Fractional order vehicle suspension system modeling and identification method based on mi-ekf and af-rls

Abstract

The application provides a fractional order automobile suspension system modeling and identification method based on MI-EKF and AF-RLS, and belongs to the technical field of automobile engineering identification. The technical scheme is as follows: step 1), a fractional order bilinear state space model of the automobile suspension system is established; and step 2), a state and parameter interactive estimation and identification process of a multiple innovation extended Kalman filter algorithm MI-EKF and an adaptive forgetting factor recursive least square algorithm AF-RLS is constructed. The fractional order bilinear state space model constructed in the application can accurately describe the automobile suspension system, the MI-EKF and AF-RLS interactive estimation algorithm proposed in the application has a faster convergence speed and higher convergence precision, and can be better applied to the state and parameter interactive identification of the automobile suspension system.

Description

Technical Field

[0001] This invention relates to the field of technology, and in particular to a method for modeling and identifying fractional-order automotive suspension systems based on MI-EKF and AF-RLS. Background Technology

[0002] With the rapid development of the automotive industry, intelligent technologies are being applied more and more widely in vehicle performance. As a crucial component of a vehicle, the suspension system plays a vital role in ensuring comfort, handling, and safety. In recent years, intelligent suspension systems have been extensively researched and applied. These systems adapt to different road conditions by adjusting damping forces in real time, effectively improving vehicle stability and comfort. However, the frequency-dependent characteristics of magnetorheological damper elements pose significant challenges to the modeling and parameter identification of suspension systems. Traditional suspension system modeling methods often rely on linear models, neglecting the complex nonlinear behavior inherent in the suspension system and failing to accurately describe its dynamic characteristics, thus affecting the performance and control effectiveness of the suspension system.

[0003] To address this technical challenge, some researchers have developed vehicle dynamics simulation models based on ADAMS / Car software and calibrated the parameters of each subsystem using measured data. However, there is a coupling relationship between parameters such as spring stiffness and damper damping, resulting in low model accuracy. Summary of the Invention

[0004] The purpose of this invention is to provide a modeling and identification method for fractional-order automotive suspension systems based on MI-EKF and AF-RLS. The proposed interactive estimation algorithm of Multi-Inspiration Extended Kalman Filter (MI-EKF) and Adaptive Forgetting Factor Recursive Least Squares (AF-RLS) has a fast convergence speed and high convergence accuracy, and can be well applied to the modeling and parameter identification of automotive suspension systems.

[0005] To achieve the aforementioned objectives, the present invention employs the following technical solution: a fractional-order automotive suspension system modeling and identification method based on MI-EKF and AF-RLS, comprising the following steps: Step 1) Establish a fractional-order bilinear state-space model of the vehicle suspension system; Step 2) Construct the state and parameter interactive estimation and identification process of the Multiple Innovation Extended Kalman Filter (MI-EKF) algorithm and the Adaptive Forgetting Factor Recursive Least Squares (AF-RLS) algorithm.

[0006] As a further optimization of the fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS provided by the present invention, the specific modeling steps of step 1) are as follows: Step 1-1) Establish a fractional-order bilinear state-space model of the vehicle suspension system, and give the general form of the fractional-order bilinear state-space system. u ( k ) is the system input signal. y ( k ) is the system output signal. It is uncorrelated process noise with zero mean. It has white noise Moving average noise, Given the system's state vector, we obtain the general form of the model: (1)

[0007] Among them, matrix , , and It is a system matrix. , and These are the parameters to be estimated. It is a fractional order. and They are unrelated, and have: , , , , , , , .

[0008] Steps 1-2) adopted The fractional derivative is defined as follows: GL is defined as: (2) in It is a discrete fractional difference operator. It is a function of fractional derivative, let ,in It is the sampling interval. It is the first k Second sampling, assuming ,definition Substituting it into equation (2), the fractional derivative is rewritten as: (3) According to equation (3), we get: (4) Substituting equation (4) into equation (1), we obtain the GL fractional-order bilinear state-space equation as follows: (5) Steps 1-3) yield the identification model of the fractional-order bilinear state-space system of the vehicle suspension: (6) In the above formula, The information vector of the system is represented as:

[0009] Let the system's parameter vector be represented as:

[0010]

[0011] When the fraction order When known, then For known terms, it is represented as:

[0012] As a further optimization of the fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS provided in this invention, the specific process of step 2) includes the following steps: Step 2-1) Initialization, given the maximum number of loops. ,make , , , , , , , ; Step 2-2) Use the actuator control signal of the vehicle suspension system as input data. u ( k Suspension displacement is used as output data. y ( k Record data; Steps 2-3) extract the state vector from the information vector. Replace with its estimated value The information vector is estimated based on equation (7). ; (7) Steps 2-4) Dynamically adjust the forgetting factor according to equation (8) ; (8) in , This is the sensitivity adjustment coefficient. .

