Tire force perception method in uncertain environment

Abstract

The application discloses a tire force sensing method in an uncertain environment, and considers that information of various uncertain working condition environments is stored in three-axis acceleration information; through interpretation of the three-axis acceleration information, mainly obtained are entropy features and dimensionless features, and then time-frequency domain features are combined to serve as input of a tire force prediction model to realize prediction, and an output result contains a prediction value and a corresponding prediction interval; wherein, the tire force prediction model is mainly established based on a deep learning architecture and a Monte Carlo method, and a mapping relationship between tire force and three-axis acceleration information interpretation features is established to complete the prediction.

Description

Technical Field

[0001] This invention belongs to the field of tire design technology, specifically relating to a method for constructing a neural network model for predicting tire force under uncertain environments. Background Technology

[0002] As the only part of a vehicle in contact with the ground, tire wear directly affects driving safety, fuel efficiency, and driving experience. With the development of intelligent transportation systems and vehicle-to-everything (V2X) technology, tire wear prediction has become an important research direction for vehicle maintenance and safety management. By predicting tire wear, early warnings can be given, reducing accident risks, extending tire life, and lowering maintenance costs. Tire wear is affected by many factors, mainly including: Driving behavior: Rapid acceleration, sudden braking, and high-speed cornering accelerate tire wear. Road conditions: Road surface materials, slope, potholes, and other road conditions have a significant impact on tire wear. Tire characteristics: The material, structure, and tire pressure of a tire determine its wear resistance. Environmental factors: Temperature, humidity, and climate conditions also affect the tire wear rate.

[0003] Road conditions are the external excitation of the tire, while tire dynamics are the direct result of tire / road interaction. Both can be further quantified into different identifiable parameters. Identifying road roughness, potholes, cracks, and road type can improve an autonomous vehicle's perception of road conditions. Estimation of tire force, tire pressure, and tire deformation are key inputs to the vehicle dynamics control module. Accurate real-time identification of the tire-road interaction state helps reduce serious traffic accidents caused by unknown road conditions and tire dynamics. Tire state information is a particularly important part of the vehicle's state information. However, tire dynamics are difficult to obtain directly, primarily because the tire-road interaction is a typically nonlinear process. Secondly, due to limitations in technology and measurement costs, some information directly related to vehicle stability, such as tire force and vehicle roll angle, cannot be directly measured.

[0004] Currently, the most common method used both domestically and internationally is to measure easily obtainable vehicle-related information using sensors, and then use subsequent algorithms to analyze or build observers to sense the tire's state parameters. However, conventional smart tires only consider a few uncertain environmental factors and lack methods for quantifying and predicting uncertainties in uncertain environments to adapt to the varying degrees of uncertainty in actual operating conditions and achieve coordinated prediction of accurate and range estimates. Summary of the Invention

[0005] Purpose of the invention: To address the technical problems existing in the prior art, this invention provides a tire force sensing method under uncertain environments. It constructs a deep prediction model structure based on the MPL architecture and Monte Carlo uncertainty quantification method, and trains the prediction model using simulated working condition data to achieve point and range prediction of tire force. The model's test error is less than 4.5%, the average tire force coverage is approximately 93.34%, and the prediction accuracy is high. It exhibits good adaptability and robustness for tire force prediction under uncertain environments, and also provides valuable insights for predicting other tire state parameters.

[0006] Technical Solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution: a tire force sensing method under uncertain conditions, comprising the following steps: S1, Collect triaxial acceleration information at the midpoint of the inner surface of the tire inner tube, the triaxial acceleration information includes: radial acceleration, circumferential acceleration and lateral acceleration at the midpoint of the inner surface of the tire inner tube; S2, preprocess the triaxial acceleration information collected in step S2. The preprocessing includes coordinate transformation (for simulation purposes), filtering, and cutting. The triaxial acceleration signal is segmented to facilitate feature identification. The original data includes multiple sets of periodic signals. After waveform analysis, statistical analysis, and simulation analysis of the triaxial acceleration signal under the above uncertain working conditions, the radial acceleration signal can be used as a synchronous reference signal, which is a better choice. Other signals are easily affected by the uncertain environment in terms of waveform shape and signal magnitude. Radial acceleration is the most stable and reliable signal among all signals.

