Parameter estimation method and system for forward and inverse models of automotive electromagnetic valve-controlled shock absorbers

Abstract

This invention discloses a parameter estimation method and system for the forward and inverse models of an automotive electromagnetic valve-controlled shock absorber. The method includes the following steps: driving the shock absorber to perform simple harmonic motion at a set stroke and frequency under different currents; constructing a parameterized model of the shock absorber based on the changes in output force during the compression and recovery strokes; constructing a parameter estimation objective function to estimate the parameters of the parameterized model; fitting the estimated parameters as a function of the current to construct the forward model of the shock absorber, which calculates the damping force based on the current state of the shock absorber; selecting key variable parameters in the forward model that change with the current to calculate the sensitivity coefficient; constructing the inverse model of the shock absorber, generating the desired damping force using the forward model, and solving for the current corresponding to the desired damping force based on the inverse model. This invention can adapt to the dynamic characteristics of CDC shock absorbers under different road conditions, accurately meet the real-time modeling needs of complex road conditions, and significantly improve the practicality and response efficiency of the model.

Description

Technical Field

[0001] This invention relates to the field of vibration damper modeling technology, specifically to a parameter estimation method and system for the forward and inverse models of an automotive electromagnetic valve-controlled vibration damper. Background Technology

[0002] The suspension system is an important component of the car chassis. The shock absorber is the core of the suspension system. The Continuous Damping Control (CDC) shock absorber is a typical example of an electromagnetically controlled shock absorber. Modeling the CDC shock absorber is the foundation of semi-active suspension control.

[0003] For CDC shock absorbers with air-cushioned pistons, under the influence of factors such as mechanical structure, hydraulic oil physical properties, and excitation, the shock absorber will generate a time delay of 5-30 ms during actual operation, including magnetic hysteresis and air hysteresis. Although some existing studies have compensated for the time delay phenomenon by using a combination of parametric models and neural networks, it is difficult to establish a simple inverse model of the shock absorber. Moreover, the black-box nature of neural networks leads to poor model interpretability, and the compensation logic for nonlinear hysteresis characteristics cannot be directly related to the physical mechanism. When the actual damping force does not match the expected damping force, it is difficult to distinguish whether it is caused by the deviation of physical parameters in the lumped parameter model or the fitting error of the neural network. This significantly increases the difficulty of control debugging and fault tracing. In addition, the generalization ability of neural networks is limited by the operating condition coverage of the training data. When faced with extreme road conditions (such as severe bumps) that were not included in the training, its compensation effect is prone to failure, resulting in insufficient robustness of current regulation.

[0004] Some solutions employ a hybrid calculation approach combining linear piecewise models and nonlinear hysteresis models when modeling CDC dampers. While this accurately describes the characteristics of the CDC damper and the nonlinear hysteresis relationship between the control current and the frequency signal, such methods rely on frequency signals, which are difficult to obtain. Furthermore, the model parameters exhibit significant frequency-varying characteristics and are in complex coupling with the control current and excitation frequency. Parameter identification requires data from multiple operating conditions, and there is a lack of unified correlation patterns among parameters under different operating conditions. If new driving scenarios need to be adapted during subsequent maintenance, large-scale parameter recalibration is required, which is costly. Summary of the Invention

[0005] To overcome the defects and shortcomings of existing technologies, this invention provides a parameter estimation method and system for the forward and inverse models of automotive electromagnetic valve-controlled shock absorbers. This invention constructs a parameterized model that does not depend on the excitation frequency while meeting the accuracy requirements of the control system. It includes a forward model of the shock absorber that calculates the damping force based on the shock absorber's velocity and displacement, and an inverse model that calculates the desired current based on the desired damping force. Specifically, based on the oil flow characteristics of the shock absorber's compression / recovery stroke, the output force is decomposed into damping force, friction force, hysteresis compensation force, and air hysteresis compensation force. The model can be constructed using displacement, velocity, acceleration, and current data, adapting to the dynamic characteristics of CDC shock absorbers under different road conditions. It can respond in real time to the differences in dynamic characteristics at different frequencies using only displacement, velocity, acceleration, and current, avoiding the cumbersome process of frequency signal acquisition and accurately adapting to the real-time modeling needs of complex road conditions, significantly improving the model's practicality and response efficiency.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a parameter estimation method for the forward and inverse models of an automotive electromagnetic valve-controlled shock absorber, comprising the following steps:

[0008] The drive damper performs simple harmonic motion at different currents with set stroke and frequency;

[0009] A parametric model of the vibration damper is constructed based on the change in output force during the compression and recovery strokes.

[0010] Construct a parameter estimation objective function to estimate the parameters of the parameterized model of the vibration damper;

[0011] The estimated parameters are fitted as a function of the current to construct a positive model of the vibration damper. The positive model of the vibration damper calculates the damping force based on the current state of the vibration damper.

[0012] The sensitivity coefficient was calculated by selecting key variable parameters in the positive model of the vibration damper that vary with current.

