CN109299491B - Meta-model modeling method based on dynamic influence graph strategy and using method - Google Patents

Abstract

A meta-model modeling method and application method based on a dynamic influence graph strategy, which belong to the field of computer application technology. The behavior of is modeled using decision nodes similar to decision makers. The steps of the construction method of the model include selecting required variables, determining simulation data, determining topological structure and probability table, checking the correctness of topological structure and probability table, and determining utility function. Model usage methods include observing the system state, what-if analysis and solving the optimal strategy. This method provides an effective technical means for simplifying the system simulation model, and solves the problems that the current meta-model does not take into account the preferences of the decision maker, the actions taken by the opponent, and cannot provide direct means to optimize the simulation output. It can be widely used in In the field of computer simulation, especially simulation modeling under high confrontation and incomplete information.

Description

A Metamodel Modeling Method and Application Method Based on Dynamic Influence Diagram Strategy

technical field

The invention belongs to the field of computer application technology, and in particular relates to a metamodel modeling method based on a dynamic influence graph strategy and a using method.

Background technique

Simulation technology is widely used in aerospace, aviation, navigation, electric power, chemical industry, nuclear energy, communication and other fields due to its advantages of economy, safety, repeatability and non-destructiveness. Modern simulation technology is not only used in traditional engineering fields, but also increasingly widely used in social, economic, biological, military and other fields, such as traffic control, urban planning, resource utilization, environmental pollution prevention, production management, market forecasting, world economic Analysis and forecasting, population control, etc. For socio-economic, military and other systems, it is difficult to conduct experiments on real systems. Therefore, it is more important to use simulation technology to study these systems.

Simple models are required for high-level reasoning and communication decision support, exploratory analysis, establishment of multi-resolution models, and fast adaptive calculations. Existing simulation organizations often have a large number of complex and effective simulation models, but lack accurate and applicable simple models. Due to the complexity of the simulation model and the lack of documentation, or the organization does not have specialized personnel to delve into the internal structure of the model, or because it takes too much time, our organization with a large simulation model cannot pass rigorous research and simplify the target model. Get much needed relatively simple models. An effective means to solve this simulation crisis is to construct a meta-model based on the simulation model.

The concept and method of meta-model is an emerging hotspot in the field of system simulation. It is suitable for low-resolution fast simulation and cross-level simulation modeling, and has a wide range of applications in industrial design and manufacturing, management science and military equipment procurement. The so-called meta-model is a simple substitute model of the simulation model, that is, a new simplified and approximate mathematical model obtained by fitting the input-output result sequence of the original simulation model, which is the relationship between the input and output of the original simulation model. Approaching. Therefore, it greatly reduces the complexity of the simulation model, and using it to replace or partly replace the simulation model for simulation experiments can greatly reduce the calculation overhead and improve the efficiency of simulation under the condition of meeting the accuracy requirements. Utilizing the meta-model can usually achieve the following five purposes: (1) increase the understanding of the real system (source system), and conveniently form valuable knowledge of the real system; (2) predict the value of the output variable or response variable; (3) Apply to high-level simulation; (4) Optimize the system or system; (5) Assist the verification and confirmation of the simulation model.

Currently common simulation meta-models include: regression model, genetic algorithm, Kriging, game model, spline model, neural network, radial basis kernel function, spatial correlation model, frequency domain model, response surface, etc. None of the above models can represent the variation of simulation state variables over time, cannot describe the relationship between simulation state variables at different times, does not take into account the preferences of decision makers, actions taken by opponents, and cannot provide direct means to optimize simulation output.

Contents of the invention

In order to overcome the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a meta-model modeling method and using method based on dynamic influence graph strategy. combined theory. The dynamic influence diagram strategy is based on the single-level influence diagram strategy and introduces the concept of time slice, which is mainly used to solve dynamic decision-making problems.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A metamodel modeling method based on dynamic influence graph strategy, comprising the following steps:

Step 1: Select the required variables from all variables, these variables include: state variables, decision variables, external variables, value variables;

Step 2: Determine the simulation data. In the dynamic influence graph game model, it can be considered that time is continuous, that is, the simulation event can occur at any time t∈[t ₀ ,t _f ], and it can be observed at [t ₀ ,t _f ] The time series simulation data of the simulation state can reflect the change of the simulation state, and the probability distribution of the simulation state can be obtained through multiple simulation estimates. Through a large amount of simulation data, a high-precision estimated probability curve of the simulation state can be obtained, and it can be used as a reference probability curve. The probability curve can be used to determine the number of discrete sampling and the sampling moment;