[0007] In other words, data segmentation processing requires identifying the triaxial acceleration signal of one revolution of the tire, calculating one revolution period based on the peak and valley points of radial acceleration according to statistical analysis, recording the time-series segmentation points, and completing the segmentation of radial acceleration while also segmenting the other acceleration signals, because the collected triaxial acceleration is time-series data.

[0008] S3. Extract time-frequency domain features, entropy information features, and dimensionless features from the preprocessed triaxial acceleration information; the entropy information features include power spectral entropy, singular spectral entropy, energy entropy, approximate entropy, sample entropy, fuzzy entropy, envelope entropy, and scatter entropy; the dimensionless features include kurtosis, skewness, waveform factor, peak factor, impulse factor, and margin factor; the time-frequency domain features include time-domain features and frequency-domain features, the time-domain features include local peak value, peak difference, peak-time difference, local mean, local variance, and signal period; the frequency-domain features include centroid frequency, amplitude skewness, and maximum amplitude value. S4, pair the extracted features of tire force and triaxial acceleration information as a sample set, and divide the sample set into a training set and a test set; S5 uses a multilayer perceptron architecture (MLP) and is based on the Monte Carlo neural network Dropout to build a tire force prediction model. S6. The tire force prediction model is trained and the network parameters are optimized using the training set obtained in step S4 to obtain the optimized tire force prediction model.

[0009] Furthermore, the tire force prediction model described in step S5 adopts a multilayer perceptron (MLP) architecture combined with a Monte Carlo neural network, which includes, in sequence: an input layer, several pairs of hidden-dropout layers, an output layer, and an MC Dropout layer. The hidden layers apply fully connected layers and the ReLU activation function. The training and computation process of the MLP is as follows:

[0010] in, , This is the weight matrix. , For bias terms, Let X be the input feature and the ReLU activation function. This is for predicting the output.

[0011] Furthermore, the number of hidden layer-dropout layers is 2-4 pairs; the number of neurons in the hidden layer is 64-256, the learning rate is 0.001-0.1, the training batch size is 50-200, and the dropout ratio is 0-0.5.

[0012] Furthermore, the entropy information features mentioned in step S3 are calculated as follows: (1) Power spectral entropy PSE, calculated by the following formula, , In the formula, P j is the normalized power spectral density of the j-th frequency component, and N is the data length; , This represents the i-th data z in the original data Z. i The frequency domain obtained by performing a Fourier transform. This represents the nth frequency component, the original data. ; fj refers to the distinguishable frequency component in the signal, corresponding to its discretized position in the frequency domain. Z(fj) is the signal representation at frequency fj in the frequency domain, and the square of the magnitude is the power at that frequency point.

[0013] (2) Singular spectral entropy (SSE) is calculated using the following formula: , , In the formula, Sk It is the k-th normalized singular value, where N is the data length; normalization factor Represents all samples z i The norm sum of squares directly reflects the influence of the original data; The singular value square is obtained by decomposing the matrix of the original data Z using SVD, which implicitly contains structural information about the data distribution. (3) Energy entropy EE, calculated by the following formula, , , Among them, E i Z is the normalized energy of the i-th sample, N is the data length, and z is the normalized energy of the i-th sample. i It is the i-th sample data; (4) The approximate entropy ApEn is calculated using the following formula: , , in, This represents the logarithmic mean of the similarity frequencies of patterns of length m at a similarity tolerance r, used to characterize the repetitive patterns of local structures in a time series; m is the pattern length, and r is the similarity tolerance. This is an indicator function; it returns 1 when the condition is met and 0 otherwise. (Original data) It is time series data; Pattern length m refers to the number of consecutive data points used to measure pattern similarity in a time series; a pattern refers to a local structure or subsequence composed of consecutive data points in a time series; and pattern length m refers to the number of consecutive data points contained in this local structure. (5) Sample entropy SampEn, calculated using the following formula: , Where A is the distance and The pattern for quantity, B is to satisfy The number of pattern pairs, r is the similarity tolerance, m is the pattern length, and the original data. It is time series data; (6) Fuzzy entropy (FuzzyEn) is calculated using the following formula: , , Where 𝑚 is the pattern length, r is the similarity tolerance, and N is the data length, representing the original data. It is a time series signal; (7) Envelope entropy EnvEn, calculated by the following formula, , In the formula, ai represents the i-th data z of the original data Z. i The envelope signal obtained by Hilbert transforming a time-domain signal. The analytic signal after the Hilbert transform is represented by its magnitude as the envelope; The power spectral density of the envelope signal difference is represented by the power spectral density obtained by performing Fourier transform (FET) spectrum analysis on the envelope signal. The normalized value of the difference power spectral density of the envelope signal is represented by M, where M represents the total number of frequency components. (8) Dispersion entropy DispEn, calculated using the following formula, , In the formula, p n Let C be the probability of the nth pattern occurring. n It is the number of times the nth mode appears in the signal, T is the total number of all observed modes, and K is the number of discrete symbols; Represents the time-domain signal z i The normalized value; It is a local minimum value to prevent the denominator from being zero; d i P represents the discrete symbol corresponding to each sample point; （j） It is d i The constructed discrete pattern.

