A parameter sensitivity analysis method for ESC virtual calibration technology

Abstract

The present application relates to a kind of parameter sensitivity analysis method for ESC virtual calibration technology, first design ESC subjective and objective evaluation system, according to the information such as vehicle body longitudinal, lateral tilt, yaw, steering, tire, ESC intervention, NVH under specific working condition ESC system performance evaluation;Second, design a kind of sensitivity analysis method based on Fourier amplitude, all adjustable parameters are analyzed, after reaching the limit of running step, the first-order influence index and total effect index of different parameters on ESC system performance evaluation are obtained, according to the transverse comparison between parameters and calibration requirements, the final sensitivity analysis result can be obtained.The method proposed in the present application compared with the sensitivity analysis method in existing virtual calibration technology considers the mutual influence between parameters, can screen out the adjustable parameters with little effect on the comprehensive performance of vehicle, so that the number of analysis parameters is reduced, and the calculation amount is greatly reduced.The use of sensitivity analysis has important promoting effect on the upgrading and optimization of vehicle virtual calibration technology.

Description

Technical Field

[0001] This invention relates to the field of automotive chassis electronic control system calibration, and in particular to a parameter sensitivity analysis method for ESC virtual calibration technology that considers the interaction between parameters. Background Technology

[0002] The ESC (Electronic Stability Control) system is a crucial chassis electronic system in automobiles, enhancing vehicle stability and safety. ESC calibration is one of the most critical steps in the virtual calibration process of intelligent vehicle chassis electronic control systems. Traditional chassis electronic control system calibration methods, relying on expert experience based on real vehicles and real-world scenarios, are inefficient and cannot perform comprehensive electromechanical performance testing of multiple intelligent chassis systems before real-world road tests. This results in long vehicle development cycles and high calibration costs, contradicting the market demand for increasingly shorter vehicle development cycles. Therefore, developing virtual calibration technology for ESC is essential. Virtual calibration is a model-based calibration technology that allows calibration to begin before vehicle road tests. Furthermore, by employing efficient automatic calibration algorithms, it can significantly shorten development cycles and reduce calibration costs.

[0003] ESC systems have numerous parameters, each with varying degrees of impact on vehicle handling stability, steering performance, and comfort. Reducing the number of parameters to be calibrated is a key issue in virtual calibration technology. Selecting effective and reasonably numerous calibration parameters, i.e., conducting parameter sensitivity analysis, is crucial for ESC virtual calibration. Current parameter sensitivity analysis methods for ESC virtual calibration do not consider the interactions between parameters. Therefore, a scientific and reasonable parameter selection process is urgently needed to identify and focus on calibrating key parameters that are critical to the control effect of the ESC system. Simultaneously, a comprehensive ESC system performance evaluation system needs to be established to guide parameter selection and calibration. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a parameter sensitivity analysis method for ESC virtual calibration technology, comprising the following steps:

[0005] Step 1

[0006] Select one or more of the following vehicle stability test conditions: serpentine test condition, fishhook test condition, and sinusoidal delay test condition.

[0007] The serpentine test is a human-vehicle closed-loop test condition for evaluating vehicle handling stability. This test condition can examine the vehicle's stability performance during continuous turning.

[0008] The described fishhook test is a driver-initiated open-loop test, which avoids the influence of the driver on the test results. During the test, the steering wheel angle quickly reaches its peak, pauses briefly at the peak, and then rapidly decreases to the opposite peak value. This invention uses it to evaluate the effectiveness of ESC in improving vehicle rollover prevention.

[0009] The sinusoidal delay test procedure is as follows: First, a test of slowly increasing the steering wheel angle is conducted in the preparatory stage. The purpose of this test is to obtain the A value required for the sinusoidal delay test. The A value is the steering wheel angle corresponding to a lateral acceleration of 0.3g. The test is conducted in two groups: one group performs a clockwise steering test, and the other group performs a counterclockwise steering test. The average value of the results from multiple tests in each group is calculated, with the steering wheel angle value accurate to 0.1°. Then, the sinusoidal delay test is performed. According to regulations, the steering wheel angle amplitude for the first sinusoidal delay test should be set to 1.5A. If the test result meets the requirements of FMVSS126 regulations, the steering wheel angle amplitude is increased by 0. The test continues until the steering wheel angle amplitude reaches 6.5A. If 6.5A is less than 270°, the sine delay test must continue until the steering wheel angle reaches 270° before stopping. If 6.5A is greater than 300°, the amplitude of the last sine delay test is 300°. If 6.5A is greater than 270° but less than 300°, the test stops when the steering wheel angle amplitude reaches 6.5A. If the results of each test meet the requirements of FMVSS126, the vehicle is considered to have passed the sine delay test.

[0010] Step Two

[0011] A virtual calibration test model was established and simulated jointly using Simulink and Carsim software. The input of the ESC black-box model was the adjustable parameter module, and the output was connected to Carsim. The input of Carsim was the ESC black-box model, and the output was the subjective and objective evaluation system module. By changing the adjustable parameter module, the performance parameters of the ESC black-box model were changed, thereby affecting the motion performance of the vehicle model in Carsim. The subjective and objective evaluation system module was used to comprehensively evaluate the dynamic subjective and objective performance of the vehicle under the current ESC parameters.

