Vehicle nonlinear dynamics state observation and parameter identification method based on pinn

Abstract

The application discloses a vehicle nonlinear dynamics state observation and parameter identification method based on PINN and belongs to the technical field of vehicle dynamics. The method comprises the following steps: a vehicle multi-degree-of-freedom nonlinear dynamics model is established; a physical information neural network containing a learnable physical sub-module is constructed to realize the prediction of dynamics variables; the derivative of the network output quantity with respect to time is calculated through an automatic differentiation technique, and the derivative is substituted into a dynamics equation to generate a physical residual term, and a multiple loss function is constructed in combination with observation data errors; an optimized model is obtained through a two-stage training strategy to realize the real-time observation and online identification of the vehicle driving state. The application solves the shortcomings that a traditional analytic model cannot adapt to time-varying characteristics such as vehicle load changes, tire wear and suspension aging, realizes the synchronous performance of state observation and parameter identification, reduces the dependence on large-scale high-quality real vehicle data, and significantly improves the generalization ability and physical interpretability of the model.

Description

Technical Field

[0001] This invention relates to the field of vehicle dynamics technology, and more specifically to a method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN. Background Technology

[0002] With the rapid development of autonomous driving and intelligent transportation systems, high-precision vehicle dynamics models have become a crucial foundation for vehicle control systems, virtual simulation, and health management. However, existing vehicle dynamics modeling methods still have significant shortcomings in handling the nonlinear dynamic behavior of complex vehicles. This is especially true for large vehicles such as buses and heavy trucks, which, due to their large overall mass, long wheelbase, high center of gravity, and often equipped with air suspension and large tires, experience significant changes in passenger or cargo distribution during operation. These factors lead to strongly nonlinear coupled dynamic behavior under steering and braking conditions. Even for ordinary passenger cars, their dynamic characteristics deviate significantly from the linear region under extreme conditions.

[0003] Traditional analytical models based on physical mechanisms (White-box) have limited accuracy when faced with nonlinearity, time-varying parameters, and sudden changes in operating conditions, and they are difficult to accurately describe complex physical processes such as tire-road contact. While pure data-driven methods (Black-box) can capture complex input-output mappings, they usually ignore constraints such as physical conservation, boundary conditions, and dynamic mechanisms, and rely heavily on large-scale, high-quality data. They are prone to producing unexplainable or physically inappropriate predictions when data is scarce or the operating conditions are unknown.

[0004] Physical Information Neural Networks (PINNs) combine physical priors with data-driven learning by incorporating physical equation residuals into the training loss, constraining the network output to satisfy known physical laws. This has led to significant progress in fluid mechanics, structural dynamics, and other fields in recent years. However, several issues still need to be addressed before PINNs can be engineered for nonlinear dynamics modeling and parameter identification in vehicles: 1. Modeling challenges of complex components: The generation mechanism of tire force and the nonlinear hysteresis characteristics of suspension in vehicle systems are extremely complex and difficult to describe completely with explicit physical equations. Directly embedding simple physical equations will lead to model mismatch.

[0005] 2. Multi-parameter time-varying characteristics: During vehicle operation, parameters such as mass, tire wear, and suspension stiffness will change over time, and traditional PINN is difficult to adapt to this parameter drift online.

[0006] 3. Training convergence problem: The vehicle dynamics equations are highly coupled, and direct training can easily lead to gradient vanishing or getting trapped in local optima.

[0007] Therefore, there is an urgent need for a modeling framework that integrates physical mechanisms and data-driven characteristics, which can achieve high-precision state observation of complex nonlinear vehicle systems while ensuring physical consistency, and at the same time complete the parameter identification of key components. Summary of the Invention

[0008] This invention provides a method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN, aiming to solve the above-mentioned problems in the existing engineering application of PINN to vehicle nonlinear dynamic modeling and parameter identification.

