Intelligent vehicle limit performance boundary modeling method based on B-PINNs

Abstract

The invention relates to a B-PINNs-based intelligent vehicle limit performance boundary modeling method. The method comprises the following steps: collecting unlabeled data and labeled data; according to the collected label-free data, constructing a vehicle dynamics model as a soft constraint for physically supervising the B-PINNs neural network model; building a trunk neural network of the B-PINNs neural network model, wherein the trunk neural network comprises an input layer, a hidden layer and an output layer; constructing a physical consistency residual term based on a physical model of vehicle dynamic characteristics; designing a loss function of the model based on the physical consistency residual term, and supervised data loss and Bayesian regularization KL divergence loss provided by combining the labeled data; according to the method, the performance boundary of the intelligent vehicle under the limiting working condition can be captured, the accuracy of modeling and predicting the external characteristics of the whole vehicle is improved, and the defects existing when a physical model or a data driving model based on a neural network is independently adopted are overcome.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent vehicle performance boundary modeling, and more specifically, relates to an intelligent vehicle extreme performance boundary modeling method based on B-PINNs. Background Art

[0002] In recent years, against the backdrop of the continuous development and iteration of intelligent vehicle technology, with the development and application of distributed drive system architectures, high-power density motors, and high-dynamic response actuators, the maneuverability of vehicles has continued to improve, and people's attention to the safety, stability, and reliability of intelligent vehicles has further increased. By accurately modeling the dynamic performance boundaries of vehicles under extreme conditions (such as high-maneuverability emergency obstacle avoidance, braking on low-adhesion roads, and large lateral acceleration cornering), it can not only guide the vehicle to make more reasonable motion plans, but also provide a reliable decision-making basis for the control system to prevent the vehicle from losing control due to exceeding physical limits. Therefore, modeling the extreme performance boundaries of intelligent vehicles is the premise and key to ensuring the safety and reliability of vehicles under extreme working conditions.

[0003] Currently, common approaches to modeling vehicle performance boundaries fall into two main categories: physical models based on vehicle dynamics and data-driven models based on neural networks. While the former offer clear physical meaning and strong interpretability, they make varying degrees of assumptions and omissions in the modeling process, making it difficult to accurately represent the strong nonlinear characteristics of the vehicle system under extreme operating conditions. Furthermore, they struggle to handle the system's time-varying characteristics and uncertainties. While the latter offers robust nonlinear fitting capabilities, they still face challenges such as a scarcity of real-world data for extreme operating conditions, insufficient coverage of long-tail scenarios, and difficulty interpreting the generalization and reliability implications of the physical basis for boundary predictions.

[0004] Physics-Informed Neural Networks (PINNs), based on a neural network architecture, embed physical laws, combining the strengths of physical and data-driven models to achieve a fusion of data-driven and physical models. They are currently being applied in other fields, such as fluid mechanics, biology, and electrical engineering. However, they have not yet been applied to modeling the performance boundaries of intelligent vehicles. This is primarily due to the complex multi-scale physical modeling involved and the coupling between different physical processes, making unified modeling difficult. Furthermore, issues such as model parameter uncertainty, noisy training data, and insufficient data have limited the application of PINNs in this area. Summary of the Invention

[0005] In response to the problems and shortcomings of the existing technology, the present invention proposes a modeling method for the extreme performance boundaries of intelligent vehicles based on B-PINNs (Bayesian Physics-Informed Neural Networks, B-PINNs). This method can capture the performance boundaries of intelligent vehicles under extreme working conditions, improve the accuracy of modeling and prediction of the external characteristics of the entire vehicle, and overcome the shortcomings of using only physical models or data-driven models based on neural networks.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs, the method comprising the following steps:

[0008] Step S1: Collect data, including unlabeled data Ω1 and labeled data Ω2; the unlabeled data Ω1 is used to constrain the constructed B-PINNs neural network model to be close to the output of the vehicle dynamics model, and the labeled data Ω2 is used to calculate the data residual loss;

[0009] Step S2: construct a vehicle dynamics model based on the unlabeled data Ω1 collected in step S1 as a soft constraint for physical supervision of the constructed B-PINNs neural network model;

[0010] Step S3: Build the backbone neural network of the B-PINNs neural network model, including an input layer, a hidden layer, and an output layer. The input layer is a mixed input of labeled and unlabeled data as described in step S1. The hidden layer is a three-layer BayesLinear layer structure with Tanh as the activation function. The output layer uses a dual-head output structure. The weights and biases in the BayesLinear layer are both Gaussian probability distributed. The main head Head1 in the dual-head output structure is used to output the mean of the vehicle limit boundary, and the secondary head Head2 is used to output the standard deviation of the corresponding mean.

