CN113204879B - An improved Hankel matrix prediction model modeling method based on fluorescent oil film and its application - Google Patents

Abstract

The invention discloses a modeling method and application of an improved Hankel matrix prediction model based on a fluorescent oil film, wherein the modeling method comprises the following steps: establishing a basic Hankel matrix prediction model; establishing an error correction prediction model according to the processing of the prediction value and the error value of the basic prediction model; and determining an improved Hankel matrix prediction model according to the prediction condition of the error correction prediction model. The modeling method can effectively solve the problems of tedious acquisition steps, time consumption and labor consumption of relation data of the gray scale of the fluorescent oil film image and the oil film thickness, more accurate data can be obtained through accurate prediction of extremely few acquired data, the complex operation of data acquisition is avoided, and a large amount of time and tool equipment are saved.

Description

An improved Hankel matrix prediction model modeling method based on fluorescent oil film and its application

technical field

The invention relates to the technical field of a modeling method for fluorescent oil film thickness and its image gray value.

Background technique

Surface frictional resistance (referred to as surface frictional resistance) is one of the most important physical quantities in aerodynamics, and it is an important part of the total resistance suffered by an aircraft during flight. one of the physical quantities. Reducing friction can not only reduce the fuel consumption of the aircraft and increase the endurance of the aircraft, but also means that the heat flow on the surface of the supersonic aircraft is reduced, the weight of the heat-resistant material is reduced, and the payload is increased. Existing studies have shown that the surface friction of a new type of civil aviation airliner accounts for about half of the total resistance when it is running stably, far exceeding other resistance factors and occupies a dominant position; while for the supersonic aircraft developed by China, the surface friction can account for the largest part. More than 50% of the total resistance has a strong impact on the stability of the supersonic aircraft operation, and is also directly related to the service life of the aircraft. Therefore, reducing surface friction is of great significance to improving aircraft performance, reducing costs and saving energy.

Most of the traditional methods of measuring friction have certain defects and limitations, such as hot film method, Preston tube method, Stanton tube method, friction balance method, and laser Doppler method, among them, the main principle of hot film method is to measure electrical Heating the heat on the metal film, by establishing a mathematical model between the Joule heat conversion rate and the fluid, so as to solve the friction resistance, but this method may cause distortion due to temperature drift; Factors such as included angle have high requirements and are difficult to use flexibly; the friction balance method installs the floating element on the displacement sensor, which can directly measure the resultant force of surface friction acting on the floating element, but the measurement accuracy is affected by environmental factors and traditional manufacturing. Factors and human factors are greatly affected; the laser Doppler measurement method uses the Doppler effect caused by the scattering of particles passing through a viscous bottom layer with streaked light, but the sampling rate is low due to the low density of tracer particles in the viscous bottom layer , which is difficult to apply in unsteady measurements.

In order to improve the above-mentioned traditional measurement method, the existing technology proposes to mix silicone oil and fluorescent molecules in a specific ratio to form a fluorescent oil film, and according to the color reaction excited by it under ultraviolet light irradiation, the thickness value of the oil film is represented by the gray value of the oil film image , and then solve the means to obtain the friction distribution.

However, if the gray value of the fluorescent oil film image and the thickness value of the oil film are obtained directly through actual measurement, it is usually more complicated and/or the amount of data collected is small. For example, in 2012, Li Peng provided a method for collecting gray value and thickness data of the fluorescent oil film , which is realized by using a sampling device built by placing an optical glass slide with high light transmittance on a flat surface platform (for the specific structure, see Li Peng "Research on Direct Measurement Technology of Global Surface Frictional Stress", Nanjing University of Aeronautics and Astronautics, 2012), and The continuous fluorescent oil film with different thickness values is solved by geometric relationship, and the sampling device satisfies:

Among them, h and s are the thickness of the point to be measured and the length of the measurement area, H and F are the height of the glass slide and the length of the acquisition area of the slope of the slide, respectively. Through this device, the thickness information of any point in the measurement area can be obtained. However, the steps of this acquisition method are relatively cumbersome, there are many mathematical conversions, and each pixel needs to be accurately located, which is time-consuming and labor-intensive. At the same time, the acquisition system used is very dependent on the flatness and smoothness of the mold. The requirements are high, and the cost of solution implementation is high.

In addition to the actual data collection, there are few studies on the relationship between the grayscale and thickness of fluorescent oil film images in the prior art, and no systematic model and modeling method for obtaining grayscale and thickness values are provided.