The optimal number of sampling times can be obtained according to the following steps:

1) Suppose j=1 and t∈[t ₀ ,t _f ], set the maximum error value ε, and the probability of variable value l∈L is represented by p ^l (t)=p(x(t)=l); L is the value range of the variable;

是 否小于ε(ε由分析者自己设定)，这里p^l(t)为参考概率，

如果满足上述条件，则跳转到步骤(5)， 否则跳转步骤(3)；2) Determine whether each approximate probability error is less than ε, namely

is less than ε (ε is set by the analyst himself), where p ^l (t) is the reference probability,

If the above conditions are met, go to step (5), otherwise go to step (3);

3) Obtain the time interval Δt, select the value k∈L that causes the largest probability error, and the time interval Δt satisfies the following equation:

这里

here

4) Make t ₀ :=t ₀ +Δt,j:=j+1, jump to step (2);

5) Obtain the optimal number of sampling times n, set n=j+1, and output n.

Once the optimal sampling times are obtained, the optimal optimal sampling time can be obtained by solving the following optimization problem:

Here T={t ₀ ,t ₁ ,...,t _f }, the number of elements |T|=n;

Step 3: Determine the topological structure and probability table. The topological structure of the influence graph strategy, that is, the relationship between variables, can be obtained according to expert knowledge, background knowledge of both parties to the strategy and the method of simulation data integration; determine the nodes of the influence graph strategy Finally, draw the original graph based on expert knowledge and background knowledge; first determine the structure of a single time segment, then determine the relationship between each time segment, obtain multiple original influence graphs, and then select one of the multiple influence graphs according to the scoring method the most suitable structure;

Step 4: Verify the correctness of the topology structure and the probability table. The principles of structure verification are as follows:

1) There are no loops in the directed graph;

2) If there is a valuable node, it has no subsequent nodes;

3) There is a path that includes all the decision nodes, and the test of the probability table generally adopts two methods of sum test and multiplication test. If the topology or probability table is incorrect, skip to step 3.

Step 5: Determine the utility function. The utility function can be set by the decision makers themselves or learned from topological structures, probability tables and simulation data.

The scoring method described is based on a trade-off between model size and probability fit obtained from the model and simulation data. If it is found from the simulation data that there is an obvious lack of fitness between the nodes, additional arcs are added between the nodes, thereby improving the original influence diagram strategy. Finally, the value nodes of both sides of the strategy are added to obtain the final influence graph strategy. Estimates of probability are based on observed frequencies, that is, the number of times a variable is observed to take on each value.

A meta-model modeling method based on a dynamic influence diagram strategy, including the following three:

Method 1: The simulation meta-model of the dynamic influence graph strategy can be used to observe the state of the system; Assume that S(t)={x ₁ (t),x ₂ (t),...,x _n (t)}, where x _i (t) (i=1,...,n) is the simulation state variable, and the time evolution of the probability distribution at a specific moment describes the change of the simulation state x _i (t) during the entire simulation period, with p( _xi (t)) said. The method of observing the state of the system is to calculate the probability of the simulated state variable x _i (t) on the value l at a specific time t, that is, p( _xi (t)=l):

Step 1: Set the parameters of the dynamic influence diagram strategy;

Step 2: Select a strategy from the player's strategy set;

Step 3: Use Bayesian theorem to calculate the probability of the state variable x _i (t) taking the value l in the case of the player choosing a strategy; Step 4: According to the specific moment t∈T={t ₁ ,.. .,t _f } the probability of taking the value l of x _i (t) to judge the state change of the system;

Method 2: The simulation meta-model of the dynamic influence diagram strategy can be used for what-if analysis;

Step 1: Set the parameters of the dynamic influence diagram strategy;

Step 2: Select a strategy from the player's strategy set;

Step 3: Use Bayesian theorem to calculate the probability of the state variable x _i (t) taking the value l in the case of the player choosing a strategy; Step 4: According to the specific moment t∈T={t ₁ ,.. .,t _f } _xi (t) takes the value l probability to judge the state change of the system.