[0014] Furthermore, step S7 is included, which involves testing the optimized tire force prediction model using a test set.

[0015] Furthermore, the cutting process in step S2 includes cutting the triaxial acceleration information according to the tire rolling cycle.

[0016] Beneficial effects: Compared with the prior art, this invention provides a tire force sensing method under uncertain environments, proposes a tire force prediction model under uncertain environments, and realizes point prediction and range prediction of tire force based on the Monte Carlo method and MPL architecture. The test error of the model is less than 4.5%, which is lower than the average absolute percentage error of existing prediction methods based on convolutional neural networks. The average tire force coverage is about 93.34%, with high prediction accuracy. It has good adaptability and robustness for tire force prediction under uncertain environments, and has reference value for the prediction of other tire state parameters. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0018] Figure 1 This is a schematic diagram of the logic flow of the tire force sensing method under uncertain conditions described in this invention.

[0019] Figure 2 This is a schematic diagram of the tire force prediction model described in this invention.

[0020] Figure 3 This is a schematic diagram of the test process for the tire force prediction model described in this invention.

[0021] Figure 4 This is the predicted result of the tire vertical force in an embodiment of the present invention.

[0022] Figure 5 This is the predicted result of the longitudinal force of the tire in an embodiment of the present invention. Detailed Implementation

[0023] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0024] Given the current lack of research on tire road information sensing methods for smart tires under uncertain environments, this invention improves the research on sensing methods for smart tires, and has certain theoretical significance and application value for the development of smart tire technology. The main research content of this invention is a method for predicting tire forces under uncertain environments. This invention constructs a deep prediction model structure based on the MPL architecture and Monte Carlo uncertainty quantification method, trains the prediction model using simulated working condition data, and evaluates the prediction performance of the prediction model.

[0025] like Figure 1 As shown, the main idea behind this invention for predicting tire parameters is as follows: Information from various uncertain operating conditions is centrally stored in triaxial acceleration information (triaxial acceleration sensor signals contain rich information that has not yet been fully interpreted). By interpreting the triaxial acceleration information, entropy features and dimensionless features are mainly obtained. These are then combined with time-frequency domain features as input to construct a tire force prediction model to achieve prediction. The output includes the predicted value and the corresponding prediction interval. The tire force prediction model is mainly based on deep learning architecture and Monte Carlo methods, establishing a mapping relationship between tire force (longitudinal force and vertical force) and the interpreted features of triaxial acceleration information to complete the prediction. The following details the process steps of the tire force sensing method under uncertain environments according to this invention: I. Extracting Data Features:

[0026] Entropy features are a generalized set of features used in information theory and nonlinear dynamics to quantify complexity, randomness, or dynamic behavior of systems. They can be categorized into classical entropy features, frequency domain entropy features, and time-domain and nonlinear entropy features. Classical entropy features include information entropy and redundancy entropy; frequency domain entropy features mainly include power spectral entropy and singular spectral entropy; and time-domain and nonlinear entropy features include energy entropy, approximate entropy, sample entropy, fuzzy entropy, envelope entropy, and scattering entropy. In signal processing and system state monitoring, entropy features are commonly used to quantify the dynamic behavior, frequency distribution, and phase relationship of signals, describing the overall characteristics or local changes of a system.

