Wheel-soil model small sample stage-by-stage bayesian inversion method

Abstract

The wheel-soil model small sample phased Bayesian inversion method solves the problems of serious parameter coupling, poor distinguishability and difficult quantification of uncertainty in the wheel-soil model parameter inversion process under small sample conditions, and belongs to the field of planetary exploration robot ground mechanics parameter identification. The model distinguishability is improved through parameter reconstruction, and the inversion process is divided into multiple stages according to the slip working conditions: first, the pressure-related parameters are estimated using low-slip data, then the shear-related parameters are estimated using high-slip data, and the uncertainty is propagated across stages. Through the above mechanism, the influence of parameter coupling can be effectively reduced under small sample conditions, and the parameter estimation results with physical interpretability and containing confidence information can be achieved, thereby providing reliable support for the motion control and environment adaptation of the exploration vehicle.

Description

Technical Field

[0001] This invention relates to a small-sample, staged Bayesian inversion method for wheel-soil models, belonging to the field of ground mechanical parameter identification for planetary exploration robots. Background Technology

[0002] As deep space exploration missions continue to advance, the assessment and control of motion performance of mobile robots on extraterrestrial surfaces has become a crucial foundational technology in the aerospace field. In the soft, deformable environment of celestial surfaces, rigid wheels remain the dominant moving components, their performance influenced by complex wheel-soil interaction mechanisms. Wheel sinking during movement alters the contact geometry and increases drag, while traction and driving torque primarily originate from soil shear deformation. Therefore, accurately understanding and predicting wheel-soil interaction processes is of great significance for improving the rovers' ability to assess mobility, adjust skidding, and ensure path planning safety under unknown terrain conditions.

[0003] Existing research typically establishes wheel-soil models based on ground mechanics theory, describing wheel-soil contact behavior through pressure-settlement relationships and shear stress laws, and these models are widely used in robot dynamics modeling and control. To ensure the effectiveness of these models in practical engineering applications, accurate acquisition of soil mechanical parameters is essential. Currently, inversion methods for wheel-soil parameters mainly fall into two categories: deterministic estimation methods and probabilistic estimation methods. Deterministic methods typically employ least squares, Newton's iteration method, robust extended Kalman filtering, and data-driven methods based on neural networks to perform point estimation of parameters. Probabilistic estimation methods, on the other hand, introduce Bayesian inference theory, treating parameters as random variables and obtaining the posterior distribution of parameters through Markov chain Monte Carlo sampling, particle filtering, and other techniques, thereby revealing the statistical dependencies and uncertainty characteristics between parameters.

[0004] However, in actual planetary exploration or soil trough experiments, due to high testing costs and limited operating conditions, the available data are usually small samples. Under these conditions, the multi-parameter coupling characteristics of the classical wheel-soil model can easily lead to unidentifiable parameter inversion problems, with different parameter combinations potentially producing similar load or torque responses. Furthermore, different slip conditions exhibit significantly different parameter sensitivities. Using single-stage joint inversion can easily lead to non-physical compensation between parameters, obscuring true physical information. In addition, traditional methods are mostly point estimates, lacking the quantification of parameter uncertainties, making it difficult to meet the model reliability requirements of autonomous decision-making. Summary of the Invention

[0005] To address the problems of severe parameter coupling, poor identifiability, and difficulty in quantifying uncertainties in the parameter inversion process of wheel-soil model under small sample conditions, this invention provides a staged Bayesian inversion method for wheel-soil model with small samples.

[0006] The present invention provides a small-sample, staged Bayesian inversion method for wheel-soil models, comprising:

[0007] S1. Establish a forward model of wheel-soil contact mechanics to describe the deterministic forward mapping from soil parameters, wheel settlement and shear displacement to vertical load and driving torque.

[0008] S2. Linearly combine the coupled parameters in the forward model into identifiable parameters, transform the bounded parameters into identifiable parameters through unbounded transformation, and then combine them with other identifiable parameters in the forward model to form a recombined identifiable parameter vector. The identifiable parameter vector includes a pressure parameter sub-vector and a shear parameter sub-vector.

[0009] S3. Conduct wheel-soil trough experiments according to different slip ratios to obtain experimental datasets. Divide the experimental datasets into low slip subsets and high slip subsets according to the slip ratio.