Method 3: The simulation meta-model of the dynamic influence graph strategy can be used to solve the optimal strategy;

Step 1: Set the parameters of the dynamic influence diagram strategy;

Step 2: Use the enumeration method or the average moving control method to calculate the optimal strategy of both countermeasures. If one of the countermeasures has selected a strategy, it can be transformed into an optimization problem.

The beneficial effects of the present invention are:

1) Information is taken into account in the meta-model, and the game theory model is used to solve the problem that other meta-models do not consider the preference information and the actions taken by the opponent.

2) The meta-model of the dynamic influence diagram adopts the optimal sampling algorithm, which simplifies the meta-model without reducing the performance. and does not provide a direct means of optimizing the simulation output.

3) Using the meta-model solution results of the dynamic influence diagram, it can provide decision makers with a direct means to optimize the simulation output.

4) The meta-model of the dynamic influence diagram can be used for what-if analysis and strategy-to-simulation evolution.

Description of drawings

Fig. 1 is the schematic diagram of the dynamic image map countermeasure model of the present invention;

Fig. 2 is the flowchart of modeling method of the present invention;

Fig. 3 is the metamodel of the dynamic influence diagram of the example;

Fig. 4 is the probability curve of example;

Figure 5 is a diagram of the hypothetical analysis results of the example.

Detailed ways

Below in conjunction with accompanying drawing, the present invention is further described:

A meta-model construction method based on an influence graph strategy, characterized in that: Step 1: Select variables; Step 2: Determine simulation data; Step 3: Determine topology and probability table; Step 4: Check the correctness of topology and probability table , if the topology or probability table is incorrect, skip to Step 3, Step 5: Determine the utility function.

The selection variables include: (1) State variables. The state variables of both sides of the game are a comprehensive and effective description of the game problem. At each moment t∈{t ₀ ,t ₁ ,...,t _f }, the simulated state of the game is represented by a discrete random variable x ⁱ (t), where i represents the player in the game. In the dynamic influence graph game model, state variables are represented by chance nodes; (2) Decision variables. Since the simulation parameters affect the evolution of the simulation, if the elements represented by the control simulation parameters are controllable, they can be represented by decision variables, while in the influence diagram model they are represented by decision nodes; (3) External variables. If the simulation parameters are uncontrollable, they are represented by external random variables, and represented by chance nodes in the influence diagram; (4) value variables. Represented in an influence diagram by a value node, which represents the player's goals. The simulation output is represented by a probability distribution of chance nodes.

The determination of simulation data includes: in the dynamic influence diagram game model, time can be considered to be continuous, that is, simulation events can occur at any time t∈[t ₀ ,t _f ]. The time series simulation data observed at [t ₀ ,t _f ] can reflect the change of the simulation state, and the probability distribution of the simulation state can be obtained through multiple simulation estimates. A high-precision estimation probability curve of the simulation state can be obtained through a large amount of simulation data, and it can be used as a reference probability curve. The reference probability curve can be used to determine the number of discrete samples and the sampling instant. If the number of sampling is large enough, the discretized probability curve can represent the change of the reference probability curve, and the discretized curve should be relatively smooth. At the same time, the larger the sampling frequency, the higher the accuracy of the meta-model but the more complex it is. In addition, the choice of discrete time is also one of the factors that affect the accuracy of the meta-model, and it is also a key consideration.

Preferably, the optimal number of sampling times is used, which can be obtained according to the following steps:

(1) Suppose j=1 and t∈[t ₀ ,t _f ], set the maximum error value ε, and the probability of variable value l∈L is represented by p ^l (t)=p(x(t)=l) ;L is the value range of the variable;

是否小于ε(ε由分析者自己设定)，这里p^l(t)为参考概率，

如果满足上述条件，则跳转到步骤(5)， 否则跳转步骤(3)；(2) Determine whether each approximate probability error is less than ε, namely

is less than ε (ε is set by the analyst himself), where p ^l (t) is the reference probability,

If the above conditions are met, go to step (5), otherwise go to step (3);

(3) Obtain the time interval Δt. Select the value k∈L that causes the largest probability error, and the time interval Δt satisfies the following equation:

这里

here

(4) make t ₀ :=t ₀ +Δt,j:=j+1, jump to step (2);

(5) Obtain the optimal sampling times n. Let n=j+1, output n.