[0027] This invention, based on experimental selection, extracts time-frequency domain features, entropy information, and dimensionless features from triaxial acceleration information and maps them to tire force to achieve the extraction of nonlinear information hidden in the signal and to describe the dynamic change law of the system.

[0028] Dimensionless features refer to feature parameters whose original units and dimensions have been eliminated through mathematical processing (such as ratios, normalization, or standardization). These features are dimensionless and can reflect the relative relationships or morphological characteristics of the data, such as kurtosis, skewness, correlation coefficient, or signal-to-noise ratio. This invention applies them to data analysis and machine learning to eliminate differences between data of different dimensions, facilitate cross-dimensional comparisons, or serve as standardized inputs for models, thereby improving the universality of the analysis and the performance of the models.

[0029] Time-frequency domain features are signal features extracted by combining time-domain and frequency-domain analysis methods, used to reveal the joint characteristics of a signal in time and frequency. Time-domain features (such as mean, variance, and peak value) describe the changes in a signal over time, while frequency-domain features (such as spectrum and energy distribution) reflect the frequency components of the signal through Fourier transform. Time-frequency domain analysis (such as wavelet transform and short-time Fourier transform) is suitable for non-stationary signals, capturing both temporal locality and frequency structure through time-spectrum analysis, and is widely used in fields such as mechanical fault diagnosis, speech recognition, and biomedical signal processing.

[0030] The main difference lies in the varying number of local peaks, peak differences, and peak-time differences in the time domain features. Local peaks include different numbers of local peak-to-peak values ​​and local peak-to-valley values. Peak differences refer to the absolute value of the difference between any two local peaks, and peak-time differences refer to the absolute value of the difference between the corresponding time points of any two local peaks.

[0031] The specific data features selected by this invention are as follows: (1) Power spectral entropy

[0032] Power Spectral Entropy (PSE) is based on the frequency domain distribution of a signal and can be used to reflect the randomness or complexity of the distribution of signal power within a frequency range.

[0033] , In the formula, Pj is the normalized power spectral density of the j-th frequency component, and M is the data length.

[0034] (2) Singular spectral entropy

[0035] Singular Spectrum Entropy (SSE) quantifies the dynamic complexity of a system by analyzing the distribution of signals in the singular value spectrum, based on Singular Value Decomposition (SVD).

[0036] , In the formula, Sk is the k-th normalized singular value, and L is the data length.

[0037] (3) Energy entropy

[0038] Energy entropy (EE) analyzes the energy distribution after signal decomposition, reflecting the degree of unevenness in the energy distribution of each sample point in the time domain signal.

[0039] , , in, It is the normalized energy of the i-th sample, and N is the data length. It is the i-th sample data.

[0040] (4) Approximate entropy

[0041] Approximate entropy (ApEn) is a statistic used to quantify the complexity and regularity of time series data. It was first proposed by Steve M. Pincus in 1991. It is suitable for short time series and can be used to measure the irregularity or unpredictability of data.

[0042] , , Where m is the pattern length and r is the similarity tolerance. This is an indicator function; it returns 1 when the condition is met and 0 otherwise. It is time series data.

[0043] (5) Sample entropy

[0044] Sample entropy (SampEn) quantifies the complexity or randomness of a signal by analyzing the similarity between patterns in a time series. It is an improvement on approximate entropy, eliminating the calculation of self-matching pairs, which can enhance the robustness of the data and make the calculation results more stable.

[0045] , Where A is the distance and The pattern for quantity, B is to satisfy The number of pattern pairs, r is the similarity tolerance, and m is the pattern length. It is time series data.

[0046] (6) Fuzzy entropy

[0047] Fuzzy entropy (FuzzyEn) makes the similarity measurement of signals more flexible and more robust to noise by introducing fuzzy membership functions.

[0048] , , Where 𝑚 is the pattern length, r is the similarity tolerance, and N is the data length. It is a time series signal.

[0049] (7) Envelope entropy

[0050] Envelope entropy (EnvEn) is a complexity measure based on the envelope characteristics of a signal, used to quantify the dynamic changes of time series signals. Its main idea is to extract the signal envelope curve and calculate the entropy value based on the distribution characteristics of the envelope signal to assess the degree of chaos or randomness of the signal.

