A Multidimensional Force Sensor Strain Prediction Method Based on Structured Hard Constraint CM-PINN

Abstract

This invention provides a strain prediction method for multidimensional force sensors based on structured hard-constraint CM-PINN. This method relies on a multidimensional force sensor strain prediction model based on structured hard-constraint CM-PINN. Addressing the practical needs of multidimensional force sensors for multi-type load branch modeling, geometric feature encoding, orthogonal projection hard embedding of strain constraint matrices, and linear superposition prediction of multiple loads, this method constructs a customized CM-PINN architecture with dedicated load branch modeling units, geometric feature encoding units, and a core physical hard constraint layer. It abandons the traditional soft-constraint loss control mode and achieves mechanical topological structured hard constraints through B-matrix orthogonal projection, balancing data-driven high-precision fitting with strict conservation of physical mechanisms. It can quickly and accurately output multi-path strain responses under multiple working conditions without relying on large-scale finite element iterations, providing efficient and reliable mechanical solution support for multidimensional force sensor structural design, performance evaluation, and intelligent optimization.

Description

Technical Field

[0001] This invention belongs to the field of strain prediction technology for multidimensional force / torque sensors, and relates to a multidimensional force sensor strain prediction method based on structured hard constraint CM-PINN. Specifically, it relates to a method that embeds the physical laws of the equivalent compliance matrix into a neural network in a network structure hard constraint manner, and uses it for multidimensional force sensor strain prediction. Background Technology

[0002] Multidimensional force sensors are core sensing components in precision robot assembly, on-orbit control in aerospace, high-end intelligent manufacturing, and force control interaction scenarios of intelligent equipment. The accurate prediction of the strain response of their elastic structure under multi-directional force / torque composite loads is the core foundation for the forward design of sensor structures, performance calibration, decoupling algorithm development, and multi-objective size optimization.

[0003] Multidimensional force sensor elastic bodies exhibit a strong coupling and high-dimensional nonlinear mechanical mapping relationship between geometric parameters, applied loads, and surface strain. Existing strain prediction methods have significant shortcomings: analytical modeling methods based on mechanics of materials and beam theory rely heavily on structural simplifications and boundary condition assumptions, and are only applicable to regular and simple elastic bodies. When faced with complex configurations such as cross beams and composite beams, the modeling error is large, and they cannot meet the requirements of parametric and refined design. Although finite element simulation (FEA) has high computational accuracy, mesh generation and load condition iteration are time-consuming, making it difficult to support large-scale parameter traversal and intelligent optimization iteration, resulting in long engineering design cycles and high computational resource consumption.

[0004] Pure data-driven neural networks can replace finite element methods to achieve rapid strain prediction, but they still have inherent defects: model fitting is highly dependent on massive amounts of high-precision simulation samples, and the generalization ability of small sample scenarios is poor; model training only relies on data loss and does not introduce mechanical prior constraints, making it difficult to guarantee physical consistency, and abnormal prediction results that violate mechanical mechanisms are prone to occur under multi-load component coupling and linear superposition conditions; at the same time, conventional network structures lack physical hierarchy design, have weak interpretability, and cannot be embedded in the hard constraint system of sensor structure optimization.

[0005] While traditional physical information neural networks (PINNs) introduce governing equations as soft-constraint losses and incorporate physical priors to some extent, they still have significant limitations: the weights of multiple loss terms are difficult to adaptively adjust, resulting in poor training convergence stability; the physical laws are only weakly constrained by loss penalties, making it easy to deviate from the actual mechanical response during the inference and prediction stage; and they have not been structurally customized for multi-load classification of multi-dimensional force sensors, structural symmetry characteristics, and the inherent topology of strain constraint matrices, making them unsuitable for engineering characteristics such as six-dimensional force multi-branch modeling, orthogonal projection hard constraints, and linear superposition of multiple loads. Summary of the Invention

[0006] To achieve the aforementioned objectives, this invention provides a strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN. This method addresses the practical needs of multidimensional force sensors for multi-type load branch modeling, geometric feature encoding, orthogonal projection hard embedding of strain constraint matrices, and linear superposition prediction of multiple loads. It constructs a customized CM-PINN architecture with dedicated load branch modeling units, geometric feature encoding units, and a core physical hard constraint layer. It abandons the traditional soft constraint loss control mode and achieves mechanical topological structured hard constraints through B-matrix orthogonal projection, balancing data-driven high-precision fitting with strict conservation of physical mechanisms. It can quickly and accurately output multi-path strain responses under multiple working conditions without relying on large-scale finite element iterations, providing efficient and reliable mechanical solution support for multidimensional force sensor structural design, performance evaluation, and intelligent optimization.

