Pneumatic support system dynamic characteristic prediction method combining mechanism knowledge and interpretable KAN machine learning drive

Abstract

The invention discloses a mechanism knowledge and explainable KAN machine learning driven pneumatic support system dynamic characteristic prediction method, which aims at the characteristics of an air spring with an additional air bag commonly used in a pneumatic support system, and comprises the following steps of: constructing a physical model consisting of compressed air and a rubber bag model; the amplitude and the frequency are used as inputs, and the rigidity difference and the lag angle difference between an experiment true value and a physical model calculation value are used as output targets for training of a KAN model; after the training is completed, replacing an activation function of the KAN model with a basic function to obtain an interpretable KAN model, and training to obtain a predicted stiffness difference, a predicted lag angle difference and a corresponding mathematical expression; the rigidity, the lag angle and the mathematical expression of the air spring with the additional air bag are superposition of a physical model and an interpretable KAN model result. The method has the advantages that the interpretable KAN model can compensate the physical model, the dynamic characteristics of the air spring with the additional air bag can be predicted more accurately, and interpretability is achieved.

Description

Technical Field

[0001] The present invention relates to a method for predicting the dynamic characteristics of a pneumatic support system, and specifically to the prediction of the dynamic characteristics of an air spring with an additional air bag commonly used in a pneumatic support system. By introducing an interpretable KAN (Kolmogorov-Arnold Network) model, the amplitude and frequency are used as input parameters, and the error between the experimental true value and the physical model calculated value is used as the output target. The KAN model is trained, and the predicted results are used to compensate the physical model, thereby improving the dynamic characteristic characterization capability of the overall model. This method can more accurately predict the dynamic characteristics of an air spring with an additional air bag, and is interpretable, which can better provide a basis for the control research of pneumatic support systems. Background Art

[0002] A pneumatic support system is a system that uses compressed air to provide support, vibration reduction, and height adjustment. It is widely used in the fields of automobiles, construction, and precision instrument vibration isolation. Air springs are the core components of pneumatic support systems, among which air springs with additional air bags are often used. An air spring with an additional air bag is a special dual-chamber throttle tube air spring. The volume of the additional air bag is variable, and the change in the volume of the air bag becomes more obvious as the amplitude increases. The air spring with an additional air bag has a wide stiffness adjustment range and is applicable to a wide range of working conditions. However, its dynamic characteristics are extremely complex due to multiple factors such as the characteristics of the rubber bladder, the expansion effect of the air bag, and the strong turbulence characteristics in the throttle tube. It is extremely difficult to establish an accurate physical model to predict its dynamic characteristics.

[0003] The Kolmogorov-Arnold Network (KAN) is an efficient, stable, and interpretable neural network with a learnable activation function. It has strong nonlinearity capture capabilities and can fit any complex function. KAN's internal structure is transparent, enabling symbolic characterization and providing a functional expression describing the relationship between input and output. Leveraging KAN's function fitting and characterization capabilities, the physical model of an air spring with an attached air bag is effectively compensated, and a mathematical expression for the dynamic characteristics of the air spring with an attached air bag is derived, making it interpretable.

[0004] The present invention proposes a method for predicting the dynamic characteristics of a pneumatic support system driven by combined mechanism knowledge and interpretable KAN machine learning. For the prediction of the dynamic characteristics of air springs with additional air bags commonly used in pneumatic support systems, this method proposes a physical model of air springs with additional air bags that does not consider the expansion effect, and combines it with an interpretable KAN model to compensate for the physical model (such as the expansion effect), which can more accurately predict the dynamic characteristics of air springs with additional air bags. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting the dynamic characteristics of a pneumatic support system driven by a combination of mechanism knowledge and explainable KAN machine learning. This method is aimed at predicting the dynamic characteristics of air springs with additional air bags that are commonly used in pneumatic support systems. By establishing a physical-KAN hybrid model, the dynamic characteristics of air springs with additional air bags can be more accurately characterized.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a method for predicting the dynamic characteristics of a pneumatic support system driven by combined mechanism knowledge and explainable KAN machine learning, including the following steps: ① The proposed method for predicting the dynamic characteristics of pneumatic support systems, driven by combined mechanism knowledge and interpretable KAN machine learning, is targeted at predicting the dynamic characteristics of air springs with attached air bags, a common type of air support system. This method is implemented by constructing a two-input, two-output physical-interpretable KAN hybrid model, where the inputs are amplitude and frequency, and the outputs are stiffness and hysteresis angle. ②. Without considering the expansion effect, a physical model consisting of a compressed air model and a rubber bladder model is constructed. The amplitude Y and frequency f are used as inputs. The calculation is performed according to the mathematical expression of the physical model, and the calculated value of the physical model, i.e., the stiffness K, is output. Z and hysteresis angle ③. Conduct dynamic characteristic test of air spring with additional air bag. According to the amplitude Y and frequency f input in step ②, obtain the corresponding experimental true value, i.e. stiffness K. G and hysteresis angle ④ Calculate the error between the calculated value of the physical model and the actual experimental value, where the stiffness difference ΔK = K G -K Z , lag angle difference ⑤. Taking amplitude Y and frequency f as input features, the corresponding stiffness difference ΔK and hysteresis angle difference To output the target, the constructed KAN model is trained; ⑥. Calculate the mean square error (MSE) of the trained KAN model. If the MSE is greater than 5e -2 , then readjust the parameters of the KAN model and return to step ⑤ to train again; if the MSE is less than or equal to 5e -2 , then save the trained KAN model; ⑦, for the trained KAN model, use the basic function library (x,x 2 ,x 3 ,x 4,tanh,sin,exp,cos,log,tan) replaces the original B-spline activation function according to the matching degree, and then performs more than 50 iterative training to obtain an interpretable KAN model; ⑧. Input the amplitude Y and frequency f in step ② into the interpretable KAN model obtained in step ⑦, and output the predicted stiffness difference ΔK N and the predicted lag angle difference And obtain the mathematical expressions composed of basic functions respectively; ⑨. The physical-interpretable KAN hybrid model is a superposition of the physical model and the interpretable KAN model, with an additional air spring stiffness K S =K Z +ΔK N , hysteresis angle Combining the physical model with the mathematical expression of the interpretable KAN model, the stiffness K is obtained. S and hysteresis angle The mathematical expression of .