[0013] Construct an inverse model of the vibration damper, use the forward model of the vibration damper to generate the desired damping force, and solve for the current corresponding to the desired damping force based on the inverse model of the vibration damper.

[0014] As a preferred technical solution, a parametric model of the vibration damper is constructed based on the changes in output force during the compression and recovery strokes, specifically including:

[0015] The damping force of the damping element is calculated based on the basic damping of the fixed damping element during the recovery stroke and the adjustable damping of the solenoid valve adjustable damping element.

[0016] The damping force of the friction element is calculated based on the friction force during the recovery stroke and the friction force during the compression stroke.

[0017] Calculate the compensation force for the recovery stroke hysteresis, and calculate the compensation forces for the compression stroke hysteresis and air hysteresis.

[0018] The output force of the vibration damper is calculated based on the damping force of the damping element, the damping force of the friction element, and the compensation force of the recovery stroke and compression stroke. A parameterized model of the vibration damper is constructed based on the change of the output force.

[0019] As a preferred technical solution, a parameter estimation objective function is constructed, specifically including:

[0020] Calculate the sum of squares of the global relative errors between the output force of the damper output from the parametric model and the measured output force of the damper;

[0021] Apply smoothing constraints to adjacent current values ​​of all parameters to construct parameter smoothing constraint terms;

[0022] The objective function for parameter estimation is constructed based on the sum of squared global relative errors and parameter smoothing constraints.

[0023] As a preferred technical solution, the parameters of the parametric model of the vibration damper are estimated, specifically including:

[0024] Fixed parameters are identified based on the initial parameter estimation, and these fixed parameters have no functional relationship with the current.

[0025] The varying parameters are determined based on quadratic parameter estimation. These varying parameters have a functional relationship with the current, and a differentiated fitting method is used to fit the varying parameters.

[0026] As a preferred technical solution, a positive model of the vibration damper is constructed, specifically represented as follows:

[0027] ;

[0028] in, This indicates the output force of the shock absorber. This indicates the adjustable damping of the adjustable damping element in the solenoid valve. This indicates the basic damping of the fixed damping element during the recovery stroke. , , The hysteresis compensation coefficient is used to restore the stroke. Indicates the speed of the shock absorber. Represents a symbolic function. The frictional force representing the return stroke. , , The hysteresis compensation coefficient is the coefficient for the compression stroke. The sluggishness coefficient is the coefficient of friction during the compression stroke. This represents the frictional force during the compression stroke. Indicates acceleration. Indicates displacement.

[0029] As a preferred technical solution, the key variable parameter selected is: The normalized sensitivity coefficients of each parameter under a given working condition are calculated based on the numerical difference method.

[0030] As a preferred technical solution, the hysteresis compensation coefficient The basic damping was fitted using a fourth-order polynomial. The hysteresis compensation coefficient can be obtained by fitting a fourth-order polynomial, or by fitting a linear function, a single sine trigonometric function, or a double trigonometric function. The stagnation coefficient is obtained by fitting a linear or quadratic function. Fitting using a quadratic function.

[0031] As a preferred technical solution, the current corresponding to the desired damping force is solved based on the inverse model of the vibration damper, specifically including:

[0032] During the recovery process, the inverse model of the shock absorber is solved iteratively based on the Newton-Raphson method;

[0033] During the compression stroke, the inverse model of the shock absorber is solved analytically using the quadratic equation root-finding formula.

[0034] As a preferred technical solution, the inverse model of the shock absorber is solved based on the bisection method during the recovery stroke.

[0035] The present invention also provides a parameter estimation system for the forward and inverse models of an automotive electromagnetic valve-controlled shock absorber, used to implement the above-mentioned parameter estimation method for the forward and inverse models of the automotive electromagnetic valve-controlled shock absorber, including: a drive module, a shock absorber parameterized model construction module, a parameter estimation module, a forward model construction module, a sensitivity coefficient calculation module, and a shock absorber inverse model construction module;

[0036] The drive module is used to drive the vibration damper to perform simple harmonic motion by setting the stroke and frequency;

[0037] The damper parameterization model building module is used to build a damper parameterization model based on the changes in output force of the damper during the compression stroke and the recovery stroke;

[0038] The parameter estimation module is used to construct a parameter estimation objective function to estimate the parameters of the damper parameterized model;

[0039] The positive model building module is used to fit the estimated parameters as a function of the current to build a positive model of the vibration damper. The positive model of the vibration damper calculates the damping force based on the current state of the vibration damper.

[0040] The sensitivity coefficient calculation module is used to select key variable parameters in the positive model of the vibration damper that change with current to calculate the sensitivity coefficient.