[0007] This invention is achieved using the following technical solution:

[0008] A strain prediction method based on a multidimensional force sensor using structured hard constraint CM-PINN includes the following steps: First, constructing the data foundation required for training and optimizing the CM-PINN prediction model, including: (1) establishing a finite element simulation model; (2) setting the range of values ​​for the variables of size and load; (3) randomly generating a sufficient finite element simulation dataset within the range of variable values, and extracting sample data from the dataset, wherein the sample data includes at least geometric parameters, load input, and path strain response. Specifically:

[0009] 4 geometric parameter vectors , , , ,in, Indicates the outer diameter of the inner ring. Indicates the beam length. Indicates the beam width. This indicates the beam height.

[0010] The load input vectors are CF1, CF2, CF3, CM1, CM2, and CM3, where CF1 represents the axial force in the X direction, CF2 represents the axial force in the Y direction, CF3 represents the axial force in the Z direction, CM1 represents the torque in the X direction, CM2 represents the torque in the Y direction, and CM3 represents the torque in the Z direction.

[0011] Path strain response S1-S16: where S1 represents the strain at strain gauge position 1, S2 represents the strain at strain gauge position 2, S3 represents the strain at strain gauge position 3, S4 represents the strain at strain gauge position 4, S5 represents the strain at strain gauge position 5, S6 represents the strain at strain gauge position 6, S7 represents the strain at strain gauge position 7, S8 represents the strain at strain gauge position 8, S9 represents the strain at strain gauge position 9, S10 represents the strain at strain gauge position 10, S11 represents the strain at strain gauge position 11, S12 represents the strain at strain gauge position 12, S13 represents the strain at strain gauge position 13, S14 represents the strain at strain gauge position 14, S15 represents the strain at strain gauge position 15, and S16 represents the strain at strain gauge position 16.

[0012] In one implementation, the samples cover multiple single-load conditions and representative points in the design space to support subsequent CM-PINN modeling training and surrogate optimization evaluation.

[0013] Then, the CM-PINN neural network is trained based on the training data.

[0014] The CM-PINN neural network is used to realize uniaxial load strain prediction and equivalent compliance matrix output, and includes at least a load-specific branch modeling unit, an input normalization unit, a geometric feature encoding unit, a core physical constraint layer, an inverse normalization unit, and an output unit.

[0015] The CM-PINN neural network specifically includes:

[0016] (1) Load-specific branch modeling unit: The load-specific branch modeling unit constructs branch models for six types of loads CF1, CF2, CF3, CM1, CM2 and CM3, including CF1 / CF2 shared model, CM1 / CM2 shared model, CF3 independent model and CM3 independent model; through symmetrical channel joint training and parameter sharing, the sample utilization efficiency is improved and the model complexity is reduced.

[0017] (2) Input standardized unit:

[0018] The input standardization unit is used to perform geometric standardization and load standardization on the 4D geometric parameters and the 6D load input vector, respectively, to obtain standardized geometric parameters and standardized load vectors. Standardization is performed on the 16D path strain response for training.

[0019] (3) Geometric feature coding unit:

[0020] The geometric feature encoding unit further expands the standardized geometric parameters into 13-dimensional engineering features through feature engineering to construct a high-dimensional interpretable feature space related to structural stiffness and cross-sectional properties.

[0021] The original geometric input contains four structural parameters, which are extended to 13 dimensions through feature engineering, resulting in 13-dimensional engineered features. By introducing derived features directly related to elastic stiffness, the learning burden on the network can be reduced, while improving physical interpretability. The 13-dimensional engineered features are shown in Table 1.

[0022] Table 1

[0023]

[0024] Subsequently, the 13-dimensional features are entered into the corresponding branch model according to the load category:

[0025] 13-dimensional engineering features are input into the encoders corresponding to each branch model:

[0026] CF Geometric Encoder: Maps 13-dimensional features to 48-dimensional latent vectors;

[0027] CM Geometric Encoder: Maps 13-dimensional features to 64-dimensional latent vectors.