[0013] Steps 2-5) Calculate the gain vector according to equation (9) The covariance matrix is ​​calculated according to equation (10). And calculate according to formula (11) ; (9) (10) (11) Steps 2-6) Calculate the parameter vector estimate according to equation (12). The system estimation matrix is ​​constructed based on equations (13), (14) and (15). , and ; (12) (13) (14) (15) Step 2-7) Calculate the predicted state value according to equation (16) The Jacobian matrix is ​​calculated according to equations (17) and (18). Covariance Predictions ; (16) (17) (18) Step 2-8) Calculate the multi-innovation matrix according to equation (19) And calculate the Kalman gain according to equation (20). According to equation (21), the Kalman filter gain is extended into a gain matrix. ; (19) (20) (twenty one) Step 2-9) Calculate the state update value according to equations (22) and (23). and update the state estimate covariance matrix ; (twenty two) (twenty three) Steps 2-9) Determine if the maximum number of iterations has been reached. If not, And jump to step 2-3), if achieved, proceed to step 2-10). Step 2-10) Output the recognition results Complete the identification.

[0014] Meanwhile, the present invention proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed, it implements the steps of the method described in the present invention.

[0015] Furthermore, the present invention proposes a computer-readable storage medium having a computer program stored thereon, the computer program being configured to implement the steps of the method described in the present invention when invoked by a processor.

[0016] Finally, the present invention proposes a computer program product, including a computer program / instructions, characterized in that the computer program / instructions, when executed by a processor, implement the steps of the method described in the present invention.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention establishes a fractional-order bilinear state-space model for automotive suspension systems, using suspension displacement as the system output and actuator control signals as the system input. Unlike traditional integer-order dynamic models, this invention, by introducing fractional-order differential operators and state-input coupling terms, can more accurately describe the long-memory characteristics and nonlinear dynamic behavior of the suspension system. Figure 4 It can be seen that this algorithm can effectively identify model parameters.

[0018] (2) The interactive identification of system state and parameters using multi-innovation extended Kalman filter (MI-EKF) and adaptive forgetting factor recursive least squares (AF-RLS) has significant advantages over the traditional single-innovation EKF and fixed forgetting factor RLS algorithms. MI-EKF reduces state estimation error by fusing observation information from multiple time points through a sliding window; the AF-RLS algorithm dynamically adjusts the forgetting factor according to the error variance to improve the accuracy of parameter identification.

[0019] (3) In this invention, parameter identification of the suspension system is a key step in the design of the suspension control strategy. The purpose of parameter identification is to estimate the unknown parameters of the system through actual measured input and output data. Fractional-order models can accurately describe the frequency dependence characteristics of intelligent damping elements, while MI-EKF and AF-RLS can efficiently estimate the state and parameters of these complex nonlinear systems in real time, so that the modeling and parameter identification of the automotive suspension system can improve both identification accuracy and convergence speed. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0021] Figure 1 This is a schematic diagram of an automotive suspension system provided by the present invention.

[0022] Figure 2 The overall flowchart of the multi-innovation extended Kalman filter and adaptive forgetting factor recursive least squares interaction algorithm provided by the present invention is shown.

[0023] Figure 3 This is a schematic diagram of the error curve between the identification parameter and the true value in Embodiment 1 of the present invention.

[0024] Figure 4 This is a comparison chart of the state estimate and the actual state value in Embodiment 1 of the present invention. Detailed Implementation

[0025] 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. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0026] Example 1: See Figures 1 to 4 This embodiment provides a technical solution: a fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS, with the following specific steps: Step 1) Establish a fractional-order bilinear state-space model of the vehicle suspension system; Step 2) Construct the state and parameter interactive estimation and identification process of the Multiple Innovation Extended Kalman Filter (MI-EKF) algorithm and the Adaptive Forgetting Factor Recursive Least Squares (AF-RLS) algorithm.

[0027] As a further optimization of the fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS provided by the present invention, the specific modeling steps of step 1) are as follows: Step 1-1) Establish a fractional-order bilinear state-space model of the vehicle suspension system, and give the general form of the fractional-order bilinear state-space system. u ( k ) is the system input signal. y ( k ) is the system output signal. It is uncorrelated process noise with zero mean. It has white noise Moving average noise, Given the system's state vector, we obtain the general form of the model: (1)

[0028] Among them, matrix , , and It is a system matrix. , and These are the parameters to be estimated. It is a fractional order. and They are unrelated, and have: , , , , , , , .

