Chassis electric control system parameter sensitivity analysis method based on deep proxy model

Abstract

The invention relates to the field of automobile chassis electric control, in particular to a chassis electric control system parameter sensitivity analysis method based on a deep agent model, which adopts a three-stage progressive strategy of'single-factor preliminary screening-modeling-Sobol analysis', and comprises the following steps: firstly, through single-factor screening, adopting a mode of adjusting parameter values one by one and observing system response; the parameters having small influence on performance are eliminated, and the range of the to-be-calibrated parameters is narrowed; a BP neural network-based system response agent model is constructed to replace a simulation model for rapid calculation, so that the calculation cost is greatly reduced while the analysis accuracy is ensured; and finally, further extracting key parameters under each working condition through Sobol global sensitivity analysis based on an agent model. According to the method, the contradiction between calculation efficiency and precision in a high-dimensional parameter space is solved, efficiency and accuracy are both considered, and standardized method support is provided for virtual calibration under complex working conditions.

Description

Technical Field

[0001] The present invention relates to the field of electronic control of automobile chassis, and particularly to a method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep surrogate model. Background Art

[0002] The calibration work of the chassis electronic control system is one of the most important links in the virtual calibration process of the intelligent automobile chassis electronic control system. Since the traditional calibration methods of the chassis electronic control system are all based on real vehicles and actual real scenarios and rely on expert experience to carry out work, the efficiency is low and the intelligent chassis multi-system electromechanical comprehensive performance test cannot be carried out before real vehicle road test, resulting in a long automobile development cycle and high calibration costs, which is contrary to the market demand for shortening the automobile development cycle. Therefore, it is very necessary to develop the virtual calibration technology of the chassis electronic control system. Virtual calibration is a model-based calibration technology, which can start the calibration work before the automobile road test. At the same time, by using an efficient automatic calibration algorithm, the development cycle can be greatly shortened and the calibration cost can be reduced.

[0003] There are a large number of parameters in the automobile chassis electronic control system, and their influence degrees on vehicle handling stability, comfort, braking performance, etc. are different. If all parameters are directly calibrated, it will lead to excessive calculation amount, low efficiency, and even may affect the reliability of the calibration result. Therefore, how to reduce the number of parameters to be calibrated in the automobile chassis electronic control system is one of the key problems of virtual calibration technology. Selecting effective and reasonable number of calibration parameters, that is, performing sensitivity analysis of parameters, is the key problem of the calibration technology of the automobile chassis electronic control system. Currently, the parameter sensitivity analysis methods for the calibration problems of the automobile chassis electronic control system often use a traversal method for screening, which takes too long. Therefore, there is an urgent need for a scientific and reasonable parameter screening method to quickly and accurately identify in a short time and focus on calibrating the key parameters that are crucial to the control effect of the automobile chassis electronic control system. Summary of the Invention

[0004] In order to solve the above technical problems, based on the Sobol global sensitivity analysis method, BP neural network and single factor analysis method, the present invention provides a method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep surrogate model. In the single factor screening stage, by adjusting each parameter value one by one and observing the system response, the parameters with less influence on performance are initially eliminated, so as to narrow the range of parameters to be calibrated and improve the efficiency of subsequent analysis; on this basis, a system response surrogate model based on BP neural network is constructed to replace the simulation model for rapid calculation, which can ensure the analysis accuracy while greatly reducing the calculation cost; then through the Sobol global sensitivity analysis based on the surrogate model, the key parameters under each working condition are further extracted.

[0005] A method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep surrogate model provided by the present invention includes the following steps:

[0006] Step 1. Single-factor screening:

[0007] For each typical working condition, use the single-factor method to adjust the parameter values one by one and observe their effects on the performance evaluation indexes of the chassis electronic control system, quantify the importance of each parameter, eliminate redundant parameters with sensitivities lower than the threshold, and narrow the parameter range for subsequent analysis;

[0008] Further steps include:

[0009] First, organize the set P = {p1, p2, … p n} of parameters to be optimized and the set M = {m1, m2, … m k} of performance evaluation indexes for evaluating system performance, where p i is the parameter to be optimized and m j is the performance evaluation index;

[0010] Next, determine the initial value or preset value of the parameter set as the reference point for subsequent comparison and evaluation;