[0028] (4) Core physical constraint layer (hard constraint)

[0029] The core physical constraint layer is used to map the intermediate representation of the network into a compliance matrix that satisfies the physical constraints, and outputs the strain result accordingly. It includes at least the following three sub-units:

[0030] 4.1) The compliance matrix generation unit maps the latent vector to a 96-dimensional flattened vector and reconstructs it into the original compliance matrix. Its dimensions are 16×6. In one implementation, the output layer of the flexibility matrix generation unit employs an unbiased linear mapping and is configured with regularization constraints to improve training stability and physical plausibility.

[0031] 4.2) Orthogonal projection elements are based on the constraint matrix B defined by the structure. Perform L2 optimal orthogonal projection to thus... Mapping to a feasible subspace that satisfies preset physical constraints yields a projective compliance matrix that satisfies the hard constraints. , .

[0032] The size and elements of the B matrix are determined by the sensor structure. Each row of the B matrix corresponds to 16 strains of the sensor under 6 loads. This unit is a deterministic computational unit, which does not introduce trainable parameters; its computation process supports gradient backpropagation, thereby achieving end-to-end training. Through this projection operation, the network output is forced to satisfy physical constraints at the structural level.

[0033] 4.3) The physical calculation unit is based on the projective compliance matrix. With standardized load vector Perform matrix multiplication to obtain the standardized strain output. ,satisfy: (5) Inverse standardization unit:

[0034] The standardized strain output is denormalized to obtain 16 physical strain channels.

[0035] (6) Output unit

[0036] The output unit is used to output:

[0037] A. Equivalent Flexibility Matrix (16×6 dimensions) and its independent parameter set, where, yes The result is obtained after inverse standardization.

[0038] The equivalent compliance matrix can serve as a physical interpretability analysis interface for analyzing structural coupling relationships, sensitivity characteristics, and parameter identifiability.

[0039] B. Strain prediction values ​​for strain paths B.16.

[0040] During the training of the CM-PINN neural network, the Adam optimizer is used to iteratively update the network parameters, and the multi-output mean squared error (MSE) loss function is used as the basic supervisory loss. Simultaneously, a zero-load physical hard constraint is introduced (transforming the physical law of "zero strain output under zero load condition" into a differentiable constraint). These two constraints are weighted and fused to calculate the total loss function, ensuring the model satisfies physical consistency. The training process employs an early stopping strategy on the validation set to prevent overfitting, and a dynamic learning rate decay mechanism (ReduceLROnPlateau) is used to adaptively adjust the learning rate. After training, the multi-dimensional force sensor strain prediction model based on structured hard constraint CM-PINN is obtained.

[0041] The multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN may also include a result analysis module.

[0042] The result analysis module interfaces with the output unit to output two types of results, which are used to verify the engineering feasibility and mechanical interpretability of the prediction results. Specifically:

[0043] Based on the equivalent compliance matrix directly output by the system, a mechanical mapping relationship between load and strain is constructed, multi-dimensional load decoupling calculation is completed, the coupling correlation law between loads of various dimensions is accurately analyzed, the degree of cross-interference of each load component on strain output is quantified, and the theoretical standard strain value is derived. In this way, the consistency verification of the prediction results at the mechanical mechanism level is completed, thereby completing the interpretability analysis of the prediction results.

[0044] Simultaneously, an engineering feasibility analysis was conducted for the 16 strain values: single-channel error quantification analysis was performed, calculating the average absolute error, mean square error, and maximum relative error between the predicted strain values ​​and the measured calibrated strain values ​​of the 16 strain paths, classifying the accuracy levels, locating strain channels with large deviations, and tracing the causes of the deviations; channel balance analysis was conducted, statistically analyzing the strain output amplitude and response characteristics of each channel, and evaluating the consistency of multi-channel outputs; static / dynamic working condition layered analysis was implemented to distinguish different load conditions and evaluate the adaptation effect of the strain prediction model.

