A Method for Identifying the Delay Coefficient of a Hysteresis Model Based on the Intersection Points of Fitted Curves

Abstract

The present invention is applicable to the technical field of automotive test data processing, and provides a method for identifying the delay coefficient of a hysteresis model based on the intersection point of fitting curves. This method respectively fits the upper and lower boundaries of the hysteresis characteristic curve and the transition process curve by the least square method, constructs their mathematical expressions and solves the intersection point coordinates. Based on the coordinate relationship of the intersection point, an analytical calculation model of the delay coefficient is established to realize the direct mathematical derivation of the parameters. This method effectively solves the influence of measurement noise and boundary curve oscillation and other interferences existing in the original test curve on the determination of the boundary switching point. At the same time, the use of mathematical analysis to solve the delay coefficient 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 have a high consistency with the actual measured transition curve, reduce the computational cost on the premise of ensuring accuracy, and can meet the needs of most practical engineering applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of automotive test data processing, and particularly relates to a method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves. Background Technique

[0002] The friction nonlinear hysteresis characteristics of automotive steering, suspension, braking and other systems will significantly affect the dynamic response quality of vehicles. In automotive 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 simulating such hysteresis characteristics. Therefore, it is very important to study a method for identifying the delay coefficient parameter with high accuracy and high robustness.

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

[0004] The above studies all use optimization algorithms to minimize the error between the simulated data and the experimental data of the boundary curve and the transition curve to obtain the delay coefficient. However, due to the interference of measurement noise, and there are large fluctuations in the boundary curve in the original experimental data, the positioning and judgment of the turning points of the loading and unloading transitions are often inaccurate, resulting in inaccurate definition of the starting and ending points of the boundary switching. Therefore, in this case, directly identifying the parameters based on the original data is likely to cause parameter errors in the loading and unloading boundary curves and affect the identification accuracy of the delay coefficient. 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 proposed in the above background technique.

[0006] The embodiments of the present invention are implemented as follows. A method for identifying the delay coefficient of a hysteresis model based on the intersection of fitting curves includes the following steps:

[0007] Step 1: For the original data of the steering wheel angle and the steering wheel torque in the hysteresis characteristic curve of the steering system obtained under three groups of measurement cycles, perform preprocessing respectively using a Butterworth low-pass filter;

[0008] 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;

[0009] Step 3: Respectively perform least square fitting on the upper and lower boundaries and the transition curves on both sides of the steering wheel torque-steering wheel angle hysteresis characteristic curve;

[0010] Step 4: Based on the fitting results of Step 3, solve the coordinates of the four intersection points between the upper and lower fitting boundary curves and the left and right fitting transition curves, and establish an analytical calculation model of the delay coefficient based on the coordinate relationship of the intersection points to achieve direct mathematical derivation of the parameters; and Based on the coordinate relationship of the intersection points, establish an analytical calculation model of the delay coefficient to achieve direct mathematical derivation of the parameters;

[0011] Step 5: Verify the accuracy of the delay coefficient parameter identification of the Fancher model.

[0012] For a further technical solution, in the said Step 1, the filter design is based on its transfer function expression:

[0013] (1);

[0014] In the formula, is a complex frequency domain variable; is the cut-off angular frequency, , corresponding to a cut-off frequency of 5 Hz; is the filter order, .

[0015] For a further technical solution, the said Step 2 includes the following specific steps:

[0016] First, calculate the maximum values , and of the steering wheel angle under each measurement cycle respectively, and take the average of the three extreme values as the maximum value of the steering wheel angle, that is: ; Calculate the minimum values , and of the steering wheel angle under each measurement cycle respectively, and take the average of the three extreme values as the minimum value of the steering wheel angle, that is: ; Finally, determine the measurement range of the steering wheel angle as , and use it as a reference for the abscissa range value when fitting the boundary curve and the transition curve subsequently.

[0017] For a further technical solution, in the step 3, for the upper and lower boundary curves, the least squares method is respectively used for fitting, and the abscissa range of the fitting curve is taken as , where the adjustment value of the steering wheel angle range is selected according to the actual abscissa range of the two side transition curves; the mathematical expressions after the upper and lower boundary fitting processes are:

[0018] (2);

[0019] In the formula, is the steering wheel angle, and ; is the steering wheel torque of the upper boundary; are the coefficients of the polynomial of the upper boundary fitting curve; is the steering wheel torque of the lower boundary; are the coefficients of the polynomial of the lower boundary fitting curve.