[0009] The present invention adopts the following technical solution: The method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN includes the following steps: Step 1: Establish a multi-degree-of-freedom nonlinear dynamic model of the vehicle to define generalized coordinates and dynamic equations; Step 2: Construct a physical information neural network containing learnable physical sub-modules to predict dynamic variables; Step 3: Calculate the derivative of the network output with respect to time using automatic differentiation technology, substitute it into the dynamic equation to generate physical residual terms, and construct a multiple loss function by combining the observation data error; Step 4: Obtain an optimized model through a two-stage training strategy to achieve real-time observation of vehicle driving status and online identification of key component parameters; Step 5: Predict vehicle attitude and assess uncertainty in real time in the vehicle ECU. When the confidence level is insufficient, switch to the safety analysis model.

[0010] Furthermore, the multi-degree-of-freedom nonlinear dynamics model of the vehicle in step 1 above is a seven-degree-of-freedom nonlinear dynamics model of the vehicle, including the vertical displacement of the vehicle's center of gravity, the vehicle's pitch angle, roll angle, and four suspension dynamic deflections.

[0011] Furthermore, the learnable physics submodule in step 2 above is used to handle nonlinear components that are difficult to model analytically, including the tire submodule and the air suspension submodule. The tire submodule adopts a parameterized magic tire formula and learns load dependence through a neural network, while the air suspension submodule learns nonlinear elastic and damping characteristics through neural network mapping.

[0012] Furthermore, the physical information neural network in step 2 above is generally a temporal convolutional network, including an input layer, a hidden layer, a physical residual calculation unit, and an output layer. The dimension of the input layer is n, the hidden layer has multiple loss functions, and the output layer is used to output the pose prediction value.

[0013] The multiple loss function in step 3 above is: ; In the formula, For multiple loss functions, The weights and bias parameters represent the neural network. Represents the set of physical parameters to be identified; Data error terms: In the formula: N d The number of labeled samples used in the data error calculation. y i For the first i The ideal output for each sample For PINN to the first i The predicted output given for each sample; Physical residuals: In the formula: N p For the number of physical points, This refers to the physical residual vector obtained by substituting the network prediction results and their time derivatives into the vehicle dynamics equations. x j For the first j The input vector corresponding to each physical collocation point; Boundary / Initial Conditions: In the formula: N b The number of samples for boundary conditions or initial conditions; y 0 is in t 0 The real or given initial state vector known at any given time; For PINN at the initial time t 0 The predicted state vector; Regularization term: ; These are the weighting coefficients for the data error term, physical residual term, boundary / initial condition term, and regularization term, respectively, using an uncertainty-weighted strategy: ; In the formula, The uncertainty parameters estimated by the network are dynamically updated as the network trains: This represents the data-driven loss term; Represents the constraint loss term in the physical equation; Represents the boundary condition loss term; This represents the network regularization loss term.

[0014] Furthermore, the two-stage training strategy in step 4 above includes: in the first stage, the network is initialized and pre-trained using a full-condition simulation dataset generated by high-fidelity simulation software; in the second stage, the network is fine-tuned online using real vehicle data collected by on-board sensors, and a replay buffer mechanism is introduced to mix historical samples for training.

[0015] Furthermore, step 5 above uses the following model to predict and simultaneously output a variance term for real-time prediction of vehicle attitude: ; in, The mean prediction of the vehicle state and key dynamic indicators at a future time (t + Δt) represents the prediction result that the model believes best conforms to physical laws and observation data under given input conditions. This represents the network's variance estimate of the prediction, used to quantify the uncertainty of the model output; The prediction confidence interval is: ; If the following conditions are met: ; This triggers a safety fallback mechanism, downgrading to a safe parsing model or limiting the input amplitude.

[0016] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following advantages: 1. This invention proposes a deep embedding architecture of learnable physical sub-modules, which designs the parameters of the tire magic formula and the nonlinear stiffness characteristics of the suspension as learnable layers in the neural network. The physical neural network not only learns the state variables, but also automatically corrects the physical parameters during backpropagation. This solves the shortcomings of traditional analytical models that cannot adapt to time-varying characteristics such as vehicle load changes, tire wear and suspension aging, and realizes the synchronous operation of state observation and parameter identification.