[0045] In existing technologies, analytical models (such as beam theory), while computationally efficient, require extensive simplification of boundary conditions, making them unsuitable for strain prediction of complex elastic bodies and resulting in significant modeling errors. Finite element analysis (FEA), while highly accurate, suffers from time-consuming mesh generation and load condition iteration, hindering rapid strain prediction. Pure data-driven neural networks are sensitive to sample size, struggle to guarantee physical consistency, and are prone to violating the linear superposition laws of mechanics under multiple loads, exhibiting weak interpretability. Traditional PINN employs a soft-constraint loss function, which suffers from difficulties in adjusting weights of multiple loss terms, instability during training, and potential deviations from physical laws during inference, all failing to meet the demands of high-precision, high-reliability, and rapid strain prediction from multi-dimensional force sensors. To address these shortcomings, this invention provides a strain prediction model based on structured hard-constraint CM-PINN, offering the following advantages:

[0046] 1. Strong physical consistency and more reliable prediction results: The CM-PINN prediction neural network of this invention uses a structured hard constraint design to directly embed the orthogonal projection of the B matrix into the core physical constraint layer of the network, realizing the mechanical topological hard constraint of the flexibility matrix. This completely abandons the soft constraint loss control mode of traditional PINN and ensures that the output strain data always strictly follows the geometric symmetry, the inherent law of the flexibility matrix and the principle of mechanical linear superposition from the neural network architecture level. This fundamentally eliminates physical violations in the inference stage and is significantly better than traditional strain prediction neural networks.

[0047] 2. High prediction accuracy and strong generalization ability: The CM-PINN prediction neural network of this invention is specially designed with geometric feature encoding units and load-specific branch structures. It is designed for classification and modeling of multiple load types of multi-dimensional force sensors. Symmetric load branches share parameters, while asymmetric load branches are modeled independently. It retains the structural symmetry constraints while taking into account the differences in mechanical response, effectively improving the strain prediction accuracy of the neural network under multi-parameter and multi-load coupled conditions. It can still maintain excellent generalization ability in small sample scenarios and achieve high-precision strain prediction without massive finite element samples.

[0048] 3. Excellent mechanical interpretability, suitable for engineering prediction needs: The CM-PINN prediction neural network of this invention is not a "black box" model. It can directly output the equivalent compliance matrix and related physical parameters, which can intuitively reflect the correspondence between the load direction of the sensor and the strain path, clearly explain the mechanical generation mechanism of the strain response, solve the pain point of insufficient interpretability of traditional data-driven prediction neural networks, and can directly provide interpretable mechanical basis for sensor-related strain prediction scenarios.

[0049] 4. High prediction efficiency and significantly reduced computational cost: After the CM-PINN prediction neural network of this invention is trained, it can quickly output the strain response under multiple working conditions and multiple paths without repeating finite element simulation. The computational efficiency is more than an order of magnitude higher than that of the traditional finite element method, effectively reducing the computational resource consumption and time cost of multi-dimensional force sensor strain prediction, and solving the pain point of low efficiency of traditional prediction methods.

[0050] 5. The neural network is highly versatile and easy to implement in engineering: The CM-PINN predictive neural network of this invention can be adapted to strain prediction scenarios of various multi-dimensional force sensors (including six-dimensional force sensors). It does not require complex modifications to the neural network structure for specific sensor configurations. It can be directly embedded into engineering processes such as sensor forward design and performance evaluation. It is easy to deploy and promote in engineering, and has a wide range of application scenarios and extremely high engineering practical value. Attached Figure Description

[0051] Figure 1 Schematic diagram of a six-dimensional force sensor model.

[0052] Figure 2 CM-PINN neural network flowchart.

[0053] Figure 3 Visualization of the equivalent flexibility matrix. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or modifications that can be made by those skilled in the art without departing from the spirit of the present invention should fall within the scope of protection of the present invention.

[0055] This embodiment provides a strain prediction method for a multidimensional force sensor based on structured hard constraint CM-PINN. This method relies on a multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN. The construction method of the multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN specifically includes: Step S1: Finite element parametric modeling and sample data construction.

[0056] The parameterized finite element simulation model based on the sensor (as shown in Figure 1) sets the value ranges of two types of variables: sensor structural dimensions and external load, and builds a complete set of load conditions; 1200 sets of simulation training samples are randomly generated within the value range of the variables.

[0057] The specific working conditions are set as follows: covering six different types of uniaxial load conditions, with 200 samples in each group. The random assignment of structural dimension parameters and the random application of uniaxial loads are completed simultaneously to achieve joint random sampling of dimension variables and uniaxial loading conditions. The simulation training sample data includes at least: (1) 4 geometric parameter vectors , , , (2) Load input vectors CF1, CF2, CF3, CM1, CM2, CM3; (3) Path strain response S1-S16.

