Six-dimensional force sensor optimization method based on cm-pinn

Abstract

The application provides a six-dimensional force sensor optimization method based on CM-PINN, which depends on a six-dimensional force sensor optimization model based on CM-PINN. The application realizes the structured hard constraint of the flexibility matrix by embedding the B matrix projection into the CM-PINN network, replaces the traditional loss function soft constraint, ensures that the mechanical properties relied on in the optimization process always strictly meet the geometric symmetry and the inherent physical law of the flexibility matrix, fundamentally eliminates the physical violation phenomenon from the architecture level, makes the optimization result more consistent with the engineering actual mechanical properties, and improves the optimization reliability; through the design of the load special branch and the symmetric joint training mechanism, the strong high-dimensional nonlinear coupling problem between the elastomer mechanical properties and the external load, the geometric structure parameters is effectively solved. The method can greatly reduce the calculation cost, shorten the design cycle, realize the efficient global optimization of the sensor geometric parameters and the load range, and adapt to the design requirements of the engineering end rapid iteration and rapid verification.

Description

Technical Field

[0001] This invention belongs to the fields of multidimensional force / torque sensor design, structural mechanics modeling, machine learning proxy modeling and engineering optimization technology. It relates to a six-dimensional force sensor optimization method based on CM-PINN, specifically a modeling and solution 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 strain prediction and multi-objective parameter optimization of six-dimensional force sensors. Background Technology

[0002] Six-dimensional force sensors, as core sensing devices in fields such as precision robotic operations, aerospace on-orbit operations, and high-end equipment manufacturing, need to simultaneously and accurately measure three-dimensional forces and three-dimensional torques. The rationality of their structural design and performance optimization directly determines their sensing accuracy, measurement range, and operational reliability, making them a crucial element in meeting the precision control requirements of high-end equipment. Currently, the structural design and multi-objective performance optimization of six-dimensional force sensors face two major bottlenecks, severely restricting rapid iteration in engineering and industrial application:

[0003] On the one hand, the optimization process requires precise capture of the strong high-dimensional nonlinear coupling relationship between the elastic body strain response and the applied load and geometric parameters. However, existing modeling methods are difficult to support the high-precision optimization requirements. Traditional analytical models (such as beam theory) are computationally efficient, but require extensive simplification of boundary conditions, making them unsuitable for the parametric optimization design of complex elastic bodies such as cross beams and composite beams, resulting in significant modeling errors. Pure data-driven neural networks can attempt to replace analytical models, but they suffer from problems such as the sensitivity of prediction accuracy to sample size, difficulty in ensuring physical consistency, easy violation of the linear superposition law of mechanics under multiple loads, and insufficient interpretability, making it difficult to directly embed them into the optimization constraint system. Traditional physical information neural networks (PINN) adopt a soft constraint mode with loss functions, which suffers from the defects of difficulty in adjusting the weights of multiple loss terms, instability in the training process, and the possibility of deviating from physical laws during the inference stage. None of these can provide high-precision and highly reliable mechanical response support for the optimization process.

[0004] On the other hand, the multi-objective optimization of six-dimensional force sensors (such as sensitivity consistency, geometric compliance, range matching, structural strength and safety, etc.) highly depends on massive finite element simulation (FEA) iterations. Each set of optimization parameters requires a complete finite element simulation calculation, which is not only costly and consumes a lot of computing resources, but also has a long iteration cycle. It cannot meet the actual needs of rapid design, rapid verification and rapid iteration in engineering, and it is difficult to achieve a balance between sensor structural performance and design efficiency.