[0012] Step 3

[0013] Based on the calibration technical specifications of the ESC system, all adjustable parameters of the ESC virtual calibration test are extracted and used as inputs for the virtual calibration test. The adjustable parameters of the ESC black box model used include five categories: longitudinal control, roll control, yaw control, steering capability, and ESC intervention. Each category includes several adjustable parameters.

[0014] Step 4

[0015] Design an ESC subjective and objective evaluation system. Based on the vehicle body longitudinal, roll, yaw, steering, tire, ESC intervention, and NVH information from the virtual calibration test under the working conditions provided in step one, establish an ESC system subjective and objective performance evaluation system.

[0016] The ESC objective performance evaluation assigns scores to each evaluation item in each test in step one. The total score for each test is the weighted average of the items in that test, and the total score is the weighted average of the total scores of the three tests.

[0017] Furthermore, the serpentine test evaluation items include average yaw rate, average steering wheel angle, average vehicle roll angle, and average lateral acceleration; the sinusoidal delay test evaluation items include yaw rate, peak lateral displacement, and lateral acceleration; the fishhook test evaluation items include roll rate, wheel ground clearance, tire bead slippage and rim contact with the ground, and anti-rollover bracket contact with the ground; the evaluation items for average yaw rate, average steering wheel angle, average vehicle roll angle, average lateral acceleration, yaw rate, and peak lateral displacement are... Lateral acceleration, roll rate, and wheel height are scored from 1 to 10, representing the degree of "problems noticed by all users" to "problems that are difficult to detect." Tire detachment and rim contact with the ground are scored 0 or 10, with 0 indicating that the tire detachment and rim contact with the ground are present and 10 indicating that the tire detachment and rim contact with the ground are not present. Rollover bracket contact with the ground is scored 0 or 10, with 0 indicating that the rollover bracket is in contact with the ground and 10 indicating that the rollover bracket is not in contact with the ground.

[0018] The subjective evaluation of ESC performance assigns scores to each item in five categories: longitudinal control, roll control, yaw control, steering capability, and ESC intervention. The total score for each category is the weighted average of the items in that category, and the total score is the weighted average of the total scores for all five categories.

[0019] Furthermore, each item in the five categories is scored from 1 to 10, representing the degree from "problems noticed by all users" to "problems that are difficult to detect." Longitudinal control includes power loss and vehicle speed loss at the end of steering; roll control includes roll angle control, roll damping, front and rear roll consistency, roll linearity, and whether the steering angle is proportional; yaw control includes yaw amount, yaw damping, yaw linearity, yaw smoothness, and confidence in yaw conditions; steering capability includes whether the steering radius is linear, whether it is the expected steering radius, left and right steering symmetry, steering torque, whether it is easy to maintain the original driving trajectory, and whether the vehicle body is easy to control; ESC intervention includes whether it intervenes, the timing of intervention, and whether the intervention is smooth.

[0020] The overall ESC performance score is shown in formula (1):

[0021] Overall performance score = α * objective score + β * subjective score (1)

[0022] In the formula, α and β are coefficients, which are assigned values ​​by experts.

[0023] Step 5

[0024] A sensitivity analysis method based on Fourier amplitude is designed. All adjustable parameters of the extracted ESC virtual calibration test are adjusted into a function with a period of 2π according to the transformation function. The Fourier coefficients are obtained by performing a Fourier series expansion on this function. The spectrum function is defined according to the Fourier coefficients, and then the first-order influence index and the total effect index are calculated.

[0025] Based on the adjustable parameters provided in step three, the comprehensive performance index function of the car is listed as shown in equation (2):

[0026] Y = f(X), X = x1, x2, ..., x n (2)

[0027] In the formula, n is the number of adjustable parameters that need to be analyzed, and Y is the overall performance score.

[0028] Let V(Y) be the total variance of the comprehensive performance index. When index x i Values At that time, the conditional variance of the vehicle's ESC performance index is denoted as... The specific form of V(Y) is shown in formula (3):

[0029] Y(Y)=E i (V -i (Y|x i ))+V i (E -i (Y|x i (3)

[0030] In the formula E i (V -i (Y|x i () represents the expected variance of X given a fixed value for Y; this part reflects the degree of dispersion of X given Y. i (E -i (Y|x i () represents the variance of the expected value of X under the condition of Y. This part reflects the degree of influence of changes in Y on the expected value of X; when x i When fluctuations occur, V i (E -i (Y|x iThe larger the value of the main effect index, the more significant the change in the overall performance of the vehicle's ESC. The two are directly proportional, so the main effect index, also known as the first-order sensitivity index, is defined as shown in formula (4):

[0031]

[0032] In the formula, S i The main effect index, also known as the first-order sensitivity index, is the ratio of the partial variance to the total variance of the overall vehicle ESC performance caused by fluctuations in the adjustable parameter values ​​of a certain ESC system. It characterizes the degree of interference to the overall performance value when the adjustable parameter values ​​fluctuate.

