physical quantity type (integer number from 1 to 16)) and numerical formulas 1-1 to 1-4 in order Means for calculating the fourth approximation coefficient D _{m1, m2, m3, m4, EC} (subscripts m1, m2, m3, m4: coefficient identification numbers (each an integer of 1 to 5)),
For the input physical quantity component to be estimated, the fourth approximation coefficient D _{m1, m2, m3, m4, EC, the} estimated input physical quantity component _{VE, VN} , and Equations 2-1 to 2-3 are used in order. by substituting a first approximation coefficient calculating means for calculating an approximate coefficient a _{m1, EC,} the output physical quantity C _M obtained from the first approximation coefficient a _{m1, EC} and the system in equation _2-4, and _EC Means for calculating four estimated input physical quantities V _{E, 1, EC} for each of the 16 output physical quantity types, and one for each output physical quantity type from the four estimated input physical quantities V _{E, 1, EC.} The means for selecting the unit and the average V _{E, av} of the estimated input physical quantity selected for each of the output physical quantity types are calculated, and the estimation of the input physical quantity component using the average V _{E, av} as the estimation target Means for making the input physical quantity V _{E, VN,} and Equation 3 _shows the first approximation coefficient _{Am1, EC} and the average V of the estimated input physical quantity _E, the estimated output physical quantity by substituting _av C _E, means for calculating the _EC, the estimated output physical quantity C _E, the output obtained from _EC and the system physical quantity C _M, the residual by substituting _EC in equation 4 Means for calculating _{CR, EC} ;
An end condition is that the magnitude of the absolute value of the residual CR _{, EC} is equal to or less than a predetermined truncation determination threshold in a predetermined number of output physical quantity types among the 16 output physical quantity types. The input physical quantity component to be estimated is newly determined when the condition is not satisfied, and the process returns to the first approximation coefficient calculation process. When the end condition is satisfied, the estimation process is terminated. Physical quantity estimation device.
(Equation 1-1)
C _{S, EC} = A ′ _{1, EC} · (V ₁ ) ⁴ + A ′ _{2, EC} · (V ₁ ) ³ + A ′ _{3, EC} · (V ₁ ) ² + A ′ _{4, EC} · (V ₁ )
+ A ' _{5, EC}
(Equation 1-2)
A ′ _{m1, EC} = B ′ _{m1,1, EC} · (V ₂ ) ⁴ + B ′ _{m1,2, EC} · (V ₂ ) ³ + B ′ _{m1,3, EC} · (V ₂ ) ²
+ B ' _{m1,4, EC}・ (V ₂ ) + B' _{m1,5, EC}
(Equation 1-3)
B ′ _{m1, m2, EC} = C ′ _{m1, m2,1, EC} · (V ₃ ) ⁴ + C ′ _{m1, m2,2, EC} · (V ₃ ) ³
_{+ C 'm1, m2,3, EC} · (V 3) 2 + C' m1, m2,4, EC · (V 3) + C 'm1, m2,5, EC
(Equation 1-4)
C ′ _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V ₄ ) ⁴ + D _{m1, m2, m3,2, EC} · (V ₄ ) ³
+ D _{m1, m2, m3,3, EC}・ (V ₄ ) ² + D _{m1, m2, m3,4, EC}・ (V ₄ )
+ D _{m1, m2, m3,5, EC}
(Equation 2-1)
C _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V _{E, 4} ) ⁴ + D _{m1, m2, m3,2, EC} · (V _{E, 4} ) ³
+ D _{m1, m2, m3,3, EC}・ (V _{E, 4} ) ² + D _{m1, m2, m3,4, EC}・ (V _{E, 4} )
+ D _{m1, m2, m3,5, EC}
(Equation 2-2)
B _{m1, m2, EC} = C _{m1, m2,1, EC} · (V _{E, 3} ) ⁴ + C _{m1, m2,2, EC} · (V _{E, 3} ) ³
+ C _{m1, m2,3, EC}・ (V _{E, 3} ) ² + C _{m1, m2,4, EC}・ (V _{E, 3} ) + C _{m1, m2,5, EC}
(Equation 2-3)
A _{m1, EC} = B _{m1,1, EC} · (V _{E, 2} ) ⁴ + B _{m1,2, EC} · (V _{E, 2} ) ³ + B _{m1,3, EC} · (V _{E, 2} ) ²
+ B _{m1,4, EC}・ (V _{E, 2} ) + B _{m1,5, EC}
(Equation 2-4)
0 = A _{1, EC}・ (V _{E, 1, EC} ) ⁴ + A _{2, EC}・ (V _{E, 1, EC} ) ³ + A _{3, EC}・ (V _{E, 1, EC} ) ²
+ A _{4, EC}・ (V _{E, 1, EC} ) + A _{5, EC} −CM _{, EC}
(Equation 3)
C _{E, EC} = A _{1, EC} · (V _{E, av} ) ⁴ + A _{2, EC} · (V _{E, av} ) ³ + A _{3, EC} · (V _{E, av} ) ²
+ A _{4, EC}・ (V _{E, av} ) + A _{5, EC}
(Equation 4)
C _{R, EC} = C _{M, EC} −C _{E, EC} A storage unit storing data of 16 types of output physical quantities output from the system due to input to the system represented by four input physical quantity components, or a storage device storing the data When estimating the four input physical quantity components based on the 16 types of output physical quantity,
