A method for online tuning of damper external characteristics based on domain recognition

Abstract

The present application relates to a kind of online tuning method of damper external characteristic based on domain recognition, belong to the technical field of automobile suspension.The key geometry and mechanical characteristics of valve system and piston assembly are abstracted as virtual structure parameters, a reversible mapping model between domain and external characteristic curve is established, equivalent structure parameters are back calculated using real-time measured damping force-velocity data, and the quick update of domain to curve domain is completed in prediction model, so that external characteristic can be online tuned with structure parameters as control variable.The present application constructs real-time representation of damper internal state with structure parameter identification, changes external characteristic tuning from traditional actuator input adjustment to curve shaping process based on domain, and determines tuning direction through sensitivity analysis, periodically updates structure parameters under closed-loop strategy, so that external characteristic continuously approximates target curve, thereby realizing real-time, adaptive optimization of damper external characteristic without changing hardware structure.

Description

Technical Field

[0001] This invention relates to an online adjustment method for the external characteristics of a shock absorber based on structural domain identification, belonging to the field of automotive suspension technology. Background Technology

[0002] In automotive engineering, shock absorbers, as the core actuators of the suspension system, directly affect a vehicle's ride comfort and handling stability through their damping force-velocity curves. The valve system structure, flow path, and valve plate mechanical properties of the shock absorber collectively determine its external characteristic shape. In engineering, the damping response that meets the vehicle's requirements is typically determined through repeated design and testing. However, traditional development and calibration processes heavily rely on bench testing and manual experience, resulting in long adjustment cycles, high costs, and difficulty in timely compensatory adjustments at the structural domain level should the vehicle's operating conditions or valve system status deviate from their intended purpose.

[0003] Among the existing publicly available technical solutions, numerous static or quasi-static optimization and design methods and computational models for valves or electromagnetic actuators have been proposed. These methods primarily aim to improve individual performance indicators to enhance output performance under specific operating conditions. For example, Chinese patent document CN120800838A discloses a shock absorber valve system calibration method, product, equipment, and storage medium based on artificial intelligence technology. This method focuses on optimizing valve structure and related parameters, which can improve valve efficiency or local response characteristics at a certain design stage. However, it does not propose a reversible implementation path based on structural parameter identification and online adjustment of the entire external characteristic curve during vehicle operation. In other words, existing solutions are mostly used for offline design and calibration, making it difficult to meet the need for real-time identification of the valve system's internal state during vehicle operation and closed-loop calibration within the structural parameter domain based on the identification results.

[0004] Most existing technologies focus on achieving instantaneous damping changes by altering actuator inputs or adjusting valve openings. However, these methods essentially remain at the level of direct control over single-point or transient conditions, failing to reversibly and traceably shape the entire external characteristic curve in real time at the structural parameter level. Therefore, in view of the above-mentioned technological status quo, there is an urgent need for a technical solution that can achieve adaptive optimization of the entire external characteristic curve of the vibration damper without changing the hardware structure. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an online adjustment method for the external characteristics of vibration dampers based on structural domain identification. It establishes a reversible mapping between structural parameters and external characteristics, uses damping force-velocity data measured during operation to inversely calculate the current equivalent structural parameters, and uses these parameters as adjustment variables to correct the external characteristics online.

[0006] The technical solution of the present invention is as follows:

[0007] A method for online adjustment of the external characteristics of a vibration damper based on structural domain identification, comprising the following steps:

[0008] (1) Virtualization of structural parameters: In order to realize the online adjustment of the external characteristics of the shock absorber, the complex valve system and piston geometry inside the shock absorber are abstracted into a continuously adjustable set of virtual structural parameters Θ. Virtualization is used to replace the multi-component coupling form that is difficult to adjust directly in the real structure with mathematical parameters, so that the throttling behavior of the shock absorber, the opening and closing behavior of the valve plate and the force conversion relationship can be described in the model with parameters of finite dimensions, thereby establishing a reversible mapping between the structural domain and the external characteristics.

[0009] (2) After building an equivalent physical model of the valve system and obtaining the set of virtual structural parameters Θ, based on the throttling flow theory, the elastic behavior of the valve plate and the pressure balance relationship of the working cylinder, construct an equivalent physical model of the damper in the compression and recovery directions. The role of this model is to express the relationship between the damping force and the piston speed in a unified, continuous and differentiable mathematical form, so that the parameter changes can directly correspond to the changes in external characteristics and meet the mathematical requirements of online identification and online adjustment.

[0010] (3) Online structural parameter identification: Under vehicle or test bench operating conditions, by solving the deviation between speed-force data and model prediction, the virtual structural parameter set Θ is continuously made closer to the actual equivalent structural characteristics during the online identification process, thus obtaining an approximately optimal parameter set. This provides a real-time and updatable structural foundation for subsequent external characteristic prediction and online calibration;

[0011] (4) Real-time prediction and adjustment of external characteristics, based on the near-optimal parameter set We construct a real-time external characteristic prediction model and design an executable online external characteristic calibration logic based on it.

[0012] (5) Online closed-loop control strategy: In the closed-loop system, the virtual structural parameter set Θ evolves as the system state variable over time, approximating the optimal parameter set. The structural state of the current cycle is input into the external characteristic prediction model, and the prediction model generates the corresponding external characteristic curve based on this state. Subsequently, the external characteristic curve and the target external characteristic The parameters are compared and a deviation function defined in the velocity domain is formed. Based on the given sensitivity linearization relationship, the calibration module obtains the parameter adjustment amount based on the deviation. Subsequently, the closed-loop controller uses a fixed step size coefficient. Update the parameters to form the parameter input for the next cycle. .

[0013] According to a preferred embodiment of the present invention, in step (1), the key structural factors affecting the formation of damping force are re-expressed as equivalent parameters with clear physical meanings, specifically including the equivalent main throttling area in the compression direction. Equivalent main throttling area in the direction of restoration The two correspond to the main throttling paths in different directions, and are used to describe the comprehensive throttling capacity formed by the throttling orifice, the valve plate opening gap and the local gap structure.