[0017] 2. This invention constructs a physical residual constraint mechanism based on automatic differentiation. It utilizes an automatic differentiation algorithm to accurately calculate the time derivative of the network output and forces it to satisfy the seven-degree-of-freedom dynamic equations. This significantly reduces the reliance on large-scale, high-quality real-vehicle data, enabling the model to output predictions that conform to physical laws even under extreme conditions where data is scarce or unseen, thus significantly improving the model's generalization ability and physical interpretability.

[0018] 3. This invention establishes an uncertainty quantification system that includes a safe fallback mechanism. Addressing the issue of uncontrollable behavior of deep learning models in unknown domains, this invention adds variance estimation to the network output, enabling real-time quantification of the reliability of the current prediction. Once the system detects high uncertainty, it immediately downgrades to a safe analytical model. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the process of the present invention.

[0020] Figure 2 This is a schematic diagram of the physical information neural network structure of the present invention. Detailed Implementation

[0021] Specific embodiments of the present invention will now be described with reference to the accompanying drawings. Many details are described below to provide a comprehensive understanding of the invention; however, those skilled in the art will not need these details to implement the invention. Well-known components, methods, and processes will not be described in detail below.

[0022] This embodiment provides a method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN, referring to... Figure 1 This includes the following steps: 1. Vehicle nonlinear dynamics modeling Establish a seven-degree-of-freedom nonlinear dynamic model for the vehicle.

[0023] The system's generalized coordinates q Defined as: ; In the formula, This represents the vertical displacement of the vehicle's center of gravity. The vehicle body pitch angle, The body roll angle, These are the dynamic deflections of the four suspensions: the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel.

[0024] The generalized dynamic equation of the vehicle is: ; in: System quality matrix; Damping and Coriolis term; : Nonlinear elastic force term; Gravity term; Force vectors of the four tires (including longitudinal and lateral components). Aerodynamic effects acting on the generalized coordinates of the vehicle body; : Road surface input excitation.

[0025] 1.1 Tire Force Model The longitudinal and lateral forces of the tire are modeled using a parametric Magic Formula model, the general form of which is: ; in, This refers to the tire slip angle; These are the parameters of the linear curve, representing the stiffness factor, shape factor, peak factor, and curvature factor, respectively.

[0026] Load dependency is defined as: ; In this invention, D 0 This refers to the inherent base peak factor of the tire model of a vehicle under standard unload conditions; These parameters are set as learnable parameters to adapt to tire characteristics under different load, tire pressure, and temperature conditions. B 0 This refers to the inherent basic stiffness factor of the tire model of a vehicle under standard unload conditions; F z This represents the actual dynamic vertical load currently borne by the tire; This refers to the vertical force on the wheels of a vehicle when it is unloaded.

[0027] 1.2 Air Suspension Model The air suspension force is determined by the airbag pressure and the suspension travel: ; In the formula, The effective area of ​​the airbag. This is the gas stiffness coefficient. The damping coefficient is... The pressure inside the airbag. This refers to the suspension travel.

[0028] In this method, Extended to a learnable function: .

[0029] In the formula, MLP ω Represents a multilayer perceptron neural network, subscript ω This represents the set of all optimizable weights and biases within the neural network. z s Represents the dynamic state variables input; p 0 This represents the input static or reference physical parameters.

[0030] 2. Design the physical information neural network structure Reference Figure 2 PINN model The input, output, and physical embedding mechanisms are as follows: 2.1 Input Definition The input vector is a combination of vehicle state, control input, and environmental conditions: ; In the formula: These are the longitudinal velocity and the lateral velocity, respectively. This refers to the yaw rate; The steering angle of the front wheels; As the driving force; The road surface adhesion coefficient; For the current estimated load; This represents the length of the time window.

[0031] 2.2 Output Definition The output includes vehicle attitude and key dynamic parameters: ; In the formula, Let be the acceleration of the vehicle's center of mass along the vertical direction. These are the vertical forces of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively.