[0041] The vibration damper inverse model construction module is used to construct the vibration damper inverse model, generate the desired damping force using the vibration damper positive model, and solve the current corresponding to the desired damping force based on the vibration damper inverse model.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] (1) The modeling process of this invention does not rely on the excitation frequency signal. By using the quadratic correlation between acceleration and frequency, the inertial effect is characterized by the air hysteresis compensation force. Under low frequency excitation, the acceleration is small and the dynamic characteristics are dominated by damping and friction. At high frequency, the acceleration increases dramatically, making the air hysteresis compensation force a key force term. It works in conjunction with the magnetic hysteresis compensation force to adapt to nonlinear characteristics. Moreover, the model does not need to collect frequency data. It can respond to the differences in dynamic characteristics at different frequencies in real time only by displacement, velocity, acceleration and current. This avoids the cumbersome process of frequency signal acquisition and can accurately adapt to the real-time modeling needs of complex road conditions, significantly improving the practicality and response efficiency of the model.

[0044] (2) The output force of this invention is strongly correlated with the stroke characteristics, the physical meaning of the parameters is clear, the model is highly interpretable, and it is easy to trace the source of the fault. Based on the difference in oil flow and force mechanism of the compression stroke and recovery stroke of the CDC shock absorber, the output force is clearly divided into four physical components: damping force, friction force, magnetic hysteresis and air hysteresis compensation force. Each component is strictly corresponding to the stroke characteristics, and the variable parameters all have clear physical meanings. The model has strong interpretability. When the control is abnormal, the corresponding physical link can be located directly through parameter deviation, which significantly simplifies the fault diagnosis and maintenance process.

[0045] (3) The objective function of the present invention integrates relative error and parameter smoothing term, which effectively improves parameter stability. Specifically, the composite objective function integrates global relative error sum of squares and parameter smoothing constraint between adjacent currents. The relative error term ensures accuracy under all working conditions, and the smoothing term suppresses the sudden change of parameters with current, avoiding parameter jumps caused by noise or overfitting, ensuring the continuity and physical rationality of parameter curves, and fundamentally improving the numerical stability and control reliability of the model.

[0046] (4) The analytical solution of the compression stroke of the present invention is fast and accurate, and the numerical iteration of the recovery stroke is efficient. It has both real-time performance and global adaptability. In view of the difference in the form of the forward model, the inverse model adopts a stroke-by-stroke solution strategy. The compression stroke utilizes the hysteresis compensation coefficient. , air stagnation compensation coefficient The low-order polynomial relationship is transformed into a quadratic equation for analytical solution, achieving millisecond-level real-time calculation. The restoring path faces high-order polynomials. The Newton-Raphson method with pre-stored tables is used to ensure fast convergence. It combines the initialization speed of the lookup table method with the global adaptability of the analytical / numerical method, overcoming the limitations of the pure lookup table method under operating conditions, and achieving real-time accurate current solution across the entire range.

[0047] (5) This invention quantitatively reveals the sensitivity law of key parameters of CDC vibration damper to current through parameter sensitivity analysis. The analysis shows that the system is most sensitive to parameter changes at low current, while the foundation damping coefficient is the most sensitive. High-sensitivity parameters are always the most influential parameters. Therefore, the accuracy of high-sensitivity parameters can be prioritized during the parameter calibration stage. During the vibration damper structural design stage, the mechanical components corresponding to high-sensitivity parameters can be optimized. During the control strategy development stage, more conservative and robust control can be adopted under high-sensitivity conditions. This significantly reduces the trial-and-error process that relies on experience in traditional methods and systematically reduces the time and cost of vibration damper development, calibration and debugging. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the parameter estimation method for the forward and inverse models of the vehicle electromagnetic valve-controlled shock absorber of the present invention.

[0049] Figure 2(a) is a schematic diagram of the force-displacement curve of the CDC vibration damper under harmonic excitation at a frequency of 1.91Hz;

[0050] Figure 2(b) is a schematic diagram of the force-velocity curve of the CDC vibration damper under harmonic excitation at a frequency of 1.91Hz;

[0051] Figure 3(a) is a schematic diagram of the force-displacement curve of the CDC vibration damper when the input current is 0.6A;

[0052] Figure 3(b) is a schematic diagram of the force-velocity curve of the CDC vibration damper when the input current is 0.6A;

[0053] Figure 4(a) is a schematic diagram of the structure of the CDC vibration damper of the present invention;

[0054] Figure 4(b) is a schematic diagram of the oil flow path of the CDC vibration damper of the present invention during the compression stroke;

[0055] Figure 4(c) is a schematic diagram of the oil flow path of the CDC vibration damper of the present invention during the recovery stroke;

[0056] Figure 5 This is a schematic diagram of the parametric model of the CDC vibration damper of the present invention;

[0057] Figure 6 This is a schematic diagram comparing the parametric model and the actual vibration damper response when the current is 0.2A.

[0058] Figure 7 This is a schematic diagram comparing the parametric model and the actual vibration damper response at a current of 1.4A.