[0011] Subsequently, make parameter adjustments one by one: for each parameter p i , while keeping other parameters fixed, only adjust the value of p i , and calculate the adjusted performance evaluation index; determine whether the predetermined number of repetitions is reached. If not, continue with parameter adjustment; if so, enter the step of calculating the influence factor. The calculation formula of the influence factor is as follows:

[0012]

[0013] where represents three values of the parameter p i ; represents the value of the jth performance evaluation index when the parameter p i takes the value s under the working condition C; m C,basej represents the reference value of the jth performance evaluation index under the working condition C; for each parameter p i , calculate the relative change amount of the performance evaluation index for all its values under the working condition C, and select the maximum value as the influence factor of the parameter p i under this working condition;

[0014]

[0015] Quantify the influence degree of each parameter on the performance evaluation index through formulas (1) and (2) to screen out the key parameters with the greatest influence on the performance evaluation index;

[0016] Normalize the influence factors of each working condition:

[0017]

[0018] Among them, is the influence factor of parameter p under condition C; I i ; I C,max and I C,min respectively represent the maximum and minimum values of the influence factors of all parameters under condition C;

[0019] Finally, select the values with large influence factors and list them in the key parameter set.

[0020] Step 2: Construct a BP neural network surrogate model:

[0021] On the basis of single-factor screening, construct a dedicated surrogate model for each condition based on the BP neural network to replace the high-fidelity simulation model and provide data for subsequent Sobol global sensitivity analysis. By using the surrogate model, the direct invocation of the high-precision simulation model in the Sobol analysis process is reduced, significantly improving the calculation efficiency while ensuring relatively high calculation accuracy.

[0022] Further steps include:

[0023] First, when constructing the BP neural network surrogate model, use the uniform sampling method as the sampling method for surrogate model training to generate high-quality input samples to cover the parameter space and provide sufficient data support for model training.

[0024] Second, perform normalization processing on the data. The calculation formula is as follows:

[0025]

[0026] Among them, z is the normalization result, x is the calculated value, x min is the minimum value in the data, and x max is the maximum value in the data.

[0027] Finally, select the relative root mean square error as the evaluation index for the model prediction performance to measure the error between the predicted value and the actual value. The calculation formula is as follows:

[0028]

[0029] Among them, RRMSE is the relative root mean square error, t i is the actual value, and y i is the estimated value.

[0030] The number of input layer nodes of the BP neural network structure is the number of parameters obtained by single-factor screening; the output of the surrogate model is the performance evaluation index value of the chassis electronic control system; the number of intermediate layers is selected as 2 - 4 according to the number of indexes, and the number of neurons is set to 20 - 80.

[0031] Step 3: Sobol global sensitivity analysis:

[0032] Based on the surrogate model, a systematic global sensitivity analysis is adopted. The first-order and total sensitivity indices are calculated through the Sobol method to quantify the main effects and interaction effects of parameters, realizing the efficient and accurate evaluation of the parameter sensitivity of the chassis electronic control system, thereby guiding the efficient and precise optimization of the chassis electronic control system and providing reliable technical support for virtual calibration under complex working conditions.

[0033] Further steps include:

[0034] First, based on the single-factor screening results, determine the input parameters and their feasible range, and define the physical constraint conditions of each parameter; adopt a uniform sampling strategy to generate a set of sample points with uniform distribution characteristics in the high-dimensional parameter space to ensure the comprehensive coverage of the parameter space.

[0035] Then, use the BP neural network surrogate model trained in Step 2 for efficient performance prediction, calculate the sensitivity index, and establish a sensitivity feedback mechanism to guide the closed-loop calibration optimization;

[0036] The steps for calculating the sensitivity index by Sobol include: The first step is to define a mathematical model, that is, first clarify a mathematical model Y = f(X), where X = (x1, x2,... x n ) represents the set of input variables to establish the relationship between the output and these inputs; the second step is to perform function decomposition, decompose the above function f(X) into a polynomial form including constant terms, first-order effect terms, second-order effect terms, and up to total effect terms, so as to quantify the influence of each input variable and its interaction on the model output in the follow-up; the third step is to determine the total variance and the contribution of each effect term to the variance by calculating the integral of each effect term, and then calculate the corresponding sensitivity indices according to these contributions, including the main effect index (first-order sensitivity index), second-order interaction effect index (second-order sensitivity index), and total effect index (total sensitivity index), so as to evaluate the importance of each input variable and the degree of influence of its interaction on the output result.