[0014] To characterize the bending and opening process of the superimposed valve plates under pressure differential, the bending stiffness, preload state, and opening / closing law of the valve plate assembly are uniformly abstracted into the equivalent stiffness of the valve plate in the compression direction. Equivalent stiffness of the directional valve plate This allows the valve plate's opening characteristics to be expressed in a continuous and differentiable manner in the mathematical model;

[0015] The compliance characteristics of a vibration damper in the low-speed range are determined by the compensating valve, through-hole, or auxiliary bypass channel. Therefore, all low-pressure bypass structures are uniformly represented by the equivalent bypass area. It is used to describe the flow capacity of oil around the main throttling channel in the low-speed region, so that the model can naturally express the linear characteristics of the low-speed region and the transition behavior between low-speed and medium-speed.

[0016] Furthermore, to unify the differences in geometric dimensions among different products, the effective pressure-bearing area formed by the piston rod diameter and the piston outer diameter is abstracted as the equivalent working area. As the only mapping area from pressure difference to damping force, it ensures that the calculation of damping force remains consistent and comparable under different structural conditions;

[0017] Through the above virtualization process, the various discrete, multi-level, and mutually coupled physical structures in the vibration damper are compressed into six continuously adjustable equivalent parameters:

[0018]

[0019] This parameter set can fully reflect the throttling behavior of the vibration damper at different speed ranges, the valve opening behavior and the force mapping relationship, and make the structural domain continuous, differentiable and identifiable, providing a unified parameterized basis for subsequent equivalent physical model construction, real-time identification of structural parameters and online adjustment of external characteristics.

[0020] According to a preferred embodiment of the present invention, in step (2), specifically, at any given time, the piston speed... v The flow rate in the chamber satisfies a volumetric continuity relationship with the flow rate in the compression direction, Q. c ,have:

[0021]

[0022] For the flow rate Q in the recovery direction r ,have:

[0023]

[0024] The flow rate within the cavity is discharged through both the main throttling path and the bypass path. The pressure difference is determined by the main throttling channel, the bypass channel, and the valve opening state. An equivalent orifice model is used to describe the main throttling flow rate. Its expression is:

[0025]

[0026] in, , respectively, represent the compression and restoration directions. This represents the specific pressure difference value obtained at a certain velocity point, and the main throttling area. It is a function of the pressure difference, and its variation is determined by the equivalent stiffness of the valve plate. For flow coefficient, For the density of the oil, This represents the equivalent stiffness of the valve plate in the corresponding direction.

[0027] Before the valve plate is opened, there is a minimum opening pressure differential. After reaching the threshold, the main throttling area increases continuously according to the following formula:

[0028]

[0029] in, This represents the initial throttling area when the valve plate is not open. As the area growth ratio coefficient, this method makes the valve opening process mathematically continuous and differentiable, so that changes in structural parameters can be directly reflected in the low-speed-medium-speed transition position and shape of the external characteristic curve.

[0030] The flow rate of the bypass channel is expressed using the equivalent orifice expression:

[0031]

[0032] The bypass path is connected in parallel with the main throttling path, and the total flow rate is... The relationship is given by the following formula:

[0033]

[0034] By combining the relationship between flow continuity and throttling flow, the pressure difference can be obtained. Implicit equation:

[0035]

[0036] The equation is given Θ and the current velocity. vUnder the given conditions, obtain the unique positive pressure difference solution. ;

[0037] Damping force Derived from the effective working area:

[0038] .

[0039] According to a preferred embodiment of the present invention, in step (3), specifically:

[0040] 3.1 Input to the forward model;

[0041] Based on the constructed equivalent physical model, given the set of virtual structural parameters Θ and the piston velocity... v Then, the pressure difference in the oil chamber in the compression or recovery direction is obtained. With damping force ,in, For pressure difference The positive real roots of the implicit equation with respect to the square root term predict the damping force as follows:

[0042]

[0043] 3.2 Objective Function Construction: Velocity-Partitioned Weighted Nonlinear Least Squares Identification;

[0044] Since different structural parameters have different effects on the force-velocity curve in different velocity ranges, it is necessary to segment the velocity axis and construct an objective function with velocity range weights.

[0045] 3.3 Gradient and Jacobian Calculation: Analytical Differentiation of Implicit Equations;

[0046] To solve the nonlinear least squares problem:

[0047] A solver combining an incremental Newton / Gauss-Newton iterative method with Levenberg-Marquardt regularization runs in parallel on the online identification cycle. To support this solver, the gradient of the objective function with respect to the parameters and the approximate Hessian matrix need to be calculated. The gradient is expressed using the chain rule as follows:

[0048]

[0049] To obtain Implicitly differentiate the implicit equation (i.e., the pressure difference implicit equation in step (2)) and for a certain velocity point and direction, let the implicit equation in the equivalent physical model be written as:

[0050]

[0051] For the j-th parameter in the parameter set Taking the partial derivative, we have:

[0052]

[0053] Obtain the implicit derivative of the pressure difference with respect to the parameters:

[0054]

[0055] The final model output partial derivatives with respect to the parameters are:

[0056]

[0057] Among them, the Kronecker function for

[0058]

[0059] All partial derivatives form the Jacobian matrix. for:

[0060]

[0061] 3.4 Nonlinear least squares solution, using incremental Levenberg–Marquardt iteration.

[0062] According to a preferred embodiment of the present invention, in step 3.2, the actual measured velocity at the i-th time moment... and damping force For a set of real-time collected observations Its target function for identification is:

[0063]

[0064] In the formula, It is a speed weighting function used to distinguish parameter-sensitive speed segments, assigning different importance to the errors of different speed segments according to the regional sensitivity of each parameter; The output is a model that calculates the directions separately based on the equivalent model and then takes the values ​​according to the observed directions; The regularization coefficient is used. This is a parameter estimate for the previous identification period.