[0011] Step S4: constructing a physical consistency residual term based on the physical model representing the vehicle dynamics characteristics in step S2;

[0012] Step S5: Based on the physical consistency residual term constructed in step S4, the supervised data loss provided by the labeled data, and the Bayesian regularized KL divergence loss, the loss function of the core part of the B-PINNs neural network model is designed; the total loss L total The mathematical expression is:

[0013] L total =L data +λ phys +Lphysics +λ KL D kL (q(w)||p(w));

[0014] Among them, L data To monitor data loss, L physics is the physical consistency loss, D KL (q(w)||p(w)) is the Bayesian regularized KL divergence loss, λ phys is the physical loss weight coefficient, λ KL is the KL divergence loss weight coefficient;

[0015] Step S6: Train the constructed B-PINNs neural network model:

[0016] Combining the labeled and unlabeled data collected in step S1, the learning rate is set to 0.001, the number of training samples (batch size) is selected to 32, the maximum gradient is limited to 8, and the KL regularization term is disabled in the first 4 rounds.

[0017] As a preferred embodiment of the present invention, the unlabeled data in step S1 Among them, v x ,v y is the longitudinal and lateral velocity of the vehicle, w is the yaw rate, δ is the front wheel angle, a x ,a y are the longitudinal and lateral accelerations of the vehicle, θ, is the vehicle pitch angle and angular velocity, φ, is the vehicle roll angle and angular velocity, z i , is the suspension displacement and velocity, F act,i is the driving force of the active suspension, u is the friction coefficient between the road and the tire, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear;

[0018] Labeled data in, Indicates the boundary point of the longitudinal and lateral acceleration limit envelope, φ max is the roll stability boundary, w max, β max It is the boundary of handling stability (yaw rate, sideslip angle of center of mass).

[0019] As a preferred embodiment of the present invention, step S2 constructs the following vehicle dynamics model:

[0020] 1) Longitudinal kinematic model:

[0021] Among them, m is the vehicle mass, m sis the sprung mass, h is the distance from the vehicle's roll axis to the center of mass, ∑F xi is the tire force acting on the vehicle in the longitudinal direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; F f is the rolling resistance;

[0022] 2) Lateral kinematic model:

[0023] Among them, ∑F yi is the tire force acting on the vehicle in the lateral direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; for The first derivative of ;

[0024] 3) Yaw kinematic model:

[0025] Among them, I z is the yaw moment of inertia, is the first-order derivative of w, I xz is the moment of inertia of the vehicle around the x and z axes, ∑M zi is the vehicle yaw moment, which is calculated as follows:

[0026]

[0027] Among them, δ f is the front wheel turning angle, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, T is the wheel track;

[0028] 4) Roll kinematic model:

[0029]

[0030] Among them, I x is the roll moment of inertia, F fl 、F fr 、F rl 、F rr are the vertical forces from the road surface acting on the left front, right front, left rear and right rear wheels of the vehicle respectively;

[0031] 5) Pitch kinematic model:

[0032]

[0033] Among them, I y is the pitch moment of inertia, h c is the height of the vehicle's center of mass, h p is the equivalent pitch rotation axis height, g is the acceleration due to gravity;

[0034] 6) Suspension dynamics model:

[0035]

[0036] in, is the vertical acceleration of the center of mass, k i ,c i is the stiffness and damping of the suspension, F i Represents the vertical force of the road surface on the i-th wheel, and i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear.

[0037] As a preferred embodiment of the present invention, the expression of the residual term in step S4 is as follows:

[0038]

[0039] Among them, 1) describes the planar motion of the vehicle, is the longitudinal acceleration residual, is the lateral acceleration residual, r w is the yaw angular acceleration residual, v x The first derivative of v y The first derivative of ; 2) describes the rolling motion, r φ is the roll angular acceleration residual,; 3) describes the pitch motion, r θ is the pitch angular acceleration residual, for The first derivative of ; 4) describes the motion of the suspension, is the residual of suspension displacement acceleration, for 5) describes the vehicle's center of mass side slip angle constraint, which is used to improve the accuracy of modeling. To avoid numerical explosion, a very small amount of ε = 10 -6 , β is the sideslip angle of the center of mass, r β is the center of mass sideslip angle residual.