[0010] S4. In the low-slip phase, Bayesian inversion is performed on the pressure parameter sub-vector using the low-slip subset to obtain the posterior sample set of the pressure parameter sub-vector.

[0011] S5. In the high-slip stage, the high-slip subset is used to perform Bayesian inversion on the shear parameter sub-vector, and the posterior sample set of the pressure parameter sub-vector obtained in S4 is used as the source of uncertainty for posterior propagation to obtain a complete posterior sample set containing pressure parameters and shear parameters.

[0012] S6. Based on the complete posterior sample set, output the posterior distribution of each soil mechanical parameter and the quantification result of its uncertainty.

[0013] Preferably, the parameters of the forward model include at least the soil cohesive deformation modulus. Friction deformation modulus Subsidence Index Soil cohesion soil internal friction angle and shear modulus ;

[0014] The coupled parameters in the forward model are linearly combined into identifiable parameters. for:

[0015]

[0016] These are the coefficients of the linear combination;

[0017] Bounded parameters are transformed into recognizable parameters through an unbounded transformation. for:

[0018]

[0019] Pressure parameter subvector is ;

[0020] The shearing parameter subvector is .

[0021] Preferably, S3 includes:

[0022] exist Groups with different slip ratios Experiments were conducted under various conditions, and the settlement amount under each working condition was recorded. Vertical load and driving torque Construct the experimental dataset:

[0023]

[0024] Among them, input Output data

[0025] Calculate the normalized sensitivity coefficient based on the identifiable parameter vector;

[0026] Calculate the normalized sensitivity coefficients of each parameter in the identifiable parameter vector to vertical load and driving torque under different working conditions, and select the slip ratio threshold based on the sensitivity difference between pressure and shear parameters. ;

[0027] Slip rate in the experimental dataset The samples were classified into the low-slip subset. ;

[0028] Slip rate in the experimental dataset The samples were classified into the high-slip subset. .

[0029] Preferably, S4 includes:

[0030] Construct the vertical load likelihood function in the low-slip subset, and obtain the posterior distribution of the pressure parameters based on the likelihood function;

[0031] A non-rotating sampler (NUTS) is used to extract samples from the posterior distribution of the pressure parameters to obtain the posterior sample set of the shear pressure parameter sub-vectors.

[0032] Preferably, the vertical load likelihood function is:

[0033]

[0034] in, For the forward model to predict vertical loads, For pressure parameter subvectors, For low-glide subsets, For vertical loads, The noise standard deviation is calibrated for the vertical load; the posterior distribution of the pressure parameters is:

[0035]

[0036] This represents the number of samples in the posterior sample set of the pressure parameter subvectors. This represents the prior distribution of the pressure parameter.

[0037] As a preferred embodiment, S5 includes:

[0038] Construct the likelihood function of the driving torque in the high slip subset;

[0039] The posterior sample set of the pressure parameter subvectors obtained in S4 is used as a representation of the uncertainty of the pressure parameters, and the posterior distribution of the shear parameters is calculated based on the constructed likelihood function.

[0040] A non-rotating sampler (NUTS) is used to extract samples from the posterior distribution of the shearing parameters to obtain the posterior sample set of the shearing parameter sub-vectors.

[0041] Calculate the conditional weight of each pressure parameter subvector posterior sample under the corresponding shear parameter subvector posterior sample. The conditional weight is equal to the high slip likelihood value of the constructed driving torque likelihood function under the combination of the pressure parameter subvector posterior sample and the corresponding shear parameter subvector posterior sample. Randomly select a pressure parameter subvector posterior sample according to the normalized conditional weight and pair it with the corresponding shear parameter subvector posterior sample. Combine the paired samples into a complete posterior sample. All paired complete posterior samples form a complete posterior sample set.

[0042] Preferably, the likelihood function of the driving torque is:

[0043]

[0044] in, For the drive torque prediction function, To calibrate the noise standard deviation of the torque sensor, For driving torque;

[0045] The posterior distribution of the shear parameter is:

[0046]

[0047] This represents the prior distribution of the shear parameters;

[0048] The high slip likelihood value of the constructed driving torque likelihood function under the combination of the posterior samples of the pressure parameter subvector and the corresponding posterior samples of the shear parameter subvector;

[0049] Let be the number of samples in the posterior sample set of the pressure parameter subvectors. Let be the number of samples in the posterior sample set of the shearing parameter subvectors. .