In order to meet the data requirements, in addition to the actual collected data, other data other than the collected data need to be used. In the further processing, the traditional interpolation method can meet the accuracy requirements when interpolating the actually collected data. When extrapolating data other than the collected data, especially when the interpolated data is far away from the collected data, the accuracy often cannot meet the requirements and even error data may appear.

On the other hand, in 2014, Mu and Chen established the Hankel matrix for system identification. The characteristic of this matrix is that it can establish a prediction model with a very small amount of data, and realize the prediction of a large amount of data other than the modeling data. This is the traditional interpolation not available in the law. However, the accuracy of the traditional Hankel matrix prediction model is low, and the deviation is large when predicting distant data, so it cannot be directly applied to the modeling of the gray value of the fluorescent oil film image and the thickness of the oil film to obtain accurate prediction results.

Contents of the invention

The purpose of the present invention is to provide a modeling method, which can predict the remaining available data with a very small amount of data, and the prediction accuracy is high, which can largely avoid the various operations of data collection and save a lot of time and tools The equipment can effectively solve the problems of cumbersome, time-consuming and labor-consuming, and less available data collection steps in the prior art for the gray scale of the fluorescent oil film image and the oil film thickness data. The purpose of the present invention is also to provide some specific application methods of the modeling method.

The present invention first discloses the following technical solutions:

A modeling method based on the improved Hankel matrix predictive model of fluorescent oil film, it comprises the following steps:

S1 establishes the basic Hankel matrix prediction model based on the collected data of fluorescent oil film;

S2 performs data prediction through the basic Hankel matrix prediction model;

S3 establishes the error correction prediction model of the basic Hankel matrix prediction model according to the processing of the predicted value obtained in step S2 and its error value;

S4 performs data prediction through the error correction prediction model, and performs model prediction accuracy and/or prediction accuracy evaluation through the prediction data;

S5 If the prediction data obtained by the error correction prediction model is accurate and/or its prediction accuracy is improved, then output the error correction prediction model as an improved Hankel matrix prediction model, if the obtained prediction data is inaccurate and/or its prediction accuracy If it is not improved, then use the error correction prediction model as the basic Hankel matrix prediction model of S1 and continue to iteratively update according to the process of S2-S5 until the improved Hankel matrix prediction model is obtained.

According to some preferred embodiments of the present invention, the processing of the predicted value and the error value includes: performing averaging processing on the error value, and correcting the predicted value by the error value after averaging.

According to some preferred embodiments of the present invention, the step S3 includes: correcting the predicted value by using the error value to obtain a corrected predicted value, and establishing the error correction forecast model by using the corrected predicted value.

According to some preferred embodiments of the present invention, the modeling method includes:

(1) Establish the basic Hankel matrix prediction model;

(2) carry out data prediction by described basic Hankel matrix prediction model;

(3) Perform mean value processing on the error value generated by prediction;

(4) Correct the forecast data according to the mean value processing result, replace the original forecast data with the corrected data, and establish the first error correction forecast model of the basic Hankel matrix forecast model;

(5) performing data prediction by the first error correction prediction model;

(6) If the data prediction is good, then output the error correction prediction model as the improved Hankel matrix prediction model, if the data prediction is wrong, then use the error correction prediction model as the basic Hankel matrix prediction model of step (1) and continue to press The process of 2)-(6) is updated iteratively until the improved Hankel matrix prediction model is obtained.

In some specific embodiments, whether the data prediction is good can be determined by checking whether the prediction accuracy of the error correction prediction model is improved compared with the basic Hankel matrix prediction model. If the prediction accuracy is improved, it is considered that the data prediction is good.

According to some preferred embodiments of the present invention, the first error correction prediction model is as follows:

Γw _(n) = [w _(n) -w _n ]+Γw _n (13),

表示模型预测结果数据组，Δε_(n)表示误差数据组，G(_ε)(z^-1)表示Δε_(n)的Z域传递函数，Δε_n表示误差数据组Δε_(n)中的误差数据，g表示脉冲数据中某时刻的灰度值，ΔG表示脉冲数据相邻两个元素的灰度值差，δ(g-n·ΔG)表示脉冲函数、当g＝n·ΔG时，δ(g-k·ΔG)＝1成立，n表示系统阶数大小，Γw_n表示修正后脉冲数据组，w_n表示w_(n)中的单个建模数据，Γw_(n)表示通过修正后的脉冲数据组替代其原脉冲数据组后得到的新的脉冲响应数据组。Among them, w(n) represents the impulse response data set used for model building, which can be specifically composed of the gray value of the pixel point in the fluorescent oil film image or its corresponding identification, such as the serial number of the pixel point, etc., and the corresponding oil film thickness value ,