[0040] As a preferred embodiment of the present invention, the supervised data loss adopts negative log-likelihood loss, which is expressed as:

[0041]

[0042] Among them, N represents the number of labeled samples, x i is the i-th input sample, y i is the i-th label, μ(x i ) and σ(x i ) is the predicted mean and standard deviation output, logσ(x i) is the regularization term.

[0043] As a preferred embodiment of the present invention, the physical consistency loss adopts the negative log-likelihood loss, which is expressed as:

[0044]

[0045] Among them, r j (x) is the jth physical residual, σ j is the corresponding residual uncertainty, logσ j is a regularization term, where M is the set of physical residuals constructed in step S4.

[0046] As a preferred embodiment of the present invention, the expression of Bayesian regularized KL divergence loss is:

[0047]

[0048] Among them, L is the number of BayesLinear layers in the neural network, and the weights and biases of the parameters in each layer are Gaussian distributed, where the posterior μ wl represents the mean value of the weight of the lth layer, Represents the variance of the weight of the first layer, the priori p(w l )~N(0,1).

[0049] As a further preferred embodiment of the present invention, the expression of the longitudinal force of the tire is:

[0050] F x =Dsin{Carctan[Bx-E(Bx-arctan(Bx))]}+S v

[0051] C=a0

[0052]

[0053] S h =a9F z +a 10

[0054] S v =0

[0055] x=λ+S h

[0056] Among them, D is the peak coefficient, C is the shape coefficient, B is the stiffness coefficient, E is the curvature coefficient, F z is the vertical load of the tire, S h is the horizontal offset of the fitting curve, λ is the longitudinal slip rate, a0 to a3 and a6 to a 10 is the fitting coefficient.

[0057] As a further preferred embodiment of the present invention, the KL divergence loss of the lth layer is:

[0058]

[0059] Among them, n l is the number of weights or bias parameters of the layer, σ i ,μ i is the standard deviation and mean of the i-th parameter.

[0060] Advantages and beneficial effects of the present invention:

[0061] (1) The method provided by the present invention can simultaneously model the physical constraints induced by vehicle dynamics and the uncertainty factors induced by external environmental changes, integrate them into Bayesian physical information neural networks (B-PINNs), and use probability distribution instead of deterministic parameters to describe network weights, thus solving the uncertainty quantification problem of traditional PINNs in modeling vehicle extreme performance boundaries.

[0062] (2) The present invention takes into account the impact of the vehicle's active suspension system on the limit boundary model, so that the proposed method can more accurately characterize the vehicle's dynamic characteristics.

[0063] (3) The present invention ultimately outputs a probability boundary as a representation of the extreme performance boundary, rather than a stability probability value or criterion. Therefore, it can cope with the uncertainty under extreme working conditions, provide guidance for avoiding driving risks from a higher dimension, and further improve the interpretability of the system.

[0064] (4) The activation function in the hidden layer of the B-PINNs neural network model constructed by the present invention is the hyperbolic tangent function (Tanh). Compared with Sigmoid and ReLu, its output range is (-1, 1), which is convenient for controlling the numerical stability of the output of each layer. Its first and second order derivatives are continuous, which can ensure that the residual term has no cusps, which is conducive to fitting complex nonlinear physical functions. Because the output is centered at zero, the error gradient is more uniform and converges faster.

[0065] (5) The present invention incorporates the vehicle's plane, roll, and pitch motions as physical constraints into the B-PINNs model, models the vehicle's dynamic characteristics in more detail, describes the vehicle's extreme performance boundaries from multiple perspectives, and further improves the interpretability and generalization ability of the neural network model.

[0066] (6) The present invention visualizes the probability boundary of the model output in the form of a heat map for reference by trajectory planning and control systems, which can more intuitively demonstrate the performance utilization and safety margin of the vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flowchart of a B-PINNs-based intelligent vehicle extreme performance boundary modeling method provided by the present invention;

[0068] Figure 2 This is a schematic diagram of the B-PINNs network structure proposed in the present invention. DETAILED DESCRIPTION

[0069] In order to enable those skilled in the art to better understand the technical solutions and advantages of the present invention, the present application is described in detail below with reference to the accompanying drawings, but this is not intended to limit the scope of protection of the present invention.