[0059] Figure 8(a) shows the parameters. A schematic diagram illustrating the fitting of the estimated values;

[0060] Figure 8(b) shows the parameters. A schematic diagram illustrating the fitting of the estimated values;

[0061] Figure 8(c) shows the parameters. A schematic diagram illustrating the fitting of the estimated values;

[0062] Figure 8(d) shows the parameters. A schematic diagram illustrating the fitting of the estimated values;

[0063] Figure 9 This is a schematic diagram of the average parameter sensitivity coefficient;

[0064] Figure 10 A schematic diagram for solving the inverse model of the vibration damper;

[0065] Figure 11 A schematic diagram illustrating the verification effect of the inverse model of the vibration damper;

[0066] Figure 12 A schematic diagram for verifying the relative error of the inverse model of the vibration damper.

[0067] Among them, 1-first lifting lug, 2-piston rod, 3-solenoid valve, 4-air chamber, 5-isolation piston, 6-second lifting lug, 7-oil reservoir, 8-piston, 9-damping valve, 10-working chamber. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 merely illustrative and not intended to limit the invention.

[0069] Example 1

[0070] like Figure 1 As shown, this embodiment provides a parameter estimation method for the forward and inverse models of an automotive electromagnetic valve-controlled shock absorber, including the following steps:

[0071] S1: Drive the vibration damper to perform simple harmonic motion at a set stroke and frequency, conduct vibration damper experiments, collect measurement data, and analyze the physical characteristics of the vibration damper;

[0072] First, determine the operating current of the vibration damper. The vibration damper controls the opening of the damping orifice through a solenoid valve. The working medium flows through the solenoid valve, which has a throttling effect. The opening of the damping orifice of the solenoid valve is different under different currents, which in turn produces an adjustment effect on the damping coefficient of the vibration damper. Therefore, when designing the experimental current, it should cover the operating current range of the CDC vibration damper. Divide the operating range of the vibration damper into m segments and determine m+1 experimental currents. The larger the value of m, the higher the accuracy of the vibration damper parameter estimation. If higher accuracy is desired, a larger value of m can be taken. However, a larger value of m will lead to more experiments and a longer experimental time. The value of m can be 5-8. In this embodiment, the preferred value of m is 6.

[0073] Secondly, determine the excitation of the test bench. Under normal operation, the vibration damper speed range is 0.3~0.5 m / s. To consider extreme cases, the maximum experimental excitation speed can be set to 1 m / s. The upper and lower ends of the CDC vibration damper are respectively installed on the upper and lower clamps of the test bench. A fixed current is input using a regulated current source, and the vibration damper is driven by a hydraulic servo system to perform simple harmonic motion with a fixed stroke and frequency.

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] in, and These are the excitation displacement and the amplitude of the excitation displacement, respectively, in meters (m). and These are the excitation velocity and the excitation velocity amplitude, respectively, in m / s; Time, in seconds; For excitation frequency, unit ; To incentivize the trip, the unit The experimental data was collected and processed using a hydraulic servo system. The experimental scheme is shown in Table 1 below:

[0079] Table 1. Experimental Scheme for Vibration Damper Characteristics

[0080]

[0081] The collected measurement data under different harmonic excitations were processed, and the force-displacement and force-velocity curves of the CDC vibration damper under different currents and frequencies were plotted, as shown in Figures 2(a)-2(b) and 3(a)-3(b), and some measurement data are given.

[0082] S2: Based on the physical characteristics of the vibration damper, construct a parametric model of the vibration damper based on the change of output force during the compression stroke and the recovery stroke;

[0083] As shown in Figures 4(a)-4(c), the first hanger 1 is connected to the frame and the second hanger 6 is connected to the axle. When the vehicle tires pass over uneven road surfaces, the suspension system is forced to move up and down, driving the piston 8 to move up and down in the shock absorber cylinder. The shock absorber moves downward with the tires as the recovery stroke and moves upward with the tires as the compression stroke. Based on the working principle of the shock absorber, the components of the output force of the shock absorber in the compression and recovery strokes are analyzed, and the simplified model is represented by components.

[0084] In this embodiment, the air chamber 4 is used to maintain the internal pressure balance when the shock absorber is working. As shown in Figure 4(b), during the compression stroke, the volume of the working chamber 10 decreases and the pressure increases, while the volume of the oil storage chamber 7 increases and the pressure decreases. The oil flows out of the working chamber and forms adjustable damping after passing through the solenoid valve 3 (path 3 in the figure).

[0085] As shown in Figure 4(c), when the shock absorber is in the recovery stroke, the volume of the oil reservoir 7 decreases and the pressure increases, while the volume of the working chamber 10 increases and the pressure decreases. The oil flows out of the oil reservoir 7 and flows into the working chamber through two paths: one path passes through the damping valve 9 on the piston to form a corresponding fixed damping (path 1 in the figure), and the other path passes through the solenoid valve 3 to form adjustable damping through the orifice of the solenoid valve 3 (path 2 in the figure).

[0086] In this embodiment, the gas chamber is filled with inert nitrogen gas. During the recovery stroke, the oil pressure below the isolation piston 5 decreases, and the isolation piston 5 moves downward. During the compression stroke, the oil pressure below the isolation piston 5 increases, and the isolation piston 5 moves upward.