[0051] , Where Pw is the normalized value of the difference power spectral density of the envelope signal, and M represents the total number of frequency components.

[0052] (8) Spread entropy

[0053] Dispersion entropy (DispEn) mainly quantifies the relative distribution of data points by symbolizing and analyzing the distribution of time series data, and extracts the pattern information and dynamic characteristics of the signal.

[0054] , Among them, the number of discrete symbols in K, Let k be the probability of the k-th pattern occurring. , It is the number of times the k-th pattern appears in the signal, and T is the total number of all observed patterns.

[0055] This invention utilizes dimensionless features to transform quantitative features with physical units into unit-independent numerical representations through data processing. This allows features to be compared and analyzed under different conditions and with different units. In general machine learning modeling, features in the original data may have different dimensions and scales, leading to some features having an excessive influence on the model during training or making the model difficult to converge. Dimensionlessness ensures that all features are at the same scale, avoiding the excessive dominance of certain features on the model. For example, this invention uses data feature normalization to make them dimensionless. Based on feature selection, this invention mainly uses the dimensionless feature calculation formulas shown in Table 1 for the dataset. The data length is N. Calculating dimensionless features such as kurtosis, skewness, waveform factor, peak factor, impulse factor, and margin factor allows for deeper understanding of the data's morphological distribution, volatility, and impulse characteristics from different perspectives of the acceleration signal. This is significant for extracting information from the triaxial acceleration signal and improving the model's accuracy and coverage.

[0056] Table 1 Formulas for Calculating Dimensionless Characteristics

[0057] II. Construction of Tire Force Prediction Model

[0058] like Figure 2 The diagram shows the structure of the constructed tire force prediction model, which employs a Multilayer Perceptron (MLP) architecture. The MLP consists of multiple hidden layers, each using fully connected layers (FC) and the ReLU activation function. Dropout layers are then added to enhance the model's non-linear expressive power, allowing the prediction model to randomly ignore some neuronal structures during training, thereby improving its generalization ability. The input layer receives the standardized input feature matrix, while the output layer outputs the prediction results, primarily the predicted tire force values. Multiple prediction values ​​are then generated through multiple sampling using MC Dropout, and the mean and standard deviation of the corresponding outputs (longitudinal force and vertical force) are calculated. The main calculation process of the MLP is as follows: , in, , This is the weight matrix. , For bias terms, Let X be the input feature and the ReLU activation function. This is for predicting the output.

[0059] At the beginning of each training cycle, data augmentation is performed by adding random noise to the input data. The training of the prediction model primarily optimizes the network parameters by minimizing the loss function. The loss function measures the error between the model's predictions and the true values; the mean squared error (MSE) is typically used as the loss function, and it is optimized using the Adam optimizer. The Adam optimizer mainly optimizes the weight matrix and bias terms to minimize the loss function (MSE). By adaptively adjusting the learning rate of each parameter, the model exhibits good convergence and robustness on the prediction task and dataset.

[0060] Monte Carlo uncertainty quantification method: The Monte Carlo Dropout (MC Dropout) used in this invention aims to estimate model uncertainty using the Monte Carlo method. It simulates Bayesian inference by repeatedly dropping out data during the prediction process to obtain an estimate of the model's uncertainty. This is particularly useful in deep learning models for estimating confidence intervals for model predictions. Dropout is a regularization technique used in this invention to prevent overfitting in neural networks. During training, Dropout randomly "drops out" neurons, setting the output of some neurons to 0 with a certain probability, forcing the network to not depend on any particular neuron, thereby improving the model's generalization ability.

[0061] Generally, Dropout is only used during training. However, in MC Dropout of this invention, Dropout is also retained during inference, which allows the model to perform Monte Carlo sampling, estimating the variance of the predictions through multiple samplings. During training, maximum likelihood estimation or maximum a posteriori estimation is typically used to find a set of optimal parameter values.

[0062] For input x, to achieve the model's prediction and its uncertainty quantification, T forward propagations can be performed, each time applying Dropout to different parts of the network. Let the neural network model be... ,in, For the output of the model, Let be the weights of the network. Then, the prediction mean and variance of MC Dropout can be calculated using the following formula: , , in, This is the mean of the prediction results obtained through n samplings. The variance of the prediction results obtained through n samplings is... This is the effective parameter configuration for the t-th sampling.