[0033] The adjustable parameters of the ESC system are X = x1, x2, ..., x. n Divided into x i and x -i x -i Indicates division by x i Other adjustable parameters besides V -i (E i (Y|x -i )) means except for x i The overall performance bias caused by fluctuations in other adjustable parameters, V(Y)-V -i (E i (Y|x -i That is, it means with x i The relevant comprehensive performance variance is defined by formula (5):

[0034]

[0035] In the formula, S i T The total effect index, also known as the total sensitivity index, characterizes the value x of a certain adjustable parameter. i The disturbance to overall performance caused by fluctuations, and the disturbance to overall performance caused by possible interactions with other adjustable parameters.

[0036] The sensitivity indices of second order and above are defined as shown in formula (6):

[0037]

[0038] In the formula, S ij This is a second-order sensitivity index, also known as a second-order interaction effect index. When the main effect index is not equal to the total effect index, it indicates that there is an interaction between this index and other indicators. ij This is used to characterize the degree of interference that the interaction between two radar system indicators causes to the overall effectiveness. ijkThe third-order sensitivity index, also known as the third-order interaction effect index, is used to characterize the interference of the interaction between three indicators on the overall effectiveness. Higher-order sensitivity indices are similar, further illustrating that the combination of specific indicators may have a specific impact on the overall effectiveness.

[0039] The relationship between the total effect index and the sensitivity indices of each order is shown in formula (7):

[0040]

[0041] The theoretical analysis of the Fourier amplitude sensitivity analysis method is as follows: after the transformation function x i (s)=G i (sin(ω i s)), After conversion, formula (2) becomes formula (8):

[0042] Y=f(x1(s),x2(s)...xn(s))=f(s) (8)

[0043] In the formula, s is a function with a period of 2π, and its Fourier series expansion is shown in formula (9):

[0044]

[0045] In the formula A k With B k These are the Fourier coefficients, where k is any integer, and A k With B k In the integer frequency domain of s∈[-π, +π], it is defined as Equation (10):

[0046]

[0047] The Fourier amplitude sensitivity analysis algorithm uses a transformation function to expand the performance evaluation model into a Fourier series and uses the output value of the performance evaluation model to calculate the Fourier coefficients. The relationship between the Fourier coefficients and the variance of the overall performance is given by formula (11):

[0048]

[0049] Define the spectrum function as formula (12):

[0050] Λ k =2(A k 2 +B k 2 (12)

[0051] When the adjustable parameters of a single ESC system fluctuate, the variance of the overall performance is calculated using the following formula (13):

[0052]

[0053] Λ pωi =2(A pωi 2 +B pωi 2 )

[0054] In the formula, parameter A pωi and B pωi It is the frequency ω i , and all its higher harmonics pω i The corresponding Fourier coefficients.

[0055] Applying the Fourier amplitude sensitivity analysis method, the i-th adjustable parameter x i The main effect index is given by formula (14):

[0056]

[0057] Transformation function x i (s)=G i (sin(ω i s)), ω in i The values ​​must satisfy a linear independence relationship, that is, the following rule must be met:

[0058]

[0059] In the formula, M is the order of influence, a i This is called the test vector, ω i The characteristic frequency is denoted as .

[0060] Step Six

[0061] Based on the magnitude of the spectral amplitude corresponding to the characteristic frequency in the spectrum obtained by the sensitivity analysis method based on Fourier amplitude, the influence of each parameter on the overall performance of the ESC system is determined. All main effect indices obtained by formula (14) in step five are used to characterize the parameters. The parameter sensitivity analysis results are obtained by comparing the main effect indices of each parameter horizontally. The adjustable parameters with large main effect indices are the parameters that have a large impact on the overall performance of the ESC.

[0062] The beneficial effects of this invention are:

[0063] Sensitivity analysis is an effective way to improve the performance of automotive chassis electronic control systems in automotive virtual calibration technology. This invention proposes a parameter sensitivity analysis method for ESC virtual calibration that can shorten the development cycle of automotive chassis electronic control systems and consider the mutual influence between parameters. First, an ESC subjective and objective evaluation system is designed, and the ESC system performance is evaluated based on information such as vehicle longitudinal direction, roll, yaw, steering, tires, ESC intervention, and NVH under specific operating conditions. Second, a sensitivity analysis method based on Fourier amplitude is designed to analyze all adjustable parameters. After reaching the limit of the number of running steps, the first-order influence index and total effect index of different parameters on the ESC system performance evaluation are obtained. The final sensitivity analysis result can be obtained based on calibration requirements and horizontal comparison between parameters. Compared with the sensitivity analysis methods in existing virtual calibration technologies, the method proposed in this invention considers the mutual influence between parameters, and can filter out adjustable parameters with minimal impact on the overall vehicle performance, thus reducing the number of analyzed parameters and significantly reducing the computational load. The application of sensitivity analysis plays an important role in promoting the upgrading and optimization of automotive virtual calibration technology. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the parameter sensitivity analysis method for ESC virtual calibration of the present invention;

[0065] Figure 2 This is a schematic diagram of the serpentine experimental working path of the present invention;

[0066] Figure 3 This is a schematic diagram of the steering wheel angle curve in the experiment of the fishhook of this invention;

[0067] Figure 4 This is a schematic diagram of the steering wheel angle curve for the sinusoidal delay test of the present invention;

[0068] Figure 5 This is a schematic diagram of the virtual calibration working condition experimental model of the present invention;

[0069] Figure 6 This is a schematic diagram of the sensitivity analysis method based on Fourier amplitude of the present invention.