[0029] Steps 1-2) adopted The fractional derivative is defined as follows: GL is defined as: (2) in It is a discrete fractional difference operator. It is a function of fractional derivative, let ,in It is the sampling interval. It is the first k Second sampling, assuming ,definition Substituting it into equation (2), the fractional derivative is rewritten as: (3) According to equation (3), we get: (4) Substituting equation (4) into equation (1), we obtain the GL fractional-order bilinear state-space equation as follows: (5) Steps 1-3) yield the identification model of the fractional-order bilinear state-space system of the vehicle suspension: (6) In the above formula, The information vector of the system is represented as:

[0030] Let the system's parameter vector be represented as:

[0031]

[0032] When the fraction order When known, then For known terms, it is represented as:

[0033] As a further optimization of the fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS provided in this invention, the specific process of step 2) includes the following steps: Step 2-1) Initialization, given the maximum number of loops. ,make , , , , , , , ; Step 2-2) Use the actuator control signal of the vehicle suspension system as input data. u ( k Suspension displacement is used as output data. y ( k Record data; Steps 2-3) extract the state vector from the information vector. Replace with its estimated value The information vector is estimated based on equation (7). ; (7) Steps 2-4) Dynamically adjust the forgetting factor according to equation (8) ; (8) in , This is the sensitivity adjustment coefficient. .

[0034] Steps 2-5) Calculate the gain vector according to equation (9) The covariance matrix is ​​calculated according to equation (10). And calculate according to formula (11) ; (9) (10) (11) Steps 2-6) Calculate the parameter vector estimate according to equation (12). The system estimation matrix is ​​constructed based on equations (13), (14) and (15). , and ; (12) (13) (14) (15) Step 2-7) Calculate the predicted state value according to equation (16) The Jacobian matrix is ​​calculated according to equations (17) and (18). Covariance Predictions ; (16) (17) (18) Step 2-8) Calculate the multi-innovation matrix according to equation (19) And calculate the Kalman gain according to equation (20). According to equation (21), the Kalman filter gain is extended into a gain matrix. ; (19) (20) (twenty one) Step 2-9) Calculate the state update value according to equations (22) and (23). and update the state estimate covariance matrix ; (twenty two) (twenty three) Step 2-10) Determine if the maximum number of iterations has been reached. If not, And jump to step 2-3), if achieved, proceed to step 2-10). Step 2-11) Output the recognition results Complete the identification.

[0035] The schematic diagram of the automotive suspension system used in this embodiment is shown below. Figure 1 As shown. The input signal... For the actuator control signal of the automobile suspension system, output signal It is suspension displacement.

[0036] Using the fractional-order bilinear state-space model mentioned above, the following model can be established for this embodiment 1: The system matrix is:

[0037] Consider fractional order We can obtain:

[0038] The parameters to be identified are combined into a parameter vector. Let the parameters to be identified be as follows:

[0039] Based on the initialization in step 2-1), a maximum number of loop iterations is given. ; Collect input and output data according to step 2-2); Construct the information vector estimate based on steps 2-3). ; Dynamically adjust the forgetting factor according to steps 2-4). ; Calculate the gain vector according to steps 2-5). Calculate the covariance matrix and ; Calculate the parameter vector estimate according to steps 2-6). and constructing the system estimation matrix , and ; Calculate the state prediction value according to steps 2-7). Calculate the Jacobian matrix Covariance Predictions ; Calculate the multi-innovation matrix according to steps 2-8). and Kalman gain And the Kalman filter gain is extended into a gain matrix. ; Calculate the state update value according to steps 2-9). and update the state estimate covariance matrix ; Complete the loop according to steps 2-10) and 2-11) and output the result.

[0040] Among them, the estimated value of the initial state is set. and the initial covariance matrix Several issues need to be considered: the initial state estimate should be as close as possible to the true value. An incorrect initial estimate may cause the filter to take longer to converge, or even cause the filter to diverge; the initial covariance matrix should be large enough to allow the algorithm to learn and adjust dynamically to the real system, but an excessively large initial covariance may cause the algorithm to be overly sensitive to measurement noise in the early stages.