[0065] According to a preferred embodiment of the present invention, in step 3.4, specifically, a Levenberg–Marquardt (LM) update step is employed. :

[0066]

[0067] in, It is the residual vector; It is a weighted matrix; I is the Levenberg damping factor; I is the identity matrix; Jacobian matrix transpose;

[0068] After obtaining the increment, the parameters are updated as follows:

[0069]

[0070] in, This is the set of current virtual structure parameters obtained in the k-th and (k-1)th iterations; The step size adjustment coefficient is the iteration result. That is, the set of approximate optimal parameters used in practice.

[0071] According to a preferred embodiment of the present invention, in step (4), specifically, in order to generate complete external characteristics, a set of discrete velocity points are selected within the velocity range. The pressure difference and damping force at each velocity point are calculated separately to obtain the real-time predicted external characteristic curve. :

[0072]

[0073] To achieve online calibration of external characteristics, a target external characteristic curve is set. This curve can be calculated from the vehicle control strategy, calibration requirements, or vehicle state. To quantify the difference between the real-time predicted curve and the target curve, the external characteristic deviation function is:

[0074]

[0075] in, It is a velocity weighting function whose value varies with the velocity range, used to emphasize the dominance of different structural parameters in different velocity ranges;

[0076] To achieve the mapping from external characteristic deviations to structural parameter adjustments, a parameter calibration relationship is constructed based on the sensitivity of the real-time prediction model to each parameter. This relationship is used to determine the deviation between the target curve and the predicted curve at any velocity point. When the changes in structural parameters are sufficiently small, the damping force becomes linear in the parameter space. Let the parameter adjustment be... The following linear approximation is obtained:

[0077]

[0078] in, Let S be the adjustment increment for the j-th virtual structure parameter; S is the sensitivity matrix, and its elements... This can be obtained through implicit differentiation. Based on the above linear relationship, the external characteristic tuning can be written in linear least squares form:

[0079]

[0080] To obtain an analytical solution, let The normal equation for the optimal solution is:

[0081]

[0082] Where the superscript T denotes the transpose of a matrix or vector;

[0083] The calculated parameter adjustments need to be controlled in steps to avoid excessive changes during a single calibration. Therefore, the following linear interpolation method is used to update the parameters:

[0084]

[0085] in, These are the structural parameters after the k-th adjustment. This is the adjustment step size factor, used to control the convergence speed of the adjustment process and ensure that the external characteristic curve approaches the target curve smoothly over multiple recognition cycles.

[0086] According to a preferred embodiment of the present invention, in step (4), to ensure that the adjusted parameters still have physical feasibility, the parameters are projected onto the engineering boundary after each adjustment to satisfy:

[0087]

[0088] in, Let j be the value of the j-th virtual structure parameter after adjustment. This represents the minimum and maximum physically feasible values ​​allowed for the j-th virtual structural parameter. This constraint ensures that even if the external characteristics of the target deviate significantly in certain velocity ranges, this module can still keep the structural parameters within an executable and computable range, avoiding physically meaningless parameter combinations.

[0089] According to a preferred embodiment of the present invention, in step (5), to describe the mathematical structure of the closed-loop controller, the external characteristic deviation of period k is first defined as:

[0090]

[0091] The error, after velocity-weighted and sensitivity-transformed, is mapped to a structural parameter correction value, which is considered as a control input. Therefore, the structural parameter update relationship is defined as:

[0092]

[0093] The control input during the kth calibration cycle The direction is determined by the error function, and its magnitude is constrained by the step size coefficient and the regularization term to ensure that the calibration is performed within the physically feasible region. To characterize the error evolution of the external characteristics over continuous periods, the closed-loop update equation is substituted into the prediction model to obtain the prediction error for the next period. Since the prediction force function is differentiable with respect to structural parameters, Taylor linearization is used to represent the error update relationship, thus yielding:

[0094] .

[0095] According to a preferred embodiment of the present invention, in step (5), in order to ensure that the control process is in a stable and feasible state in both numerical and engineering terms, a dual convergence criterion is introduced;

[0096] Firstly, to ensure that the overall external characteristics closely approximate the target curve, the maximum deviation in the velocity domain must satisfy:

[0097]

[0098] Where V represents the set of velocity domains considered during the calibration process; ε is the deviation threshold of the external characteristic curve, used to determine whether the predicted external characteristic has sufficiently approximated the target curve;

[0099] Secondly, to avoid over-updating or oscillation issues, the structural parameter correction amounts must meet the following requirements:

[0100]

[0101] Where 𝛿 is the convergence threshold of the structural parameter correction amount;

[0102] The calibration process is considered convergent when both conditions are met simultaneously. If either condition is not met, the process proceeds to the next calibration cycle, continuing the measurement, identification, and prediction process. Furthermore, to prevent structural parameters from drifting to non-physical regions, adjustments are made after each update. Apply the physical feasible region projection D:

[0103]

[0104] To ensure that the calibrated structural parameters always meet manufacturing and motion constraints, and to enhance robustness under different working conditions, a step size adaptive strategy based on the error change rate is adopted. When the error decreases slowly or signs of oscillation appear, the step size is automatically adjusted to keep the closed-loop controller monotonically convergent.

[0105] This invention abstracts the key geometric and mechanical characteristics of the valve system and piston assembly into virtual structural parameters, establishes a reversible mapping model between the structural domain and the external characteristic curve, and uses real-time measured damping force-velocity data to inversely derive the equivalent structural parameters. The prediction model then rapidly updates the structural domain to the curve domain, enabling online adjustment of the external characteristics using structural parameters as control variables. This method identifies and constructs a real-time representation of the damper's internal state using structural parameters, transforming external characteristic adjustment from traditional actuator input regulation to a curve shaping process based on the structural domain. Sensitivity analysis determines the adjustment direction, and the structural parameters are periodically updated under a closed-loop strategy, continuously bringing the external characteristics closer to the target curve. Therefore, real-time, adaptive optimization of the damper's external characteristics can be achieved without changing the hardware structure.

