Method for identifying delay coefficient of hysteresis model based on fitting curve intersection point

Abstract

The invention is suitable for the technical field of automobile test data processing, and provides a fitting curve intersection point-based hysteresis model delay coefficient identification method, which comprises the following steps of: respectively fitting upper and lower boundaries of a hysteresis characteristic curve and a transition process curve through a least square method, constructing mathematical expressions of the upper and lower boundaries and the transition process curve, and solving an intersection point coordinate of the mathematical expressions. Based on the coordinate relation of the intersection points, an analytical calculation model of the delay coefficient is established, and direct mathematical derivation of parameters is achieved. According to the method, the influence of interference such as measurement noise and boundary curve oscillation in an original test curve on boundary switching point judgment is effectively solved, meanwhile, the delay coefficient is solved through mathematical analysis, the calculation cost of a complex optimization algorithm is avoided, and the parameter identification efficiency is improved. By adopting the delay coefficient identified by the method, the model simulation curve and the actually measured transition curve have high consistency, the calculation cost is reduced on the premise of ensuring the precision, and most actual engineering requirements can be met.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile test data processing, and in particular relates to a method for identifying a delay coefficient of a hysteresis model based on an intersection of a fitting curve. Background Art

[0002] The friction nonlinear hysteresis characteristics of the vehicle steering, suspension, braking and other systems will significantly affect the dynamic response quality of the vehicle. In the vehicle dynamics modeling and simulation, it is very important to establish a high-fidelity hysteresis model. At present, the Fancher model is mostly used to characterize such nonlinear hysteresis characteristics. A very important parameter in the Fancher model is the delay coefficient. The accurate identification of the delay coefficient parameter is the key to accurately simulate such hysteresis characteristics. Therefore, it is very important to study a high-precision and high-robust delay coefficient parameter identification method.

[0003] For the identification of the delay coefficient of the Fancher model, the Marquardt optimization algorithm is used to find the parameter vector in the document "Physical Mechanism and Parameter Identification of Leaf Spring Fancher Model". The objective function is designed based on the simulated suspension vertical load corresponding to the suspension deformation and the experimental test data with the minimum error. The coefficients of the upper and lower boundary polynomials of the envelope and the fitting value of the delay coefficient are solved at one time. In the document "Study on the Fitting Accuracy of Dynamic Stiffness of Leaf Spring Based on Fancher Model", the initial value of the delay coefficient is obtained according to the mean point of the loading and unloading boundary derivatives. Finally, the delay coefficient is optimized based on the minimum error between the test and fitting loads.

[0004] The above studies all use optimization algorithms to minimize the error between the simulation data and the test data of the boundary curve and transition curve to obtain the delay coefficient. However, due to the interference of measurement noise and the large fluctuations and oscillations of the boundary curve in the original test data, the positioning judgment of the turning points of loading and unloading migration is often inaccurate, making it impossible to accurately define the starting and ending points of the boundary switching. Therefore, in this case, directly performing parameter identification based on the original data is prone to errors in the parameters of the loading and unloading boundary curves, and at the same time affects the accuracy of delay coefficient identification. Summary of the invention

[0005] The purpose of the embodiments of the present invention is to provide a method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves, aiming to solve the problems raised in the above-mentioned background technology.

[0006] The embodiment of the present invention is implemented as follows: a method for identifying a delay coefficient of a hysteresis model based on an intersection of a fitting curve comprises the following steps: Step 1: The original data of steering wheel angle and steering wheel torque in the steering system hysteresis characteristic curve obtained under three sets of measurement cycles are preprocessed using a Butterworth low-pass filter respectively; Step 2: Calculate the maximum and minimum values ​​of the steering wheel angle data after low-pass filtering preprocessing in step 1, that is, determine the measurement range covered by the steering wheel angle; Step 3: The upper and lower boundaries of the steering wheel torque-steering wheel angle hysteresis characteristic curve and the transition curves on both sides are fitted by the least square method; Step 4: Based on the fitting processing results of step 3, solve the four intersection points between the upper and lower fitting boundary curves and the left and right fitting transition curves and Based on the coordinate relationship of the intersection points, an analytical calculation model of the delay coefficient is established to achieve direct mathematical derivation of the parameters. Step 5: Verify the accuracy of the delay coefficient parameter identification of the Fancher model.