[0087] In this embodiment, when the shock absorber is working, the output force of the piston rod 2 mainly consists of damping force, friction force, and elastic force, and is also affected by magnetic hysteresis and gas hysteresis. The elastic force is generated by the elastic deformation of the valve plate in the piston 8, and is usually small and negligible. The damping force accounts for the largest proportion of the output force of the CDC shock absorber, and is composed of two parts: hydraulic oil flowing through the piston and changes in gas volume. When the input current of the CDC shock absorber changes, the opening degree of the internal solenoid valve changes, and the fluid flow resistance changes; when the shock absorber speed and acceleration change, the hydraulic oil flow rate and the movement state of the nitrogen in the gas chamber both change, such as... Figure 5 As shown, the shock absorber is considered as an adjustable damping element of a solenoid valve. Fixed damping element during the recovery stroke , Restoration stroke friction element Compression stroke friction element Hysteresis element and lag elements composition;

[0088] According to the working principle description, in the recovery phase, in addition to the adjustable damping at the solenoid valve, the mechanical valve will generate additional damping. Therefore, the damping force generated by the damping element is expressed as:

[0089] ;

[0090] in, It is the adjustable damping generated by the solenoid valve. It is the basic damping generated by the mechanical valve on the solenoid valve piston during the return stroke. It is a sign function; when the shock absorber is in the compression stroke, , It doesn't work.

[0091] Because the piston sealing rings deform differently during compression and recovery strokes, resulting in different coefficients of friction, the frictional force generated by the friction element is divided into recovery stroke friction force. and friction during compression stroke The damping force generated by the friction element can be expressed as:

[0092] ;

[0093] in, The speed at which the shock absorber moves;

[0094] In this embodiment, the hysteresis loop of the shock absorber exhibits significant differences during the recovery and compression strokes. During the recovery stroke, due to the two channels of the oil (path 1 and path 2), the oil compensation in the working chamber is rapid, and the pressure difference between the upper and lower parts of the piston in the gas chamber is small. At this time, the hysteresis loop is mainly affected by magnetic hysteresis. During the compression stage, the oil flows to the oil reservoir through only one channel (path 3), and because gas is more easily compressed, a portion of the oil pushes the piston in the gas chamber towards the gas bladder. During this process, the effect of gas hysteresis is amplified. In summary, considering only the effect of magnetic hysteresis during the recovery stroke, the resulting compensation force is... The compression stroke takes into account both magnetic hysteresis and pneumatic hysteresis, and the corresponding compensation forces are respectively and .

[0095] The compensating force corresponding to the recovery stroke hysteresis can be expressed as:

[0096] ;

[0097] in, , It is a parameter;

[0098] The compensating forces corresponding to magnetic hysteresis and air hysteresis during compression stroke are expressed as follows:

[0099] ;

[0100] ;

[0101] in, , It is acceleration. It is a parameter;

[0102] The output force of the shock absorber is:

[0103] ;

[0104] Therefore, this embodiment, based on the oil flow characteristics of the damper's compression and recovery strokes, clearly decomposes its output force into damping force, friction force, hysteresis compensation force, and air hysteresis compensation force. Among them, the air hysteresis compensation force is related to the damper's acceleration, the recovery stroke only considers the influence of hysteresis, while the compression stroke considers the influence of both hysteresis and air hysteresis.

[0105] S3: Model Parameter Estimation

[0106] In step S2, the parametric model of the vibration damper was determined based on its working principle. This step uses experimental data to evaluate all parameters in the parametric model. Make an estimate;

[0107] The objective function for parameter estimation is the sum of squared errors or the sum of absolute errors between the model values ​​and experimental values. Firstly, the control system requires a small relative error between the model and the actual model, rather than simply pursuing the minimum sum of squared errors. Secondly, at each current, the model is prone to instability of parameters at each current in an attempt to minimize the objective function. To address these two issues, this embodiment proposes the following objective function:

[0108] ;

[0109] Where n represents the total number of experimental data points, This represents the output force of the damper calculated by the parametric model under the damper state corresponding to the i-th data point. Indicates the first The output force of the vibration damper was experimentally measured under the conditions corresponding to each data point. It is a small positive number used to prevent the denominator from being zero. To smooth the weighting coefficient, a value of 0.005 to 0.05 can be used. This value can be fine-tuned through a small number of preliminary experiments. In this embodiment, a value of 0.005 is preferred to balance accuracy and stability. m represents the number of segments in the working range of the vibration damper. Indicates the first The parameter in the first... Estimated values ​​under group current, parameter smoothing term This is used to constrain the numerical abrupt changes of the same parameter between adjacent currents, achieving smoothness across the entire range. The first term in the above equation considers global relative error to ensure modeling accuracy, while the second term penalizes parameter jumps, smoothing parameter values ​​under adjacent currents. This design eliminates the need to predict which parameter or current range will be unstable, automatically applying smoothing constraints to adjacent current values ​​for all parameters. The smoothing term only penalizes abrupt changes in value with current, without affecting the reasonable trend of parameter changes with current. Taking the smaller value can preserve the original precision to the maximum extent.