[0106] Where this invention is not detailed, existing technologies may be used.

[0107] The beneficial effects of this invention are as follows:

[0108] 1. The virtual structural parameter space and equivalent physical model constructed by this invention enable external characteristics to no longer rely on static test calibration, but to inversely determine the structural state through real-time data, realizing a two-way mapping from structural parameters to external characteristic curves. This breaks through the inherent limitation of "unidentifiable structure" in the traditional vibration damper development process. This model can not only describe the combined effect of valve system flow area, valve plate stiffness and piston assembly, but also capture the influence of structural changes on the shape of damping force curves in the entire velocity domain, making external characteristic prediction more accurate and controllable.

[0109] 2. This invention introduces a sensitivity-based structural tuning mechanism, shifting external characteristic tuning from single-point adjustment to curve domain shaping. By combining speed weighting, regularization constraints, and structural domain mapping, it can effectively coordinate the damping requirements of different speed ranges, making the adjusted external characteristics approach the target curve as a whole. Compared with the traditional method of generating instantaneous damping changes by changing the actuator input, this invention directly adjusts within the structural parameter domain, making the tuning more physically meaningful and not limited by the hardware execution range.

[0110] 3. The online closed-loop structure identification and adjustment strategy proposed in this invention enables the vibration damper to periodically update its structural parameters during operation, realizing dynamic feedback of "state identification - prediction - adjustment - update". This closed-loop mechanism gives the vibration damper an adaptive capability similar to an electronic control system, enabling it to automatically compensate for external characteristic deviations caused by wear, temperature drift or changes in operating conditions, thereby maintaining stable damping performance without replacing the hardware structure. Attached Figure Description

[0111] Figure 1 This is a flowchart of the method of the present invention;

[0112] Figure 2This is a comparison chart of the damping force-velocity characteristic curves of the vibration damper of the present invention. Detailed Implementation

[0113] The present invention will be further described below with reference to the embodiments and accompanying drawings, but is not limited thereto.

[0114] Example 1:

[0115] like Figure 1 As shown in the figure, this embodiment provides an online adjustment method for the external characteristics of a vibration damper based on structural domain identification. The steps are as follows:

[0116] (1) Virtualization of structural parameters: In order to realize the online adjustment of the external characteristics of the shock absorber, the complex valve system and piston geometry inside the shock absorber are abstracted into a continuously adjustable set of virtual structural parameters Θ. Virtualization is used to replace the multi-component coupling form that is difficult to adjust directly in the real structure with mathematical parameters, so that the throttling behavior of the shock absorber, the opening and closing behavior of the valve plate and the force conversion relationship can be described in the model with parameters of finite dimensions, thereby establishing a reversible mapping between the structural domain and the external characteristics.

[0117] The key structural factors affecting the formation of damping force are re-expressed as equivalent parameters with clear physical meaning, specifically including the equivalent main throttling area in the compression direction. Equivalent main throttling area in the direction of restoration The two correspond to the main throttling paths in different directions, and are used to describe the comprehensive throttling capacity formed by the throttling orifice, the valve plate opening gap and the local gap structure.

[0118] To characterize the bending and opening process of the superimposed valve plates under pressure differential, the bending stiffness, preload state, and opening / closing law of the valve plate assembly are uniformly abstracted into the equivalent stiffness of the valve plate in the compression direction. Equivalent stiffness of the directional valve plate This allows the valve plate's opening characteristics to be expressed in a continuous and differentiable manner in the mathematical model;

[0119] The compliance characteristics of a vibration damper in the low-speed range are determined by the compensating valve, through-hole, or auxiliary bypass channel. Therefore, all low-pressure bypass structures are uniformly represented by the equivalent bypass area. It is used to describe the flow capacity of oil around the main throttling channel in the low-speed region, so that the model can naturally express the linear characteristics of the low-speed region and the transition behavior between low-speed and medium-speed.

[0120] Furthermore, to unify the differences in geometric dimensions among different products, the effective pressure-bearing area formed by the piston rod diameter and the piston outer diameter is abstracted as the equivalent working area. As the only mapping area from pressure difference to damping force, it ensures that the calculation of damping force remains consistent and comparable under different structural conditions;

[0121] Through the above virtualization process, the various discrete, multi-level, and mutually coupled physical structures in the vibration damper are compressed into six continuously adjustable equivalent parameters:

[0122]

[0123] This parameter set can fully reflect the throttling behavior of the vibration damper at different speed ranges, the valve opening behavior and the force mapping relationship, and make the structural domain continuous, differentiable and identifiable, providing a unified parameterized basis for subsequent equivalent physical model construction, real-time identification of structural parameters and online adjustment of external characteristics.

[0124] (2) After building an equivalent physical model of the valve system and obtaining the set of virtual structural parameters Θ, based on the throttling flow theory, the elastic behavior of the valve plate and the pressure balance relationship of the working cylinder, construct an equivalent physical model of the damper in the compression and recovery directions. The role of this model is to express the relationship between the damping force and the piston speed in a unified, continuous and differentiable mathematical form, so that the parameter changes can directly correspond to the changes in external characteristics and meet the mathematical requirements of online identification and online adjustment.