Once the optimal sampling times are obtained, the optimal optimal sampling time can be obtained by solving the following optimization problem:

Here T={t ₀ ,t ₁ ,...,t _f }, the number of elements |T|=n.

The said determined topology and probability table include: the topology of the influence graph strategy, that is, the relationship between variables, can be obtained according to expert knowledge, background knowledge of both parties to the strategy, and simulation data integration. After determining the nodes of the strategy of the influence diagram, the original diagram is drawn according to expert knowledge and background knowledge. First determine the structure of a single time segment, then determine the relationship between each time segment, obtain multiple original influence diagrams, and then select a most suitable structure from multiple influence diagrams according to the scoring method. The scoring method is based on a trade-off between model size and the probability match obtained from the model and the simulation data. If there is a clear lack of fitness between nodes found from simulation data learning, additional arcs are added between nodes, thereby improving the original influence diagram strategy. Finally, the value nodes of both sides of the strategy are added to obtain the final influence graph strategy. Estimates of probability are based on observed frequency, that is, the number of times a variable is observed to take on each value. In an influence diagram game, there is a conditional probability table for each variable x _i (t). The conditional probability table provides the conditional probability p( _xi (t)|Φ _i =l _Φ ) of each value combination of the parent node of each node, then the conditional probability θ _l =p( _xi (t)=l| The estimated value of Φ _i =l _Φ ) is:

Here N _l is the observed number of times _xi (t)=l and Φ _i =l _Φ in the simulation, and N _Φ is the number of observed Φ _i =l _Φ in the simulation.

的值，将两者相加，如果等于或接近1，说明数值 接近真实，否则要重新获取；(2)乘测试：设C₁是C₂唯一的一个父结 点，则P(C₂)＝∑P(C₁)P(C₂|C₁)，可以先获取P(C₁)和P(C₂|C₁)的值，然后获取 P(C₂)，测试上式两边接近或相等，如果是，则结果可信，否则重新获 取。The correctness check of the topology structure and the probability table includes: the correctness check of the dynamic influence diagram countermeasure model needs to check two aspects of the structure and the probability table. The structure check is based on the following three criteria: (1) the directed graph has no loops; (2) if there is a valuable node, it has no subsequent nodes; (3) there is a path that includes all decision nodes. The test of the probability table generally adopts two methods of sum test and multiplication test. (1) Sum test: The sum test is to check whether all the probabilities of a node satisfy the normalization. Let C be a binary node, first determine the value of P(C), after a certain period of time, then determine

If it is equal to or close to 1, it means that the value is close to the real value, otherwise it needs to be obtained again; (2) multiplication test: Let C ₁ be the only parent node of C ₂ , then P(C ₂ ) ＝∑P(C ₁ )P(C ₂ |C ₁ ), you can first obtain the values of P(C ₁ ) and P(C ₂ |C ₁ ), then obtain P(C ₂ ), and test that both sides of the above formula are close to or Equal, if yes, the result is trusted, otherwise re-fetch.

The determined utility function may be set by the decision maker or learned from the topology, probability table and simulation data.

There are three ways to use the simulation meta-model based on the dynamic influence diagram strategy, as follows:

这里局中 人1、2的策略分别为

D¹(i)和D²(j)分别为局中 人1、2的策略集.。条件概率分布描述了策略选择后仿真结果随时间 变化的情况。如果变量有期望值，则它的平均值可以用期望值代替， 期望值的计算公式为：Approach 1: The simulation meta-model of the dynamic influence graph strategy can be used to observe the state of the system. Suppose S(t)={x ₁ (t), x ₂ (t), ..., x _n (t)}, where x _i (t) (i=1, ..., n) is the simulation state variable. In the influence graph game model, the time evolution of the probability distribution at a specific time t ∈ T = {t ₁ ,...,t _f } describes the change of the simulation state throughout the simulation period, with p(S(t)) express. In other words, the influence diagram game is used to calculate the probability of a state variable at time t∈T, ie p(S(t)=l _S ). Studying a single simulated variable, p( _xi (t)) can be tracked. Moreover, specific values of state variables can be tracked by p( _xi (t)=l) (l∈L _i ). The observation probability p( _xi (t)=l) can be used to analyze the likelihood of a given simulated event occurring. In order to analyze the strategies that players can adopt, influence diagram games can be used to evaluate the conditional probability distribution of each player's strategy