[0032] 2.3 Network Layer Structure The network is a Temporal Convolutional Network (TCN), and its layer structure includes: an input layer (dimension n), hidden layers (including multiple loss functions), physical residual calculation units (through automatic differentiation), and an output layer (pose prediction values).

[0033] 3. Constructing physical residuals and design loss functions 3.1 Definition of Physical Residual The core of PINN lies in using Automatic Differentiation (AD) to calculate the time derivative of the network output and then substituting it into the dynamic equation to construct the residual.

[0034] Taking the equation of pitch motion as an example: ;

[0035] In the formula, For pitch rotation inertia, F z,i For the first i The vertical support force acting on the sprung mass of the vehicle body by each axle is the dynamic vertical load corresponding to the axle. These are the distances from the front and rear axles to the vehicle's center of gravity. For the overall vehicle quality, It is the height of the center of mass relative to the center of tilt.

[0036] Pitch angle output by the network The second-order time derivative is obtained through automatic differentiation: ; The corresponding physical residual is: ; Similarly, the vertical and lateral residuals are as follows: ; ; In the formula, The moment of inertia is the tilting motion. It is half the wheel track.

[0037] 3.2 Design of Multiple Loss Functions The multiple loss function of PINN is: ; In the formula, For multiple loss functions, The weights and bias parameters representing a neural network are core variables that need to be optimized during network training. This represents the set of physical parameters to be identified.

[0038] The definitions are as follows: Data error terms: ; N d The number of labeled samples used in the data error calculation. y i For the first i The ideal output for each sample For PINN to the first i The predicted output given for each sample.

[0039] Physical residuals: In the formula, N p For the number of physical points, This refers to the physical residual vector obtained by substituting the network prediction results and their time derivatives into the vehicle dynamics equations. x j For the first j The input vector corresponding to each physical collocation point.

[0040] Boundary / Initial Conditions: In the formula, N b The number of samples for boundary conditions or initial conditions; y 0 is in t 0 The real or given initial state vector known at any given time; For PINN at the initial time t 0 The predicted state vector.

[0041] Regularization term: ; These are the weighting coefficients for the data error term, physical residual term, boundary / initial condition term, and regularization term, respectively, using an uncertainty-weighted strategy: ; In the formula, The uncertainty parameters estimated by the network are dynamically updated as the network trains: This represents the data-driven loss term; Represents the constraint loss term in the physical equation; Represents the boundary condition loss term; This represents the network regularization loss term.

[0042] 4. Design a learnable physics submodule (embedded submodule) 4.1 Tire Submodule The nonlinear load dependence of the tire is implemented using a small neural network: ; The network parameters are included in the overall parameter set. The total loss function is used for joint optimization.

[0043] 4.2 Air Suspension Submodule The air suspension forces for each wheel are given by a learnable mapping network: ; Its output is consistent with the vehicle dynamics equations. Joint constraints enable the network to automatically learn nonlinear aeroelastic and damping characteristics.

[0044] 5. Two-stage multi-fidelity training and transfer learning strategy 5.1 Two-stage training framework Phase 1: Simulation pre-training.

[0045] Generate a multi-condition dataset using the TruckSim + Simulink simulation platform: ; In the formula, D sim This indicates the simulation pre-training dataset used in Phase 1, which contains data generated by the dynamics simulation software. N sim Group input x i Compared to ideal output y i A set of.

[0046] Optimize on this data: .

[0047] In the formula, L sim This is the total loss function for the simulation pre-training phase; L data,sim This is the monitoring error term for the simulation data; L physics This is the physical residual loss term; η 1_1 and η 2_1 These represent the weighting coefficients corresponding to the data error term and the physical residual term, respectively.

[0048] Phase Two: Fine-tuning of real vehicle data.

[0049] Collect real vehicle data: ; In the formula, D real This is a training dataset for real vehicles; x j For the j-th input sample; y j For the corresponding output sample; N real This represents the total number of actual vehicle data samples.

[0050] Perform small-batch online training: ; In the formula, L real This is the total loss function during the actual vehicle fine-tuning stage; L data,real This is the error term for monitoring real vehicle data; η 1_2 These are the weighting coefficients corresponding to the supervision error terms of real vehicle data; η 2_2 The weighting coefficients are the weighting coefficients corresponding to the physical residual terms.