[0070] Figure 7 This is a schematic diagram of the adjustable parameters of the present invention after transformation function. Detailed Implementation

[0071] like Figure 1 As shown in the figure, this embodiment provides a parameter sensitivity analysis method for ESC virtual calibration technology, which includes the following steps:

[0072] Step 1

[0073] Referring to GB / T 6323-2014 and FMVSS No.126, three representative vehicle stability test conditions were selected: serpentine test condition, fishhook test condition, and sinusoidal delay test.

[0074] Specifically, the slalom test is a human-vehicle closed-loop test condition for evaluating vehicle handling stability. This test condition examines the vehicle's stability performance during continuous cornering. The slalom test can be used for both subjective and objective evaluation. In objective evaluation, testers can objectively assess vehicle handling performance based on test data such as yaw rate. The slalom test path is as follows: Figure 2 As shown in the figure, L represents the distance between the two piles. In accordance with the requirements of GB / T6323-2014, L is set to 30 meters in this embodiment. The serpentine test was also conducted on both high-adhesion and low-adhesion road surfaces.

[0075] The fishhook test is an open-loop test conducted by the driver, thus avoiding any influence from the driver on the test results. Named for the resemblance of the vehicle's trajectory to a fishhook, the fishhook test is a legally established test in the United States for evaluating a vehicle's rollover resistance. The prescribed steering wheel angle curve for the test is as follows: Figure 3 As shown in the diagram, during the test, the steering wheel angle quickly reaches its peak value, and after a brief pause at the peak, it rapidly decreases to the opposite peak value. The fishhook test is characterized by a large steering wheel angle amplitude and high steering speed, making it prone to rollover during the test. This invention uses it to evaluate the effectiveness of ESC in improving vehicle rollover prevention capabilities.

[0076] The sinusoidal delay test procedure is as follows: First, in the preparatory stage, a test is conducted by slowly increasing the steering wheel angle. The car is traveling at a speed of 80 km / h, such as... Figure 4The steering wheel angle is slowly increased at a rate of 13.5 deg / s until the lateral acceleration of the car reaches 0.5g. The purpose of this test is to determine the A value required for the sinusoidal delay test. The A value is the steering wheel angle corresponding to a lateral acceleration of 0.3g. This experiment needs to be conducted in two groups: one group performs a clockwise steering test, and the other group performs a counterclockwise steering test. The average value of the results from multiple tests in each group is calculated, with the steering wheel angle value accurate to 0.1°. Then, the sinusoidal delay test is performed. According to regulations, the steering wheel angle amplitude for the first sinusoidal delay test should be set to 1.5A. If the result of this test meets the requirements of FMVSS126 regulations, the steering wheel angle amplitude is increased by 0.5A before the next test, until the steering wheel angle amplitude reaches 6.5A. If 6.5A is less than 270°, the sinusoidal delay test must continue until the steering wheel angle reaches 270° before stopping; if 6.5A is greater than 300°, the amplitude of the final sinusoidal delay test is 300°; if 6.5A is greater than 270° but less than 300°, the test stops when the steering wheel angle amplitude reaches 6.5A. If each test result meets the requirements of FMVSS126, the vehicle is considered to have passed the sinusoidal delay test.

[0077] Step Two

[0078] like Figure 5 As shown, a virtual calibration test model was established, and Simulink and Carsim software were used for joint simulation. The input of the ESC black-box model was the adjustable parameter module, and the output was connected to Carsim; the input of Carsim was the ESC black-box model, and the output was the subjective and objective evaluation system module. By changing the adjustable parameter module, the performance parameters of the ESC black-box model were altered, thereby affecting the motion performance of the vehicle model in Carsim. The subjective and objective evaluation system module was used to comprehensively evaluate the dynamic subjective and objective performance of the vehicle under the current ESC parameters.

[0079] Step 3

[0080] According to the calibration technical specifications of the ESC system, all adjustable parameters of the ESC virtual calibration test are extracted and used as input for the virtual calibration test. The adjustable parameters of the ESC black box model used include five categories: longitudinal control, roll control, yaw control, steering capability, and ESC intervention. In this embodiment, longitudinal control includes power loss and vehicle speed loss at the end of steering; roll control includes roll angle control, roll damping, front and rear roll consistency, roll linearity, and whether the steering angle is proportional; yaw control includes yaw amount, yaw damping, yaw linearity, yaw smoothness, and confidence in the yaw situation; steering capability includes whether the steering radius is linear, whether it is according to the expected steering radius, left and right steering symmetry, steering torque, whether it is easy to maintain the original driving trajectory, and whether the vehicle body is easy to control; ESC intervention includes whether to intervene, intervention timing, and intervention smoothness, for a total of 21 adjustable parameters.