[0125] At any given moment, the piston speed v The flow rate in the chamber satisfies a volumetric continuity relationship with the flow rate in the compression direction, Q. c ,have:

[0126]

[0127] For the flow rate Q in the recovery direction r ,have:

[0128]

[0129] The flow rate within the cavity is discharged through both the main throttling path and the bypass path. The pressure difference is determined by the main throttling channel, the bypass channel, and the valve opening state. An equivalent orifice model is used to describe the main throttling flow rate. Its expression is:

[0130]

[0131] in, , respectively, represent the compression and restoration directions. This represents the specific pressure difference value obtained at a certain velocity point, and the main throttling area. It is a function of the pressure difference, and its variation is determined by the equivalent stiffness of the valve plate. For flow coefficient, For the density of the oil, This represents the equivalent stiffness of the valve plate in the corresponding direction.

[0132] Before the valve plate is opened, there is a minimum opening pressure differential. After reaching the threshold, the main throttling area increases continuously according to the following formula:

[0133]

[0134] in, This represents the initial throttling area when the valve plate is not open. As the area growth ratio coefficient, this method makes the valve opening process mathematically continuous and differentiable, so that changes in structural parameters can be directly reflected in the low-speed-medium-speed transition position and shape of the external characteristic curve.

[0135] The flow rate of the bypass channel is expressed using the equivalent orifice expression:

[0136]

[0137] The bypass path is connected in parallel with the main throttling path, and the total flow rate is... The relationship is given by the following formula:

[0138]

[0139] By combining the relationship between flow continuity and throttling flow, the pressure difference can be obtained. Implicit equation:

[0140]

[0141] The equation is given Θ and the current velocity. v Under the given conditions, obtain the unique positive pressure difference solution. ;

[0142] Damping force Derived from the effective working area:

[0143] .

[0144] (3) Online structural parameter identification: Under vehicle or test bench operating conditions, by solving the deviation between speed-force data and model prediction, the virtual structural parameter set Θ is continuously made closer to the actual equivalent structural characteristics during the online identification process, thus obtaining an approximately optimal parameter set. This provides a real-time and updatable structural foundation for subsequent external characteristic prediction and online calibration;

[0145] 3.1 Input to the forward model;

[0146] Based on the constructed equivalent physical model, given the set of virtual structural parameters Θ and the piston velocity... v Then, the pressure difference in the oil chamber in the compression or recovery direction is obtained. With damping force ,in, For pressure difference The positive real roots of the implicit equation with respect to the square root term predict the damping force as follows:

[0147]

[0148] 3.2 Objective Function Construction: Velocity-Partitioned Weighted Nonlinear Least Squares Identification;

[0149] Since different structural parameters have different effects on the force-velocity curve in different velocity segments, it is necessary to segment the velocity axis and construct an objective function with velocity segment weights. The actual measured velocity at time i... and damping force For a set of real-time collected observations Its target function for identification is:

[0150]

[0151] In the formula, It is a speed weighting function used to distinguish parameter-sensitive speed segments, assigning different importance to the errors of different speed segments according to the regional sensitivity of each parameter; The output is a model that calculates the directions separately based on the equivalent model and then takes the values ​​according to the observed directions; The regularization coefficient is used. For parameter estimation of the previous identification period;

[0152] For ease of implementation and explanation, the speed weighting function Piecewise constants or smoothing window functions can be used. A typical implementation divides the velocity axis into three segments: a low-speed segment... Transition section High-speed section And set weights Each of the three segments corresponds to a certain condition, such that... The relevant low-speed segments are given a higher weight than other segments to facilitate bypass parameter identification; and The relevant transition section has a medium weight to identify valve opening characteristics; the relevant high-speed section has the highest weight to ensure identification of the main throttling area. Velocity segmentation threshold. The characteristic speed point of the product was obtained from engineering experience.

[0153] 3.3 Gradient and Jacobian Calculation: Analytical Differentiation of Implicit Equations;

[0154] To solve the nonlinear least squares problem:

[0155] A solver combining an incremental Newton / Gauss-Newton iterative method with Levenberg-Marquardt regularization runs in parallel on the online identification cycle. To support this solver, the gradient of the objective function with respect to the parameters and the approximate Hessian matrix need to be calculated. The gradient is expressed using the chain rule as follows:

[0156]

[0157] To obtain Implicitly differentiate the implicit equation (i.e., the pressure difference implicit equation in step (2)) and for a certain velocity point and direction, let the implicit equation in the equivalent physical model be written as:

[0158]

[0159] For the j-th parameter in the parameter set Taking the partial derivative, we have:

[0160]

[0161] Obtain the implicit derivative of the pressure difference with respect to the parameters:

[0162]

[0163] The final model output partial derivatives with respect to the parameters are:

[0164]

[0165] Among them, the Kronecker function for

[0166]

[0167] All partial derivatives form the Jacobian matrix. for:

[0168]

[0169] 3.4 Nonlinear least squares solution using incremental Levenberg-Marquardt iteration;

[0170] Using Levenberg–Marquardt (LM) update steps :

[0171]

[0172] in, It is the residual vector; It is a weighted matrix; I is the Levenberg damping factor; I is the identity matrix; Jacobian matrix transpose;

[0173] After obtaining the increment, the parameters are updated as follows:

[0174]

[0175] in, This is the set of current virtual structure parameters obtained in the k-th and (k-1)th iterations; The step size adjustment coefficient is the iteration result. That is, the set of approximate optimal parameters used in practice.

[0176] (4) Real-time prediction and adjustment of external characteristics, based on the near-optimal parameter set We construct a real-time external characteristic prediction model and design an executable online external characteristic calibration logic based on it.