[0041] The parameter identification results using the fractional-order vehicle suspension system modeling and identification method based on MI-EKF and AF-RLS in this embodiment are as follows: Figure 3 As shown, the state estimate is compared with the true state. Figure 4 As shown in the figure. The method in this embodiment has high identification accuracy, small parameter identification error, and the estimated value of the parameter to be identified is very close to the true value. It also has high convergence accuracy, and the state estimate can track the true state well. This also shows that the identification method has good applicability to the state and parameter interaction estimation of the vehicle suspension system.

[0042] Example 2: This example proposes an electronic system, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method steps of the present invention.

[0043] Example 3: This example proposes a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the steps of the method described in this invention, which will not be repeated here.

[0044] Example 4: This example proposes a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, they implement the steps of the method described in this invention, which will not be repeated here.

[0045] It should be noted that the processing flow of embodiments 2-4 corresponds to the specific steps of the method provided in embodiment 1 of the present invention, and has the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in embodiment 1 of the present invention.

[0046] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modeling and identifying fractional-order automotive suspension systems based on MI-EKF and AF-RLS, characterized in that, Includes the following steps: Step 1) Establish a fractional-order bilinear state-space model of the vehicle suspension system; Step 2) Construct the state and parameter interactive estimation and identification process of the Multi-Inspiration Extended Kalman Filter (MI-EKF) algorithm and the Adaptive Forgetting Factor Recursive Least Squares (AF-RLS) algorithm.

2. The method for modeling and identifying fractional-order vehicle suspension systems based on MI-EKF and AF-RLS according to claim 1, characterized in that, Step 1) includes the following steps: Step 1-1) Establish a fractional-order bilinear state-space model of the vehicle suspension system, and give the general form of the fractional-order bilinear state-space system. u ( k ) is the system input signal. y ( k ) is the system output signal. It is uncorrelated process noise with zero mean. It has white noise Moving average noise, Given the system's state vector, we obtain the general form of the model: (1)； ； Among them, matrix , , and It is a system matrix. and These are the parameters to be estimated. It is the fractional order. and They are unrelated, and have: , , , , , , , ; Steps 1-2) Use the Grünwald-Letnikov definition of fractional derivatives, i.e., the GL definition, to solve for the fractional derivative. GL is defined as: (2)； in, It is a discrete fractional difference operator. It is a function of fractional derivative, let ,in It is the sampling interval. It is the first k Second sampling, assuming ,definition Substituting it into equation (2), the fractional derivative is rewritten as: (3)； According to equation (3), we get: (4)； Substituting equation (4) into equation (1), we obtain the GL fractional-order bilinear state-space equation as follows: (5)； Steps 1-3) yield the identification model of the fractional-order bilinear state-space system of the vehicle suspension: (6)； In the above formula, The information vector of the system is represented as: ； Let the system's parameter vector be represented as: ； ； When the fraction order When known, then For known terms, it is represented as:

3. The method for modeling and identifying fractional-order vehicle suspension systems based on MI-EKF and AF-RLS according to claim 1, characterized in that, Step 2) includes the following steps: Step 2-1) Initialization, given the number of loops Define data length ,make , , , , , , , ; Step 2-2) Use the actuator control signal of the vehicle suspension system as input data. u ( k Suspension displacement is used as output data. y ( k Record data; Steps 2-3) extract the state vector from the information vector. Replace with its estimated value The information vector is estimated based on equation (7). ; (7)； Steps 2-4) Dynamically adjust the forgetting factor according to equation (8) ; (8)； in , This is the sensitivity adjustment coefficient; Steps 2-5) Calculate the gain vector according to equation (9) The covariance matrix is ​​calculated according to equation (10). And calculate according to formula (11) ; (9)； (10)； (11)； Steps 2-6) Calculate the parameter vector estimate according to equation (12). The system estimation matrix is ​​constructed based on equations (13), (14) and (15). and ; (12)； (13)； (14)； (15)； Step 2-7) Calculate the predicted state value according to equation (16) The Jacobian matrix is ​​calculated according to equations (17) and (18). Covariance Predictions ; (16)； (17)； (18)； Step 2-8) Calculate the multi-innovation matrix according to equation (19) And calculate the Kalman gain according to equation (20). According to equation (21), the Kalman filter gain is extended into a gain matrix. ; (19)； (20)； (21)； Step 2-9) Calculate the state update value according to equations (22) and (23). and update the state estimate covariance matrix ; (22)； (23)； Steps 2-9) Determine if the maximum number of iterations has been reached. If not, And jump to step 2-3), if achieved, proceed to step 2-10). Step 2-10) Output the recognition results Complete the identification.

4. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed, it implements the steps of the method as described in any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is configured to implement the steps of the method according to any one of claims 1 to 3 when invoked by a processor.

6. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 3.

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