[0007] In step ①, the air spring with additional air bag is composed of three parts: the main air chamber, a single throttle tube and the additional air bag. The additional air bag is made of elastic material, has ductility, and its volume is variable.

[0008] In step ①, the physical-interpretable KAN hybrid model of the air spring with additional air bag is used to predict the stiffness K of the air spring with additional air bag. S and hysteresis angle And be able to give the corresponding mathematical expressions.

[0009] In step ②, the stiffness K obtained by the physical model Z and hysteresis angle The expression is:

[0010]

[0011] Among them, K A 、 are the stiffness and hysteresis angle calculated by the compressed air model; K R 、 These are the stiffness and hysteresis angle calculated for the rubber bag model.

[0012] In step ②, the stiffness K calculated by the compressed air model A and hysteresis angle The expression is:

[0013]

[0014]

[0015] N=-(p0-p atm )αV r0 V s0 R t +p0γβA s0 V r0 R t ; M=-(p0-p atm )α(V s0 RT0γ+RT0γV r0 )+p0γβA s0 RT0γ

[0016] O=V s0 RT0γ+RT0γV r0 ; P = V r0 V s0 R t

[0017]

[0018]

[0019] Among them, p0 and T0 are the initial pressure and initial temperature of the air spring with additional air bag respectively; α, β, V s0 、A s0 are the effective area change rate, effective volume change rate, effective volume, and effective area of the main air chamber respectively; V r0 is the effective volume of the additional air bag; p atm , R, γ are atmospheric pressure, thermodynamic constant, and specific heat ratio respectively; ω is the angular frequency, ω=2πf; y0 is the excitation amplitude; L t 、D t 、A t are the length, diameter and cross-sectional area of the throttling tube respectively; R t is the throttling coefficient; t is the loss coefficient along the way; in ,ζ out are the inlet local loss coefficient and the outlet local loss coefficient respectively; Re is the Reynolds number; ε is the equivalent roughness of the throttling tube.

[0020] In the step ②, the rubber bladder model is composed of the Coulomb friction model and the fractional derivative Kelvin-Voigt model. The stiffness K obtained by the rubber bladder model is R and hysteresis angle The expression is:

[0021]

[0022]

[0023]

[0024] Among them, K C and K V is the Coulomb model stiffness and the Kelvin-Voigt model stiffness; and are the hysteresis angles of the Coulomb model and the Kelvin-Voigt model respectively; μ = F fs / F fm ; y0 is the amplitude of the input excitation; y is the displacement applied to the air spring; F fm represents the maximum friction force in the Coulomb friction model; y2 is the maximum friction force to reach F fm / 2 when the displacement value; F fs is the initial force; F f0 is the steady-state force; K e is the linear elastic stiffness; c is the fractional derivative damping coefficient; q is the fractional derivative order.

[0025] In step 3, the data obtained from the dynamic characteristics experiment of the air spring with an additional air bag is divided into a training set and a test set. The training set data is used to train the KAN model; the test set data is not used to train the KAN model and is only used to test the model's prediction accuracy under unknown inputs.