[0020] For the two side transition curves, the least squares method is respectively used for fitting. The abscissa range of the left fitting transition curve is ; the abscissa range of the right fitting transition curve is ; the mathematical expressions after the two side transition curve fitting processes are:

[0021] (3);

[0022] In the formula, is the steering wheel angle; is the adjustment value of the abscissa range of the fitting curve, i.e., the steering wheel angle range; is the steering wheel torque of the left transition curve; are the coefficients of the polynomial of the left transition curve fitting curve; is the steering wheel torque of the right transition curve; are the coefficients of the polynomial of the right transition curve fitting curve.

[0023] For a further technical solution, in the step 4, the intersection points of the upper and lower boundary curves and the left transition curve are respectively , and the intersection points of the upper and lower boundary curves and the right transition curve are respectively ; the intersection point is used as the actual boundary switching point, i.e., the turning point of the steering wheel angle during the process of switching from unloading to loading or from loading to unloading; the intersection point is used as the end point of the loading and unloading transition process;

[0024] In the Fancher model, the angle passing through the 95% transition curve is defined as , where is the delay coefficient. When loading, the delay coefficient is calculated as:

[0025] (4);

[0026] In the formula, is the abscissa value of the intersection point , is the abscissa value of the intersection point ;

[0027] When unloading, the delay coefficient is calculated as:

[0028] (5);

[0029] In the formula, is the abscissa value of the intersection point , is the abscissa value of the intersection point ;

[0030] is a simplified modeling parameter, and to reduce the parameter identification error, it is default that the delay coefficients during loading and unloading are the same. Then, the delay coefficient of the Fancher model takes the mean value of the delay coefficient during loading and the delay coefficient during unloading. The delay coefficient of the Fancher model is calculated as:

[0031] (6).

[0032] A further technical solution is that the step 5 includes the following specific steps:

[0033] Use the Fancher model to simulate the hysteresis characteristics of the steering wheel torque - steering wheel angle relationship curve. Take the identified delay coefficient as the input and compare the simulation curve with the original data.

[0034] A method for identifying the delay coefficient of a hysteresis model based on the intersection points of fitting curves provided by an embodiment of the present invention effectively solves the influence of interference 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, this method uses a delay coefficient solving method based on mathematical analysis, avoiding the computational cost of complex optimization algorithms and improving the parameter identification efficiency. The delay coefficient identified by this method can make the model simulation curve highly consistent with the actual measured transition curve, reducing the computational cost on the premise of ensuring accuracy and meeting the needs of most practical engineering. Description of the Drawings

[0035] Figure 1Flow chart of a method for identifying the delay coefficient of a hysteresis model based on the intersection point of a fitting curve provided by an embodiment of the present invention;

[0036] Figure 2 Schematic diagram of the fitting curve of the steering wheel torque - steering wheel angle hysteresis characteristic;

[0037] Figure 3 Comparison diagram of the simulation curve of the steering wheel torque - steering wheel angle hysteresis characteristic and the original test data. Specific implementation mode

[0038] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to 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 used to limit the present invention.

[0039] The following describes in detail the specific implementation of the present invention with reference to specific embodiments.

[0040] As Figure 1 shown, a method for identifying the delay coefficient of a hysteresis model based on the intersection point of a fitting curve provided by an embodiment of the present invention includes the following steps:

[0041] Step 1: Respectively perform preprocessing on the original data of the steering wheel angle and the steering wheel torque in the steering system hysteresis characteristic curves obtained under three groups of measurement cycles by using a Butterworth low - pass filter;

[0042] Step 2: Calculate the maximum value and the minimum value in the steering wheel angle data after the low - pass filtering preprocessing in Step 1, that is, determine the measurement range covered by the steering wheel angle;

[0043] Step 3: Respectively perform fitting processing on the upper and lower boundaries and the transition curves on both sides of the steering wheel torque - steering wheel angle hysteresis characteristic curve by using the least - squares method;

[0044] Step 4: Based on the fitting processing results in Step 3, solve the coordinates of the four intersection points and between the upper and lower fitting boundary curves and the left and right fitting transition curves. Based on the coordinate relationship of the intersection points, establish an analytical calculation model for the delay coefficient to realize the direct mathematical derivation of the parameters;

[0045] Step 5: Verify the accuracy of the parameter identification of the Fancher model delay coefficient.