[0005] In summary, existing optimization methods for six-dimensional force sensors either suffer from unreliable results due to insufficient modeling accuracy and poor physical consistency, or are difficult to adapt to engineering requirements due to low computational efficiency and long iteration cycles. These methods fail to meet the core requirements of high-end equipment for high-precision, high-reliability, and rapid sensor design. Therefore, there is an urgent need for a six-dimensional force sensor optimization method that combines high precision, strong physical consistency, high interpretability, and high optimization efficiency. This method would address the pain points of inaccurate modeling, low computational efficiency, and poor constraint adaptability in existing optimization techniques, and promote the intelligent and efficient upgrading of six-dimensional force sensor structural design. Summary of the Invention

[0006] To achieve the above-mentioned objectives, this invention provides an optimization method for a six-dimensional force sensor based on CM-PINN. This method can be used for the design of structural parameters of multi-dimensional force / torque sensors.

[0007] The technical solution adopted by the present invention to solve the above problems is as follows:

[0008] A six-dimensional force sensor optimization method based on CM-PINN relies on a six-dimensional force sensor optimization model based on CM-PINN. The model specifically includes: a surrogate evaluation module for uniaxial load prediction and linear superposition, a differential evolution optimization module, and a convergence determination and output module.

[0009] (1) The surrogate evaluation module for uniaxial load prediction and linear superposition includes: an optimization variable construction unit, a uniaxial load prediction unit, a combined load condition linear superposition unit, an objective function calculation unit, and a constraint violation calculation unit.

[0010] 1.1) Optimization Variable Construction Unit: The optimization variable construction unit performs symmetric dimensionality reduction on the original 10-dimensional optimization variables (4-dimensional geometric parameters and 6-dimensional load range parameters) to construct an 8-dimensional design vector.

[0011] This is used to generate candidate solutions.

[0012] in, The load ranges corresponding to CF2 are equal; The load ranges of CM1 and CM2 are equal. This indicates the load range of CF3. This indicates the load range of CM3. Indicates the sensor size, i=1-4 respectively correspond to , , , .

[0013] 1.2) Uniaxial load prediction unit: The uniaxial load prediction unit calls the CM-PINN solver for each candidate solution to calculate the strain response under six types of uniaxial load conditions and obtain the single load prediction result.

[0014] 1.3) Combined working condition linear superposition unit: The combined working condition linear superposition unit is based on the principle of linear superposition and synthesizes the prediction results of six types of uniaxial loads into a combined working condition response, which is used to replace the finite element combined solution.

[0015] 1.4) Objective Function Calculation Unit: The objective function calculation unit calculates a multi-objective weighted function based on the combined operating condition response.

[0016]

[0017] in For sensitivity consistency, For geometric deviation terms, This is the range deviation term; Different weights, i=1-3, represent the weights of the sensitivity consistency term, geometric deviation term, and range deviation term, respectively.

[0018] The calculation formula is:

[0019]

[0020] in, It is the mean of the representative values ​​after taking the logarithm; The mean strain value corresponding to the i-th load type; As the zero offset; n is the number of effective load types (the types of loads that can produce an actual response to the current strain gauge);

[0021] The calculation formula is:

[0022]

[0023] The geometric deviation term can bring optimized geometric parameters closer to preset engineering feasible values, avoiding extreme dimensions, wherein: The current geometric parameters for the i-th load type; These are the preset target geometric parameters for the i-th load type; i = 1-4, corresponding to load types CF1 and CF2, load types CM1 and CM2, load type CF3, and load type CM3, respectively.

[0024] The calculation formula is:

[0025]

[0026] The range deviation term ensures that the load range is close to the actual application requirements, avoiding being too large (wasting sensitivity) or too small (insufficient); among which: For the current load range of the i-th load type, The preset target load range for the i-th load type; i = 1-4, corresponding to load types CF1 and CF2, load types CM1 and CM2, load type CF3, and load type CM3, respectively.

[0027] 1.5) Constraint Violation Calculation Unit: The constraint violation calculation unit calculates the sum of the violation degree of seven types of constraints, including: minimum measurable strain constraint, single load stress safety constraint, size boundary constraint, beam length patch constraint, inner flange geometric validity constraint, combined load sensitive path strength constraint, and channel order-of-magnitude hard constraint.