[0081] Step 4

[0082] Design an ESC subjective and objective evaluation system. Based on the information on vehicle body longitudinal, roll, yaw, steering, tires, ESC intervention, NVH and other information from the virtual calibration test under the working conditions provided in step one, establish an ESC system subjective and objective performance evaluation system.

[0083] The ESC performance objective evaluation assigns scores to each evaluation item in the three tests: slalom test, sinusoidal delay test, and fishhook test. In this embodiment, the slalom test evaluation items include average yaw rate, average steering wheel angle, average body roll angle, and average lateral acceleration; the sinusoidal delay test evaluation items include yaw rate, peak lateral displacement, and lateral acceleration; and the fishhook test evaluation items include roll rate, wheel ground clearance, tire bead slippage and rim contact with the ground, and anti-rollover bracket contact with the ground. The scores for average yaw rate, average steering wheel angle, average body roll angle, and average lateral acceleration are also assessed. Average lateral acceleration, yaw rate, peak lateral displacement, lateral acceleration, roll rate, and wheel height are scored from 1 to 10, representing the severity from "problems noticed by all users" to "problems that are difficult to detect." Tire rim slippage and rim contact issues are scored either 0 or 10, with 0 indicating both conditions and 10 indicating none. Rollover brace contact issues are also scored either 0 or 10, with 0 indicating both conditions and 10 indicating none. The total score for each test is the weighted average of the scores for that test, and the final score is the weighted average of the total scores for all three tests.

[0084] The subjective evaluation of ESC performance assigns scores from 1 to 10 to each item in five categories: longitudinal control, roll control, yaw control, steering ability, and ESC intervention. Scores from 1 to 10 represent the degree of "problems noticed by all users" to "problems that are difficult to detect." In this embodiment, longitudinal control includes power loss and vehicle speed loss at the end of steering; roll control includes roll angle control, roll damping, front and rear roll consistency, roll linearity, and whether the steering angle is proportional; yaw control includes yaw amount, yaw damping, yaw linearity, yaw smoothness, and confidence in yaw conditions; steering ability includes whether the steering radius is linear, whether it is the expected steering radius, left and right steering symmetry, steering torque, whether it is easy to maintain the original driving trajectory, and whether the vehicle body is easy to control; and ESC intervention includes whether it intervenes, the timing of intervention, and the smoothness of intervention. The total score for each category is the weighted average of the items in that category, and the total score is the weighted average of the total scores for all five categories.

[0085] The objective evaluation table for ESC performance is shown in Table 1, and the subjective evaluation table for ESC performance is shown in Table 2.

[0086] Table 1 Objective Evaluation Table of ESC Performance

[0087]

[0088] Table 2 Subjective Evaluation Table of ESC Performance

[0089]

[0090] The overall ESC performance score is shown in formula (1):

[0091] Overall performance score = 0.7 * objective score + 0.3 * subjective score (1)

[0092] In this embodiment, the coefficients 0.7 and 0.3 are assigned by experts.

[0093] Step 5

[0094] like Figure 6 As shown, a sensitivity analysis method based on Fourier amplitude is designed to adjust all adjustable parameters of the extracted ESC virtual calibration test into functions with a period of 2π according to the transformation function, such as... Figure 7 As shown. The Fourier coefficients are obtained by performing a Fourier series expansion on this function, and a spectrum function is defined based on the Fourier coefficients. Then, the first-order influence index and the total effect index are calculated.

[0095] The Fourier amplitude sensitivity analysis method is explained as follows: It is a global sensitivity analysis based on variance. It mainly studies the magnitude of the variance of the output fluctuation caused by the fluctuation of the input to demonstrate the impact of the input fluctuation on the output. It can be characterized by several different types of sensitivity indices.

[0096] Based on the adjustable parameters provided in step three, the comprehensive performance index function of the car is listed as shown in equation (2):

[0097] Y = f(X), X = x1, x2, ..., x n (2)

[0098] In the formula, n is the number of adjustable parameters that need to be analyzed, and Y is the overall performance score.

[0099] Let V(Y) be the total variance of the comprehensive performance index. When index x i Values At that time, the conditional variance of the vehicle's ESC performance index is denoted as... The specific form of V(Y) is shown in formula (3):

[0100] Y(Y)=E i (V -i (Y|x i ))+V i (E -i (Y|x i (3)

[0101] In the formula E i (V -i (Y|x i () represents the expected variance of X given a fixed value for Y; this part reflects the degree of dispersion of X given Y. i (E -i (Y|x i () represents the variance of the expected value of X under the condition of Y. This part reflects the degree of influence of changes in Y on the expected value of X; when x i When fluctuations occur, V i (E -i (Y|x i The larger the value of the main effect index, the more significant the change in the overall performance of the vehicle's ESC. The two are directly proportional, so the main effect index, also known as the first-order sensitivity index, is defined as shown in formula (4):

[0102]

[0103] In the formula, S iThe main effect index, also known as the first-order sensitivity index, is the ratio of the partial variance to the total variance of the overall vehicle ESC performance caused by fluctuations in the adjustable parameter values ​​of a certain ESC system. It characterizes the degree of interference to the overall performance value when the adjustable parameter values ​​fluctuate.