[0037] Among them, Y = f(X) represents the model to be analyzed, which has an n-dimensional vector input X = (x1, x2,... x n );x i represents the input of the model; V represents the total variance of the output of the model f(X) when all input values fluctuate; V i represents the partial variance of the model output when a single input value fluctuates; represents the partial variance generated by the interaction between multiple input variables on the model output;

[0038] The calculation formula for the main effect index is as follows:

[0039]

[0040] Among them, S i represents the main effect index or first-order sensitivity index of x i and is used to measure the independent influence of the fluctuation of a single input variable x i on the output; E represents the expected value;

[0041] The calculation formula for the second-order interaction effect index is as follows:

[0042]

[0043] Among them, S ij represents the second-order interaction effect index or second-order sensitivity index of x i and x j and is used to measure the degree of influence of the interaction between input variables x i and x j on the output;

[0044] The calculation formula for the total effect index is as follows:

[0045]

[0046] Among them, represents the total effect index or total sensitivity index and is used to measure the contribution degree of this input to the total variance of the output when the value of x i fluctuates. The larger is, the greater the influence of this parameter in all scenarios.

[0047] Finally, set the screening threshold for the total effect index. For a certain performance index, if the total effect index of a certain parameter is greater than the screening threshold, it is included in the range of parameters to be calibrated, that is, the key parameter set; if is less than the screening threshold, it is not included in the range of parameters to be calibrated.

[0048] Advantages of the present invention:

[0049] The present invention adopts a three - level progressive strategy of "single - factor preliminary screening - modeling - Sobol analysis". First, through single - factor screening, parameters with less impact on system performance are eliminated to avoid redundancy in global analysis. Then, a surrogate model is used to replace high - precision simulation to accelerate calculation, dynamically optimize the sample distribution, and reduce the computational complexity of high - dimensional sensitivity analysis. Finally, Sobol global sensitivity analysis is adopted to quantify the main effects and interaction effects, comprehensively evaluate the influence degree of parameters on system performance under different working conditions, extract key parameters from numerous parameters, and lay a foundation for subsequent parameter calibration work. It solves the contradiction between computational efficiency and accuracy in high - dimensional parameter space, takes both efficiency and accuracy into account, and provides a standardized method support for virtual calibration under complex working conditions. Description of the Drawings

[0050] Figure 1 It is a schematic diagram of the overall process of the parameter sensitivity analysis method for the chassis electronic control system based on the deep surrogate model of the present invention;

[0051] Figure 2 It is a schematic diagram of the single - factor screening process of the parameters of the present invention;

[0052] Figure 3 It is a schematic diagram of the BP neural network structure of the present invention;

[0053] Figure 4 It is a schematic diagram of the Sobol global sensitivity analysis process of the present invention;

[0054] Figure 5 It is a schematic diagram of the calculation steps of the Sobol sensitivity index of the present invention. Detailed Embodiment

[0055] As Figure 1 shown, a parameter sensitivity analysis method for the chassis electronic control system based on the deep surrogate model provided by the present invention. In this embodiment, taking the ABS system as an example, the analysis method includes the following steps:

[0056] Step 1: Single - factor screening:

[0057] The screening process is as Figure 2 shown. For each typical working condition, the single - factor method is used to adjust the parameter values one by one and observe their influence on the ABS performance evaluation index, so as to quantify the importance of each parameter, quickly eliminate redundant parameters with sensitivity lower than the threshold, narrow the parameter range for subsequent analysis, and significantly reduce the parameter dimension for subsequent analysis;

[0058] The further steps include:

[0059] First, organize the set P = {p1, p2,... p n} of parameters to be optimized for the ABS system and the set M = {m1, m2,... mk}, where p i is the parameter to be optimized in the ABS system, and m j is the performance evaluation index;

[0060] Next, determine the initial value or preset value of the parameter set as the reference point for subsequent comparison and evaluation;