[0070] like Figure 1 、 Figure 2 As shown, this embodiment provides a method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs, which includes the following steps:

[0071] Step S1: Collect data:

[0072] In this embodiment, data needs to be collected in the early stage for training the constructed B-PINNs neural network model. The collected data is called data samples and is divided into two categories: unlabeled data Ω1 and labeled data Ω2. Among them, the unlabeled data Ω1 is used to constrain the constructed B-PINNs neural network model to be close to the output of the vehicle dynamics model, that is, to ensure the constraint of physical characteristics; while the labeled data Ω2 is used to calculate the data residual loss.

[0073] Furthermore, due to the difficulty in collecting and accurately evaluating the amount of labeled extreme performance boundary data, this embodiment collects the state quantities of the first five data frames when the vehicle loses control in real scenarios and simulation scenarios as label data.

[0074] Specifically, unlabeled data Among them, v x ,v y is the longitudinal and lateral velocity of the vehicle, w is the yaw rate, δ is the front wheel angle, a x ,a y are the longitudinal and lateral accelerations of the vehicle, θ, is the vehicle pitch angle and angular velocity, φ, is the vehicle roll angle and angular velocity, z i , is the suspension displacement and velocity, F act,i is the driving force of the active suspension, u is the friction coefficient between the road and the tire, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear.

[0075] Labeled data in, Indicates the boundary point of the longitudinal and lateral acceleration limit envelope, φ max is the roll stability boundary, w max, β max It is the boundary of handling stability (yaw rate, sideslip angle of center of mass).

[0076] Step S2: construct a vehicle dynamics model based on the unlabeled data Ω1 collected in step S1 as a soft constraint for physical supervision of the constructed B-PINNs neural network model;

[0077] In this embodiment, in order to more accurately describe the motion of a highly maneuverable vehicle, the vehicle's planar, roll, and pitch motions are modeled. On this basis, considering that when the vehicle is driving under extreme conditions, the active suspension system will intervene to provide active suspension force to suppress load transfer between tires and improve tire contact with the ground, the suspension model and tire model are also taken into consideration.

[0078] Specifically, the following vehicle dynamics model is established:

[0079] 1) Longitudinal kinematic model:

[0080] Among them, m is the vehicle mass, m s is the sprung mass, h is the distance from the vehicle's roll axis to the center of mass, ∑F xi is the tire force acting on the vehicle in the longitudinal direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; F f is the rolling resistance.

[0081] 2) Lateral kinematic model:

[0082] Among them, ∑F yi is the tire force acting on the vehicle in the lateral direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; for The first derivative of .

[0083] 3) Yaw kinematic model:

[0084] Among them, I z is the yaw moment of inertia, is the first-order derivative of w, I xz is the moment of inertia of the vehicle around the x and z axes, ∑M zi is the vehicle yaw moment, which is calculated as follows:

[0085]

[0086] Among them, δf is the front wheel turning angle, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, and T is the wheel track.

[0087] 4) Roll kinematic model:

[0088]

[0089] Among them, I x is the roll moment of inertia, F fl 、F fr 、F rl 、F rr are the vertical forces acting on the left front, right front, left rear and right rear wheels of the vehicle respectively.

[0090] 5) Pitch kinematic model:

[0091]

[0092] Among them, I y is the pitch moment of inertia, h c is the height of the vehicle's center of mass, h p is the equivalent pitch rotation axis height, and g is the acceleration due to gravity.

[0093] 6) Suspension dynamics model:

[0094]

[0095] in, is the vertical acceleration of the center of mass, k i ,c i is the stiffness and damping of the suspension, F i Represents the vertical force of the road surface on the i-th wheel, and i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear.

[0096] 7) Tire model:

[0097] In this embodiment, the lateral and longitudinal forces acting on the tire need to be accurately calculated during calculations 1)-6). Therefore, the Pacejka magic formula tire model, which has a strong applicability, is adopted in this embodiment. A set of trigonometric functions of the same form are used to express tire forces in different directions. The expression for the longitudinal force of the tire is:

[0098] F x =Dsin{Carctan[Bx-E(Bx-arctan(Bx))]}+S v

[0099] C=a0

[0100]

[0101] S h =a9F z +a 10

[0102] S v =0

[0103] x=λ+S h

[0104] Among them, D is the peak coefficient, C is the shape coefficient, B is the stiffness coefficient, E is the curvature coefficient, F z is the vertical load of the tire, S h is the horizontal offset of the fitting curve, λ is the longitudinal slip rate, a0 to a3 and a6 to a 10 is the fitting coefficient; the lateral force of the tire can be calculated similarly.