Indicates the model prediction result data group, Δε _(n) represents the error data group, G( _ε )(z ^-1 ) represents the Z-domain transfer function of Δε _(n) , and Δε _n represents the error data in the error data group Δε _(n) , g represents the gray value at a certain moment in the pulse data, ΔG represents the gray value difference between two adjacent elements of the pulse data, δ(gn·ΔG) represents the pulse function, when g=n·ΔG, δ(gk· ΔG)=1 is established, n represents the order of the system, Γw _n represents the corrected pulse data set, w _n represents the single modeling data in w _(n) , Γw _(n) represents the replacement of other The new impulse response data set obtained after the original impulse data set.

According to some preferred embodiments of the present invention, the step S3 includes: correcting the predicted value by the error value to obtain a corrected predicted value, adding the corrected predicted value to the set of predicted values, The extended prediction value is obtained, and the error correction prediction model is established through the corrected prediction value.

According to some preferred embodiments of the present invention, the modeling method includes:

(1) set up described basic Hankel matrix prediction model;

(2) Carry out data prediction through the basic Hankel matrix prediction model;

(3) Perform mean value processing on the error value generated by prediction;

(4) Correct the predicted data according to the mean value processing result, add the corrected data in the original predicted data, obtain the expanded data, and establish the second error correction forecast model of the basic Hankel matrix forecast model with the expanded data;

(5) evaluating the accuracy of the second error correction prediction model;

(6) If the prediction accuracy improves, then output the error correction prediction model as an improved Hankel matrix prediction model, if the prediction accuracy does not improve, then use the error correction prediction model as the basic Hankel matrix prediction model of step (1) and continue to press ( The process of 2)-(6) is updated iteratively until the improved Hankel matrix prediction model is obtained.

According to some preferred embodiments of the present invention, the second error correction prediction model is as follows:

G(z ^-1 )＝w ₁ z ^-1 +w ₂ z ^-2 +...w _n z ^-n (17)

表示模型预测结果数据组，Δε_(n)表示误差数据组，G(z^-1)表示Δε_(n)的Z域传递函数，Δε_n表示误差数据组Δε_(n)中的误差数据，g表示脉冲数据中某时刻的灰度值，ΔG表示脉冲数据相邻两个元素的灰度值差，δ(g-n·ΔG)表示脉冲函数、当g＝n·ΔG时，δ(g-k·ΔG)^＝1成立，n表示系统阶数大小，Γw_n表示修正后脉冲数据组，w_n表示w_(n)中的单个建模数据，Γw_(n)表示第r次迭代得到的扩展后脉冲响应数据组，

表示第r+1次迭代中得到的扩展后的脉冲响应数据组，

表示通过传递函数G(z^-1)预测的数据，r表示迭代次数，

表示收敛条件。Among them, w _(n) represents the impulse response data set used for model building, which can be specifically composed of the gray value of the pixel point in the fluorescent oil film image or its corresponding identification, such as the serial number of the pixel point, etc., and the corresponding oil film thickness value ,

Indicates the model prediction result data group, Δε _(n) represents the error data group, G(z ^-1 ) represents the Z-domain transfer function of Δε _(n) , Δε _n represents the error data in the error data group Δε _(n) , and g represents The gray value at a certain moment in the pulse data, ΔG represents the gray value difference between two adjacent elements of the pulse data, δ(gn·ΔG) represents the pulse function, when g=n·ΔG, δ(gk·ΔG) ^{= 1} is established, n represents the order of the system, Γw _n represents the corrected impulse data set, w _n represents the single modeling data in w _(n) , Γw _(n) represents the extended impulse response data set obtained in the rth iteration ,

Represents the extended impulse response data set obtained in the r+1th iteration,

Represents the data predicted by the transfer function G(z ^-1 ), r represents the number of iterations,

Indicates the convergence condition.

According to some preferred embodiments of the present invention, the evaluation method of the prediction accuracy is: subtracting the predicted data from the original data to obtain the error data, taking the percentage value of the error data and its corresponding original data as the error rate, and taking the error The size of the rate represents the prediction accuracy.