[0063] To further quantify the uncertainty of the model's predictions, calculating the prediction range is a crucial step. Assume the predicted value obtained from T sampling iterations is... Based on the distribution of predicted values, the upper and lower limits of the prediction interval for a confidence level of α are: , , in, It is the lower limit of the prediction interval. It is the upper limit of the prediction interval. It is a set of predicted values ​​obtained through multiple MC Dropout samplings, where Percentile means finding a given percentage of the predicted values.

[0064] Data augmentation methods:

[0065] Data augmentation methods primarily increase the diversity of training data through noise injection. Specifically, at the beginning of each training epoch, a certain amount of Gaussian noise is added to the input dataset (feature matrix). This technique helps the model learn better and perform more robustly on unknown data. Noise injection is a technique that increases the diversity of training data by adding random perturbations to the input data. Its basic principle is to simulate the uncertainty or variation that may exist in the input data, helping the model become more robust, especially when the input data contains noise or incomplete information. Noise injection can improve the model's tolerance to noise, perturbations, and various small variations, reducing the risk of overfitting. Assuming the input layer of the prediction model contains... The characteristic, noise injection, can be represented as: , in, The noise is sampled from a Gaussian distribution and added to each data point to simulate data perturbation. To control the intensity of noise, Features after noise injection.

[0066] By adding noise, the model can adapt to perturbations in the input data, improving its robustness to unknown data and making the training samples more diverse. This helps avoid overfitting the model to the training data, thereby improving the model's performance on the test set. At the same time, increasing the diversity of samples effectively expands the dataset, providing more training samples. Noise enhancement makes the data features learned by the model more universal, avoiding dependence on specific samples.

[0067] Hyperparameter optimization algorithm: This invention primarily utilizes Bayesian optimization of hyperparameters. Bayesian optimization (BO) is a sequential design strategy for finding the optimal parameters of a black-box function, suitable for evaluating functions that are costly or computationally complex. It combines Bayesian inference and probabilistic modeling, guiding the search process by constructing a probabilistic model of the objective function, thus exploring the hyperparameter space more efficiently. The core of Bayesian optimization lies in using a Gaussian process (GP) or other probabilistic models as surrogate models to approximate the unknown objective function. GP provides a natural way to express the uncertainty about the shape of the objective function and can predict the objective value and its variance at any input point. As more observational data is added, GP continuously updates its beliefs, gradually approximating the true objective function.

[0068] Given training data and the corresponding output Gaussian processes assume the objective function is... It comes from a multivariate normal distribution: , in, It is the mean function. It is the covariance function. For any test point The predicted distribution is: , , , Where K is the covariance matrix calculated from the covariance function. It is the observation noise variance, where I is the identity matrix. To predict the mean, To predict variance.

[0069] For the minimization problem, the expected improvement (EI) can be expressed as: , in, This is the best observed function value. When the predicted distribution is normally distributed, EI can be calculated using an analytical formula: , , in, , These are the cumulative distribution function and probability density function of the standard normal distribution, respectively, and Z is the variable for calculating the standardized expected improvement (EI).

[0070] These formulas are used to guide the selection of hyperparameters in the Bayesian optimization process, ensuring that a solution close to the global optimum is found within a finite number of iterations.

[0071] III. Testing Process

[0072] like Figure 3 As shown, the test process of the tire force prediction method of the present invention is as follows: Based on simulation data, after data processing, a dataset for tire force prediction is obtained. The input features used include not only basic time-domain features and frequency-domain features, but also entropy features and dimensionless features after feature filtering. Using the corresponding feature calculation formula, a dataset of triaxial acceleration features of 78 working conditions is obtained. Then, the dataset is divided, and the 15 test working conditions selected are shown in Table 2. These are the selected test samples for the tire force prediction model, which fully consider the uniformity of data distribution and take into account the data breadth for training the prediction model.