[0105] In summary, equations 1) to 7) complete the system physical model foundation in the B-PINNs neural network model.

[0106] It should be pointed out that although the suspension system is dynamically modeled, the vertical body posture state quantity is not included in the proposed B-PINNs neural network, but is only used as an intermediate item in the vehicle dynamics calculation. The reason is that the purpose of detailed vertical dynamics modeling is mainly to evaluate the vehicle's comfort and carefully analyze the coupling mechanism relationship between various systems. The present invention focuses more on the extreme boundary modeling problem of the vehicle in planar motion. Therefore, the vertical motion characteristics of the vehicle are implicitly represented in the model to ensure a balance between computational efficiency and accuracy.

[0107] Step S3: Build the backbone neural network of the B-PINNs neural network model, including the input layer, hidden layer, and output layer;

[0108] The significance of this step is to embed the data and physical constraints in the above steps S1 and S2 into the B-PINNs neural network model, and establish a mapping relationship between the vehicle state, external environment, suspension mechanical characteristics and the boundary representation of the vehicle's extreme performance; among them, the input layer is a mixed input of labeled and unlabeled data described in step S1, the hidden layer is a three-layer BayesLinear layer structure, the activation function is Tanh, and the output layer selects a Dual-head output structure, which allows the model to output prediction results with confidence and supports physical supervision training of unlabeled samples.

[0109] Furthermore, the weights of a common Linear layer are fixed values, while the weights and biases in the BayesLinear layer used in this embodiment are both Gaussian probability distributed and are defined as follows:

[0110] Among them, W ij is the jth weight of the i-th layer, b j is the corresponding j-th bias, u ij is the j-th weight mean of the i-th layer, is the jth weight standard deviation of the i-th layer, u bj is the corresponding j-th bias mean, is the corresponding j-th bias standard deviation;

[0111] When performing forward propagation, the sample value is calculated from the distribution of weights, including the following parameters in each layer: μ w —weight mean matrix, representing the average connection strength of learning; σ w —weight logarithmic standard deviation matrix, which can be decoded into standard deviation; μ b —bias mean vector; σ b —Bias logarithmic standard deviation matrix. The forward propagation follows the reparameterized sampling principle, as follows:

[0112] W(s)=μ w +σ w ⊙ w , w ~N(0,1)

[0113] b(s)=μ b +σ b ⊙ b , b ~N(0,1)

[0114] y=W(s)x+b(s)

[0115] Among them, W(s) is the weight sampling, b(s) is the bias sampling, ⊙ represents element-level multiplication, that is, Hadamard product, ∈ w ,∈ b is a random noise term sampled from a standard normal distribution, y and x are the output and input of the current BayesLinear layer respectively; this formula defines the forward propagation process of the BayesLinear layer, which introduces uncertainty through reparameterization while maintaining differentiability.

[0116] In this way, the gradient of the loss with respect to μ and σ can be calculated through automatic differentiation. This is suitable for mixed labels of collected data and is more robust under the influence of limited data volume and data uncertainty. The KL divergence is combined as a regularization term to guide a reasonable model distribution.

[0117] Furthermore, the activation function selected by the present invention is the hyperbolic tangent function (Tanh). Compared with Sigmoid and ReLu, its output range is (-1, 1), which is convenient for controlling the numerical stability of each layer output. Its first and second order derivatives are continuous, which can ensure that the residual term has no cusp, which is conducive to fitting complex nonlinear physical functions. Because the output is centered at zero, the error gradient is more uniform and converges faster. It is suitable for the B-PINNs framework proposed in this invention. Its mathematical expression is as follows:

[0118]

[0119] Furthermore, the output layer is designed as a dual-head structure, sharing a set of hidden layers. Head 1 outputs the mean of the vehicle's limit boundary, while Head 2 outputs the standard deviation of the corresponding mean, representing the distribution width of the prediction uncertainty. In practice, most neural networks use softplus to output standard deviations to ensure positive values. However, considering that the vehicle limit boundary modeling problem involved in this invention does not require a maximum confidence dynamic range, a linear scaling method can be used to map the aforementioned Tanh output value to a positive standard deviation, expressing a relative uncertainty indicator to measure the credibility of the output limit boundary model.