Here the strategies of players 1 and 2 are respectively

D ¹ (i) and D ² (j) are the strategy sets of players 1 and 2 respectively. The conditional probability distribution describes how the simulation results change over time after the strategy is chosen. If the variable has an expected value, its average value can be replaced by the expected value, and the formula for calculating the expected value is:

以及观测到在时刻t上状态l，计算条件概率

分析概率随时间的变化。表示仿真参数的 外部随机变量也用相似的方法进行分析。假设外部变量为z_j＝h，则用p(S(t)|z_j＝h)或者p(x_i(t)|z_j＝h)对状态变量进行更新，检验这些条件概率 看是否仿真受这些外部变量的影响。如果同时分析外部变量与策略对 的影响，则可以计算条件概率

在假设分析 中的条件概率也可以用于计算在时间t∈T上仿真状态的条件期望，计 算公式如下：Method 2: The simulation meta-model of the dynamic influence diagram strategy can be used for what-if analysis. In what-if analysis, the influence diagram strategy is used to determine the conditional probability p(S(t)| _xi (t)=l), that is, to fix the values of several random variables and observe the changes of the joint probability of other simulated variables. The conditional probability thus reveals the link between the observed simulation state and the evolution of the simulation over time. The same analysis can also be used for the effect of the player strategy on the decision node on the simulation state, that is, when the choice strategy

And observe the state l at time t, calculate the conditional probability

Analyze changes in probabilities over time. External random variables representing simulation parameters are also analyzed in a similar way. Assuming that the external variable is z _j =h, then use p(S(t)|z _j =h) or p( _xi (t)|z _j =h) to update the state variable, and check these conditional probabilities to see if they are simulated affected by these external variables. Conditional probabilities can be calculated if the effects of external variables and policy pairs are analyzed simultaneously

The conditional probability in what-if analysis can also be used to calculate the conditional expectation of the simulated state at time t ∈ T, the calculation formula is as follows:

Method 3: The simulation meta-model of the dynamic influence graph game can be used to solve the optimal strategy. Solving an influence diagram game is to observe how pairs of strategies affect utility nodes. Since the two sides of the strategy cannot cooperate, and both parties obtain relevant information at the same time, they can maximize the payment of the non-zero sum influence graph strategy at the same time, and find out the Pareto balance from the strategy pair. If the model is relatively simple, enumeration method can be used. If the model is complex, the moving average control method can be used, that is, the calculation of the decision vector of each stage only considers the previous stages of decision-making, and the calculation process is repeated until the end of the strategy. On the other hand, the influence diagram game also retains important information for further research on the impact of different utility functions on Pareto equilibrium. If one player chooses a strategy, the other player can maximize the expected utility to find the strategy with the greatest utility, which is no different from solving the influence diagram.