[0177] To generate complete external characteristics, a set of discrete velocity points is selected within the velocity range. The pressure difference and damping force at each velocity point are calculated separately to obtain the real-time predicted external characteristic curve. :

[0178]

[0179] To achieve online calibration of external characteristics, a target external characteristic curve is set. This curve can be calculated from the vehicle control strategy, calibration requirements, or vehicle state. To quantify the difference between the real-time predicted curve and the target curve, the external characteristic deviation function is:

[0180]

[0181] in, It is a velocity weighting function whose value varies with the velocity range, used to emphasize the dominance of different structural parameters in different velocity ranges;

[0182] To achieve the mapping from external characteristic deviations to structural parameter adjustments, a parameter calibration relationship is constructed based on the sensitivity of the real-time prediction model to each parameter. This relationship is used to determine the deviation between the target curve and the predicted curve at any velocity point. When the changes in structural parameters are sufficiently small, the damping force becomes linear in the parameter space. Let the parameter adjustment be... The following linear approximation is obtained:

[0183]

[0184] in, Let S be the adjustment increment for the j-th virtual structure parameter; S is the sensitivity matrix, and its elements... This can be obtained through implicit differentiation. Based on the above linear relationship, the external characteristic tuning can be written in linear least squares form:

[0185]

[0186] To obtain an analytical solution, let The normal equation for the optimal solution is:

[0187]

[0188] Where the superscript T denotes the transpose of a matrix or vector;

[0189] The calculated parameter adjustments need to be controlled in steps to avoid excessive changes during a single calibration. Therefore, the following linear interpolation method is used to update the parameters:

[0190]

[0191] in, These are the structural parameters after the k-th adjustment. This is the adjustment step size factor, used to control the convergence speed of the adjustment process and ensure that the external characteristic curve approaches the target curve smoothly over multiple recognition cycles.

[0192] To ensure that the adjusted parameters remain physically feasible, the parameters are projected onto the engineering boundary after each adjustment to satisfy the following conditions:

[0193]

[0194] in, Let j be the value of the j-th virtual structure parameter after adjustment. This represents the minimum and maximum physically feasible values ​​allowed for the j-th virtual structural parameter. This constraint ensures that even if the external characteristics of the target deviate significantly in certain velocity ranges, this module can still keep the structural parameters within an executable and computable range, avoiding physically meaningless parameter combinations.

[0195] (5) Online closed-loop control strategy: In the closed-loop system, the virtual structural parameter set Θ evolves as the system state variable over time, approximating the optimal parameter set. The structural state of the current cycle is input into the external characteristic prediction model, and the prediction model generates the corresponding external characteristic curve based on this state. Subsequently, the external characteristic curve and the target external characteristic The parameters are compared and a deviation function defined in the velocity domain is formed. Based on the given sensitivity linearization relationship, the calibration module obtains the parameter adjustment amount based on the deviation. Subsequently, the closed-loop controller uses a fixed step size coefficient. Update the parameters to form the parameter input for the next cycle. .

[0196] To describe the mathematical structure of the closed-loop controller, we first define the external characteristic deviation with period k as:

[0197]

[0198] The error, after velocity-weighted and sensitivity-transformed, is mapped to a structural parameter correction value, which is considered as a control input. Therefore, the structural parameter update relationship is defined as:

[0199]

[0200] The control input during the kth calibration cycle The direction is determined by the error function, and its magnitude is constrained by the step size coefficient and the regularization term to ensure that the calibration is performed within the physically feasible region. To characterize the error evolution of the external characteristics over continuous periods, the closed-loop update equation is substituted into the prediction model to obtain the prediction error for the next period. Since the prediction force function is differentiable with respect to structural parameters, Taylor linearization is used to represent the error update relationship, thus yielding:

[0201] .

[0202] Therefore, it can be seen that when the parameter adjustment direction is consistent with the deviation direction, the error will decrease in the next cycle; if the step size coefficient is appropriately selected so that the spectral radius of the error update mapping is less than 1, the entire closed-loop system will exhibit monotonically convergent characteristics. Since this embodiment introduces the velocity segment weight matrix W in the three modules of parameter identification, external characteristic prediction and calibration, it essentially enhances the effective rank of the sensitivity matrix, thereby ensuring that the closed-loop error has convergence in each velocity segment.

[0203] To ensure that the control process is in a stable and feasible state both numerically and in an engineering sense, a dual convergence criterion is introduced;

[0204] Firstly, to ensure that the overall external characteristics closely approximate the target curve, the maximum deviation in the velocity domain must satisfy:

[0205]

[0206] Where V represents the set of velocity domains considered during the calibration process; ε is the deviation threshold of the external characteristic curve, used to determine whether the predicted external characteristic has sufficiently approximated the target curve;

[0207] Secondly, to avoid over-updating or oscillation issues, the structural parameter correction amounts must meet the following requirements:

[0208]

[0209] Where 𝛿 is the convergence threshold of the structural parameter correction amount;

[0210] The calibration process is considered convergent when both conditions are met simultaneously. If either condition is not met, the process proceeds to the next calibration cycle, continuing the measurement, identification, and prediction process. Furthermore, to prevent structural parameters from drifting to non-physical regions, adjustments are made after each update. Apply the physical feasible region projection D:

[0211]

[0212] To ensure that the calibrated structural parameters always meet manufacturing and motion constraints, and to enhance robustness under different working conditions, a step size adaptive strategy based on the error change rate is adopted. When the error decreases slowly or signs of oscillation appear, the step size is automatically adjusted to keep the closed-loop controller monotonically convergent.

[0213] The closed-loop control strategy in this embodiment executes in the following order within each cycle: First, force-velocity data for the current cycle is collected; then, the latest structural parameters are obtained through online structural parameter identification; subsequently, these parameters are input into the external characteristic prediction model to obtain a complete predicted external characteristic curve; then, the deviation is compared with the target external characteristic, and the calibration module calculates the parameter adjustment amount based on the deviation; finally, the parameter update for this cycle is completed under the constraint of the parameter feasible region. The above closed-loop iterative process is continuously executed during vehicle operation, causing the external characteristic to approach the target curve cycle by cycle.