[0051] The total loss is: ; In the formula, L total Let this be the total loss function for network training; L sim This represents the total loss function during the simulation phase. w sim Weights are applied to the simulation data. L real This is the total loss function for the actual vehicle stage; w real Weighting is applied to real vehicle data loss. Weights are dynamically adjusted: .

[0052] in, Represents the number of simulation data samples. This represents the number of real vehicle data samples. This weight is used to balance the data contribution during the simulation pre-training and real vehicle data fine-tuning stages, thereby achieving knowledge transfer from simulation to real vehicles.

[0053] 5.2 Replay Buffer and Anti-Forgotten Mechanism To prevent the loss of prior simulation knowledge during online updates, a replay buffer strategy is adopted to periodically mix in old data samples: ; in, This is the sampling scale factor.

[0054] 6. Uncertainty Quantification and Safety Rollback The model predicts and outputs a variance term simultaneously: ; in, The mean prediction of the vehicle state and key dynamic indicators at a future time (t + Δt) represents the prediction result that the model believes best conforms to physical laws and observation data under given input conditions. The variance estimate of the prediction given by the network is used to quantify the uncertainty of the model output and reflects the reliability of the network's current prediction result. The smaller the value, the more reliable the model considers the predicted value to be; The larger the value, the more likely the current operating conditions are outside the training data distribution, and the lower the reliability of the prediction.

[0055] The prediction confidence interval is: ; If the following conditions are met: ; This triggers a safety fallback mechanism, downgrading to a safe parsing model or limiting the input amplitude.

[0056] 7. Edge deployment and online updates After training, the model parameters After pruning, quantization, and knowledge processing, a lightweight version is generated: ; Deployed in the vehicle's edge control unit (ECU), it enables millisecond-level real-time prediction. During the online phase, parameters can be fine-tuned based on new data to maintain the model's adaptability to load changes and wear.

[0057] Although the above embodiments use a seven-degree-of-freedom model, in specific applications, this physical constraint architecture can be extended to a fourteen-degree-of-freedom vehicle model to include wheel rotation dynamics, thereby more accurately handling anti-lock braking (ABS) conditions; or in scenarios with limited computing resources, it can be simplified to a three-degree-of-freedom model, focusing only on the vehicle's lateral stability and center-of-gravity sideslip angle estimation, to adapt to the deployment requirements of low-computing-power edge computing devices.

[0058] The above physical information neural network infrastructure uses a multi-layer residual network or a temporal convolutional network (TCN). In other implementations, a long short-term memory network (LSTM) or a gated recurrent unit (GRU) can be used to process time-series data, utilizing its gating mechanism to capture long-term vehicle dynamic dependencies; alternatively, a Transformer architecture can be used to process vehicle sensor data in parallel using a self-attention mechanism, improving the feature extraction capability for sudden road surface stimuli.

[0059] In addition to using the Magic Formula, the tire submodule of the above-mentioned learnable submodules can also build learnable layers based on the Dugoff tire model or the Brush model to adapt to the physical characteristics of different types of tires (such as off-road tires and engineering tires); while the suspension submodule can also model the electromagnetic valve response characteristics or hydraulic system damping characteristics in the control algorithm of the active suspension system as a learnable neural network layer, thereby realizing the state monitoring of the active chassis system.

[0060] For lightweight deployment platforms, in addition to the model pruning and quantization techniques mentioned in the above embodiments, knowledge distillation can also be used. A trained large-scale PINN model can be used as a teacher network to guide a simpler student network in learning, thus running on an extremely low-power microcontroller (MCU). Furthermore, the deployment platform is not limited to in-vehicle ECUs; it can also be deployed on cloud servers, utilizing cloud computing power for large-scale digital twin modeling and remote health monitoring of the fleet.