[0026] Compared with the existing technology, the present invention has the following advantages: the dynamic characteristics prediction method of the pneumatic support system driven by the combined mechanism knowledge and interpretable KAN machine learning can more accurately predict the dynamic characteristics changes of the air spring with an additional air bag compared with the traditional physical model modeling method; the dynamic characteristics prediction method of the pneumatic support system driven by the combined mechanism knowledge and interpretable KAN machine learning is more efficient, stable and transparent than other physical-data hybrid models; the dynamic characteristics prediction method of the pneumatic support system driven by the combined mechanism knowledge and interpretable KAN machine learning can more accurately give the mathematical expression of the dynamic characteristics of the air spring with an additional air bag, which is beneficial to the control and optimization of the pneumatic support system. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a mechanism diagram of the physical-interpretable KAN hybrid model in the present invention.

[0028] Figure 2 This is the flow chart of the physical-interpretable KAN hybrid model in the present invention.

[0029] Figure 3 It is a flow chart of building a physical model in the present invention.

[0030] Figure 4 This is a flowchart of constructing an interpretable KAN model in the present invention.

[0031] Figure 5 It is a schematic diagram of the mathematical expression of the stiffness and hysteresis angle of the interpretable KAN model in the present invention.

[0032] Figure 6 This is a schematic diagram comparing the predicted values of the KAN model training set and the actual experimental values in the present invention.

[0033] Figure 7 This is a schematic diagram comparing the predicted values of the physical-interpretable KAN hybrid model in the present invention with the actual experimental values. DETAILED DESCRIPTION

[0034] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0035] like Figure 1 A method for predicting dynamic characteristics of a pneumatic support system driven by combined mechanism knowledge and explainable KAN machine learning is shown, comprising the following steps: ① The proposed method for predicting the dynamic characteristics of pneumatic support systems, driven by combined mechanism knowledge and interpretable KAN machine learning, is targeted at predicting the dynamic characteristics of air springs with attached air bags, a common type of air support system. This method is implemented by constructing a two-input, two-output physical-interpretable KAN hybrid model, where the inputs are amplitude and frequency, and the outputs are stiffness and hysteresis angle. ②. Without considering the expansion effect, a physical model consisting of a compressed air model and a rubber bladder model is constructed. The amplitude Y and frequency f are used as inputs. The calculation is performed according to the mathematical expression of the physical model, and the calculated value of the physical model, i.e., the stiffness K, is output. Z and hysteresis angle ③. Conduct dynamic characteristic test of air spring with additional air bag. According to the amplitude Y and frequency f input in step ②, obtain the corresponding experimental true value, i.e. stiffness K. G and hysteresis angle ④ Obtain the error between the calculated value of the physical model and the actual experimental value, where the stiffness difference ΔK = K G -K Z , lag angle difference ⑤. Taking amplitude Y and frequency f as input features, the corresponding stiffness difference ΔK and hysteresis angle difference To output the target, the constructed KAN model is trained; ⑥. Calculate the mean square error (MSE) of the trained KAN model. If the MSE is greater than 5e -2 , then readjust the parameters of the KAN model and return to step ⑤ to train again; if the MSE is less than or equal to 5e -2 , then save the trained KAN model; ⑦, for the trained KAN model, use the basic function library (x,x 2 ,x 3 ,x 4 ,tanh,sin,exp,cos,log,tan) replaces the original B-spline activation function according to the matching degree, and then performs more than 50 iterative training to obtain an interpretable KAN model; ⑧. Input the amplitude Y and frequency f in step ② into the interpretable KAN model obtained in step ⑦, and output the predicted stiffness difference ΔK N and the predicted lag angle difference And obtain the predicted stiffness difference ΔK respectively N and the predicted lag angle difference Mathematical expressions composed of basic functions; ⑨. The physical-interpretable KAN hybrid model is a superposition of the physical model and the interpretable KAN model, with an additional air spring stiffness K S =K Z +ΔK N , hysteresis angle Combining the physical model with the mathematical expression of the interpretable KAN model, the stiffness K is obtained. S and hysteresis angle The mathematical expression of .