[0110] Next, fixed parameters are identified through initial parameter estimation, and experimental data under different currents are used to refine the parameters. An estimate was made, and it was found that Since the changes are not significant and there is no obvious functional relationship with the current, these seven parameters can be treated as fixed parameters. After taking their mean value and substituting it into the model, the remaining parameters can be estimated again using the least squares method, which can improve the accuracy of the model.

[0111] In this embodiment, particle swarm optimization, SQP, or Levenberg-Marquardt algorithm can be used to estimate the parameters.

[0112] After initial parameter estimation, the identified fixed parameters and their values ​​are shown in Table 2 below:

[0113] Table 2. Fixed parameters and their values ​​after initial estimation

[0114]

[0115] like Figure 6 and Figure 7 As shown, the fitting results between the parametric model after quadratic parameter estimation and the real vibration damper are presented under low current (0.2A) and high current (1.4A).

[0116] S4: Fit the variable parameters and establish the positive model of the vibration damper;

[0117] The variable parameters estimated in step S3 are fitted as functions of current to construct a positive model of the vibration damper. , , , Fitted as a function of current;

[0118] , Since the current varies widely, the accuracy of a simple quadratic function fitting method is poor, resulting in a significant loss of accuracy in the final positive model of the vibration damper. To balance the generalization ability of the fitting function, this embodiment proposes to use a fourth-order polynomial for fitting, thereby improving the fitting accuracy, expressed as:

[0119] ;

[0120] ;

[0121] To reduce the number of fitting parameters, parameters affecting the compression stroke damping characteristics will be... and Fit the data using both linear and quadratic functions.

[0122] ;

[0123] ;

[0124] The estimated values ​​of each parameter are fitted as shown in Figures 8(a)-8(d), and the parameter results are shown in Table 3 below:

[0125] Table 3 Parameter Fitting Results

[0126]

[0127] In this embodiment, the parameters Alternatively, linear functions, single sine trigonometric functions, or double trigonometric functions can be used for fitting, and the parameters can be adjusted. A quadratic function can also be used for fitting;

[0128] The displacement, velocity, and acceleration signals of the shock absorber need to be filtered before participating in the positive model calculation. In this embodiment, a moving average filter is used with a window length of 55. Of course, weighted moving average filter, median filter, or Gaussian filter can also be used to filter the displacement, velocity, and acceleration signals.

[0129] In summary, the positive model of the vibration damper is:

[0130] ;

[0131] in, For fixed parameters, the value is the average value under various currents. It is a variable parameter. It is the hysteresis compensation coefficient for restoring the stroke. It is the hysteresis compensation coefficient for the compression stroke. It is the basic damping coefficient. It is the air stagnation compensation coefficient. The relationship between the variable parameter representing displacement and the current is as follows:

[0132] ;

[0133] ;

[0134] ;

[0135] ;

[0136] S5: Based on the established parameterized model, conduct parameter sensitivity analysis of the model;

[0137] Based on the establishment of the positive model of the vibration damper, sensitivity analysis is performed on the key parameters of the model to quantify the influence of each parameter on the output force of the vibration damper, thereby clarifying the priority of parameter calibration, identifying the key components that have the greatest impact on performance, and providing a robust design basis for the vibration damper control strategy under different current conditions.

[0138] The local sensitivity analysis method is used to evaluate the impact of parameter changes on the model output by calculating the partial derivatives of the output force with respect to the model parameters through numerical difference. The specific steps are as follows:

[0139] First, we select four key parameters in the positive model that vary with current for analysis. Then, we analyze one parameter of the positive model. Its sensitivity coefficient under a given operating condition is defined as:

[0140] ;

[0141] in, It is the nominal value of the parameter, referring to the estimated value of the parameter under a certain current in step S4; It is the nominal output force, which refers to the output force of the vibration damper under a given working condition; The disturbance amplitude can be obtained by the model numerical difference method, and the disturbance amplitude is set to ±1% of the parameter value. Based on the experimental data collected in step S1, the average sensitivity coefficient of each parameter during the entire working stroke is calculated using the measured velocity, displacement and acceleration data under three typical control currents: low (0.2A), medium (0.8A) and high (1.4A).

[0142] like Figure 9 As shown, the sensitivity analysis conclusions are as follows:

[0143] (1) Foundation damping coefficient It exhibits the highest sensitivity (1.38–0.74) across all currents, which is consistent with its physical meaning. The basic damping force generated by the mechanical valve during the recovery stroke is directly characterized and is the main contributor to the damping force of the shock absorber.

[0144] (2) Hysteresis compensation coefficient It exhibits high sensitivity (0.91–0.75) at low and medium currents, indicating that the hysteresis effect plays an important role in the recovery stroke, especially under low current (corresponding to soft damping mode) conditions;

[0145] (3) Hysteresis compensation coefficient The sensitivity is moderate (0.67–0.33), reflecting the degree of influence of hysteresis effect during the compression stroke;

[0146] (4) The sensitivity of the gas stagnation compensation coefficient k is the lowest (0.10~0.22), indicating that the gas stagnation effect has a relatively small impact on the model, which is consistent with the physical characteristics of nitrogen in the gas chamber being relatively easy to compress.