[0061] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN, characterized in that, Includes the following steps: Step 1: Establish a multi-degree-of-freedom nonlinear dynamic model of the vehicle to define generalized coordinates and dynamic equations; Step 2: Construct a physical information neural network containing learnable physical sub-modules to predict dynamic variables; Step 3: Calculate the derivative of the network output with respect to time using automatic differentiation technology, substitute it into the dynamic equation to generate physical residual terms, and construct a multiple loss function by combining the observation data error; Step 4: Obtain an optimized model through a two-stage training strategy to achieve real-time observation of vehicle driving status and online identification of key component parameters; Step 5: Predict vehicle attitude and assess uncertainty in real time in the vehicle ECU. When the confidence level is insufficient, switch to the safety analysis model.

2. The method for observing and identifying vehicle nonlinear dynamic states based on PINN as described in claim 1, characterized in that: The multi-degree-of-freedom nonlinear dynamics model of the vehicle in step 1 is a seven-degree-of-freedom nonlinear dynamics model of the vehicle, including the vertical displacement of the vehicle's center of gravity, the vehicle's pitch angle, roll angle, and four suspension dynamic deflections.

3. The method for observing and identifying vehicle nonlinear dynamic states based on PINN as described in claim 1, characterized in that: The learnable physics submodule in step 2 is used to handle nonlinear components that are difficult to model analytically. It includes a tire submodule and an air suspension submodule. The tire submodule uses a parameterized magic tire formula and learns load dependence through a neural network, while the air suspension submodule learns nonlinear elastic and damping characteristics through neural network mapping.

4. The method for observing and identifying vehicle nonlinear dynamic states based on PINN as described in claim 1, characterized in that: The physical information neural network in step 2 is a temporal convolutional network, which includes an input layer, a hidden layer, a physical residual calculation unit, and an output layer. The input layer has a dimension of n, the hidden layer has multiple loss functions, and the output layer is used to output the pose prediction value.

5. The method for observing and identifying nonlinear vehicle dynamics states based on PINN as described in claim 1, characterized in that: The multiple loss function in step 3 is: ； In the formula: For multiple loss functions, The weights and bias parameters represent the neural network. Represents the set of physical parameters to be identified; Data error terms: In the formula: N d The number of labeled samples used in the data error calculation. y i For the first i The ideal output for each sample For PINN to the first i The predicted output given for each sample; Physical residuals: In the formula: N p For the number of physical points, This refers to the physical residual vector obtained by substituting the network prediction results and their time derivatives into the vehicle dynamics equations. x j For the first j The input vector corresponding to each physical collocation point; Boundary / Initial Conditions: In the formula: N b The number of samples for boundary conditions or initial conditions; y 0 is in t 0 The real or given initial state vector known at any given time; For PINN at the initial time t 0 The predicted state vector; Regularization term: ; These are the weighting coefficients for the data error term, physical residual term, boundary / initial condition term, and regularization term, respectively, using an uncertainty-weighted strategy: ； In the formula, The uncertainty parameters estimated by the network are dynamically updated as the network trains: This represents the data-driven loss term; Represents the constraint loss term in the physical equation; Represents the boundary condition loss term; This represents the network regularization loss term.

6. The method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN as described in claim 5, characterized in that: The two-stage training strategy in step 4 includes: in the first stage, the network is initialized and pre-trained using a full-condition simulation dataset generated by high-fidelity simulation software; in the second stage, the network is fine-tuned online using real vehicle data collected by on-board sensors, and a replay buffer mechanism is introduced to mix historical samples for training.

7. The method for observing and identifying the nonlinear dynamic state of a vehicle based on PINN as described in claim 5, characterized in that, Step 5 uses the following model to predict and simultaneously outputs a variance term for real-time prediction of vehicle attitude: ； in, The mean prediction of the vehicle state and key dynamic indicators at a future time (t + Δt) represents the prediction result that the model believes best conforms to physical laws and observation data under given input conditions. This represents the network's variance estimate of the prediction, used to quantify the uncertainty of the model output; The prediction confidence interval is: ； If the following conditions are met: ； This triggers a safety fallback mechanism, downgrading to a safe parsing model or limiting the input amplitude.

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