The present invention further proposes some applications of the modeling method, such as obtaining more accurate fluorescent oil film thickness data and its image grayscale data on the basis of a small amount of collected data through the modeling method.

The invention can be further applied to the analysis of surface frictional resistance based on the thickness data of the fluorescent oil film and its image grayscale data.

Compared with the uncorrected error function of the traditional Hankel matrix prediction model, the generated errors will continue to accumulate and amplify. The error is generated by the system itself, and may also include problems such as rounding calculation errors. The present invention establishes an improved Hankel matrix prediction model, such as The first error correction prediction model or the matrix error correction prediction model as described in the specific embodiment, the second error correction prediction model or the Hankel matrix high-order iterative error correction prediction model as described in the specific embodiment can greatly eliminate the influence of errors and realize Improvement of model prediction accuracy.

The modeling method of the present invention can effectively solve the problem that the collection steps of the relationship data between the gray scale of the fluorescent oil film image and the thickness of the oil film are cumbersome, time-consuming and labor-intensive, and the remaining desired data can be predicted through a very small amount of data. Higher precision, thus avoiding the various operations of data collection to a great extent, saving a lot of time and tools and equipment.

Description of drawings

Fig. 1 is a collection device for data collection application in a specific embodiment.

Fig. 2 is a specific establishment process of the improved Hankel matrix prediction model described in the present invention.

Fig. 3 is another specific establishment process of the improved Hankel matrix prediction model described in the present invention.

FIG. 4 is a schematic flowchart of a specific data collection method adopted in a specific embodiment.

FIG. 5 is a schematic diagram of specific working conditions for data collection in Example 1.

FIG. 6 is a schematic diagram of pixel value averaging processing in Embodiment 1. FIG.

Fig. 7 is the real collection picture obtained in embodiment 1.

Detailed ways

The present invention will be described in detail below in conjunction with the embodiments and drawings, but it should be understood that the embodiments and drawings are only used for exemplary description of the present invention, and do not constitute any limitation on the protection scope of the present invention. All reasonable transformations and combinations within the scope of the gist of the present invention fall within the protection scope of the present invention.

According to the technical scheme of the present invention, some specific modeling methods of the improved Hankel matrix predictive model include:

S1 establishes the basic Hankel matrix prediction model;

S2 performs data prediction through the basic Hankel matrix prediction model;

S3 establishes an error correction prediction model of the basic Hankel matrix prediction model according to the processing of the prediction value generated by the prediction and/or its error value;

S4 Carry out data prediction or prediction accuracy evaluation through error correction prediction model;

S5 If the prediction data obtained by the error correction prediction model is accurate and/or its prediction accuracy is improved, then output the error correction prediction model as an improved Hankel matrix prediction model, if the prediction data obtained by the error correction prediction model is inaccurate or its prediction accuracy is not If it is improved, the error correction forecasting model is used as the basic Hankel matrix forecasting model in step (2) and continues to be iteratively updated according to the process of S2-S5, until the final improved Hankel matrix forecasting model is obtained.

Among them, the basic theory of the Hankel matrix prediction model is as follows:

Let the Z-domain transfer function of the Hankel matrix prediction model be shown in formula (2), where [b ₁ , b ₂ ... b _n ] is the numerator coefficient, [a ₁ , a ₂ ... a _n ] is the denominator coefficient, and n is The order size of the Z-domain transfer function is determined by the highest power of the numerator and denominator coefficients:

Carry out power series expansion on formula (2), and get the following formula (3):

[w ₁ ,w ₂ ...w _n ] in formula (3) is the coefficient of the constant term obtained by expansion, that is, the pulse coefficient. Put formula (3) into formula (2) to get formula (4):

Further expand and simplify formula (5):

Perform product transformation on formula (5) and simplify the same power-level term, namely:

By equalizing the coefficients corresponding to the same power-level items on both sides of the equal sign, the matrix relationship between the impulse response data and the transfer function numerator coefficient b _n and denominator coefficient a _n is constructed, as shown in formula (7):

Construct the coefficient of the power series on the right side of equation (7) into a Hankel matrix form:

Then the solution matrix of the denominator coefficient a _n of the transfer function is shown in formula (9):

It can be seen that by constructing the Hankel matrix for the impulse response data, the numerator coefficient b _n and the denominator coefficient a _n of the transfer function can be obtained, and then the Z-domain transfer function prediction model can be obtained.