[0073] Table 2 Test Samples for Tire Force Prediction Model Wheel speed (km / h) Wear (mm) Tire pressure (MPa) longitudinal slip Side slip angle Load (N) 60 0 0.23 5% 4° 4000 80 0 0.25 5% 2° 4000 80 0 0.25 3% 2° 4500 80 0 0.25 3% 4° 5000 80 0 0.25 7% 4° 5500 60 2.5 0.23 5% 4° 4000 80 2.5 0.25 5% 2° 4000 80 2.5 0.25 5% 2° 4500 80 2.5 0.25 3% 4° 5000 80 2.5 0.25 7% 4° 5500 60 5 0.23 9% 6° 4000 80 5 0.25 1% 6° 4500 80 5 0.25 3% 2° 4500 80 5 0.25 5% 2° 4500 80 5 0.25 3% 0° 4500

[0074] like Figure 3 The diagram illustrates the main testing process. After reading the dataset, 103 input features are selected, and the input data undergoes table transformation. The processed data is then input into the prediction structure, which trains the model and its parameter configuration. Hyperparameters are then optimized using Bayesian methods. The hyperparameter search space range is as follows: the number of hidden layer neurons ranges from 64 to 256; the learning rate is 0.001 to 0.1; the training batch size is 50 to 200; the number of hidden layers is 2 to 4; and the Dropout ratio is 0 to 0.5. In each iteration, the next set of hyperparameters is selected based on the current surrogate model, and cross-validation is used to evaluate performance. After optimization, the final prediction model is retrained based on the optimal hyperparameter combination, providing the predicted tire force value and prediction interval, along with corresponding prediction result evaluation metrics. The evaluation metrics primarily use Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and coverage. RMSE and MAPE primarily measure the difference between the predicted point value and the true value, while coverage primarily measures the coverage of the true value by the prediction interval. The formula for calculating MAPE is as follows: , In the formula, n is the number of data points. It is the true value of the i-th data point. It is the predicted value of the i-th data point.

[0075] IV. Analysis of Implementation Results:

[0076] The tire force prediction model, trained on a dataset of uncertain operating conditions, was tested using 15 sets of sample operating condition data to evaluate its predictive performance. Figure 4 The image shows the predicted vertical force of the tire. Figure 5 These are the prediction results for the longitudinal force of the tire. The figures show both the actual and predicted values ​​of the tire force, as well as the prediction range for the corresponding tire force prediction uncertainty quantification.

[0077] The specific predictive performance evaluation indicators are shown in Table 3. The average absolute percentage error of the predicted tire force point values ​​is within 4.5%, which is lower than the average absolute percentage error of existing prediction methods based on convolutional neural networks. The root mean square error of the predicted tire force point values ​​is less than 100N, which is also lower than the error of 830N of the known prediction methods. The average coverage of the predicted tire force range is about 93.34%, which can achieve a high coverage rate. The results show that the prediction model can achieve good prediction performance overall.

[0078] Table 3 Results of Tire Force Prediction Evaluation Indicators Tire force RMSE (N) MAPE Coverage vertical force 83.57 1.54% 100% Longitudinal force 92.82 4.20% 86.67%

[0079] The prediction effect of the prediction method is evaluated by assessment indicators and compared with the indicators of existing prediction methods. The results show that the tire force prediction model established in this invention has a better overall prediction effect.

[0080] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for tire force sensing under uncertain conditions, characterized in that... Includes the following steps: S1, Collect triaxial acceleration information at the midpoint of the inner surface of the tire inner tube, the triaxial acceleration information includes: radial acceleration, circumferential acceleration and lateral acceleration at the midpoint of the inner surface of the tire inner tube; S2, preprocess the triaxial acceleration information collected in step S2, the preprocessing includes coordinate transformation, filtering and cutting; S3. Extract time-frequency domain features, entropy information features, and dimensionless features from the preprocessed triaxial acceleration information; the entropy information features include power spectral entropy, singular spectral entropy, energy entropy, approximate entropy, sample entropy, fuzzy entropy, envelope entropy, and scatter entropy; the dimensionless features include kurtosis, skewness, waveform factor, peak factor, impulse factor, and margin factor; the time-frequency domain features include time-domain features and frequency-domain features, the time-domain features include local peak value, peak difference, peak-time difference, local mean, local variance, and signal period; the frequency-domain features include centroid frequency, amplitude skewness, and maximum amplitude value. S4, pair the extracted features of tire force and triaxial acceleration information as a sample set, and divide the sample set into a training set and a test set; S5 uses a multilayer perceptron architecture (MLP) and is based on the Monte Carlo neural network Dropout to build a tire force prediction model. S6. The tire force prediction model is trained and the network parameters are optimized using the training set obtained in step S4 to obtain the optimized tire force prediction model.