[0007] According to a further technical solution, in step 1, the filter design is based on its transfer function expression: (1); In the formula, is a complex frequency domain variable; is the cut-off angular frequency, , corresponding to the cut-off frequency 5Hz; is the filter order, .

[0008] According to a further technical solution, step 2 comprises the following specific steps: First, calculate the maximum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the maximum value of the steering wheel angle ,Right now: ; Calculate the minimum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the minimum value of the steering wheel angle ,Right now: ; Finally, the measurement range of the steering wheel angle is determined to be , which will be used as a reference for the range of horizontal coordinates when fitting the boundary curve and transition curve.

[0009] A further technical solution is that in step 3, the upper and lower boundary curves are fitted by the least square method, and the horizontal coordinate range of the fitting curve is , where the steering wheel angle range adjustment value The selection is based on the actual horizontal coordinate range of the transition curves on both sides; the mathematical expressions of the upper and lower boundaries after fitting are: (2); In the formula, is the steering wheel angle, and ; is the steering wheel torque at the upper boundary; are the coefficients of the upper boundary fitting curve polynomial; is the steering wheel torque at the lower boundary; are the coefficients of the lower boundary fitting curve polynomial.

[0010] For the transition curves on both sides, the least squares method is used for fitting. The horizontal coordinate range of the left fitting transition curve is ; The horizontal coordinate range of the right fitting transition curve is ; The mathematical expression after fitting of the transition curves on both sides is: (3); In the formula, is the steering wheel angle; is the adjustment value of the horizontal coordinate range of the fitting curve, i.e. the steering wheel angle range; is the steering wheel torque of the left transition curve; The coefficients of the fitting curve polynomial for the left transition curve; is the steering wheel torque of the right transition curve; The coefficients of the fitting curve polynomial for the right transition curve.

[0011] In a further technical solution, in step 4, the intersection points of the upper and lower boundary curves with the left transition curve are The intersection points of the upper and lower boundary curves with the right transition curve are ; Intersection As the actual boundary switching point, it is the turning point of the steering wheel angle during the process of switching from unloading to loading or from loading to unloading; intersection point As the end point of the loading and unloading transition process; In the Fancher model, the angle passing through the 95% transition curve is defined as ,in is the delay coefficient, then the delay coefficient during loading Calculated as: (4); In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of ; Delay factor during unloading Calculated as: (5); In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of ; In order to simplify the modeling parameters and reduce the parameter identification error, the default delay coefficients during loading and unloading are the same, so the delay coefficient of the Fancher model is the delay coefficient during loading. and the delay factor during unloading The mean value of the Fancher model delay coefficient is calculated as: (6).

[0012] According to a further technical solution, step 5 comprises the following specific steps: The Fancher model is used to simulate the hysteresis characteristics of the steering wheel torque-steering wheel angle relationship curve. The identified delay coefficient is used as input, and the simulation curve is compared with the original data.

[0013] The embodiment of the present invention provides a method for identifying the delay coefficient of a hysteresis model based on the intersection of a fitting curve. The method effectively solves the influence of interferences such as measurement noise and boundary curve oscillation in the original test curve on the determination of the boundary switching point. At the same time, the method adopts a delay coefficient solution method based on mathematical analysis, which avoids the computational cost of complex optimization algorithms and improves the parameter identification efficiency. The delay coefficient identified by this method can make the model simulation curve and the actual measured transition curve have a high consistency, reduce the computational cost while ensuring accuracy, and meet most actual engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flowchart of a method for identifying a delay coefficient of a hysteresis model based on an intersection of a fitting curve provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of the fitting curve of the steering wheel torque-steering wheel angle hysteresis characteristic; Figure 3 This is a comparison chart of the steering wheel torque-steering wheel angle hysteresis characteristic simulation curve and the original test data. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0016] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0017] like Figure 1 As shown, a method for identifying a delay coefficient of a hysteresis model based on the intersection of a fitting curve is provided in one embodiment of the present invention, comprising the following steps: Step 1: The original data of steering wheel angle and steering wheel torque in the steering system hysteresis characteristic curve obtained under three sets of measurement cycles are preprocessed using a Butterworth low-pass filter respectively; Step 2: Calculate the maximum and minimum values ​​of the steering wheel angle data after low-pass filtering preprocessing in step 1, that is, determine the measurement range covered by the steering wheel angle; Step 3: The upper and lower boundaries of the steering wheel torque-steering wheel angle hysteresis characteristic curve and the transition curves on both sides are fitted by the least square method; Step 4: Based on the fitting processing results of step 3, solve the four intersection points between the upper and lower fitting boundary curves and the left and right fitting transition curves and Based on the coordinate relationship of the intersection points, an analytical calculation model of the delay coefficient is established to achieve direct mathematical derivation of the parameters. Step 5: Verify the accuracy of the delay coefficient parameter identification of the Fancher model.