[0104] The adjustable parameters of the ESC system are X = x1, x2, ..., x. n Divided into x i and x -i x -i Indicates division by x i Other adjustable parameters besides V -i (E i (Y|x -i )) means except for x i The overall performance bias caused by fluctuations in other adjustable parameters, V(Y)-V -i (E i (Y|x -i That is, it means with x i The relevant comprehensive performance variance is defined by formula (5):

[0105]

[0106] In the formula, S i T The total effect index, also known as the total sensitivity index, characterizes the value x of a certain adjustable parameter. i The disturbance to overall performance caused by fluctuations, and the disturbance to overall performance caused by possible interactions with other adjustable parameters.

[0107] Similarly, sensitivity indices of second order and above can be defined as shown in formula (6):

[0108]

[0109] In the formula, S ij This is a second-order sensitivity index, also known as a second-order interaction effect index. When the main effect index is not equal to the total effect index, it indicates that there is an interaction between this index and other indicators. ij This is used to characterize the degree of interference that the interaction between two radar system indicators causes to the overall effectiveness. ijk The third-order sensitivity index, also known as the third-order interaction effect index, is used to characterize the interference of the interaction between three indicators on the overall effectiveness. Higher-order sensitivity indices are similar, further illustrating that the combination of specific indicators may have a specific impact on the overall effectiveness.

[0110] The relationship between the total effect index and the sensitivity indices of each order is shown in formula (7):

[0111]

[0112] The theoretical analysis of the Fourier amplitude sensitivity analysis method is as follows: Figure 6 After transformation function x i (s)=G i (sin*ω i s)), After conversion, formula (2) becomes formula (8):

[0113] Y = f(x1(s), x2(s), ..., x n (s))=f(s) (8)

[0114] In the formula, s is a function with a period of 2π, and its Fourier series expansion is shown in formula (9):

[0115]

[0116] In the formula A k With B k These are the Fourier coefficients, where k is any integer, and A k With B k In the integer frequency domain of s∈[-π, +π], it is defined as Equation (10):

[0117]

[0118] The Fourier amplitude sensitivity analysis algorithm uses a transformation function to expand the performance evaluation model into a Fourier series and uses the output value of the performance evaluation model to calculate the Fourier coefficients. The relationship between the Fourier coefficients and the variance of the overall performance is given by formula (11):

[0119]

[0120] Define the spectrum function as formula (12):

[0121] Λ k =2(A k 2 +B k 2 (12)

[0122] When the adjustable parameters of a single ESC system fluctuate, the variance of the overall performance is calculated using the following formula (13):

[0123]

[0124] Λ pωi =2(A pωi 2 +B pωi 2 )

[0125] In the formula, parameter A pωi and B pωi It is the frequency ω i , and all its higher harmonics pω i The corresponding Fourier coefficients.

[0126] Applying the Fourier amplitude sensitivity analysis method, the i-th adjustable parameter x i The main effect index is given by formula (14):

[0127]

[0128] Figure 6 The transformation function x in i (s)=G i (sin(ω i s)), ω in i The values ​​must satisfy a linear independence relationship, that is, the following rule must be met:

[0129]

[0130] In the formula, M is the order of influence, which is usually taken as 4, a i This is called the test vector, ω i The characteristic frequency is denoted as .

[0131] This embodiment uses the ESC black-box model with 21 adjustable parameters as an example, and the selected feature frequencies are:

[0132]

[0133] Step Six

[0134] The influence of each parameter on the overall performance of the ESC system is determined by the magnitude of the spectral amplitude corresponding to the characteristic frequency in the spectrum obtained by the sensitivity analysis method based on Fourier amplitude. The main effect index is used to characterize the effect. The parameter sensitivity analysis results are obtained by comparing the main effect indices of each parameter.

[0135] Specifically, the main effect indices of all adjustable parameters obtained from formula (14) in step five are sorted. The adjustable parameters with larger main effect indices are those that have a greater impact on the overall performance of ESC. When improving the virtual calibration of ESC, the adjustment of these adjustable parameters can be the focus and they can be used as optimization targets.