According to the direct relationship between the denominator coefficient a _n of the transfer function and the impulse response data in the above model, the denominator coefficient a _n is optimized. If the impulse response data directly acting on the denominator coefficient a _n is corrected, a better result can be obtained prediction effect.

Based on the above findings, the error correction prediction model can be further selected from:

A. The first error correction prediction model, the process of obtaining the improved Hankel matrix prediction model based on this model is as shown in accompanying drawing 2, and it specifically includes:

(1) Establish the basic Hankel matrix prediction model;

(2) Carry out data prediction through the basic Hankel matrix prediction model;

(3) Perform mean value processing on the error value generated by prediction;

(4) Correct the forecast data according to the mean value processing result, replace the original forecast data with the corrected data, and establish the first error correction forecast model of the basic Hankel matrix forecast model;

(5) performing data prediction by the first error correction prediction model;

(6) If the data prediction is good, then output the error correction prediction model as the improved Hankel matrix prediction model, if the data prediction is wrong, then use the error correction prediction model as the basic Hankel matrix prediction model of step (2) and continue to press The process of 2)-(6) is iteratively updated until the final improved Hankel matrix prediction model is obtained.

Whether the data is predicted well can be determined by whether the accuracy of the first error correction prediction model is improved relative to the basic Hankel matrix prediction model. If the accuracy is improved after correction, it is considered that the data prediction is good.

The first error correction prediction model can be further specifically constructed as follows:

表示模型对w(n)的预测结果数据组，则可得到式(10)所示的误差数据组：Let w(n) denote the impulse response data set used for model building,

represents the prediction result data set of the model for w(n), then the error data set shown in formula (10) can be obtained:

Among them, Δε _(n) represents the error data set.

Based on the above basic theory of Hankel matrix prediction model, the Z-domain transfer function G( _ε )(z ^-1 ) of Δε _(n) is established, and according to the characteristics of the Z-domain transfer function, it is expressed as the following impulse model:

In formula (11), Δε _n represents the data in the error data group Δε _(n) , g represents the gray value at a certain moment in the pulse data, ΔG represents the gray value difference between two adjacent elements of the pulse data, δ(gn· ΔG) represents an impulse function, and when g=n·ΔG, δ(gk·ΔG)=1 holds true.

Analyzing equations (7), (8) and (9), considering that w _n is a single modeling data, and w _n directly affects the denominator coefficient a _n , after error correction processing, the following corrected pulse data set can be obtained Γw _n :

Update the obtained corrected pulse data Γw _n to the original sequence to obtain a new data set Γw(n) and establish the following data correction model, as follows:

Γw _(n) = [w _(n) -w _n ]+Γw _n (13).

The corrected data group obtained through the data correction model is used as the impulse response data group data of the Hankel matrix prediction model, and its corresponding Z-domain transfer function is obtained, that is, the first error correction prediction model is obtained.

B. The second error correction prediction model, that is, a high-order iterative error correction prediction model.

In order to improve the accuracy of the prediction model, the present invention also includes the process of establishing a high-order system transfer function model in an iterative manner, that is, expanding on the basis of the first error correction prediction model, for example, predicting the first error correction prediction model to obtain The data added to the original pulse data series to expand the amount of pulse data to establish a higher order prediction model. In this process, the supplementary prediction data is the data after error correction, which reduces the cumulative effect of errors and makes the follow-up prediction results on the right track. At the same time, the Hankel matrix is constructed with the supplementary new pulse data and the improved Prediction model, through iterative calculation until the accuracy of the model gradually improves to the convergence state, and finally predictive analysis.

The process of obtaining the improved Hankel matrix prediction model based on the model is shown in Figure 3, which specifically includes:

(1) Establish the basic Hankel matrix prediction model;

(2) Carry out data prediction through the basic Hankel matrix prediction model;

(3) Perform mean value processing on the error value generated by prediction;

(4) Correct the predicted data according to the mean value processing result, add the corrected data in the original predicted data, obtain the expanded data, and establish the second error correction forecast model of the basic Hankel matrix forecast model with the expanded data;

(5) Evaluate the accuracy of the second error correction prediction model. The specific accuracy evaluation method can be as follows: the error data can be obtained by subtracting the original data from the predicted data, and the error data is divided by the corresponding original data and converted into a percentage The form display is convenient for intuitive analysis, and finally the percentage error is analyzed as the criterion of accuracy;

(6) If the prediction accuracy improves, then output the error correction prediction model as an improved Hankel matrix prediction model, if the prediction accuracy does not improve, then use the error correction prediction model as the basic Hankel matrix prediction model of step (1) and continue to press ( The process of 2)-(6) is iteratively updated until the final improved Hankel matrix prediction model is obtained.