[0018] As a preferred embodiment of the present invention, in step 1, the filter design is based on its transfer function expression: (1); In the formula, is a complex frequency domain variable; is the cut-off angular frequency, , corresponding to the cut-off frequency 5Hz; is the filter order, ; As a preferred embodiment of the present invention, step 2 includes the following specific steps: First, calculate the maximum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the maximum value of the steering wheel angle ,Right now: ; Calculate the minimum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the minimum value of the steering wheel angle ,Right now: ; Finally, the measurement range of the steering wheel angle is determined to be , which will be used as a reference for the range of horizontal coordinates when fitting the boundary curve and transition curve.

[0019] As a preferred embodiment of the present invention, in step 3, the upper and lower boundary curves are fitted by the least square method, and the fitting polynomial order can be appropriately selected according to the actual fitting effect. In order to reduce the influence of the transition curves on the fitting effect, the horizontal coordinate range of the upper and lower boundary fitting curves should be appropriately reduced based on the maximum range of the steering wheel angle. Referring to the minimum and maximum values ​​of the steering wheel angle calculated in step 2, the horizontal coordinate range of the fitting curve can be taken as , where the steering wheel angle range adjustment value It can be appropriately selected according to the actual horizontal coordinate range of the transition curves on both sides. The mathematical expressions of the upper and lower boundaries after fitting are: (2); In the formula, is the steering wheel angle, and ; is the steering wheel torque at the upper boundary; are the coefficients of the upper boundary fitting curve polynomial; is the steering wheel torque at the lower boundary; are the coefficients of the lower boundary fitting curve polynomial.

[0020] For the transition curves on both sides, the least squares method is used for fitting respectively, and the fitting polynomial degree can be appropriately selected according to the actual fitting effect. The horizontal coordinate range of the left fitting transition curve can be appropriately adjusted to the minimum value of the steering wheel angle calculated in step 2. , so that it can cover the actual horizontal coordinate range of the transition curve data on the left as much as possible; the horizontal coordinate range of the fitting transition curve on the right is , so that it can cover the actual horizontal coordinate range of the transition curve data on the right as much as possible. The mathematical expression of the transition curves on both sides after fitting is: (3); In the formula, is the steering wheel angle; is the adjustment value of the horizontal coordinate range of the fitting curve, i.e. the steering wheel angle range; is the steering wheel torque of the left transition curve; The coefficients of the fitting curve polynomial for the left transition curve; is the steering wheel torque of the right transition curve; The coefficients of the fitting curve polynomial for the right transition curve.

[0021] like Figure 2As shown in FIG. 1 , as a preferred embodiment of the present invention, the intersection points of the upper and lower boundary curves with the left transition curve are respectively The intersection points of the upper and lower boundary curves with the right transition curve are . Intersection As the actual boundary switching point, it is the turning point of the steering wheel angle during the process of switching from unloading to loading or from loading to unloading; intersection point Serves as the end point of the loading and unloading transition process.

[0022] In the Fancher model, the angle passing through the 95% transition curve is defined as ,in is the delay coefficient, then the delay coefficient during loading is calculated as: (4); In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of ; Delay factor during unloading is calculated as: (5); In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of .

[0023] In order to simplify the modeling parameters and reduce the parameter identification error, the default delay coefficients during loading and unloading are the same, so the delay coefficient of the Fancher model is the delay coefficient during loading. and the delay factor during unloading The mean value of the Fancher model delay coefficient is calculated as: (6).

[0024] As a preferred embodiment of the present invention, step 5 includes the following specific steps: The Fancher model is used to simulate the hysteresis characteristics of the steering wheel torque-steering wheel angle relationship curve, and the identified delay coefficient is used as input to compare the simulation curve with the original data. Figure 3 As shown in the figure, the simulation curve is highly consistent with the actually measured transition curve, and can more accurately describe the nonlinear hysteresis characteristics of the steering system. This step verifies the effectiveness and accuracy of the method.