[0046] As a preferred embodiment of the present invention, in Step 1, the filter design is based on its transfer function expression:

[0047] (1);

[0048] In the formula, is a complex frequency domain variable; is the cut-off angular frequency, , corresponding to the cut-off frequency of 5 Hz; is the filter order, ;

[0049] As a preferred embodiment of the present invention, step 2 includes the following specific steps:

[0050] First, calculate the maximum values , and of the steering wheel angle in each measurement cycle respectively. Take the average of the three extreme values as the maximum value of the steering wheel angle, that is: ; Calculate the minimum values , and of the steering wheel angle in each measurement cycle respectively. Take the average of the three extreme values as the minimum value of the steering wheel angle, that is: ; Finally, determine the measurement range of the steering wheel angle as , and use it as a reference for the abscissa range value when fitting the boundary curve and the transition curve subsequently.

[0051] As a preferred embodiment of the present invention, in step 3, for the upper and lower boundary curves, the least squares method is respectively used for fitting processing, and the degree of the fitting polynomial can be appropriately selected according to the actual fitting effect. In order to reduce the influence of the two side transition curves on the fitting effect, the abscissa range of the upper and lower boundary fitting curves should be appropriately reduced based on the maximum and minimum value ranges of the steering wheel angle. Referring to the minimum and maximum values of the steering wheel angle calculated in step 2, the abscissa range of the fitting curve can be taken as , where the steering wheel angle range adjustment value can be appropriately selected according to the actual abscissa range of the two side transition curves. The mathematical expressions after the upper and lower boundary fitting processing are:

[0052] (2);

[0053] In the formula, is the steering wheel angle, and ; is the steering wheel torque of the upper boundary; is the coefficient of the upper boundary fitting curve polynomial; is the steering wheel torque of the lower boundary; is the coefficient of the lower boundary fitting curve polynomial.

[0054] For the transition curves on both sides, the least squares method is used for fitting respectively, and the degree of the fitting polynomial can be appropriately selected according to the actual fitting effect. The abscissa range of the left fitting transition curve can be appropriately adjusted with reference to the minimum value of the steering wheel angle calculated in step 2 to , so that it can cover the actual abscissa range of the left transition curve data as much as possible; the abscissa range of the right fitting transition curve is , so that it can cover the actual abscissa range of the right transition curve data as much as possible. The mathematical expressions after fitting the transition curves on both sides are:

[0055] (3);

[0056] In the formula, is the steering wheel angle; is the adjustment value of the abscissa range of the fitting curve, that is, the steering wheel angle range; is the steering wheel torque of the left transition curve; is the coefficient of the fitting curve polynomial of the left transition curve; is the steering wheel torque of the right transition curve; is the coefficient of the fitting curve polynomial of the right transition curve.

[0057] As Figure 2 shown, as a preferred embodiment of the present invention, the intersection points of the upper and lower boundary curves and the left transition curve are respectively , and the intersection points of the upper and lower boundary curves and the right transition curve are respectively . The intersection point is used as the actual boundary switching point, that is, the turning point of the steering wheel angle during the process of changing from unloading to loading or from loading to unloading; the intersection point is used as the end point of the loading and unloading transition process.

[0058] In the Fancher model, the angle passing through the 95% transition curve is defined as , where is the delay coefficient, then the delay coefficient during loading is calculated as:

[0059] (4);

[0060] In the formula, is the abscissa value of the intersection point , is the abscissa value of the intersection point ;

[0061] The delay coefficient during unloading is calculated as:

[0062] (5);

[0063] In the formula, is the abscissa value of the intersection point , is the abscissa value of the intersection point .

[0064] For simplifying the modeling parameters and reducing the parameter identification error, assuming that the delay coefficients during loading and unloading are the same, the delay coefficient of the Fancher model is taken as the mean of the delay coefficient during loading and the delay coefficient during unloading. The delay coefficient of the Fancher model is calculated as:

[0065] (6).

[0066] As a preferred embodiment of the present invention, step 5 includes the following specific steps:

[0067] Use the Fancher model to simulate the hysteresis characteristics of the steering wheel torque - steering wheel angle relationship curve. Take the identified delay coefficient as the input and compare the simulation curve with the original data. As Figure 3 shown, the simulation curve has a high consistency with the actually measured transition curve and can accurately describe the nonlinear hysteresis characteristics of the steering system. The effectiveness and accuracy of this method are verified through this step.