[0028] Constraint 1: Minimum measurable strain constraint

[0029] Ensure that the strain on the sensitive path is not lower than the measurement threshold under minimum rated load:

[0030]

[0031] Where: k represents the k-th type of load, specifically including CF1, CF2, CF3, CM1, CM2, and CM3 loads; This represents the minimum measurable strain under the k-th type of load; This represents the set of sensitive strain paths for the k-th type of load; For the maximum range; Minimum measurable load , This represents the strain value generated on the i-th strain path under the k-th load condition. .

[0032] Constraint 2, Single Load Stress Safety Constraint

[0033] Hot spot stress at the location of maximum stress under maximum load for all paths Not exceeding allowable stress

[0034] Where: K=2 represents the stress amplification factor, that is, the strain gauge stress obtained within the linear elastic range is amplified to the position of maximum stress of the elastic beam of the sensor; E is the Young's modulus of the sensor, specifically, if the sensor material is aluminum, E=69e9; , For yield strength, This is for the safety factor.

[0035] Constraint 3, Dimensional Boundary Constraints

[0036] Size upper and lower limits: sensor model greater than 100mm and less than 350mm

[0037]

[0038] in, and These represent the beam length and the outer diameter of the sensor's inner flange, respectively.

[0039] Constraint 4, Beam Length Patch Constraint

[0040] The beam length is greater than twice the strain gauge length to meet the patching requirements.

[0041]

[0042] For strain gauge dimensions

[0043] Constraint 5: Geometric validity constraint of the inner flange

[0044] Sensor inner flange dimensions inner diameter From outer diameter The wall thickness was reduced by 20mm to ensure geometric validity.

[0045]

[0046] Constraint 6, Combined Load Strength Constraint

[0047] For the sensitive path, the combined stress under simultaneous six-axis loads satisfies the strength constraint:

[0048]

[0049] This represents the combined strain on the i-th sensitive strain path under simultaneous six-axis loading. This represents the combined stress on the i-th sensitive strain path under simultaneous six-axis loading. This represents the strain value generated on the i-th sensitive strain path under the k-th load condition.

[0050] Table 1 below shows the configuration and number of sensitive strain paths corresponding to each load component.

[0051] Table 1

[0052] CF1 Primary response groups: {1, 2, 3, 4}, {9, 10, 11, 12}; Secondary response groups: {6, 16}, {8, 14} 12 CF2 Primary response groups: {5, 6, 7, 8}, {13, 14, 15, 16}; Secondary response groups: {4, 10}, {2, 12} 12 CF3 Path {1, 3, 5, 7, 9, 11, 13, 15} 8 CM1 The path {5,7,13,15} 4 CM2 The path {1, 3, 9, 11} 4 CM3 Path {2, 4, 6, 8, 10, 12, 14, 16} 8

[0053] Constraint 7: Channel order of magnitude constraint

[0054] With the sensitivity of each channel on the same order of magnitude, this constraint is a hard constraint that must be met, compared to the order-of-magnitude objective in the objective function. The objective function then provides optimization space.

[0055]

[0056] Define the mean strain value of the k-th load channel, where max represents the maximum value and min represents the minimum value.

[0057] (2) The differential evolution optimization module includes: a parameter initialization unit, a population generation unit, and an iterative optimization unit.

[0058] 2.1) Parameter initialization unit: The parameter initialization unit sets the boundary of optimization variables, the weights of different objectives in the multi-objective weighting function, constraint rules and differential evolution parameters, including population size, mutation factor, crossover probability and maximum number of iterations.

[0059] 2.2) Population generation unit: The population generation unit generates an initial candidate population in an 8-dimensional design space.

[0060] 2.3) Iterative optimization unit: The iterative optimization unit is used to call the differential evolution algorithm library to iteratively update the current candidate population; in each iteration, the surrogate evaluation module of single-axis load prediction and linear superposition is called for the candidate solution to calculate its corresponding multi-objective weighted function value and constraint violation amount, and the candidate population is updated according to the preset superiority and inferiority comparison rules, thereby gradually approaching the global optimal solution.