[0120] Step S4: Based on the physical model representing the vehicle dynamics in step S2, a physical consistency residual term is constructed. That is, the vehicle's planar motion, roll and pitch motion, and suspension constraints are embedded in the B-PINNs neural network model. The residual term construction is mainly divided into four parts: (1) the neural network predicts the state variables; (2) automatic differentiation obtains its derivatives; (3) constructs the residual function corresponding to each variable; (4) the residual squares are summed as part of the loss;

[0121] Specifically, the residual term is as follows:

[0122]

[0123] Among them, 1) describes the planar motion of the vehicle, is the longitudinal acceleration residual, is the lateral acceleration residual, r w is the yaw angular acceleration residual, v x The first derivative of v y The first derivative of ; 2) describes the rolling motion, r φ is the roll angular acceleration residual,; 3) describes the pitch motion, r θ is the pitch angular acceleration residual, for The first derivative of ; 4) describes the motion of the suspension, is the residual of suspension displacement acceleration, for 5) describes the vehicle's center of mass side slip angle constraint, which is used to improve the accuracy of modeling. To avoid numerical explosion, a very small amount of ε = 10 -6 , β is the sideslip angle of the center of mass, r β It should be noted that the tire model is not considered in the residual modeling of the B-PINNs neural network model described in the present invention. The reason is that the Pacejka model is highly nonlinear and it is difficult to ensure the stability of the input and output range.

[0124] Step S5: Based on the physical consistency residual term constructed in step S4, and the supervised data loss and Bayesian regularized KL divergence loss provided by the labeled data, the loss function of the core part of the B-PINNs neural network model is designed.

[0125] Furthermore, the total loss L total The mathematical expression is as follows: L total =L data +λ phys L physics +λ KL D KL (q(w)||p(w));

[0126] Among them, L data To monitor data loss, L phyiscs is the physical consistency loss, D KL (q(w)||p(w)) is the Bayesian regularized KL divergence loss, λ phys is the physical loss weight coefficient, λ KL is the KL divergence loss weight coefficient, set Prevent the KL term from over-dominantly dominating the optimization;

[0127] In the above formula, for labeled samples, the output is the mean and standard deviation of the Gaussian distribution, and the supervised data loss uses the negative log-likelihood (NLL) loss, which is expressed as:

[0128]

[0129] Among them, N represents the number of labeled samples, x i is the i-th input sample, y i is the i-th label, μ(x i ) and σ(x i ) is the predicted mean and standard deviation output, logσ(x i ) is the regularization term;

[0130] Similarly, the physical consistency loss adopts the same NLL form, combined with the physical residual term constructed in step S4, and the specific form is as follows:

[0131]

[0132] Among them, r j (x) is the jth physical residual, σ j is the corresponding residual uncertainty, logσ j is a regularization term, where M is the set of physical residuals constructed in step S4, which has 7 items in total. In order to avoid manually setting the hyperparameter weights of each residual term, the present invention introduces a dynamic weight mechanism based on uncertainty, that is, the weight j is Dynamically learn the importance of each residual.

[0133] In this embodiment, in order to constrain the distribution of all learnable parameters to not deviate from the Gaussian prior during training, prevent overfitting and improve generalization ability, it is necessary to consider the Bayesian regularized KL divergence loss in the loss function design. The specific mathematical form is as follows:

[0134]

[0135] Among them, L is the number of BayesLinear layers in the neural network, and the weights and biases of the parameters in each layer are Gaussian distributed, where the posterior μ wl represents the mean value of the weight of the lth layer, Represents the variance of the weight of the first layer, the priori p(w l )~N(0,1), further, the KL divergence loss of the lth layer is:

[0136]

[0137] Among them, n l is the number of weights or bias parameters of the layer, σ i ,μ i is the standard deviation and mean of the i-th parameter.

[0138] Step S6: Train the constructed B-PINNs neural network model:

[0139] In this step, it is necessary to combine the labeled data and unlabeled data collected in step S1. When training the B-PINNs neural network proposed in this invention, the Adam optimizer is selected, the learning rate is set to 0.001, the number of training samples (batch size) is selected to 32, and the maximum gradient is limited to 8 to prevent gradient explosion. The KL regularization term is disabled in the first four rounds to speed up the initial fitting.

[0140] In this example, the Tanh activation function was selected, and given the numerical range of the input variables, data normalization was required. Z-score normalization was employed to focus the input within the most sensitive range of the activation function gradient, ensuring stable and efficient training. Furthermore, Monte Carlo (MC) sampling was employed in the subsequent inference phase, sampling the weights multiple times to obtain multiple output prediction samples to calculate the prediction distribution and model uncertainty. All sampled values ​​were saved for subsequent visualization of the prediction distribution.