Its specific construction can further include:

Let w _(n) be the impulse response data set to be modeled, and the constructed Hankel matrix H(w) can be obtained as:

表示传递函数预测模型G(z^-1)预测的数据，r为迭代次数。结合式(12)、(13)的数据修正模型，并将修正后的数据补入原脉冲响应数据组中，可得如下的扩展后修正脉冲数据组

如式(15)所示：Based on the formula (14), establish the transfer function prediction model G(z ^-1 )=w ₁ z ^-1 +w ₂ z ^-2 +...w _n z ^-n (17), and establish the iterative formula, where

Indicates the data predicted by the transfer function prediction model G(z ^-1 ), and r is the number of iterations. Combining the data correction model of formulas (12) and (13), and adding the corrected data into the original impulse response data set, the following extended corrected impulse data set can be obtained

As shown in formula (15):

The obtained expanded and corrected impulse data set is used as the impulse response data set data of the Hankel matrix prediction model, and its corresponding Z-domain transfer function is obtained, and iterated until the error data set obtained by formula (10) satisfies the following convergence conditions:

The corresponding Z-domain transfer function in the final convergence state is obtained, that is, the second error correction prediction model is obtained.

The present invention further provides some specific data acquisition and correlation methods of the image gray value and oil film thickness value of the fluorescent oil film that can be used for the above-mentioned model establishment, which can be realized by the existing acquisition device as shown in accompanying drawing 1, including as attached The process shown in Figure 4 is as follows:

Calibrate the photographic equipment required for data collection, such as a camera, to obtain its internal and external parameters, including internal parameters such as camera focal length, focus coordinates, and radial distortion parameters, and external parameters such as rotation matrix and translation matrix, which determine the world coordinate system to the camera coordinate system conversion;

Obtain the fluorescent oil film and ultraviolet light source, and carry out the ultraviolet color reaction of the oil film, such as filling the oil film through the fluorescent oil film collection system, and turning on the ultraviolet light source to carry out the reaction;

Acquisition of grayscale images of the oil film through photographic equipment such as a camera;

Judging whether the effect of the image is good, if it is not good, the oil film preparation and color reaction will be carried out again, if the effect is good, the next gray value collection will be carried out;

Collect the gray value of the gray image with good effect, including: pose calculation, complete the conversion between pixel coordinates and the world coordinate system, and collect the gray point set of the required oil film;

Perform pixel ratio and geometric conversion on the collected gray points to obtain the oil film thickness corresponding to each point in the point set.

Example 1

The collection and correlation test of the gray value of the image of the fluorescent oil film and the thickness of the oil film is carried out through the data collection and correlation method described in the specific embodiment.

Among them, the photographic equipment uses a Canon EOS 550D camera with a horizontal and vertical resolution of 72dpi and a bit depth of 24. It has the characteristics of high resolution, fast acquisition speed, and easy operation. The ultraviolet light source used is JZFZ -220/18-001 machine vision ultraviolet light lamp, its effective power is 18W±10%, and it has the characteristics of emitting more uniform ultraviolet light.

During the test, when the fluorescent oil film is in an excited state, in order to eliminate the interference of stray light such as ultraviolet light source and ambient light, a 520nm optical filter is installed on the lens of the camera to improve the accuracy of pixel gray value.

In the device used as shown in Figure 1, the slide glass is an international standard slide glass, with a length of 76.20 mm, a width of 25.40 mm, and a height of 0.95 mm. The specific collection steps carried out by this device are:

Place a glass slide 2 on a smooth and opaque platform, which can ensure its smoothness and flatness through high-precision machining;

Pour an appropriate amount of fluorescent oil film on the area on the smooth platform that is not in direct contact with slide glass 2, take another slide glass 1 with a light transmittance above 95%, make it touch the smooth platform at one end, and put slide glass 2 on the other end , forming a slope, and by pressing the glass slide 1, the fluorescent oil film under it is filled with the gap formed by the slide glass 1, the slide glass 2 and the smooth platform;

Turn on the ultraviolet light, and collect the grayscale image of the oil film through the acquisition condition shown in Figure 5. Under this acquisition condition, a spatial rectangular coordinate system is established with the end point at the left end of the slide glass as the origin, and the effective acquisition area is from the origin to The length of the oil film extension is 70.00mm, that is, the space coordinates of the initial collection point are (0,0,0), the space coordinates of the end point are (7,0,0), the unit is cm, and the height of the ultraviolet light source is 50cm, that is, its space coordinates is (0,0,50).