[0061] (3) The convergence determination module includes a convergence determination unit and a result output unit.

[0062] 3.1) The convergence determination unit is responsible for calculating the improvement amount of the optimal multi-objective weighted function value, the stability of the feasible solution in consecutive iterations, and the current iteration number during the iteration process. When determining whether the convergence condition is met, the convergence condition includes: the improvement amount of the optimal multi-objective weighted function value is lower than a preset threshold, the maximum iteration number is reached, and the feasible optimal solution remains stable within several consecutive iterations.

[0063] 3.2) The result output unit is used to output the optimal geometric parameters and range configuration, as well as the corresponding multi-objective weighted function value and constraint violation amount when at least one convergence condition is met; and to perform sensitivity, stress, size and order of magnitude verification.

[0064] The CM-PINN solver works as follows:

[0065] The CM-PINN solver is used to predict uniaxial load strain and includes at least a load-specific branch modeling unit, a normalized unit, a geometric feature encoding unit, a core physical constraint layer, an inverse normalized unit, and an output unit.

[0066] The CM-PINN neural network module is as follows: Figure 2 As shown, it specifically includes:

[0067] (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, where CF1 / CF2 are shared models, CM1 / CM2 are shared models, CF3 is an independent model, and CM3 is an independent model; through symmetrical channel joint training and parameter sharing, the sample utilization efficiency is improved and the model complexity is reduced. Among them, CF1, CF2, CF3, CM1, CM2, and CM3 represent the axial force and torque in the x, y, and z directions, respectively.

[0068] (2) Standardized unit:

[0069] The standardization unit is used to standardize the 4D geometric parameters and the 6D load vector respectively, to obtain standardized 4D geometric parameters and standardized 6D load vector.

[0070] The standardized 4D geometric parameters are fed into the corresponding branch model according to the load category:

[0071] (3) Geometric feature coding unit

[0072] The geometric feature encoding unit includes a CF encoder and a CM encoder, used to encode geometric parameters into latent vectors according to the payload type; specifically:

[0073] The standardized geometric parameters are sent to the corresponding encoder according to the load type:

[0074] CF encoder: maps geometric features to 48-dimensional latent vectors;

[0075] CM encoder: maps geometric features to 64-dimensional latent vectors.

[0076] (4) Core physical constraint layer

[0077] The core physical constraint layer is used to map the intermediate representations (latent vectors) 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:

[0078] 4.1) The compliance matrix generation unit maps the latent vectors to 96-dimensional flattened vectors and reconstructs them 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.

[0079] 4.2) Orthogonal Projection Unit: The orthogonal projection unit projects the data according to the B matrix. Perform L2 optimal orthogonal projection mapping, and The projection compliance matrix is ​​obtained by traversing the feasible subspace that satisfies the preset physical constraints. .

[0080] Where matrix B is:

[0081]

[0082] The size and elements of matrix B All are determined by the sensor structure. Each row of the B matrix corresponds to one of the 16 strains of the sensor under six 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.

[0083] 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: , where the dimension is (16×6)@ (6×1) -> (16×1). (5) Inverse normalized unit:

[0084] The standardized strain output is denormalized to obtain 16 physical strain channels.

[0085] (6) Output unit

[0086] Used to output strain prediction values ​​for 16 strain paths;

[0087] The specific training method for the CM-PINN solver is as follows:

[0088] First, the data foundation required for training and optimizing the CM-PINN solver is constructed, including: (1) establishing the sensor parameterized geometric model and finite element simulation model; (2) setting the range of design variables and load conditions; (3) extracting sample data, which includes at least geometric parameters, load input, and path strain response (4 geometric parameter vectors). , , , Load input vectors CF1, CF2, CF3, CM1, CM2, CM3; path strain response S1-S16).

[0089] 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.