[0050] The beneficial effects of this invention are as follows: This application presents a staged Bayesian inversion and uncertainty quantification method for wheel-soil mechanics models with identifiable constraints. It improves model identifiability through parameter reconstruction and divides the inversion process into multiple stages based on slip conditions: first, pressure-related parameters are estimated using low-slip data; second, shear-related parameters are estimated using high-slip data; and third, uncertainty propagation across stages is achieved. Through this mechanism, the influence of parameter coupling can be effectively reduced under small sample conditions, resulting in parameter estimation results with physical interpretability and confidence information, thus providing reliable support for the motion control and environmental adaptation of the exploration vehicle. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the method described in this application. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0055] This implementation first establishes a wheel-soil contact mechanics model. By integrating the contact arcs of normal and tangential stresses, a deterministic positive mapping is established from soil parameters, wheel settlement and slip ratio to vertical load and driving torque. To address the parameter coupling and structural unidentification issues in the model, the original parameters are reorganized, and a combined pressure modulus and internal friction angle transformation are introduced to construct an identifiable parameter vector.

[0056] Furthermore, based on the influence characteristics of slip ratio on the wheel-soil interaction mechanism, the working conditions are divided into low-slip and high-slip stages, clarifying the sensitivity differences of pressure-related and shear-related parameters under different working conditions, thus providing a basis for staged inversion. On this basis, using small-sample experimental data, pressure parameter sub-vectors are inverted based on vertical load in the low-slip stage, and NUTS sampling is used to obtain posterior samples; in the high-slip stage, the uncertainty of pressure parameters is propagated to the shear parameter inversion process through posterior propagation, constructing a complete full posterior distribution.

[0057] Finally, posterior predictions are performed using the complete posterior sample set to quantify the uncertainty of the prediction results. The inversion results are then evaluated using Markov chain convergence diagnostics and residual analysis to obtain parameter estimation results that are physically interpretable and contain confidence information. Specifically, the small-sample, staged Bayesian inversion method for the wheel-soil model in this embodiment includes:

[0058] Step 1: Establish a forward model of wheel-soil contact mechanics to describe the deterministic forward mapping from soil parameters, wheel settlement and shear displacement to vertical load and driving torque;

[0059] A deterministic forward mapping model of a rigid wheel traveling on soft terrain is constructed, dividing the contact arc between the wheel and the soil into an entry zone and an exit zone, with the normal and tangential stress distributions as follows:

[0060] (1)

[0061] (2)

[0062] in, Indicates the wheel radius. Indicates the width of the wheel. Indicates soil cohesion. Indicates the cohesive deformation modulus of soil. Indicates the frictional deformation modulus. Indicates the subsidence index. Indicates the contact entry angle. Indicates the angle of maximum stress. Indicates the contact exit angle. Indicates the internal friction angle of the soil. Let be the angle of any point on the contact arc with reference to the vertical line. Indicates shear modulus. This represents the cumulative shear displacement. When... To enter the area, This is for exiting the zone.

[0063] The macroscopic mechanical response obtained by integration is:

[0064] (3)

[0065] (4)

[0066] in, Indicates vertical load. This indicates the driving torque.

[0067] Step 2: Linearly combine the coupled parameters in the forward model into identifiable parameters, transform the bounded parameters into identifiable parameters through unbounded transformation, and then combine them with other identifiable parameters in the forward model to form a recombined identifiable parameter vector. This identifiable parameter vector includes a pressure parameter sub-vector and a shear parameter sub-vector.

[0068] For the six-parameter vector in the model built in step one The structural non-identifiability problem existing under the condition of fixed wheel width is addressed by parameter reorganization.

[0069] Due to wheel width Keep constant during the experiment. and Since the normal stress expression only appears in linear combination form, a combination parameter is introduced:

[0070] (5)

[0071] To avoid periodic boundary problems, the internal friction angle is... Transform into unbounded parameters:

[0072] (6)

[0073] The recombined recognizable parameter vector is:

[0074] (7)

[0075] The physical interpretation of each model parameter after recombination and its role in the Bayesian network are shown in the table below.

[0076] Table 1. Physical Interpretation of Parameters and Their Role in Bayesian Networks

[0077]

[0078] Step 3: Conduct wheel-soil trough experiments according to different slip ratios to obtain experimental datasets. Divide the experimental datasets into low slip subsets and high slip subsets according to the slip ratio.