2. The tire force sensing method under uncertain conditions according to claim 1, characterized in that: The tire force prediction model described in step S5 adopts a multilayer perceptron (MLP) architecture combined with a Monte Carlo neural network, which includes, in sequence: an input layer, several pairs of hidden-dropout layers, an output layer, and an MC Dropout layer. The hidden layers apply fully connected layers and the ReLU activation function. The training and computation process of the MLP is as follows: ， in, , This is the weight matrix. , For bias terms, Let X be the input feature and the ReLU activation function. This is for predicting the output.

3. The tire force sensing method under uncertain conditions according to claim 2, characterized in that: The number of hidden layer-dropout layers is 2-4 pairs; the number of neurons in the hidden layer is 64-256, the learning rate is 0.001-0.1, the training batch size is 50-200, and the dropout ratio is 0-0.

5.

4. The tire force sensing method under uncertain conditions according to claim 2, characterized in that: The entropy information features mentioned in step S3 are calculated as follows: (1) Power spectral entropy PSE, calculated by the following formula, ， In the formula, P j is the normalized power spectral density of the j-th frequency component, and N is the data length; , This represents the i-th data z in the original data Z. i The frequency domain obtained by performing a Fourier transform. This represents the nth frequency component, the original data. ; (2) Singular spectral entropy (SSE) is calculated using the following formula: ， ， In the formula, S k It is the k-th normalized singular value, where N is the data length; normalization factor Represents all samples z i The norm sum of squares directly reflects the influence of the original data; The singular value square is obtained by decomposing the matrix of the original data Z using SVD, which implicitly contains structural information about the data distribution. (3) Energy entropy EE, calculated by the following formula, ， ， Among them, E i Z is the normalized energy of the i-th sample, N is the data length, and z is the normalized energy of the i-th sample. i It is the i-th sample data; (4) The approximate entropy ApEn is calculated using the following formula: ， ， in, This represents the logarithmic mean of the similarity frequencies of patterns of length m at a similarity tolerance r, used to characterize the repetitive patterns of local structures in a time series; m is the pattern length, and r is the similarity tolerance. This is an indicator function; it returns 1 when the condition is met and 0 otherwise. (Original data) It is time series data; (5) Sample entropy SampEn, calculated using the following formula: ， Where A is the distance and The pattern for quantity, B is to satisfy The number of pattern pairs, r is the similarity tolerance, m is the pattern length, and the original data. It is time series data; (6) Fuzzy entropy (FuzzyEn) is calculated using the following formula: ， ， Where 𝑚 is the pattern length, r is the similarity tolerance, and N is the data length, representing the original data. It is a time series signal; (7) Envelope entropy EnvEn, calculated by the following formula, ， In the formula, ai represents the i-th data z of the original data Z. i The envelope signal obtained by Hilbert transforming a time-domain signal. The analytic signal after the Hilbert transform is represented by its magnitude as the envelope; The power spectral density of the envelope signal difference is represented by the power spectral density obtained by performing Fourier transform (FET) spectrum analysis on the envelope signal. The normalized value of the difference power spectral density of the envelope signal is represented by M, where M represents the total number of frequency components. (8) Dispersion entropy DispEn, calculated using the following formula, ， In the formula, p n Let C be the probability of the nth pattern occurring. n It is the number of times the nth mode appears in the signal, T is the total number of all observed modes, and K is the number of discrete symbols; Represents the time-domain signal z i The normalized value; It is a local minimum value to prevent the denominator from being zero; d i P represents the discrete symbol corresponding to each sample point; （j） It is d i The constructed discrete pattern.

5. The tire force sensing method under uncertain conditions according to claim 2, characterized in that: It also includes step S7, which involves testing the optimized tire force prediction model using a test set.

6. The tire force sensing method under uncertain conditions according to claim 2, characterized in that: The cutting process described in step S2 includes cutting the triaxial acceleration information according to the tire rolling cycle.

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