Claims

1. A method for predicting the dynamic characteristics of a pneumatic support system driven by combined mechanism knowledge and explainable KAN machine learning, including the following steps: ① The proposed method for predicting the dynamic characteristics of pneumatic support systems, driven by combined mechanism knowledge and interpretable KAN machine learning, is targeted at predicting the dynamic characteristics of air springs with attached air bags, a common type of air support system. This method is implemented by constructing a two-input, two-output physical-interpretable KAN hybrid model, where the inputs are amplitude and frequency, and the outputs are stiffness and hysteresis angle. ②. Without considering the expansion effect, a physical model consisting of a compressed air model and a rubber bladder model is constructed. The amplitude Y and frequency f are used as inputs. The calculation is performed according to the mathematical expression of the physical model, and the calculated value of the physical model, i.e., the stiffness K, is output. Z and hysteresis angle ③. Conduct dynamic characteristic test of air spring with additional air bag. According to the amplitude Y and frequency f input in step ②, obtain the corresponding experimental true value, i.e. stiffness K. G and hysteresis angle ④ Calculate the error between the calculated value of the physical model and the actual experimental value, where the stiffness difference ΔK = K G -K Z , lag angle difference ⑤. Taking amplitude Y and frequency f as input features, the corresponding stiffness difference ΔK and hysteresis angle difference To output the target, the constructed KAN model is trained; ⑥. Calculate the mean square error (MSE) of the trained KAN model. If the MSE is greater than 5e -2 , then readjust the parameters of the KAN model and return to step ⑤ to train again; if the MSE is less than or equal to 5e -2 , then save the trained KAN model; ⑦, for the trained KAN model, use the basic function library (x,x 2 ,x 3 ,x 4 ,tanh,sin,exp,cos,log,tan) replaces the original B-spline activation function according to the matching degree, and then performs more than 50 iterative training to obtain an interpretable KAN model; ⑧. Input the amplitude Y and frequency f in step ② into the interpretable KAN model obtained in step ⑦, and output the predicted stiffness difference ΔK N and the predicted lag angle difference And obtain the mathematical expressions composed of basic functions respectively; ⑨. The physical-interpretable KAN hybrid model is a superposition of the physical model and the interpretable KAN model, with an additional air spring stiffness K S =K Z +ΔK N , hysteresis angle Combining the physical model with the mathematical expression of the interpretable KAN model, the stiffness K is obtained. S and hysteresis angle The mathematical expression of .

2. The physical-interpretable KAN hybrid model of the air spring with additional air bag according to claim 1 is characterized in that The air spring with additional air bag is composed of three parts: a main air chamber, a single throttle tube and an additional air bag. The additional air bag is made of elastic material, has ductility and its volume is variable.

3. The physical-interpretable KAN hybrid model of the air spring with additional air bag according to claim 1 is characterized in that The model is used to predict the stiffness K of the air spring with an additional air bag S and hysteresis angle And be able to give the corresponding mathematical expressions.

4. The physical model according to claim 1, characterized in that The stiffness K obtained by the physical model Z and hysteresis angle The expression is: Among them, K A 、 are the stiffness and hysteresis angle calculated by the compressed air model; K R 、 These are the stiffness and hysteresis angle calculated for the rubber bag model.

5. The compressed air model according to claim 1, characterized in that The stiffness K calculated by the compressed air model A and hysteresis angle The expression is: I=-(p0-p atm )αV r0 V s0 R t +p0γβA s0 V r0 R t ;M=-(p0-p atm )α(V s0 RT0γ+RT0γV r0 )+p0γβA s0 RT0c O=V s0 RT0γ+RT0γV r0 ;P=V r0 V s0 R t Among them, p0 and T0 are the initial pressure and initial temperature of the air spring with additional air bag respectively; α, β, V s0 、A s0 are the effective area change rate, effective volume change rate, effective volume, and effective area of the main air chamber respectively; V r0 is the effective volume of the additional air bag; p atm , R, γ are atmospheric pressure, thermodynamic constant, and specific heat ratio respectively; ω is the angular frequency, ω=2πf; y0 is the excitation amplitude; L t 、D t 、A t are the length, diameter and cross-sectional area of the throttling tube respectively; R t is the throttling coefficient; t is the loss coefficient along the way; in ,ζ out are the inlet local loss coefficient and the outlet local loss coefficient respectively; Re is the Reynolds number; ε is the equivalent roughness of the throttling tube.

6. The rubber bladder model according to claim 1, characterized in that The rubber bladder model is composed of the Coulomb friction model and the fractional derivative Kelvin-Voigt model. The stiffness K obtained by the rubber bladder model is R and hysteresis angle The expression is: Among them, K C and K V is the Coulomb model stiffness and the Kelvin-Voigt model stiffness; and are the hysteresis angles of the Coulomb model and the Kelvin-Voigt model respectively; μ = F fs / F fm ; y0 is the amplitude of the input excitation; y is the displacement applied to the air spring; F fm represents the maximum friction force in the Coulomb friction model; y2 is the maximum friction force to reach F fm / 2 when the displacement value; F fs is the initial force; F f0 is the steady-state force; K e is the linear elastic stiffness; c is the fractional derivative damping coefficient; q is the fractional derivative order.

7. The KAN model according to claim 1, characterized in that The KAN model in step ⑤ is a Kolmogorov-Arnold Network model, and the activation function is a learnable B-spline activation function.

8. The KAN model according to claim 1, characterized in that The data from the dynamic characteristics experiment of the air spring with an additional air bag is divided into a training set and a test set. The training set data is used to train the KAN model; the test set data is not used to train the KAN model and is only used to test the model's prediction accuracy under unknown inputs.

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