[0061] Subsequently, perform parameter adjustment one by one: for each parameter p i , while keeping other parameters fixed, only adjust the value of p i , and calculate the adjusted performance evaluation index; determine whether the predetermined number of repetitions is reached. If not, continue with parameter adjustment; if so, enter the step of calculating the influence factor. The calculation formula of the influence factor is as follows:

[0062]

[0063] where represents three values of the parameter p i ; represents the value of the j-th performance evaluation index when the parameter p i takes the value s under the working condition C; m C,basej represents the reference value of the j-th performance evaluation index under the working condition C; for each parameter p i , calculate the relative change amount of the performance evaluation index for all its values under the working condition C, and select the maximum value as the influence factor of the parameter p i under this working condition;

[0064]

[0065] Quantify the influence degree of each parameter on the performance evaluation index through formulas (1) and (2) to screen out the key parameters that have the greatest influence on the performance evaluation index;

[0066] Since the order of magnitude of the influence factors of parameters may vary greatly under different working conditions, to ensure the comparability of the influence factors under different working conditions, the present invention normalizes the influence factors of each working condition:

[0067]

[0068] where is the influence factor of the parameter p i under the working condition C; I C,max and I C,min respectively represent the maximum and minimum values of the influence factors of all parameters under the working condition C;

[0069] Finally, select the values with large influence factors and list them in the key parameter set.

[0070] Step 2: Construct a BP neural network surrogate model:

[0071] Based on the single-factor screening, a dedicated surrogate model for each working condition is constructed based on the BP neural network to replace the high-fidelity simulation model. In this embodiment, it is used to replace the complex ABS simulation model to provide data for the subsequent Sobol global sensitivity analysis. By using the surrogate model, the direct invocation of the high-precision simulation model in the Sobol analysis process is reduced, and the computational time is reduced by more than 90% on the premise of ensuring accuracy, thus significantly improving the computational efficiency while ensuring relatively high computational accuracy.

[0072] Further steps include:

[0073] First, when constructing the BP neural network surrogate model, high-quality input samples need to be generated to cover the parameter space and provide sufficient data support for model training. Due to the complex characteristics of the ABS system with multiple parameters and multiple outputs, efficient sampling should be achieved under limited computational resources. Therefore, the uniform sampling method is used as the sampling method for surrogate model training.

[0074] Secondly, since various control parameters of the ABS system are index values with different dimensions and the value ranges vary greatly, in order to avoid some variables having too much influence on the results during network training, accelerate the model convergence speed and improve the prediction accuracy, the present invention normalizes the data, and the calculation formula is as follows:

[0075]

[0076] where z is the normalization result, x is the calculated value, x min is the minimum value in the data, x max is the maximum value in the data.

[0077] Finally, the relative root mean square error is selected as the evaluation index for the model prediction performance to measure the error between the predicted value and the actual value. The calculation formula is as follows:

[0078]

[0079] where RRMSE is the relative root mean square error, t i is the actual value, y i is the estimated value.

[0080] The structure diagram of the said BP neural network is as Figure 3As shown, the input data of each working condition surrogate model are the parameters obtained through single-factor screening. Therefore, the number of input layer nodes should be the number of parameters obtained through single-factor screening. The output of the surrogate model is the value of the ABS performance evaluation index, and the specific number of output nodes is determined by the number of evaluation indexes adopted for the working condition. The number of hidden layers is selected as 2 - 4 according to the number of indexes, and the number of neurons is set to 20 - 80. The specific values are adjusted through experiments to find the optimal configuration.

[0081] Step 3: Sobol global sensitivity analysis:

[0082] Based on the surrogate model, systematic global sensitivity analysis is adopted. The first-order and total effect sensitivity indexes are calculated through the Sobol method to quantify the main effects and interaction effects of the parameters, thereby guiding the efficient and accurate optimization of the ABS system.

[0083] Further steps include:

[0084] First, based on the single-factor screening results, determine the input parameters and their feasible region ranges, and define the physical constraint conditions of each parameter. Adopt a uniform sampling strategy to generate a set of sample points with uniform distribution characteristics in the high-dimensional parameter space to ensure comprehensive coverage of the parameter space.