Under the above collection steps, the thickness of the oil film at different positions can be obtained, as follows:

Where h represents the thickness of the oil film to be measured, s represents the length of the measurement area, H and F represent the height of the slide and the length of the slope collection area of the slide 1, respectively.

In order to improve the stability of pixel gray value, average value processing is adopted for the pixel value to be measured, that is, a total of 8 pixels around the pixel to be measured and the measurement pixel are collected to form a 3×3 square area, and then The pixel values of the 9 pixel points in this area are processed as the average value to represent the pixel value of the measured pixel point, as shown in Fig. 6 . The number of pixels collected is 22, and the grayscale images collected are analyzed with MATLAB software to establish a pixel value coordinate matrix. The spatial coordinates and pixel coordinates of the initial collection points are (0,0,0), respectively. (610,1020), the space coordinates and pixel coordinates of the end point are (7,0,0) and (2418,1020) respectively. Because there are decimals after the average gray value processing, it is correspondingly converted to an integer. For example, the gray value obtained by the average gray value processing is 76.11, and the thickness is 78.09961. When the gray value is converted to 76, the corresponding thickness This translates to 77.98673. After the thickness values of the 22 collection points are calculated by formula (1), the pixel coordinates of the 22 collection points on the pixel coordinate system are obtained according to the pose calculation, and the pixel coordinates of the 22 collection points are read by using MATLAB software. Pixel values can be used to obtain the fluorescent oil film grayscale and thickness data including Table 1 and Table 2:

Table 1 Fluorescent oil film grayscale-thickness test data

Table 2 Fluorescent oil film grayscale-thickness test data (data used for modeling)

serial number 1* 2* 3* 4* 5* 6* Oil film gray value Pixel 100 96 92 88 84 80 Oil film thickness value μm 301.9912 235.6195 178.0973 142.1460 117.2566 96.23890

After conversion, the pixel scale coefficient λ of this test is 38.71289μm/Pixel. During the collection process, the brightness of the fluorescent oil film reaches saturation when the thickness is about 320μm, that is, the brightness does not increase any more, so the maximum thickness collected is about 300μm, and the collected The order of the points is from right to left, that is, starting with the saturated gray value point. The real collection picture taken is shown in Figure 7, and the collected data is shown in Table 1 and Table 2.

Example 2

Based on the modeling data obtained in Example 1 Table 2, with (serial number value, thickness value) as w (n), through the traditional Hankel matrix model described in the specific embodiment of the present invention, the first error correction prediction model of the present invention ( Hankel matrix error correction model) and the second error correction prediction model (higher-order iterative Hankel matrix error correction model) modeling process to obtain the corresponding transfer function, as shown in equations (17), (18) and (19), respectively:

It can be seen that the prediction model established in the form of Hankel matrix can well meet the special background of modeling with a small amount of data to predict other data and maintain high accuracy.

Further experimental data show that the prediction accuracy of the traditional Hankel model can reach 76.69%, and the prediction accuracy of the improved algorithm Hankel matrix error correction model and the Hankel matrix high-order iterative error correction model are 85.69% and 89.25%, respectively, compared with the traditional Hankel The accuracy of the array model is increased by 9% and 12.56%, respectively, and the system converges when the iteration of the high-order iteration error correction model reaches the fourth order. In the measurement of global friction, the thickness measurement of the fluorescent oil film is extremely important, and the thickness measurement has reached the micron level, so the accuracy improvement of the improved algorithm has great application value in engineering practice.