An example of air combat simulation analysis is used to illustrate the construction and application of influence diagram countermeasures. The two sides of the air battle are red and blue, each with an aircraft, and both are equipped with two missiles. The initial state of the air battle is that the red plane is in the upper hand, and the red plane is close to the blue plane and is preparing to launch a missile to attack the blue plane. Using the method disclosed in the present invention, an influence diagram strategy is established. The air combat simulation state at time t is represented by two state variables S(t)={x ₁ (t), x ₂ (t)}, which are represented by chance nodes in Figure 3 . These two variables have their own indicators respectively as "survival of red machines at time t" and "survival of blue machines at time t". When the state variables are binary, their set of values is L ₁ ＝L ₂ ＝{0, 1}, and the two variables can define 4 states of air combat: (1) Red machine advantage: Red machine survives and blue machine was shot down, that is, x ₁ (t)=1, x ₂ (t)=0; (2) blue machine advantage: the blue machine survives and the red machine is shot down, that is, x ₁ (t)=0, x ₂ (t )=1; (3) balance of power: both sides survive, that is, x ₁ (t)=1, x ₂ (t)=1; (4) unfavorable: both sides are shot down, that is, x ₁ (t)=0, x ₂ (t)=0. Both red and blue have two strategies to choose from: attack strategy and defense strategy, which are represented by decision nodes in Figure 3. The attack strategy is to shoot down the opponent regardless of the opponent's posture, while the defense strategy is to attack the opponent only when he is in an advantage, otherwise, evade first, seize a favorable position and then attack. In the process of constructing an influence diagram strategy, the simulation data is used to first estimate the probability curve of the state variables. The simulation is repeated 2000 times, and the condition for each termination is that the red and blue sides are shot down or the time reaches the termination time t _f =300s. According to the set accuracy ε=0.03 and the algorithm disclosed in the present invention, the number of time segments can be determined as |T|=10, and the position of the optimal moment is T={0, 56, 79, 89, 97, 121, 132 , 185, 230, 300}. The influence diagram strategy model is shown in Figure 3. In Fig. 3, the black arrows represent the original influence diagram strategies, while the white arrow arcs represent additional arcs added using simulated data. Figure 4 is a simulation estimation curve, and the dotted line is a reference estimation curve. It can be seen from the figure that the effect of the meta-model is ideal. Figure 4 depicts how the air battle progresses when both sides choose an attack strategy. The probability curve shows no significant change in the probability distribution of the state variables before 79 seconds and after 185 seconds. Therefore, the most noticeable change occurs between 79 seconds and 185 seconds. The probability of "red advantage" and "blue advantage" has two peaks between 89 seconds and 132 seconds. The reason is that the red team launched the missile first, and then the blue team also fired the missile before it was shot down. In this case, both sides always attack each other regardless of the situation. At 89 seconds, the red team launches the missile first, and the probability of shooting down the blue team before 97 seconds is 0.45. However, the blue team also had time to launch the missile before it was shot down. At the end of the simulation, the probability of the red team's advantage is 0.303, the blue team's advantage is 0.184, both unfavorable is 0.378, and the balance of power is 0.135. Using the influence diagram game meta-model, it is easy to analyze the progress of the simulation.

In order to study the relationship between the different values of the simulation state at different times, the meta-model of the strategy of the influence diagram can be used for hypothesis analysis. For example, assuming that at time t=89s, both red and blue are still alive, the blue team chooses an attack strategy, and the red team chooses two strategies respectively, that is, x ₁ (89)=1.x ₂ (89)=1, d ^B = {aggressive} and d ^R {aggressive, defensive}. The approximate curve is shown in Figure 4. From Figure 5, it can be seen that if the red team's first missile does not hit the blue team, it is relatively bad to adopt a defensive strategy. In this case, the blue team has a probability of winning the air battle of 0.514, while the red team has only 0.288.

Table 1 Probability distribution of each state of utility nodes

The third application of the influence diagram game is to obtain the optimal strategy of both sides of the game. If the blue team chooses an attack strategy, the probability distribution of each state of the utility node is shown in Table 1. Three utility functions are proposed in Table 2. The utility function f ₁ (·) indicates that the decision maker’s goal is the survival of the red team, and f ₂ ( ) means only interested in shooting down the blue side, and f ₃ (·) means the red side wins. Table 2 also shows that different utility functions produce different optimal decisions. If f ₁ (·) and f ₃ (·) are chosen, the defensive strategy is more suitable. And choosing the utility function f ₂ (·), the decision maker is more inclined to the attack strategy. If the red and the blue have two strategies to choose from, then the Pareto equilibrium is the solution of the non-zero-sum game. Assuming that both sides of the countermeasure choose the utility function f ₁ (·), then the defense strategy is the optimal strategy for both sides. The calculation results are shown in Table 3, and both sides should choose the defense strategy.

Table 2 The optimal decision of the red square under different utility functions

Table 3 Optimal solutions for both sides of the game

In summary, it is only a preferred example of the present invention, and is not used to limit the scope of the present invention. All methods and steps according to the scope of the claims of the present invention should be included in the scope of the claims of the present invention.

Claims (3)

1. A metamodel modeling method based on dynamic influence graph countermeasures, characterized in that, comprising the following steps: Step 1: Select required variables from all variables, these variables include: state variables, decision variables, external variables, value variables; Step 2: Determine the simulation data. In the dynamic influence graph game model, it can be considered that time is continuous, that is, the simulation event can occur at any time t∈[t ₀ ,t _f ], and it can be observed at [t ₀ ,t _f ] The time series simulation data of the simulation state can reflect the change of the simulation state, and the probability distribution of the simulation state can be obtained through multiple simulation estimates. Through a large amount of simulation data, a high-precision estimated probability curve of the simulation state can be obtained, and it can be used as a reference probability curve. The probability curve can be used to determine the number of discrete sampling and the sampling moment; The optimal number of sampling times can be obtained according to the following steps: 1) Suppose j=1 and t∈[t ₀ ,t _f ], set the maximum error value ε, and the probability of variable value l∈L is represented by p ^l (t)=p(x(t)=l); L is the value range of the variable; 2) Determine whether each approximate probability error is less than ε, namely

is less than ε (ε is set by the analyst himself), where p ^l (t) is the reference probability,