[0079] To verify the identifiability of the recombined parameters, the normalized sensitivity coefficient was calculated:

[0080] (8)

[0081] in, , for The amount.

[0082] Based on the sensitivity analysis results, the slip ratio threshold was selected. The actual working conditions are divided into low-slip and high-slip conditions. In the low-slip condition ( Under vertical load right , Highly sensitive, and to , , Low sensitivity; in high slip conditions ( Under these conditions, the driving torque right , , Highly sensitive, and to The sensitivity is low, and the specific sensitivity is shown in Table 2. This decoupling characteristic provides a theoretical basis for staged inversion.

[0083] Table 2. Mechanism-dependent parameter sensitivity and its impact on staged Bayesian inversion.

[0084]

[0085] A small sample dataset was obtained using a single-wheel earth trough experimental platform or simulation experiments. The wheel radius was set. ,width For a fixed value, in Groups with different slip ratios Experiments were conducted under various conditions, and the settlement amount under each working condition was recorded. Vertical load and driving torque Constructing the experimental dataset:

[0086] (9)

[0087] in, , .

[0088] The dataset was divided into low-slip subsets based on the slip ratio. With high-glide subsets .

[0089] (10)

[0090] (11)

[0091] Step 4: In the low-slip phase, Bayesian inversion is performed on the pressure parameter sub-vector using the low-slip subset to obtain the posterior sample set of the pressure parameter sub-vector;

[0092] In low-glide subsets Above, using vertical load Inverted pressure parameter subvector .

[0093] The likelihood function is based on the measurement error of the vertical load:

[0094] (12)

[0095] in, This is the prediction of vertical load by the forward model.

[0096] According to Bayes' theorem, the posterior distribution is:

[0097] (13)

[0098] To prevent the simulation from encountering physically impossible boundaries, bijective, strictly differentiable mapping functions can be used to map bounded physical parameters. Projecting onto unconstrained Euclidean coordinate space:

[0099] (14)

[0100] The posterior was sampled using NUTS to obtain posterior samples The specific process is as follows:

[0101] Determine the prior Configure the non-rotating sampler (NUTS).

[0102] Definition phase A parameter vector ;

[0103] According to equation (12), the likelihood function of the vertical load in stage A is obtained:

[0104] The posterior distribution of the pressure parameters in stage A is defined according to equation (13);

[0105] If the pressure parameters have physical boundaries, the constrained parameters are converted to the unconstrained space according to equation (14), and then mapped back to the physical space after sampling.

[0106] Samples are drawn from the posterior distribution using a non-retrograde sampler (NUTS). After convergence, the samples from each chain are merged, and the preheating iteration samples are discarded to obtain the posterior sample set of the pressure parameter subvectors.

[0107] Step 5: In the high-slip stage, Bayesian inversion is performed on the shear parameter sub-vector using the high-slip subset, and the posterior sample set of the pressure parameter sub-vector obtained in S4 is used as the source of uncertainty for posterior propagation to obtain a complete posterior sample set containing pressure parameters and shear parameters.

[0108] Phase B utilizes high-glide subsets Estimating shear parameters At the same time, the pressure parameters of stage A remain uncertain.

[0109] The likelihood function of the driving torque is:

[0110] (15)

[0111] in, For the drive torque prediction function, Calibrate the noise standard deviation for the torque sensor.

[0112] The propagation formula for the full posterior distribution is:

[0113] (16)

[0114] Simplifying it to discrete form, we get:

[0115] (17)

[0116] The posterior was sampled using NUTS to obtain posterior samples The specific algorithm is as follows:

[0117] Prior determination of drive torque And configure NUTS;

[0118] Definition phase B parameter vector ;

[0119] The likelihood function of the driving torque is defined according to equation (15);

[0120] The posterior distribution of stage B is defined according to equations (16) and (17);

[0121] If the shearing parameters have physical boundaries, the constrained parameters are transformed into the unconstrained space according to equation (14), and then mapped back to the physical space after sampling.

[0122] A non-rotating sampler (NUTS) is used to extract samples from the posterior distribution of the shearing parameters to obtain the posterior sample set of the shearing parameter sub-vectors.