For each of the four input physical quantity components, the input physical quantity V _VN for each of the four input physical quantity components acquired as a sample in advance (subscript VN: input physical quantity component identification number (integer of 1 to 4)) and the 16 Output physical quantity C _{S, EC for each} output physical quantity type (however, subscript EC: identification number of output physical quantity type (integer number from 1 to 16)) and numerical formulas 1-1 to 1-4 in order Means for calculating the fourth approximate coefficient D _{m1, m2, m3, m4, EC} (subscripts m1, m2, m3, m4: coefficient identification numbers (integers 1 to 5 respectively)),
For the input physical quantity component to be estimated, the fourth approximation coefficient D _{m1, m2, m3, m4, EC, the} estimated input physical quantity component _{VE, VN} , and Equations 2-1 to 2-3 are used in order. first approximation coefficient calculating means for calculating an approximate coefficient a _{m1, EC,} the first approximation coefficient in equation 2-4 a _{m1, EC} and obtained from the system output physical quantity C _M, said substituted and _EC Means for calculating four estimated input physical quantities V _{E, 1, EC} for each of the 16 output physical quantity types, one for each output physical quantity type from the four estimated input physical quantities V _{E, 1, EC} Means for selecting, an average V _{E, av} of estimated input physical quantities selected for each type of output physical quantity _, and calculating the estimated input physical quantity V for an input physical quantity component having the average V _{E, av} as the estimation target _E, means to _VN, the first approximation coefficients in equation 3 a _{m1, EC} and average V _E of the estimated input physical _quantity, the _av generations Calculating means, the estimated output physical quantity C _E in Equation _{4, EC} and output physical quantity C _M obtained from the _system, residual C _R by substituting the _EC, the _EC of calculating the estimated output physical quantity C _E, the _EC and Function as a means to
An end condition is that the magnitude of the absolute value of the residual CR _{, EC} is equal to or less than a predetermined truncation determination threshold in a predetermined number of output physical quantity types among the 16 output physical quantity types. If not, the input physical quantity component to be estimated is newly determined and the process returns to the first approximation coefficient calculation process. If the end condition is satisfied, the estimation process is terminated. Input physical quantity estimation program.
(Equation 1-1)
C _{S, EC} = A ′ _{1, EC} · (V ₁ ) ⁴ + A ′ _{2, EC} · (V ₁ ) ³ + A ′ _{3, EC} · (V ₁ ) ² + A ′ _{4, EC} · (V ₁ )
+ A ' _{5, EC}
(Equation 1-2)
A ′ _{m1, EC} = B ′ _{m1,1, EC} · (V ₂ ) ⁴ + B ′ _{m1,2, EC} · (V ₂ ) ³ + B ′ _{m1,3, EC} · (V ₂ ) ²
+ B ' _{m1,4, EC}・ (V ₂ ) + B' _{m1,5, EC}
(Equation 1-3)
B ′ _{m1, m2, EC} = C ′ _{m1, m2,1, EC} · (V ₃ ) ⁴ + C ′ _{m1, m2,2, EC} · (V ₃ ) ³
_{+ C 'm1, m2,3, EC} · (V 3) 2 + C' m1, m2,4, EC · (V 3) + C 'm1, m2,5, EC
(Equation 1-4)
C ′ _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V ₄ ) ⁴ + D _{m1, m2, m3,2, EC} · (V ₄ ) ³
+ D _{m1, m2, m3,3, EC}・ (V ₄ ) ² + D _{m1, m2, m3,4, EC}・ (V ₄ )
+ D _{m1, m2, m3,5, EC}
(Equation 2-1)
C _{m1, m2, m3, EC} = D _{m1, m2, m3,1, EC} · (V _{E, 4} ) ⁴ + D _{m1, m2, m3,2, EC} · (V _{E, 4} ) ³
+ D _{m1, m2, m3,3, EC}・ (V _{E, 4} ) ² + D _{m1, m2, m3,4, EC}・ (V _{E, 4} )
+ D _{m1, m2, m3,5, EC}
(Equation 2-2)
B _{m1, m2, EC} = C _{m1, m2,1, EC} · (V _{E, 3} ) ⁴ + C _{m1, m2,2, EC} · (V _{E, 3} ) ³
+ C _{m1, m2,3, EC}・ (V _{E, 3} ) ² + C _{m1, m2,4, EC}・ (V _{E, 3} ) + C _{m1, m2,5, EC}
(Equation 2-3)
A _{m1, EC} = B _{m1,1, EC} · (V _{E, 2} ) ⁴ + B _{m1,2, EC} · (V _{E, 2} ) ³ + B _{m1,3, EC} · (V _{E, 2} ) ²
+ B _{m1,4, EC}・ (V _{E, 2} ) + B _{m1,5, EC}
(Equation 2-4)
0 = A _{1, EC}・ (V _{E, 1, EC} ) ⁴ + A _{2, EC}・ (V _{E, 1, EC} ) ³ + A _{3, EC}・ (V _{E, 1, EC} ) ²
+ A _{4, EC}・ (V _{E, 1, EC} ) + A _{5, EC} −CM _{, EC}
(Equation 3)
C _{E, EC} = A _{1, EC} · (V _{E, av} ) ⁴ + A _{2, EC} · (V _{E, av} ) ³ + A _{3, EC} · (V _{E, av} ) ²
+ A _{4, EC}・ (V _{E, av} ) + A _{5, EC}
(Equation 4)
C _{R, EC} = C _{M, EC} −C _{E, EC}