If the above conditions are met, then jump to step (5), otherwise jump to step (3); 3) Obtain the time interval Δt, select the value k∈L that causes the largest probability error, and the time interval Δt satisfies the following equation:

here

4) Make t ₀ :=t ₀ +Δt,j:=j+1, jump to step (2); 5) Obtain the optimal number of sampling times n, make n=j+1, and output n; Once the optimal sampling times are obtained, the optimal optimal sampling time can be obtained by solving the following optimization problem:

Here T={t ₀ ,t ₁ ,...,t _f }, the number of elements |T|=n; Step 3: Determine the topological structure and probability table. The topological structure of the influence graph strategy, that is, the relationship between variables, can be obtained according to expert knowledge, background knowledge of both parties to the strategy and the method of simulation data integration; determine the nodes of the influence graph strategy Finally, draw the original graph based on expert knowledge and background knowledge; first determine the structure of a single time segment, then determine the relationship between each time segment, obtain multiple original influence graphs, and then select one of the multiple influence graphs according to the scoring method the most suitable structure; Step 4: Verify the correctness of the topology structure and the probability table. The principles of structure verification are as follows: 1) There are no loops in the directed graph; 2) If there is a valuable node, it has no subsequent nodes; 3) There is a path that includes all decision nodes, and the probability table is generally checked by two methods: sum test and multiplication test; if the topology or probability table is incorrect, skip to step 3; Step 5: Determine the utility function; the utility function can be set by the decision maker or learned according to the topology, probability table and simulation data. 2. A meta-model modeling method based on a dynamic influence graph strategy according to claim 1, wherein the scoring method is based on a trade-off between the model scale and the probability matching degree obtained from the model and simulation data ; If it is found from the simulation data that there is an obvious lack of fitness between the nodes, add additional arcs between the nodes to improve the original influence graph strategy; finally, add the value nodes of both sides of the strategy to obtain the final Influence diagram strategy; estimates of probabilities are based on observed frequencies, that is, the number of times a variable is observed to take on each value. 3. A method for using meta-model modeling based on dynamic influence diagram countermeasures, characterized in that it includes the following three types: Method 1: The simulation meta-model of the dynamic influence graph strategy can be used to observe the state of the system; suppose S(t)={x ₁ (t),x ₂ (t),...,x _n (t)}, where x _i (t) (i=1,...,n) is the simulation state variable, and the time evolution of the probability distribution at a specific moment describes the change of the simulation state x _i (t) during the entire simulation period, with p( _xi (t)) means that the method of observing the state of the system is to calculate the probability of the simulated state variable x _i (t) on the value l at a specific moment t, that is, p( _xi (t)=l): Step 1: Set the parameters of the dynamic influence diagram strategy; Step 2: Select a strategy from the player's strategy set; Step 3: Use Bayes theorem to calculate the probability of the state variable x _i (t) taking the value l in the case of the player choosing a strategy; Step 4: Judging the state change of the system according to the probability that x _i (t) takes value l at a specific moment t∈T={t ₁ ,...,t _f }; Method 2: The simulation meta-model of the dynamic influence diagram strategy can be used for what-if analysis; Step 1: Set the parameters of the dynamic influence diagram strategy; Step 2: Select a strategy from the player's strategy set; Step 3: Use Bayesian theorem to calculate the probability of the state variable x _i (t) taking the value l in the case of the player choosing a strategy; Step 4: According to the specific moment t∈T={t ₁ ,.. .,t _f } x _i (t) value l probability to judge the state change of the system; Method 3: The simulation meta-model of the dynamic influence graph strategy can be used to solve the optimal strategy; Step 1: Set the parameters of the dynamic influence diagram strategy; Step 2: Use the enumeration method or the average moving control method to calculate the optimal strategy of both countermeasures. If one of the countermeasures has already selected a strategy, it can be transformed into an optimization problem.

Images