Claims

1. A parameter sensitivity analysis method for ESC virtual calibration technology, characterized in that: Includes the following steps: Step 1 Select one or more of the following vehicle stability test conditions: serpentine test condition, fishhook test condition, and sinusoidal delay test condition; Step Two A virtual calibration test model was established and simulated jointly using Simulink and Carsim software. The input of the ESC black-box model was the adjustable parameter module, and the output was connected to Carsim. The input of Carsim was the ESC black-box model, and the output was the subjective and objective evaluation system module. By changing the adjustable parameter module, the performance parameters of the ESC black-box model were changed, thereby affecting the motion performance of the vehicle model in Carsim. The subjective and objective evaluation system module was used to comprehensively evaluate the dynamic subjective and objective performance of the vehicle under the current ESC parameters. Step 3 According to the calibration technical specifications of the ESC system, all adjustable parameters of the ESC virtual calibration test are extracted and used as input for the virtual calibration test. The adjustable parameters of the ESC black box model used include five categories: longitudinal control, roll control, yaw control, steering capability, and ESC intervention. Each category includes several adjustable parameters. Step 4 Design an ESC subjective and objective evaluation system. Based on the vehicle body longitudinal, roll, yaw, steering, tire, ESC intervention, and NVH information from the virtual calibration test under the working conditions provided in step one, establish an ESC system subjective and objective performance evaluation system. The ESC performance objective evaluation assigns scores to each evaluation item in each test in step one. The total score for each test is the weighted average of the items in that test, and the total score is the weighted average of the total scores of the three tests. The subjective evaluation of ESC performance assigns scores to each item in five categories: longitudinal control, roll control, yaw control, steering capability, and ESC intervention. The total score for each category is the weighted average of the items in that category, and the total score is the weighted average of the total scores for all five categories. The overall ESC performance score is shown in formula (1): Overall performance score = α * objective score + β * subjective score (1) In the formula, α and β are coefficients, which are assigned by experts; Step 5 A sensitivity analysis method based on Fourier amplitude is designed. All adjustable parameters of the extracted ESC virtual calibration test are adjusted into a function with a period of 2π according to the transformation function. The Fourier coefficients are obtained by performing a Fourier series expansion on this function. The spectrum function is defined according to the Fourier coefficients, and then the first-order influence index and the total effect index are calculated. Based on the adjustable parameters provided in step three, the comprehensive performance index function of the car is listed as shown in equation (2): Y=f(X),X=x1,x2......x n (2) In the formula, n is the number of adjustable parameters that need to be analyzed, and Y is the overall performance score; Let V(Y) be the total variance of the comprehensive performance index. When index x i Values At that time, the conditional variance of the vehicle's ESC performance index is denoted as... The specific form of V(Y) is shown in formula (3): Y(Y)=E i (V -i (Y|x i ))+V i (AND -i (Y|x i )) (3) In the formula E i (V -i (Y|x i () represents the expected variance of X given a fixed value for Y; this part reflects the degree of dispersion of X given Y. i (E -i (Y|x i () represents the variance of the expected value of X under the condition of Y. This part reflects the degree of influence of changes in Y on the expected value of X; when x i When fluctuations occur, V i (E -i (Y|x i The larger the value of the main effect index, the more significant the change in the overall performance of the vehicle's ESC. The two are directly proportional, so the main effect index, also known as the first-order sensitivity index, is defined as shown in formula (4): In the formula, S i The main effect index, also known as the first-order sensitivity index, is the ratio of the partial variance to the total variance of the overall vehicle ESC performance caused by fluctuations in the adjustable parameter values ​​of a certain ESC system. It represents the degree of interference to the overall performance value when the adjustable parameter values ​​fluctuate. The adjustable parameters of the ESC system are X = x1, x2, ..., x. n Divided into x i and x -i x -i Indicates division by x i Other adjustable parameters besides V -i (E i (Y|x -i )) means except for x i The overall performance bias caused by fluctuations in other adjustable parameters, V(Y)-V -i (E i (Y|x -i That is, it means with x i The relevant comprehensive performance variance is defined by formula (5): In the formula, The total effect index, also known as the total sensitivity index, characterizes the value x of a certain adjustable parameter. i The disturbance to overall performance caused by fluctuations alone, and the disturbance to overall performance caused by possible interactions with other adjustable parameters; The sensitivity indices of second order and above are defined as shown in formula (6): In the formula, S ij S is a second-order sensitivity index. ij Used to characterize the degree of interference between the interaction between two radar system indicators on overall effectiveness; S ijk It is a third-order sensitivity index, used to characterize the interference of the interaction between the three indicators on the overall effectiveness; The relationship between the total effect index and the sensitivity indices of each order is shown in formula (7): The theoretical analysis of the Fourier amplitude sensitivity analysis method is as follows: after the transformation function... After conversion, formula (2) becomes formula (8): Y=f(x1(s),x2(s)......x n (s))=f(s) (8) In the formula, s is a function with a period of 2π, and its Fourier series expansion is shown in formula (9): In the formula A k With B k These are the Fourier coefficients, where k is any integer, and A k With B k In the integer frequency domain of s∈[-π, +π], it is defined as Equation (10): The Fourier amplitude sensitivity analysis algorithm uses a transformation function to expand the performance evaluation model into a Fourier series and uses the output value of the performance evaluation model to calculate the Fourier coefficients. The relationship between the Fourier coefficients and the variance of the overall performance is given by formula (11): Define the spectrum function as formula (12): L k =2(a k 2 +B k 2 ) (12) When the adjustable parameters of a single ESC system fluctuate, the variance of the overall performance is calculated using the following formula (13): L pωi =2(A pωi 2 +B pωi 2 ) In the formula, parameter A pωi and B pωi It is the frequency ω i , and all its higher harmonics pω i The corresponding Fourier coefficients; Applying the Fourier amplitude sensitivity analysis method, the i-th adjustable parameter x i The main effect index is given by formula (14): Transformation function ω in i The values ​​must satisfy a linear independence relationship, that is, the following rule must be met: In the formula, M is the order of influence, and a i This is called the test vector, ω i Characteristic frequency; Step Six Based on the magnitude of the spectral amplitude corresponding to the characteristic frequency in the spectrum obtained by the sensitivity analysis method based on Fourier amplitude, the influence of each parameter on the overall performance of the ESC system is determined. All main effect indices obtained by formula (14) in step five are used to characterize the parameters. The parameter sensitivity analysis results are obtained by comparing the main effect indices of each parameter horizontally. The adjustable parameters with large main effect indices are the parameters that have a large impact on the overall performance of the ESC.