[0085] Then, use the BP neural network surrogate model trained in Step 2 for efficient performance prediction, calculate the sensitivity index, and establish a sensitivity feedback mechanism to guide the closed-loop calibration optimization;

[0086] The steps for calculating the Sobol sensitivity index include: Step 1: Define a mathematical model, that is, first clarify a mathematical model Y = f(X), where X = (x1, x2,... x n ) represents the set of input variables to establish the relationship between the output and these inputs; Step 2: Decompose the function. Decompose the above function f(X) into a polynomial form including constant terms, first-order effect terms, second-order effect terms, and up to total effect terms, so as to be able to quantify the influence of each input variable and its interaction on the model output in the follow-up; Step 3: Determine the total variance and the contribution of each effect term to the variance by calculating the integral of each effect term, and then calculate the corresponding sensitivity indexes according to these contributions, including the main effect index (first-order sensitivity index), second-order interaction effect index (second-order sensitivity index), and total effect index (total sensitivity index), so as to evaluate the importance of each input variable and the influence degree of its interaction effect on the output result. This series of operations ultimately helps to identify the key influencing factors and optimize the model parameters.

[0087] Among them, Y = f(X) represents the model being analyzed, which has an n-dimensional vector input X = (x1, x2,... x n );x iX represents the input of the model; V represents the total variance of the output of the model f(X) when all input values fluctuate; V i represents the partial variance of the model output when a single input value fluctuates; represents the partial variance of the model output caused by the interaction between multiple input variables;

[0088] The formula for calculating the main effect index is as follows:

[0089]

[0090] where S i represents the main effect index or first-order sensitivity index of x i to measure the independent impact of the fluctuation of a single input variable x i on the output; E represents the expected value;

[0091] The formula for calculating the second-order interaction effect index is as follows:

[0092]

[0093] where S ij represents the second-order interaction effect index or second-order sensitivity index of x i and x j to measure the degree of influence of the interaction between input variables x i and x j on the output;

[0094] The formula for calculating the total effect index is as follows:

[0095]

[0096] where represents the total effect index or total sensitivity index, used to measure the contribution degree of this input to the total variance of the output when the value of x i fluctuates. The larger is, the greater the influence of this parameter in all scenarios.

[0097] Set the screening threshold of the total effect index. For a certain performance index, if the total effect index of a certain parameter is greater than the screening threshold, it is included in the range of parameters to be calibrated, that is, the key parameter set; if is less than the screening threshold, it is not included in the range of parameters to be calibrated, so as to improve the calculation efficiency and ensure the pertinence of the calibration work.

[0098] Finally, through the combination of sampling strategy optimization, surrogate model integration and statistical verification, the efficient and accurate evaluation of the parameter sensitivity of the ABS system is realized, providing reliable technical support for virtual calibration under complex working conditions.