[0068] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall 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 point of a fitting curve, characterized in that It includes the following steps: Step 1: For the original data of the steering wheel angle and the steering wheel torque in the steering system hysteresis characteristic curves obtained under three groups of measurement cycles, preprocess them respectively using Butterworth low-pass filters; Step 2: Calculate the maximum value and the minimum value in the steering wheel angle data after the low-pass filtering preprocessing in Step 1, that is, determine the measurement range covered by the steering wheel angle; Step 3: Respectively perform fitting processing on the upper and lower boundaries and the transition curves on both sides of the steering wheel torque-steering wheel angle hysteresis characteristic curve using the least squares method; Step 4: Based on the fitting result in Step 3, solve the coordinates of the four intersection points between the upper and lower fitting boundary curves and the left and right fitting transition curves, and establish an analytical calculation model for the delay coefficient based on the coordinate relationship of the intersection points to achieve direct mathematical derivation of the parameters; and Based on the coordinate relationship of the intersection points, establish an analytical calculation model for the delay coefficient to achieve direct mathematical derivation of the parameters; Step 5: Verify the accuracy of the parameter identification of the delay coefficient of the Fancher model; The said Step 2 includes the following specific steps: First, calculate the maximum values of the steering wheel angle for each measurement cycle respectively. , and . Take the average of the three extreme values as the maximum value of the steering wheel angle , that is: ; Calculate the minimum values of the steering wheel angle for each measurement cycle respectively , and . Take the average of the three extreme values as the minimum value of the steering wheel angle , that is: ; Finally, determine the measurement range of the steering wheel angle as , which will be used as a reference for the abscissa range value when fitting the boundary curve and the transition curve in the follow-up. In the step 3, for the upper and lower boundary curves, the least square method is respectively used for fitting, and the abscissa range of the fitting curve is taken as , where the adjustment value of the steering wheel angle range is selected according to the actual abscissa range of the two side transition curves; the mathematical expressions after the upper and lower boundary fitting are: ； Wherein, is the steering wheel angle, and ; is the steering wheel torque at the upper boundary; are the coefficients of the polynomial of the fitting curve at the upper boundary; is the steering wheel torque at the lower boundary; are the coefficients of the polynomial of the fitting curve at the lower boundary; For the transition curves on both sides, the least squares method is used for fitting respectively. The abscissa range of the left fitting transition curve is ; The abscissa range of the right fitting transition curve is ; The mathematical expressions of the transition curves on both sides after fitting are: ； Wherein, is the steering wheel angle; is the adjustment value of the abscissa range of the fitting curve, i.e., the steering wheel angle range; is the steering wheel torque of the left transition curve; are the coefficients of the polynomial of the fitting curve of the left transition curve; is the steering wheel torque of the right transition curve; are the coefficients of the polynomial of the fitting curve of the right transition curve; In the said step 4, the intersection points of the upper and lower boundary curves with the left transition curve are respectively , and the intersection points of the upper and lower boundary curves with the right transition curve are respectively ; The intersection point serves as the actual boundary switching point, that is, the turning point of the steering wheel angle during the process of changing from unloading to loading or from loading to unloading; The intersection point serves as the end point of the transition process between loading and unloading In the Fancher model, the angle passing through the 95% transition curve is defined as , where is the delay coefficient. Then, when loading, the delay coefficient is calculated as: ； Wherein, is the abscissa value of the intersection point , and is the abscissa value of the intersection point . Delay coefficient during unloading Calculated as: ； In the formula, is the abscissa value of the intersection point , and is the abscissa value of the intersection point . To simplify the modeling parameters and reduce the parameter identification error, the delay coefficients during default loading and unloading are assumed to be the same. Then, the delay coefficient of the Fancher model is taken as the delay coefficient during loading and the delay coefficient during unloading The mean value of the delay coefficient of the Fancher model is calculated as follows: 。 2. The method for identifying the delay coefficient of the hysteresis model based on the intersection point of the fitting curves according to claim 1, wherein In the said Step 1, the filter design is based on its transfer function expression: ； wherein, is a complex frequency domain variable; is the cut-off angular frequency, rad / s, corresponding to a cut-off frequency of 5 Hz; is the filter order, .

3. The method for identifying the delay coefficient of the hysteresis model based on the intersection point of the fitting curve according to claim 1, characterized in that The said Step 5 includes the following specific steps: Use the Fancher model to simulate the hysteresis characteristics of the steering wheel torque-steering wheel angle relationship curve, take the identified delay coefficient as the input, and compare the simulation curve with the original data.

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