2. The parameter sensitivity analysis method for ESC virtual calibration technology according to claim 1, characterized in that: The serpentine test is a human-vehicle closed-loop test condition for evaluating vehicle handling stability. This test condition can examine the stability performance of the vehicle during continuous turning. The fishhook test is a driver-initiated open-loop test, which also avoids the influence of the driver on the test results. In the test, the steering wheel angle quickly reaches its peak value, and after a brief stay at the peak value, it quickly decreases to the opposite peak value. It is used to evaluate the effectiveness of ESC in improving the vehicle's anti-rollover capability. The sinusoidal delay test procedure is as follows: First, a test of slowly increasing the steering wheel angle is conducted in the preparatory stage. The purpose of this test is to obtain the A value required for the sinusoidal delay test. The A value is the steering wheel angle corresponding to a lateral acceleration of 0.3g. This is conducted in two groups: one group performs a clockwise steering test, and the other group performs a counterclockwise steering test. The average value of the results from multiple tests in each group is calculated, with the steering wheel angle value accurate to 0.1°. Then, the sinusoidal delay test is performed. According to regulations, the steering wheel angle amplitude for the first sinusoidal delay test should be set to 1.5A. If the test results meet FMVSS126... The regulations require that the steering wheel angle amplitude be increased by 0.5A before the next test, until the steering wheel angle amplitude reaches 6.5A. If 6.5A is less than 270°, the sine delay test must continue until the steering wheel angle reaches 270° before stopping. If 6.5A is greater than 300°, the amplitude of the last sine delay test is 300°. If 6.5A is greater than 270° but less than 300°, the test stops when the steering wheel angle amplitude reaches 6.5A. If the results of each test meet the requirements of FMVSS126, the vehicle is considered to have passed the sine delay test.

3. The parameter sensitivity analysis method for ESC virtual calibration technology according to claim 1, characterized in that: In step four, the objective evaluation of ESC performance includes the following evaluation items: slalom test (mean yaw rate, average steering wheel angle, average body roll angle, average lateral acceleration); sinusoidal delay test (mean yaw rate, peak lateral displacement, lateral acceleration); and hook test (mean roll rate, wheel ground clearance, tire bead slippage and rim contact with the ground, and anti-rollover bracket contact with the ground). The evaluation items for average yaw rate, average steering wheel angle, average body roll angle, average lateral acceleration, yaw rate, and peak lateral displacement are also considered. Lateral displacement, lateral acceleration, roll rate, and wheel height are scored from 1 to 10, representing the degree of "problems noticed by all users" to "problems that are difficult to detect." Tire detachment and rim contact with the ground are scored 0 or 10, with 0 indicating that tire detachment and rim contact with the ground are present, and 10 indicating that tire detachment and rim contact with the ground are not present. Rollover bracket contact with the ground is scored 0 or 10, with 0 indicating that rollover bracket contact with the ground is present, and 10 indicating that rollover bracket contact with the ground is not present.

4. The parameter sensitivity analysis method for ESC virtual calibration technology according to claim 1, characterized in that: In step four, the subjective evaluation of ESC performance assigns scores of 1-10 to each item in the five categories. Scores of 1-10 represent the degree of "problems noticed by all users" to "problems that are difficult to detect". Longitudinal control includes power loss and vehicle speed loss at the end of steering; roll control includes roll angle control, roll damping, front and rear roll consistency, roll linearity, and whether the steering angle is proportional; yaw control includes yaw amount, yaw damping, yaw linearity, yaw smoothness, and confidence in yaw conditions; steering ability includes whether the steering radius is linear, whether it is the expected steering radius, left and right steering symmetry, steering torque, whether it is easy to maintain the original driving trajectory, and whether the vehicle body is easy to control; ESC intervention includes whether it intervenes, the timing of intervention, and whether the intervention is smooth.

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