Claims

1. A method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep proxy model, characterized in that: It includes the following steps: Step 1, single-factor screening: For each typical working condition, the single-factor method is used to adjust the parameter values one by one and observe their effects on the performance evaluation indexes of the chassis electronic control system, quantify the importance of each parameter, eliminate redundant parameters with sensitivity lower than the threshold, and narrow the parameter range; Step 2, construct a BP neural network surrogate model: On the basis of single-factor screening, a dedicated surrogate model for each working condition is constructed based on the BP neural network to replace the high-fidelity simulation model; first, when constructing the BP neural network surrogate model, the uniform sampling method is used as the sampling method for surrogate model training; second, the data is normalized; finally, the relative root mean square error is selected as the evaluation index for the model prediction performance; Step 3, Sobol global sensitivity analysis: First, based on the single-factor screening results, determine the input parameters and their feasible region ranges, define the physical constraint conditions of each parameter, and adopt the uniform sampling strategy to generate a sample point set with uniform distribution characteristics in the high-dimensional parameter space to ensure comprehensive coverage of the parameter space; Then, use the BP neural network surrogate model trained in Step 2 for efficient performance prediction, adopt a systematic global sensitivity analysis, calculate the sensitivity index through the Sobol method, quantify the main effect and interaction effect of the parameters, and establish a sensitivity feedback mechanism to guide the closed-loop calibration optimization; The steps for calculating sensitivity indices using the Sobol method are as follows: First step, define a mathematical model, that is, first clarify a mathematical model Y = f(X), where X = (x1, x2,... x n ) represents the set of input variables to establish the relationship between the output and these inputs; Second step, perform function decomposition, decompose the above function f(X) into a polynomial form including constant terms, first-order effect terms, second-order effect terms up to total effect terms, so as to be able to quantify the influence of each input variable and its interaction on the model output in the follow-up; Third step, determine the total variance and the contribution of each effect term to the variance by calculating the integral of each effect term, and then calculate the corresponding sensitivity indices according to these contributions, including main effect indices, second-order interaction effect indices and total effect indices, so as to evaluate the importance of each input variable and the degree of influence of its interaction on the output result; Among them, Y = f(X) represents the model to be analyzed, which has an n-dimensional vector input X = (x1, x2,... x n ); x i represents the input of the model; V represents the total variance of the output of the model f(X) when all input values fluctuate; V i represents the partial variance of the model output when a single input value fluctuates; represents the partial variance of the model output due to the interaction between multiple input variables; The calculation formula for the main effect index is as follows: Among them, S i represents the main effect index or the first-order sensitivity index of x i ; E represents the expected value; The calculation formula for the second-order interaction effect index is as follows: Among them, S ij represents the second-order interaction index or second-order sensitivity index of x i and x j ; The calculation formula for the total effect index is as follows: Among them, represents the full effect index or the total sensitivity index; Finally, set the screening threshold of the total effect index. For a certain performance index, if the total effect index of a certain parameter is greater than the screening threshold, it is included in the range of parameters to be calibrated, that is, the key parameter set; if is less than the screening threshold, it is not included in the range of parameters to be calibrated; to achieve an efficient and accurate evaluation of the parameter sensitivity of the chassis electronic control system.

2. The method for analyzing the parameter sensitivity of the chassis electronic control system based on the deep proxy model according to claim 1, characterized in that: The steps of the single-factor screening described in Step 1 include: First, organize the set P = {p1, p2, … p n} of parameters to be optimized and the set M = {m1, m2, … m k} of performance evaluation metrics for evaluating the system performance, where p i is the parameter to be optimized and m j is the performance evaluation metric; Next, determine the initial value or preset value of the parameter set as the reference point for subsequent comparison and evaluation; Subsequently, parameter-by-parameter adjustment is performed: for each parameter p i , while keeping other parameters fixed, only the value of p i is adjusted, and the performance evaluation index after adjustment is calculated; it is judged whether the predetermined number of repetitions is reached. If not, the parameter adjustment continues; if it is reached, the step of calculating the influence factor is entered, and the calculation formula of the influence factor is as follows: Among them, represents three values of parameter p i ; represents the value of the j-th performance evaluation index when the value of parameter p i is s under condition C; m C,basej represents the reference value of the j-th performance evaluation index under condition C; for each parameter p i , calculate the relative change of the performance evaluation index for all values of it under condition C, and select the maximum value as the influence factor of parameter p i under this condition; Screen out the key parameters that have the greatest impact on the performance evaluation index by quantifying the impact degree of each parameter on the performance evaluation index through Formula (1) and Formula (2); Normalize the influence factors of each working condition: Among them, is the influence factor of parameter p under condition C; i I C,max and I C,min respectively represent the maximum and minimum values of the influence factors of all parameters under condition C; Finally, select the values with large influence factors and list them in the key parameter set.

3. A method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep proxy model according to claim 1, characterized in that: The calculation formula for normalizing the data described in Step 2 is as follows: Among them, z is the normalization result, x is the calculated value, x min is the minimum value in the data, x max is the maximum value in the data.

4. A method for analyzing the parameter sensitivity of a chassis electronic control system based on a deep proxy model according to claim 1, characterized in that: The calculation formula for the relative root mean square error described in Step 2 is as follows: where RRMSE is the relative root mean square error, t i is the actual value, and y i is the estimated value.

5. The method for analyzing the parameter sensitivity of the chassis electronic control system based on the deep proxy model according to claim 1, characterized in that: The number of input layer nodes of the BP neural network structure described in Step 2 is the number of parameters obtained by single-factor screening; the output of the surrogate model is the value of the performance evaluation index of the chassis electronic control system; the number of intermediate layers is selected as 2-4 according to the number of indexes, and the number of neurons is set to 20-80.

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