[0214] Figure 2 This paper demonstrates the overall effect of the online structural parameter identification and external characteristic adjustment module of the present invention. The horizontal axis represents piston velocity, and the vertical axis represents damping force. The four curves in the figure correspond to the initial measured external characteristics, the predicted external characteristics obtained based on virtual structural parameter identification, the adjusted predicted external characteristics, and the target external characteristics, respectively. The identified predicted external characteristics are highly consistent with the initial measured curve across the entire speed range, verifying that the structural parameter virtualization model and online identification algorithm of this embodiment can accurately reflect the equivalent physical characteristics of the actual valve system. Based on this, the external characteristic adjustment module maps the curve deviation to the virtual structural parameter space. The updated predicted external characteristics significantly approach the target curve, especially in the medium and high speed ranges, where the curve slope and force level are effectively adjusted, forming a convergence trend of "measurement—identification—adjustment—target" approaching step by step. This result proves that this embodiment can achieve real-time shaping and adaptive optimization of the external characteristic curve without changing the hardware structure.

Claims

1. A method for online tuning of an external characteristic of a shock absorber based on domain recognition, characterized by, The steps are as follows: (1) Structure parameter virtualization, the internal valve system of the shock absorber and the piston geometric characteristics are abstracted into a set of continuous adjustable virtual structure parameters Θ, and a reversible mapping between the structure domain and the external characteristics is established; (2) Build an equivalent physical model of the valve system. After obtaining the virtual structure parameter set Θ, based on the throttle flow theory, valve plate elastic behavior and working cylinder pressure balance relationship, the equivalent physical model of the shock absorber in compression and recovery directions is constructed, and the relationship between damping force and piston speed is expressed in mathematical form, so that the parameter change directly corresponds to the change of external characteristics, meeting the mathematical requirements of online identification and online tuning; (3) Online structural parameter identification, under the vehicle or bench running conditions, the deviation between the speed-force data and the model prediction is solved, so that the virtual structural parameter set Θ is constantly approximated to the actual equivalent structural characteristics in the online identification process, and the approximately optimal parameter set is obtained ; (4) Real-time prediction and tuning of external characteristics, based on an approximately optimal parameter set , a real-time external characteristic prediction model is constructed, and on this basis, an executable online external characteristic tuning logic is designed; (5) Online closed-loop control strategy, in the closed-loop system, the virtual structure parameter set Θ evolves as the system state over time, approximating the optimal parameter set The structure state of the current cycle is input into the external characteristic prediction model, and the prediction model generates a corresponding external characteristic curve according to the state , then the external characteristic curve is compared with the target external characteristic , and a deviation function defined on the speed domain is formed, based on the given sensitivity linearization relationship, the parameter adjustment amount is obtained by the tuning module based on the deviation , then the closed-loop controller updates the parameters with a fixed step coefficient to form the parameter input of the next cycle .

2. The method of claim 1, wherein the online tuning of the damper force versus displacement characteristic is based on a domain recognition. In step (1), the key structural factors affecting the damping force formation are expressed as equivalent parameters with clear physical meanings, specifically, the equivalent main throttling area in the compression direction and the equivalent main throttling area in the recovery direction , both of which correspond to the main throttling paths in different directions and are used to describe the comprehensive throttling capacity formed by the throttling orifice, the valve piece opening gap and the local gap structure. ​ To depict the deflection and opening process of the superimposed valve disc under the action of pressure difference, the bending stiffness, pre-tightening state and opening and closing law of the valve disc group are uniformly abstracted as the equivalent stiffness of the valve disc in the compression direction and the equivalent stiffness of the valve disc in the recovery direction ; The low pressure bypass structure is represented as a bypass equivalent area for describing the throughflow capacity of the oil to bypass the main throttle passage in the low speed range Furthermore, to unify the differences in geometry among different products, the effective area of compression formed by the piston rod diameter and the piston outer diameter is abstracted as an equivalent working area as the only mapping area of the differential pressure to the damping force; Through virtualization processing, the discrete, multi-level and mutually coupled physical structure in the shock absorber is compressed into six continuous adjustable equivalent parameters: 。 3. The method of claim 2, wherein the online tuning of the damper force versus displacement characteristic is based on the identified structural parameter. In step (2), specifically, at any time, the piston velocity v satisfies the volume continuity relation between the chamber flow rate Q c , and has: For the flow Q in the direction of recovery r there is: The flow in the cavity is discharged through the main throttle path and the bypass path, and the differential pressure is determined by the main throttle channel, the bypass channel and the opening state of the valve plate. The main throttle flow is described by using an equivalent hole model The expression is: wherein, , respectively, represent the compression and recovery directions, represents the specific differential pressure value obtained at a certain speed point, the main throttle area is a function of the differential pressure, the change of which is determined by the equivalent stiffness of the valve plate, is the flow coefficient, is the oil density, is the equivalent stiffness of the valve plate in the corresponding direction; The valve disc, before opening, has a minimum opening pressure difference After the threshold is reached, the main throttle area continuously increases according to the following equation: wherein, represents the initial throttling area when the valve plate is not opened, is the area growth proportionality coefficient; The flow of the bypass channel is expressed by the equivalent hole expression: The bypass path is in parallel with the main throttle path, and the total flow The relationship is given by the equation: The flow continuity and the throttle flow relationship are solved to obtain the implicit equation of differential pressure : This equation gives the unique positive pressure difference solution v for given Θ and current velocity ; Damping force From the effective working area: 。 4. The method of claim 3, wherein the online tuning of the damper force versus displacement characteristic is based on the identified structural parameter. In step (3), specifically: 3.1 Input of the forward model; According to the equivalent physical model, the piston velocity v is given a set of virtual structure parameters Θ, the pressure difference of the oil chamber in the compression or recovery direction is obtained and the damping force wherein is the pressure difference The positive real root of the implicit equation with respect to the square root term predicts the damping force as: 3.2 Objective function construction: nonlinear least squares identification with speed partition weighted; Due to the different effects of different structure parameters on the force-speed curve in different speed sections, the speed axis needs to be segmented and a target function with speed section weight is constructed; 3.3 Gradient and Jacobian calculation: analytical derivation of implicit equations; An incremental Newton / Gauss-Newton type iterative method combined with Levenberg-Marquardt regularization is used to solve the solver running in parallel with the online identification cycle. To support the solver, the gradient and approximate Hessian matrix of the objective function with respect to the parameters need to be calculated. The gradient is expressed by the chain rule as: To obtain The implicit equation is implicitly differentiated with respect to the velocity point and direction, and the implicit equation in the equivalent physical model is written as for the jth parameter in the set of parameters Taking the partial derivative, we have: The implicit derivative of the pressure difference with respect to the parameter is obtained: The partial derivative of the final model output with respect to the parameter is: where the Kronecker function is All partial derivatives form the Jacobian matrix is: 3.4 Nonlinear least squares solution, incremental Levenberg-Marquardt iteration is used.