[0141] Step S7: In steps S1-S6, the preparation of preliminary data, construction of the vehicle dynamics model, establishment of the B-PINNS neural network, design of the physical residual and loss function, and training strategy are completed respectively; then the trained model is used for prediction, and the vehicle limit performance boundary modeling results predicted by the B-PINNs neural network model are directly output and visualized.

[0142] Furthermore, according to the description of the model, the output results are probabilistic boundary indicators, including the output side longitudinal acceleration boundary, the center of mass sideslip angle limit, the limit yaw rate and the roll stability limit (LTR). The output forms are the mean and the standard deviation describing the uncertainty of the mean. The collected data are saved and the results can be visualized by the particle swarm optimization method to draw the acceleration envelope diagram a x -a y , handling stability boundary map Lateral stability boundary v x -δ-LTR, which expresses the uncertainty of the boundary in the form of a heat map.

[0143] The vehicle limit boundaries output by the present invention can be applied to the vehicle's longitudinal control, lateral control, stability control, motion planning module, and driving risk prediction systems. Since it provides boundary estimates with confidence, the boundaries can be dynamically optimized and adjusted according to different objectives, thereby improving the flexibility and personalization of the system.

[0144] The above description is merely a preferred embodiment of the present invention and therefore cannot be used to limit the scope of the present invention. In other words, equivalent changes and modifications made according to the scope of the patent application and the contents of the specification should still fall within the scope of the patent of the present invention.

Claims

1. A B-PINNs-based intelligent vehicle extreme performance boundary modeling method, characterized by: The steps include: Step S1: Collect data, including unlabeled data Ω1 and labeled data Ω2; the unlabeled data Ω1 is used to constrain the constructed B-PINNs neural network model to be close to the output of the vehicle dynamics model, and the labeled data Ω2 is used to calculate the data residual loss; Step S2: construct a vehicle dynamics model based on the unlabeled data Ω1 collected in step S1 as a soft constraint for physical supervision of the constructed B-PINNs neural network model; Step S3: Build the backbone neural network of the B-PINNs neural network model, including an input layer, a hidden layer, and an output layer. The input layer is a mixed input of labeled and unlabeled data as described in step S1. The hidden layer is a three-layer BayesLinear layer structure with Tanh as the activation function. The output layer uses a dual-head output structure. The weights and biases in the BayesLinear layer are both Gaussian probability distributed. The main head Head1 in the dual-head output structure is used to output the mean of the vehicle limit boundary, and the secondary head Head2 is used to output the standard deviation of the corresponding mean. Step S4: constructing a physical consistency residual term based on the physical model representing the vehicle dynamics characteristics in step S2; Step S5: Based on the physical consistency residual term constructed in step S4, the supervised data loss provided by the labeled data, and the Bayesian regularized KL divergence loss, the loss function of the core part of the B-PINNs neural network model is designed; the total loss L total The mathematical expression is: L total =L data +λ phys L physics +λ KL D KL (q(w)||p(w)); Among them, L data To monitor data loss, L physics is the physical consistency loss, D KL (q(w)||p(w)) is the Bayesian regularized KL divergence loss, λ phys is the physical loss weight coefficient, λ KL is the KL divergence loss weight coefficient; Step S6: Train the constructed B-PINNs neural network model: Combining the labeled and unlabeled data collected in step S1, the learning rate is set to 0.001, the number of training samples is selected as 32, the maximum gradient is limited to 8, and the KL regularization term is disabled in the first 4 rounds.

2. The B-PINNs-based intelligent vehicle extreme performance boundary modeling method according to claim 1, characterized in that: Unlabeled data in step S1 Among them, v x ,v y is the longitudinal and lateral velocity of the vehicle, w is the yaw rate, δ is the front wheel angle, a x ,a y are the longitudinal and lateral accelerations of the vehicle, are the vehicle pitch angle and angular velocity, are the vehicle roll angle and angular velocity, is the suspension displacement and velocity, F act,i is the driving force of the active suspension, u is the friction coefficient between the road and the tire, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; Labeled data in, Indicates the boundary point of the longitudinal and lateral acceleration limit envelope, φ max is the roll stability boundary, w max, β max is the yaw rate and sideslip angle boundary of the center of mass.