[0123] Calculate the conditional weight of each pressure parameter subvector posterior sample under the corresponding shear parameter subvector posterior sample. The conditional weight is equal to the high-slip likelihood value of the constructed driving torque likelihood function under the combination of the pressure parameter subvector posterior sample and the corresponding shear parameter subvector posterior sample. Randomly select a pressure parameter subvector posterior sample according to the normalized conditional weight and pair it with the corresponding shear parameter subvector posterior sample. The paired samples are combined into a complete posterior sample, and all paired complete posterior samples are... Form a complete posterior sample set .

[0124] Step 6: Output the posterior distribution of each soil mechanical parameter and its uncertainty quantification results based on the complete posterior sample set.

[0125] Using the complete posterior sample set generated in step 5 It can input any new working condition. The process involves making model predictions and quantifying the uncertainty of the prediction results. This process is called the posterior prediction distribution.

[0126] For a new input Its posterior prediction distribution is defined as the expected distribution of the model output for all possible parameter values. Its Monte Carlo approximation calculation method is as follows:

[0127] First, calculate the posterior prediction mean as the best estimate of the model output:

[0128] (18)

[0129] in, It is the forward model established in step one. It comes from the complete posterior sample set. The One sample. This estimate. By combining all possible parameter combinations, the most reliable prediction value is given.

[0130] Secondly, the posterior prediction covariance is calculated to quantify the uncertainty of the prediction. This uncertainty consists of two parts: the posterior uncertainty of the parameters themselves, and the uncertainty of the model's observation noise. The calculation formula is as follows:

[0131] (19)

[0132] in, It is the deviation between the predicted value and the predicted mean of a single parameter sample; This is the observation noise covariance matrix defined in step five. From this, the marginal prediction variances of the vertical load and driving torque can be obtained:

[0133] (20)

[0134] Through the above calculations, the predicted values ​​of load and torque under any working condition and their confidence intervals can be given, thus achieving a complete quantification of the uncertainty of model prediction.

[0135] Step Nine: Diagnosis and Evaluation.

[0136] To ensure the reliability of the inversion results and the effectiveness of the method, the entire inversion process and results are diagnosed and evaluated using methods such as Markov chain convergence diagnosis, standardized residual analysis, and Fisher information matrix.

[0137] This application solves the problem of unidentifiable parameters caused by multi-parameter coupling in the wheel-soil interaction model by reconfiguring parameters and imitating constraints, making the inversion problem mathematically unique and avoiding the ambiguity of different parameter combinations producing the same response. Simultaneously, based on sensitivity analysis, the working conditions are divided into low-slip and high-slip stages, enabling staged Bayesian inversion of pressure and shear parameters. This fully utilizes the differentiated excitation of parameters under various working conditions, significantly improving parameter identification accuracy under small sample conditions.

[0138] Furthermore, to address the issue that small sample data is insufficient to support traditional joint inversion, this application inverts pressure-related parameters during the low slip phase and, during the high slip phase, transmits the uncertainty of pressure parameters to the shear parameter inversion process through posterior propagation, thus achieving complete quantification of uncertainty throughout the entire process. The final output is parameter estimation results containing confidence information, providing a reliable and credible basis for the motion control and environmental adaptation of the probe.

[0139] Furthermore, this application calculates the predicted values ​​of load and torque under arbitrary working conditions and their confidence intervals through posterior prediction distribution, and evaluates the inversion results by combining Markov chain convergence diagnosis, standardized residual analysis and other methods, forming a complete diagnostic evaluation system. This effectively ensures the reliability of the inversion results and the engineering applicability of the method, and provides key support for the mobility assessment and autonomous decision-making of extraterrestrial star surface mobile robots under unknown terrain conditions.

[0140] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A small-sample, staged Bayesian inversion method for wheel-soil models, characterized in that, include: S1. Establish a forward model of wheel-soil contact mechanics to describe the deterministic forward mapping from soil parameters, wheel settlement and shear displacement to vertical load and driving torque. S2. Linearly combine the coupled parameters in the forward model into identifiable parameters, transform the bounded parameters into identifiable parameters through unbounded transformation, and then combine them with other identifiable parameters in the forward model to form a recombined identifiable parameter vector. The identifiable parameter vector includes a pressure parameter sub-vector and a shear parameter sub-vector. S3. Conduct wheel-soil trough experiments according to different slip ratios to obtain experimental datasets. Divide the experimental datasets into low slip subsets and high slip subsets according to the slip ratio. S4. In the low-slip phase, Bayesian inversion is performed on the pressure parameter sub-vector using the low-slip subset to obtain the posterior sample set of the pressure parameter sub-vector. S5. In the high-slip stage, the high-slip subset is used to perform Bayesian inversion on the shear parameter sub-vector, and the posterior sample set of the pressure parameter sub-vector obtained in S4 is used as the source of uncertainty for posterior propagation to obtain a complete posterior sample set containing pressure parameters and shear parameters. S6. Based on the complete posterior sample set, output the posterior distribution of each soil mechanical parameter and the quantification result of its uncertainty.

2. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 1, characterized in that, The parameters of the forward model include at least the soil cohesive deformation modulus. Friction deformation modulus Subsidence Index Soil cohesion soil internal friction angle and shear modulus ; The coupled parameters in the forward model are linearly combined into identifiable parameters. for: ； These are the coefficients of the linear combination; Bounded parameters are transformed into recognizable parameters through an unbounded transformation. for: ； Pressure parameter subvector is ; The shearing parameter subvector is .

3. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 2, characterized in that, S3 include: exist Groups with different slip ratios Experiments were conducted under various conditions, and the settlement amount under each working condition was recorded. Vertical load and driving torque Construct the experimental dataset: ； Among them, input Output data ; Calculate the normalized sensitivity coefficient based on the identifiable parameter vector; Calculate the normalized sensitivity coefficients of each parameter in the identifiable parameter vector to vertical load and driving torque under different working conditions, and select the slip ratio threshold based on the sensitivity difference between pressure and shear parameters. ; Slip rate in the experimental dataset The samples were classified into the low-slip subset. ; Slip rate in the experimental dataset The samples were classified into the high-slip subset. .

4. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 3, characterized in that, S4 include: Construct the vertical load likelihood function in the low-slip subset, and obtain the posterior distribution of the pressure parameters based on the likelihood function; A non-rotating sampler (NUTS) is used to extract samples from the posterior distribution of the pressure parameters to obtain the posterior sample set of the shear pressure parameter sub-vectors.

5. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 4, characterized in that, The likelihood function for the vertical load is: ； in, This is the prediction of vertical load by the forward model; For pressure parameter subvectors, The noise standard deviation is calibrated for vertical loads; The posterior distribution of the pressure parameter is: ； This represents the number of samples in the posterior sample set of the pressure parameter subvectors; This represents the prior distribution of the pressure parameter.

6. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 3, characterized in that, S5 include: Construct the likelihood function of the driving torque in the high slip subset; The posterior sample set of the pressure parameter subvectors obtained in S4 is used as a representation of the uncertainty of the pressure parameters, and the posterior distribution of the shear parameters is calculated based on the constructed likelihood function. A non-rotating sampler (NUTS) is used to extract samples from the posterior distribution of the shearing parameters to obtain the posterior sample set of the shearing parameter sub-vectors. Calculate the conditional weight of each pressure parameter subvector posterior sample under the corresponding shear parameter subvector posterior sample. The conditional weight is equal to the high slip likelihood value of the constructed driving torque likelihood function under the combination of the pressure parameter subvector posterior sample and the corresponding shear parameter subvector posterior sample. Randomly select a pressure parameter subvector posterior sample according to the normalized conditional weight and pair it with the corresponding shear parameter subvector posterior sample. Combine the paired samples into a complete posterior sample. All paired complete posterior samples form a complete posterior sample set.

7. The small-sample, staged Bayesian inversion method for the wheel-soil model according to claim 6, characterized in that, The likelihood function of the driving torque is: ； in, This is the drive torque prediction function; Calibrate the noise standard deviation for the torque sensor; The posterior distribution of the shear parameter is: ； This represents the prior distribution of the shear parameters; The high slip likelihood value of the constructed driving torque likelihood function under the combination of the posterior samples of the pressure parameter subvector and the corresponding posterior samples of the shear parameter subvector; The number of samples in the posterior sample set of the pressure parameter subvectors; The number of samples in the posterior sample set of the shearing parameter subvectors; 。 8. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the small-sample, staged Bayesian inversion method for the wheel-soil model as described in any one of claims 1 to 7.

9. A staged Bayesian inversion device for small samples of a wheel-soil model, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the small-sample, staged Bayesian inversion method for the wheel-soil model as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the small-sample, staged Bayesian inversion method for the wheel-soil model as described in any one of claims 1 to 7.

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