[0058] in Indicates the outer diameter of the inner ring. Indicates the beam length. Indicates the beam width. The following parameters represent the beam height: CF1 represents the axial force in the X direction, CF2 represents the axial force in the Y direction, CF3 represents the axial force in the Z direction, CM1 represents the moment in the X direction, CM2 represents the moment in the Y direction, CM3 represents the moment in the Z direction, S1 represents the strain at strain gauge 1, S2 represents the strain at strain gauge 2, S3 represents the strain at strain gauge 3, S4 represents the strain at strain gauge 4, S5 represents the strain at strain gauge 5, S6 represents the strain at strain gauge 6, S7 represents the strain at strain gauge 7, S8 represents the strain at strain gauge 8, S9 represents the strain at strain gauge 9, S10 represents the strain at strain gauge 10, S11 represents the strain at strain gauge 11, S12 represents the strain at strain gauge 12, S13 represents the strain at strain gauge 13, S14 represents the strain at strain gauge 14, S15 represents the strain at strain gauge 15, and S16 represents the strain at strain gauge 16.

[0059] In one implementation, the sample set covers both symmetric load conditions and asymmetric representative points to improve the model's generalization ability.

[0060] Step S2: Construct and train a payload-specific CM-PINN network.

[0061] like Figure 2 The CM-PINN network includes: a load-dedicated branch modeling unit, an input normalization unit, a geometric feature encoding unit, a core physical constraint layer, an inverse normalization unit, and an output unit.

[0062] S2.1 Using load-specific branch modeling elements for branch modeling

[0063] The load-specific branch modeling unit constructs branch models based on load classification;

[0064] Specifically, for the six load conditions CF1, CF2, CF3, CM1, CM2, and CM3, a four-branch structure is adopted:

[0065] CF1 and CF2 share branches and are trained jointly;

[0066] CM1 and CM2 share branches and are trained jointly;

[0067] CF3 uses an independent branch;

[0068] CM3 employs independent branches. Symmetrical relationship constraints are achieved through parameter sharing in symmetric channels, while the ability to express differences is preserved through independent modeling of asymmetric channels.

[0069] S2.2 Input Normalization and Feature Encoding

[0070] 1. Use input normalization units to perform geometric normalization and load normalization on 4D geometric parameters and 6D load inputs respectively;

[0071] 2. Standardize the 16-dimensional path strain response for training;

[0072] 3. The standardized 4-dimensional geometric parameters are extended into 13-dimensional engineering features using geometric feature coding units, as shown in Table 1.

[0073] Table 1

[0074]

[0075] 4. The 13-dimensional engineering features are entered into the corresponding branch model according to the load type;

[0076] 13-dimensional engineering features are input into the encoders corresponding to each branch model:

[0077] CF Geometric Encoder: 13D→48D, used to map 13-dimensional features to 48-dimensional latent vectors;

[0078] CM Geometric Encoder: 13D→64D, used to map 13-dimensional features to 64-dimensional latent vectors.

[0079] S2.3 Core Physical Constraint Layer (Hard Constraints)

[0080] This layer consists of three sub-units: a flexibility matrix generation unit, an orthogonal projection unit, and a physical calculation unit.

[0081] 1) The compliance matrix generation unit is used to map the latent vector to a 96-dimensional flattened vector and reconstruct it into the original compliance matrix. , .

[0082] This represents the original compliance matrix, which does not contain physical laws.

[0083] Its output layer uses an unbiased linear mapping and can be enhanced with regularization terms.

[0084] 2) Orthogonal projection elements are defined according to the constraint matrix B of the structure (see...). Figure 1 (structural relationship) Performing L2 optimal orthogonal projection yields the projection compliance matrix that satisfies the hard constraints:

[0085]

[0086] in Let B be the feasible subspace defined by the B matrix. This process is a deterministic differentiable operation, does not introduce trainable parameters, and can participate in backpropagation.

[0087] The B matrix is ​​specifically represented as follows:

[0088]

[0089] The size and elements of matrix B All are determined by the sensor structure (e.g.) Figure 1 In the figure, s1-s16 correspond to the strains collected by 16 strain gauges. Each row of matrix B corresponds to 16 strains (S1-S16 from front to back) of the sensor under 6 loads (from top to bottom: axial force in the x direction, axial force in the y direction, axial force in the z direction, torque in the x direction, torque in the y direction, torque in the z direction).