[0147] Based on the above sensitivity analysis, it can be concluded that, on the one hand, parameter calibration priority should prioritize ensuring... and The high accuracy of identification, especially in the low current range (0.2–0.8 A), means that even a small identification error will lead to a large deviation in the model output. On the other hand, the lower the current, the more sensitive the model is to parameter changes, indicating that even small parameter deviations can easily cause large fluctuations in the output force. Therefore, higher precision is required for accurate modeling and control at low currents.

[0148] The analysis results further confirm the variable parameters of the recovery stroke. , The overall sensitivity is higher than that of the compression stroke parameter. , On average, it is about 70% higher, which is consistent with the physical mechanism that there are two channels for oil flow during the recovery process.

[0149] S6: Construct the numerical inverse model for restoring the travel and the analytical inverse model for compressing the travel;

[0150] Since the positive model of the vibration damper is monotonically reversible, a lookup table method can be established with a step size of 0.01A to quickly match the desired damping force with the current state of the vibration damper (displacement, velocity, acceleration). For the current, this method is a lookup table method, but the lookup table method can only cover the predefined state range. It cannot obtain the corresponding value when encountering extreme working conditions. However, the analytical method of calculating the ideal current corresponding to the desired output force of the vibration damper based on the current state of the vibration damper can be directly calculated in real time without relying on pre-stored data, and it is convenient for subsequent model optimization.

[0151] like Figure 10 As shown, in the inverse model of the vibration damper:

[0152] (1) Reconstructing the itinerary ( )

[0153] The positive model of the shock absorber for recovery stroke includes , Since an analytical solution cannot be derived for a fifth-degree polynomial, this embodiment uses the Newton-Raphson method for numerical solution. The initial values ​​are obtained by interpolation from a pre-stored table. , Substituting the positive model of the recovery stroke damper, we construct the error function:

[0154] ;

[0155] in, This indicates the desired output force of the vibration damper;

[0156] Solution objective: The solution steps are as follows:

[0157] Determine the initial value using the current-damping force pre-stored table.

[0158] Iteration formula:

[0159] ;

[0160] in, express right The derivative;

[0161] Convergence threshold or ;

[0162] If the iteration value exceeds 0.2~1.4A, take the endpoint of the interval as the optimal solution;

[0163] (2) Compression stroke ( )

[0164] Will The positive model of the vibration damper at that time can be written in the following form:

[0165] ;

[0166] parameter , With current The coupling relationship is a low-order polynomial, which can be transformed into a quadratic equation in one variable and solved directly, expressed as:

[0167] ;

[0168] make , , Calculate using the quadratic formula :

[0169] ;

[0170] Since the positive model of the vibration damper is monotonically reversible, the above equation applies. There is a unique solution.

[0171] In this embodiment, the Newton-Raphson method can be replaced by the bisection method for numerical solution. When a=0, the equation degenerates into a linear function and I=-P / N can be solved directly, further simplifying the calculation.

[0172] To verify the accuracy of the CDC vibration damper inverse model established above, a random current signal of 0.2-1.4A and a sinusoidal velocity signal with an amplitude of 0.3m / s and a period of 10s were input into the forward model. The damping force output by the forward model was used to simulate the desired damping force. Then, the current corresponding to the desired damping force was solved using the vibration damper inverse model, and then input into the forward model as the actual damping force. The results are as follows. Figure 11 and 12 As shown, its root mean square error (RMSE) is 9.56. Figure 12 In the 0.5s interval around 0s and 10s, the damper error is relatively large. However, the damper speed is relatively small at this time, and the increase in damping force error has little impact on the vehicle control effect. It can be considered that the established CDC damper inverse model can meet the accuracy requirements.

[0173] Example 2

[0174] This embodiment provides a parameter estimation system for the forward and inverse models of an automotive electromagnetic valve-controlled shock absorber, used to implement the parameter estimation method for the forward and inverse models of the automotive electromagnetic valve-controlled shock absorber in Embodiment 1. The system includes: a drive module, a shock absorber parameterized model construction module, a parameter estimation module, a forward model construction module, a sensitivity coefficient calculation module, and a shock absorber inverse model construction module.

[0175] In this embodiment, the drive module is used to drive the vibration damper to perform simple harmonic motion with a set stroke and frequency under different currents;

[0176] In this embodiment, the damper parameterization model building module is used to build a damper parameterization model based on the changes in output force of the damper during the compression stroke and the recovery stroke;

[0177] In this embodiment, the parameter estimation module is used to construct a parameter estimation objective function to estimate the parameters of the damper parameterized model;

[0178] In this embodiment, the positive model building module is used to fit the estimated parameters as a function of the current to build a positive model of the vibration damper. The positive model of the vibration damper calculates the damping force based on the current state of the vibration damper.