The above examples are only preferred implementations of the present invention, and the scope of protection of the present invention is not limited to the above examples. All technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims (6)

1. An improved Hankel matrix prediction model modeling method based on a fluorescent oil film is characterized by comprising the following steps: the method comprises the following steps:

s1, establishing a basic Hankel matrix prediction model based on fluorescence oil film collected data;

s2, carrying out data prediction through the basic Hankel matrix prediction model to obtain prediction data;

s3: correcting the prediction data through the error value to obtain corrected prediction data, and establishing a first error correction prediction model through the corrected prediction data, wherein the first error correction prediction model specifically comprises the following steps:

s31: averaging the error value generated by prediction to obtain an averaging result;

s32: correcting the prediction data according to the equalization processing result, replacing the original prediction data with the correction data, and establishing a first error correction prediction model of a basic Hankel matrix prediction model;

s4: performing data prediction through the first error correction prediction model;

s5: if the prediction data obtained through the first error correction prediction model is good, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the data prediction is wrong, taking the error correction prediction model as a basic Hankel matrix prediction model of S1 and continuously performing iterative updating according to the processes of S2-S5 until the improved Hankel matrix prediction model is obtained;

the fluorescence oil film acquisition data comprise pixel point gray values of fluorescence oil film images and corresponding oil film thickness values, and the prediction data are thicknesses of the fluorescence oil films.

2. The modeling method of claim 1, wherein: the first error-corrected prediction model is as follows:

Γw_(n)＝[w_(n)-w_n]+Γw_n (13)，

wherein, w_(n)Representing the impulse response data set used for model building,

representing model prediction result data set, Δ ε_(n)Representing error data set, G_(ε)(z^-1) Represents Delta epsilon_(n)Z-domain transfer function of_nRepresenting error data set Δ ε_(n)In the error data, G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, δ (G-k · Δ G) =1 holds when G = n · Δ G, n represents a system order size, and Γ ww =1 holds_nRepresenting the corrected pulse data set, w_nDenotes w_(n)Of (3) single modeling data, Γ w_(n)Representing a new impulse response data set obtained by replacing its original impulse data set with the modified impulse data set.

3. The modeling method of claim 1, wherein: the step S3 includes: and correcting the prediction data through the error value to obtain corrected prediction data, adding the corrected prediction data into a set of original prediction data to obtain expanded prediction data, and establishing the error correction prediction model through the expanded prediction data.

4. A modeling method in accordance with claim 3, wherein: the modeling method comprises the following steps:

(1) Establishing the basic Hankel matrix prediction model;

(2) Carrying out data prediction through the basic Hankel matrix prediction model;

(3) Averaging the error value generated by prediction;

(4) Correcting the predicted data according to the averaging processing result, adding the corrected data into the original predicted data to obtain expanded data, and establishing a second error correction prediction model of the basic Hankel matrix prediction model according to the expanded data;

(5) Evaluating the accuracy of the second error correction prediction model;

(6) And (3) if the prediction precision is improved, outputting the error correction prediction model as an improved Hankel matrix prediction model, and if the prediction precision is not improved, taking the error correction prediction model as the basic Hankel matrix prediction model in the step (1) to continuously carry out iterative updating according to the processes from (2) to (6) until the improved Hankel matrix prediction model is obtained.

5. The modeling method of claim 4, wherein: the second error-corrected prediction model is as follows:

G(z^-1)＝w₁z^-1+w₂z^-2+…w_nz^-n (17)

wherein w_(n)Representing the impulse response data set used for model building,

data set representing model prediction results, Δ ε_(n)Indicating an error data set, G (z)^-1) Denotes. DELTA.. Di_(n)Z-domain transfer function of_nRepresenting error data set Δ ε_(n)Wherein G represents a gray scale value at a certain time in the pulse data, Δ G represents a gray scale value difference between two adjacent elements in the pulse data, δ (G-n · Δ G) represents a pulse function, δ (G-k · Δ G) =1 holds when G = n · Δ G, n represents a system order size, and Γ ww =1_nRepresenting the corrected pulse data set, w_nDenotes w_(n)Of (3) single modeling data, Γ w_(n)Representing the expanded impulse response data set obtained from the r-th iteration,

representing the extended impulse response data set obtained in the (r + 1) th iteration,

represents the passage of a transfer function G (z)^-1) The predicted data, r, represents the number of iterations,

the convergence condition is indicated.

6. A modeling method as claimed in claim 4 or 5, characterized in that: the method for evaluating the prediction precision comprises the following steps: and subtracting the original data from the predicted data to obtain error data, and representing the prediction precision by the error rate by taking the percentage value of the error data and the corresponding original data as the error rate.

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