[0090] This represents the projective compliance matrix, which contains physical laws.

[0091] 3) The physical calculation unit will standardize the load vector. With the projective compliance matrix Multiply to obtain the standardized strain :

[0092]

[0093] S2.4 Inverse Standardization

[0094] The standardized strain is standardized by the inverse standardization unit to obtain 16 micro-strain prediction outputs.

[0095] S2.5 Model Output

[0096] The output unit is used to output the results, including: A. Equivalent compliance matrix and its independent parameter set (used for interpretability analysis, such as coupling relationships, sensitivity orientation, and identifiability analysis) such as Figure 3 Equivalent Flexibility Matrix Specifically, it is determined by the projected compliance matrix. After inverse standardization, the strain can be directly obtained by interacting with the load; B. 16-path strain path prediction.

[0097] During the training of the CM-PINN neural network, the Adam optimizer is used to iteratively update the network parameters, and the multi-output mean squared error (MSE) loss function is used as the basic supervision loss. Simultaneously, zero-load physical hard constraints are incorporated as auxiliary constraint losses to ensure the model meets physical consistency requirements. The training process employs an early stopping strategy on the validation set to prevent overfitting, and a dynamic learning rate decay mechanism (ReduceLROnPlateau) is used to adaptively adjust the learning rate. After training, the multi-dimensional force sensor strain prediction model based on structured hard constraints CM-PINN is obtained.

[0098] The multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN may also include a result analysis module, which is used to verify the engineering feasibility and mechanical interpretability of the prediction results.

[0099] Combined with equivalent compliance matrix heatmap ( Figure 3 The following mechanical interpretability analyses can be performed:

[0100] (1) Load-strain mapping orthogonality analysis: The equivalent compliance matrix shows a clear distribution characteristic of the main load response channels. The main response paths of each load component do not overlap, which verifies the matching degree between the sensor structure and the load components and provides a basis for decoupled measurement.

[0101] (2) Coupling interference quantification analysis: The degree of cross-coupling between load components can be directly quantified by the values ​​of non-principal response terms in the equivalent compliance matrix. Combined with the amplitude comparison of principal response terms, the decoupling performance of the sensor can be evaluated.

[0102] (3) Identifiability and sensitivity analysis: There are no completely linear correlation terms in the response modes of each load component on the 16 strain paths, indicating that the load components can be identified independently, and the difference in compliance value reflects the difference in sensitivity of loads in different dimensions.

[0103] (4) Physical consistency verification: The alternating positive and negative distribution of the equivalent flexibility matrix and the symmetrical response mode are highly consistent with the mechanical properties of the elastic body structure, and can be directly verified. (where F is the applied load) Derivation of theoretical strain values Consistency verification is performed between the model prediction results and the actual results.

[0104] Simultaneously, engineering feasibility analysis can be conducted on 16 strain values:

[0105] Single-channel error quantification analysis was performed, calculating the average absolute error, mean square error, and maximum relative error between the predicted strain values ​​and the measured calibrated strain values ​​of the 16 strain paths, classifying the accuracy levels, locating strain channels with large deviations, and tracing the causes of the deviations; channel balance analysis was conducted, statistically analyzing the strain output amplitude and response characteristics of each channel, and evaluating the consistency of multi-channel output; static / dynamic working condition layered analysis was implemented to distinguish different load conditions and evaluate the adaptation effect of the strain prediction model.