[0179] In this embodiment, the sensitivity coefficient calculation module is used to select key variable parameters in the positive model of the vibration damper that change with the current to calculate the sensitivity coefficient;

[0180] In this embodiment, the damper inverse model construction module is used to construct the damper inverse model, generate the desired damping force using the damper positive model, and solve for the current corresponding to the desired damping force based on the damper inverse model.

[0181] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A parameter estimation method of a positive and inverse model of a solenoid valve controlled shock absorber for a vehicle, characterized by, The method comprises the following steps: driving the damper to make a simple harmonic motion at a set stroke and frequency under different currents; constructing a damper parameterization model based on the change of the damper output force in the compression stroke and the recovery stroke, specifically comprising: calculating the damping force of the damping element based on the base damping of the fixed damping element in the recovery stroke and the adjustable damping of the electromagnetic valve adjustable damping element; calculating the damping force of the friction element based on the friction force in the recovery stroke and the friction force in the compression stroke; calculating the compensation force of the recovery stroke hysteresis, and calculating the compensation force of the compression stroke hysteresis and air hysteresis; calculating the damper output force based on the damping force of the damping element, the damping force of the friction element, and the compensation force of the recovery stroke and the compression stroke, and constructing a damper parameterization model based on the change of the output force; constructing a parameter estimation objective function to estimate the parameters of the damper parameterization model; fitting the estimated parameters as a function of current to construct a damper positive model, and calculating the damping force according to the current state of the damper by the damper positive model; constructing a damper positive model, specifically represented as: ； wherein denotes the output force of the shock absorber, denotes the adjustable damping of the electromagnetic valve adjustable damping element, denotes the base damping of the fixed damping element in the rebound stroke, is the hysteresis compensation factor for the rebound stroke, denotes the movement speed of the shock absorber, denotes the sign function, denotes the friction in the rebound stroke, is the hysteresis compensation factor for the compression stroke, is the air hysteresis factor for the compression stroke, denotes the friction in the compression stroke, denotes the acceleration, denotes the displacement;​​​​ selecting key variable parameters that change with current in the damper positive model to calculate the sensitivity coefficient; The selected key variable parameters are The normalized sensitivity coefficients of each parameter under the given working condition are calculated based on the numerical difference method. constructing a damper inverse model, generating the expected damping force by the damper positive model, and solving the current corresponding to the expected damping force based on the damper inverse model.

2. The method according to claim 1, wherein constructing a parameter estimation objective function, specifically comprising: calculating the global relative error sum of squares between the damper output force output by the damper parameterization model and the measured damper output force; applying a smoothing constraint to the adjacent current values of all parameters to construct a parameter smoothing constraint term; constructing a parameter estimation objective function based on the global relative error sum of squares and the parameter smoothing constraint term.

3. The method of claim 1, wherein estimating the parameters of the damper parameterization model, specifically comprising: identifying fixed parameters based on the initial parameter estimation, the fixed parameters having no functional relationship with current; determining variable parameters based on the secondary parameter estimation, the variable parameters having a functional relationship with current, and fitting the variable parameters by a differential fitting method.

4. The method of claim 1, wherein hysteresis compensation coefficient by a fourth order polynomial fit, base damping by a fourth order polynomial fit, or by any one of a linear function, a single sine triangle function, a double triangle function, hysteresis compensation coefficient by a linear or quadratic function fit, gas hysteresis coefficient by a quadratic function fit.

5. The method of claim 1, wherein solving the current corresponding to the expected damping force based on the damper inverse model, specifically comprising: in the recovery stroke, the damper inverse model is iteratively solved based on the Newton-Raphson method; in the compression stroke, the damper inverse model is analytically solved by the quadratic equation root formula.

6. The method of claim 5, wherein in the recovery stroke, the damper inverse model is solved based on the bisection method instead of the Newton-Raphson method.

7. A parameter estimation system of a positive and inverse model of a solenoid valve controlled shock absorber for a vehicle, characterized by, The parameter estimation method for realizing the damper positive and inverse model of the electromagnetic valve controlled damper for vehicles according to any one of claims 1-6 comprises a driving module, a damper parameterization model construction module, a parameter estimation module, a positive model construction module, a sensitivity coefficient calculation module, and a damper inverse model construction module; the driving module is used to drive the damper to make a simple harmonic motion at a set stroke and frequency under different currents; the damper parameterization model construction module is used to construct a damper parameterization model based on the change of the damper output force in the compression stroke and the recovery stroke; the parameter estimation module is used to construct a parameter estimation objective function to estimate the parameters of the damper parameterization model; The positive model construction module is configured to fit the estimated parameters as a function of the current, construct a damper positive model, and calculate a damping force according to a current state of the damper; The sensitivity coefficient calculation module is configured to select a key variable parameter that changes with the current in the damper positive model to calculate a sensitivity coefficient; The damper inverse model construction module is configured to construct a damper inverse model, generate a desired damping force by using the damper positive model, and solve a current corresponding to the desired damping force based on the damper inverse model.

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