[0025] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for identifying the delay coefficient of a hysteresis model based on the intersection of a fitting curve, characterized in that: The following steps are involved: Step 1: The original data of steering wheel angle and steering wheel torque in the steering system hysteresis characteristic curve obtained under three sets of measurement cycles are preprocessed using a Butterworth low-pass filter respectively; Step 2: Calculate the maximum and minimum values ​​of the steering wheel angle data after low-pass filtering preprocessing in step 1, that is, determine the measurement range covered by the steering wheel angle; Step 3: The upper and lower boundaries of the steering wheel torque-steering wheel angle hysteresis characteristic curve and the transition curves on both sides are fitted by the least square method; Step 4: Based on the fitting processing results of step 3, solve the four intersection points between the upper and lower fitting boundary curves and the left and right fitting transition curves and Based on the coordinate relationship of the intersection points, an analytical calculation model of the delay coefficient is established to achieve direct mathematical derivation of the parameters. Step 5: Verify the accuracy of the delay coefficient parameter identification of the Fancher model.

2. The method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves according to claim 1, characterized in that: In step 1, the filter design is based on its transfer function expression: （1）； In the formula, is a complex frequency domain variable; is the cut-off angular frequency, , corresponding to the cut-off frequency 5Hz; is the filter order, .

3. The method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves according to claim 1, characterized in that: The step 2 comprises the following specific steps: First, calculate the maximum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the maximum value of the steering wheel angle ,Right now: ; Calculate the minimum value of the steering wheel angle in each measurement cycle , and , take the average of the three extreme values ​​and take it as the minimum value of the steering wheel angle ,Right now: ; Finally, the measurement range of the steering wheel angle is determined to be , which will be used as a reference for the range of horizontal coordinates when fitting the boundary curve and transition curve.

4. The method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves according to claim 3, characterized in that: In step 3, the upper and lower boundary curves are fitted using the least squares method, and the horizontal coordinate range of the fitting curve is , where the steering wheel angle range adjustment value The selection is based on the actual horizontal coordinate range of the transition curves on both sides; the mathematical expressions of the upper and lower boundaries after fitting are: （2）； In the formula, is the steering wheel angle, and ; is the steering wheel torque at the upper boundary; are the coefficients of the upper boundary fitting curve polynomial; is the steering wheel torque at the lower boundary; are the coefficients of the lower boundary fitting curve polynomial; For the transition curves on both sides, the least squares method is used for fitting. The horizontal coordinate range of the left fitting transition curve is ; The horizontal coordinate range of the right fitting transition curve is ; The mathematical expression after fitting of the transition curves on both sides is: （3）； In the formula, is the steering wheel angle; is the adjustment value of the horizontal coordinate range of the fitting curve, i.e. the steering wheel angle range; is the steering wheel torque of the left transition curve; The coefficients of the fitting curve polynomial for the left transition curve; is the steering wheel torque of the right transition curve; The coefficients of the fitting curve polynomial for the right transition curve.

5. The method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves according to claim 4, characterized in that: In step 4, the intersection points of the upper and lower boundary curves with the left transition curve are The intersection points of the upper and lower boundary curves with the right transition curve are ; Intersection As the actual boundary switching point, it is the turning point of the steering wheel angle during the process of switching from unloading to loading or from loading to unloading; intersection point As the end point of the loading and unloading transition process; In the Fancher model, the angle passing through the 95% transition curve is defined as ,in is the delay coefficient, then the delay coefficient during loading Calculated as: （4）； In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of ; Delay factor during unloading Calculated as: （5）； In the formula, For intersection The horizontal axis value of For intersection The horizontal axis value of ; In order to simplify the modeling parameters and reduce the parameter identification error, the default delay coefficients during loading and unloading are the same, so the delay coefficient of the Fancher model is the delay coefficient during loading. and the delay factor during unloading The mean value of the Fancher model delay coefficient Calculated as: （6）。 6. The method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves according to claim 5, characterized in that: The step 5 comprises the following specific steps: The Fancher model is used to simulate the hysteresis characteristics of the steering wheel torque-steering wheel angle relationship curve. The identified delay coefficient is used as input, and the simulation curve is compared with the original data.

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