3. The method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs according to claim 1, characterized in that: The supervised data loss uses negative log-likelihood loss, which is expressed as: Among them, N represents the number of labeled samples, x i is the i-th input sample, y i is the i-th label, μ(x i ) and σ(x i ) is the predicted mean and standard deviation output, logσ(x i ) is the regularization term.

4. The method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs according to claim 1, characterized in that: The physical consistency loss uses negative log-likelihood loss, which is expressed as: Among them, r j (x) is the jth physical residual, σ j is the corresponding residual uncertainty, logσ j is a regularization term, where M is the set of physical residuals constructed in step S4.

5. The method for modeling the limit performance boundary of an intelligent vehicle based on B-PINNs according to claim 1, characterized in that: The expression of Bayesian regularized KL divergence loss is: Among them, L is the number of BayesLinear layers in the neural network, and the weights and biases of the parameters in each layer are Gaussian distributed, where the posterior μ wl represents the mean value of the weight of the lth layer, Represents the variance of the weight of the first layer, the priori p(w l )~N(0,1).

6. The method for modeling the limit performance boundary of an intelligent vehicle based on B-PINNs according to claim 2, characterized in that: Step S2 constructs the following vehicle dynamics model: 1) Longitudinal kinematic model: Among them, m is the vehicle mass, m s is the sprung mass, h is the distance from the vehicle's roll axis to the center of mass, ∑F xi is the tire force acting on the vehicle in the longitudinal direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; F f is the rolling resistance; 2) Lateral kinematic model: Among them, ∑F yi is the tire force acting on the vehicle in the lateral direction, where i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear; for The first derivative of ; 3) Yaw kinematic model: Among them, I z is the yaw moment of inertia, is the first-order derivative of w, I xz is the moment of inertia of the vehicle around the x and z axes, ∑M zi is the vehicle yaw moment, which is calculated as follows: Among them, δ f is the front wheel turning angle, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, T is the wheel track; 4) Roll kinematic model: Among them, I x is the roll moment of inertia, F fl 、F fr 、F rl 、F rr are the vertical forces from the road surface acting on the left front, right front, left rear and right rear wheels of the vehicle respectively; 5) Pitch kinematic model: Among them, I y is the pitch moment of inertia, h c is the height of the vehicle's center of mass, h p is the equivalent pitch rotation axis height, g is the acceleration due to gravity; 6) Suspension dynamics model: in, is the vertical acceleration of the center of mass, k i ,c i is the stiffness and damping of the suspension, F i Represents the vertical force of the road surface on the i-th wheel, and i∈{fl,fr,rl,rr} represents the left front, right front, left rear, and right rear.

7. The method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs according to claim 5, characterized in that: The KL divergence loss of layer l is: Among them, n l is the number of weights or bias parameters of the layer, σ i ,μ i is the standard deviation and mean of the i-th parameter.

8. The method for modeling the extreme performance boundary of an intelligent vehicle based on B-PINNs according to claim 6, characterized in that: The expression of the longitudinal force of the tire is: F x =Dsin{Carctan[Bx-E(Bx-arctan(Bx))]}+S v C=a0 <h2 style=";text-align:left;direction:ltr">D=a1F<h2 style=";text-align:left;direction:ltr"> z <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a2F<h2 style=";text-align:left;direction:ltr"> z E=a6F z 2 +a7F z +a8 S h =a9F z +a 10 S v ＝0 x=λ+S h Among them, D is the peak coefficient, C is the shape coefficient, B is the stiffness coefficient, E is the curvature coefficient, F z is the vertical load of the tire, S h is the horizontal offset of the fitting curve, λ is the longitudinal slip rate, a0 to a3 and a6 to a 10 is the fitting coefficient.

9. The method for modeling the limit performance boundary of an intelligent vehicle based on B-PINNs according to claim 6, characterized in that: The expression of the residual term in step S4 is as follows: Among them, 1) describes the planar motion of the vehicle, is the longitudinal acceleration residual, is the lateral acceleration residual, r w is the yaw angular acceleration residual, v x The first derivative of v y The first derivative of ; 2) describes the rolling motion, r φ is the roll angular acceleration residual; 3) describes the pitch motion, r θ is the pitch angular acceleration residual, for The first derivative of ; 4) describes the motion of the suspension, is the residual of suspension displacement acceleration, for The first derivative of ; 5) describes the vehicle's center of mass side slip angle constraint, the minimum ε = 10 -6 , β is the sideslip angle of the center of mass, r β is the center of mass sideslip angle residual.

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