5. The method of online tuning of the damper's external characteristics based on the structural recognition according to claim 4, characterized by, In step 3.2, the actual measured velocity at the i-th time instant and the damping force , for a set of real-time collected observations , which identifies the objective function as: wherein, is a speed weighting function, used to distinguish parameter sensitive speed segments, giving different importance to the error of different speed segments according to the regional sensitivity of each parameter; is the model output based on the equivalent model, calculated for each direction respectively and valued according to the observation direction; is a regularization coefficient; is the parameter estimation of the last identification period.

6. The method of online tuning of the damper force characteristic based on the recognition of the structure according to claim 5, characterized in that, In step 3.4, specifically, the Levenberg-Marquardt update step is used : wherein is a residual vector; is a weighting matrix; is a Levenberg damping factor; I is an identity matrix; is a Jacobian matrix is a transpose; After obtaining the increment, the parameters are updated as follows: wherein, is the current virtual structure parameter set obtained for the k, k-1th iteration; is a step adjustment coefficient, the iteration result is the approximate optimal parameter set as actually used.

7. The method of online tuning of the damper force characteristic based on the recognition of the structure according to claim 6, characterized in that, In step (4), specifically, in order to generate the complete external characteristic, a set of discrete speed points is selected in the speed interval , and the differential pressure and damping force are respectively solved at each speed point to obtain the real-time predicted external characteristic curve : To achieve online tuning of the outer characteristic, a target outer characteristic curve is set To quantify the difference between the real-time predicted curve and the target curve, an outer characteristic deviation function is wherein is a speed weighting function; To realize the mapping from the external characteristic deviation to the structural parameter adjustment, the parameter adjustment relationship is constructed based on the sensitivity of the real-time prediction model to each parameter. In any speed point, the deviation between the target curve and the prediction curve is In the case where the structural parameter variation is small enough, the damping force is linearized in the parameter space. Let the parameter adjustment amount be The following linear approximation is obtained: wherein, is the tuning increment for the jth virtual structure parameter; S is the sensitivity matrix, and its elements Based on the linear relationship, the external characteristic tuning is written in the form of linear least squares: To get the analytical solution, let The normal equation of the optimal solution is Where the superscript T represents the transpose of the matrix or vector; The calculated parameter adjustment amount needs to be step controlled to avoid large changes in one tuning. Therefore, the parameters are updated using the following linear interpolation method: wherein, is the structure parameter after the kth adjustment, is an adjustment step factor, used to control the convergence speed of the adjustment process, ensuring that the external characteristic curve approaches the target curve in a smooth manner within multiple identification cycles.

8. The method of online tuning of the damper force characteristic based on the recognition of the structure according to claim 7, characterized in that, In step (4), to ensure that the tuned parameters still have physical feasibility, the parameters are projected to the engineering boundary after each tuning to meet: wherein, is the value of the j-th virtual structure parameter after the adjustment, denotes the minimum and maximum physically feasible values allowed for the j-th virtual structure parameter.

9. The method of online tuning of the damper's external characteristics based on the structural recognition according to claim 8, characterized by, In step (5), to express the mathematical structure of the closed-loop controller, first define the external characteristic deviation of period k as: The error is mapped to a structure parameter correction after a speed weighting and a sensitivity transformation, the correction being considered as a control input Thus, the structure parameter update relation is defined as: control input quantity of the kth tuning cycle The direction of the update is determined by the error function, and its magnitude is jointly constrained by the step size coefficient and the regularization term, ensuring that the tuning is performed within the physically feasible region. To characterize the error evolution of the external characteristics in the continuous cycle, the closed-loop update equation is substituted into the prediction model to obtain the predicted error of the next cycle. Since the prediction function is differentiable with respect to the structural parameters, the Taylor linearization is used to represent the update relationship of the error, resulting in: 。 10. The method of online tuning of the damper force characteristic based on the recognition of the structure according to claim 9, characterized in that, In step (5), to ensure that the control process is stable and feasible in both numerical and engineering sense, double convergence criteria are introduced; First, to ensure that the overall external characteristic curve approximates the target curve, the maximum deviation in the speed domain must satisfy: Where V represents the speed domain set considered in the tuning process; ε is the deviation threshold of the external characteristic curve, used to determine whether the predicted external characteristic has sufficiently approximated the target curve; Second, to avoid excessive updating or oscillation problems, the structure parameter correction amount must satisfy: Where δ is the convergence threshold of the structure parameter correction amount; When both conditions are satisfied, the calibration process is considered to be converged. If either condition is not satisfied, the next calibration cycle is entered, and the measurement, identification, and prediction processes are continued. In addition, to avoid the structural parameters drifting to non-physical regions, a physical feasible region projection D is applied after each update. Applying a physical feasible region projection D: To ensure that the tuned structure parameters always meet the manufacturing and motion constraints, a step size adaptive strategy based on error change rate is used to enhance the robustness in different working conditions. When the error decreases slowly or shows signs of oscillation, the step size is automatically adjusted to ensure that the closed-loop controller converges monotonically.

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