Claims

1. A strain prediction method based on a multidimensional force sensor using structured hard-constraint CM-PINN, characterized in that, This relies on a multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN. The construction method of the multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN is as follows: First, a finite element simulation model is established, and the range of values ​​for the dimensions and loads is set. Within the range of variable values, a sufficient finite element simulation dataset is randomly generated. The sample data in the finite element simulation dataset includes geometric parameter vectors, load vectors, and path strain responses. Then, the geometric parameter vector and load vector are used as inputs to the CM-PINN neural network, and the path strain response is used as the output of the CM-PINN neural network to train and obtain the multi-dimensional force sensor strain prediction model based on structured hard constraint CM-PINN. The multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN includes a load-dedicated branch modeling unit, an input normalization unit, a geometric feature encoding unit, a core physical constraint layer, an inverse normalization unit, and an output unit. During the training process of the multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN, branch models are constructed for six types of loads: The load-specific branch modeling unit is used to construct branch models according to load classification; branch models corresponding to the same type of load share model parameters. The input standardization unit is used to standardize the geometric parameter vector and the load vector respectively; The geometric feature encoding unit is used to expand the standardized geometric parameter vector into a 13-dimensional engineering feature, and the 13-dimensional engineering feature enters the corresponding branch model according to the load type. Each branch model uses a geometric encoder to map the 13-dimensional engineering features into latent vectors; The core physical constraint layer is used to map the latent vectors into a projected compliance matrix that satisfies the physical constraints, and thereby obtain the standardized strain result. The inverse normalization unit is used to inverse normalize the strain result to obtain the strain response; The output unit is used to output the strain response and the equivalent compliance matrix, which is obtained by inverse normalization of the projected compliance matrix.

2. The strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN according to claim 1, characterized in that, The geometric parameter vector includes the outer diameter of the inner ring. Beam length Beam width and beam height The load vector includes axial force CF1 in the X direction, axial force CF2 in the Y direction, axial force CF3 in the Z direction, moment CM1 in the X direction, moment CM2 in the Y direction, and moment CM3 in the Z direction; the path strain response includes the strain at all strain gauge locations.

3. The strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN according to claim 2, characterized in that, The load classification is as follows: the six load types are divided into four categories according to load type; CF1 and CF2 are divided into one category, which share a branch model and are jointly trained; CM1 and CM2 are divided into one category, which share a branch model and are jointly trained; CF3 and CM3 are trained separately using separate branch models.

4. The strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN according to claim 2, characterized in that, The geometric feature encoding unit is used to expand the standardized geometric parameter vector into 13-dimensional engineering features. Specifically, the 13-dimensional engineering features include the original four types of geometric parameters and derived features directly related to elastic mechanical stiffness obtained based on the original four types of geometric parameters. The original four types of geometric parameters include the outer diameter of the cylinder, the length of the beam, the width of the beam, and the thickness of the beam. The derived features specifically include the cylinder wall thickness, the inner diameter of the cylinder, the cross-sectional area A, the moment of inertia I1, the moment of inertia I2, the polar moment of inertia Ip, the sensor position, the neutral axis distance z, and the neutral axis distance y.

5. The strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN according to claim 2, characterized in that, The core physical constraint layer includes a compliance matrix generation unit, an orthogonal projection unit, and a physical calculation unit. This core physical constraint layer maps each latent vector to a projected compliance matrix that satisfies the physical constraints, and obtains the standardized strain result accordingly. The specific method is as follows: The flexibility matrix generation unit maps the latent vector to a 96-dimensional flattened vector and reconstructs the 96-dimensional flattened vector into the original flexibility matrix; the output layer of the flexibility matrix generation unit adopts an unbiased linear mapping and is configured with regularization constraints. The orthogonal projection unit is used to perform optimal orthogonal projection of the original compliance matrix in the L2 sense based on the B matrix to obtain the projected compliance matrix, which satisfies the structural hard constraints; each row of the B matrix corresponds to 16 strains under six loads of the sensor. The physical calculation unit performs matrix multiplication based on the projected compliance matrix and the standardized load vector to obtain the standardized strain.

6. The strain prediction method for multidimensional force sensors based on structured hard constraint CM-PINN according to claim 1, characterized in that, The multi-dimensional force sensor strain prediction model based on structured hard constraint CM-PINN also includes a result analysis module. The result analysis module connects to the two types of output results of the output unit to verify the engineering feasibility and mechanical interpretability of the prediction results.

7. The strain prediction method for a multidimensional force sensor based on structured hard constraint CM-PINN according to claim 1, wherein during the training process of the multidimensional force sensor strain prediction model based on structured hard constraint CM-PINN, the Adam optimizer is used to iteratively update the model parameters; and the multi-output mean square error loss is used as the basic supervision loss, while a zero-load physical hard constraint loss term is introduced, and the two are weighted and fused to calculate the total loss function to ensure that the model satisfies physical consistency, wherein, The zero-load physical hard constraint specifically transforms the physical law that "the strain output is zero under zero load conditions" into a differentiable constraint; the training process employs a validation set early stopping strategy to prevent overfitting, and uses a dynamic learning rate decay mechanism to adaptively adjust the learning rate.

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