[0090] Then, for the six load conditions, a four-branch structure is used for training, with each branch corresponding to one of the four load types. Symmetrical constraints are achieved through parameter sharing in symmetric channels, while independent modeling in asymmetric channels preserves the ability to express differences. Specifically, the branch models corresponding to symmetric load types (such as x / y force and x / y bending moment) use a parameter sharing mechanism to achieve structural symmetry constraints; the branch models corresponding to asymmetric load types (such as z-force and z-bending moment) use independent modeling to preserve the asymmetric differences in their mechanical responses. The geometric encoder, core physical constraint layer, and inverse normalized unit structure of each branch model are consistent. (Physical Constraints and Training) The physical constraint layer is used to map each latent vector to a compliance matrix that satisfies the physical constraints, and outputs 16-way normalized strain accordingly. During training, the Adam optimizer is used to iteratively update the model parameters, and an early stopping strategy is used to prevent overfitting, ensuring that the model has good generalization ability under unseen geometric and load conditions.

[0091] After training, the model's strain prediction accuracy under different geometric parameters and load conditions is verified through a test set to ensure that the model meets the preset error threshold. When the model's prediction error converges to the target range, the training is complete, and the trained CM-PINN solver is obtained.

[0092] In existing technologies, analytical models (such as beam theory), while computationally efficient, require simplified boundary conditions, making them difficult to adapt to complex structures and parametric design requirements, and thus unable to provide reliable support for the structural optimization of six-dimensional force sensors. While the finite element method offers high accuracy, it requires extensive repetitive simulations during multivariate and multi-objective optimization, resulting in high computational costs and lengthy design cycles. Pure data-driven neural networks struggle to directly support engineering parameters and optimization constraint design, exhibiting poor physical consistency and easily leading to optimization results deviating from actual mechanical properties. Traditional PINNs often employ soft constraints based on loss functions, which suffer from difficulties in adjusting the weights of multiple loss terms and instability in the training process, failing to support efficient and reliable optimization iterations. To address the shortcomings of the existing technologies, the technical solution provided by this invention offers the following beneficial effects:

[0093] 1. Strong physical consistency and more reliable optimization basis: This invention embeds the B matrix projection into the CM-PINN network to realize the structured hard constraint of the compliance matrix, replacing the traditional soft constraint of the loss function. This ensures that the mechanical properties on which the optimization process depends always strictly satisfy the inherent physical laws of geometric symmetry and compliance matrix, fundamentally eliminating physical violations at the architectural level. This makes the optimization results more consistent with the actual mechanical properties of engineering and improves the reliability of optimization.

[0094] 2. More targeted optimization and more accurate results: By designing a dedicated load branch and a symmetrical joint training mechanism, the problem of strong high-dimensional nonlinear coupling between the mechanical properties of the elastic body and the external load and geometric parameters is effectively solved. It can accurately capture the influence of each parameter on the sensor performance during the optimization process, ensuring the accuracy of the optimization direction, and making the optimized sensor better in core performance such as sensitivity consistency and range matching.

[0095] 3. Significantly improved optimization efficiency and good engineering adaptability: The CM-PINN surrogate model, trained with a small amount of limited metadata, can completely replace the large number of repeated finite element simulations in traditional multi-objective optimization. Through the surrogate evaluation mechanism of "single load mechanical property calculation + linear superposition", it greatly reduces the computational cost and shortens the design cycle, realizing efficient global optimization of sensor geometric parameters and load range, and adapting to the design requirements of rapid iteration and rapid verification in engineering. Attached Figure Description

[0096] Figure 1 Flowchart of multi-objective optimization of multi-dimensional force sensor based on CM-PINN solver optimization algorithm.

[0097] Figure 2 Schematic diagram of a six-dimensional force sensor model

[0098] Figure 3 Flowchart of the optimization method for a six-dimensional force sensor based on CM-PINN. Detailed Implementation

[0099] 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.

[0100] This embodiment provides an optimization method for a six-dimensional force sensor based on CM-PINN.

[0101] like Figure 1 As shown, this method relies on an optimization algorithm based on the CM-PINN solver. The method specifically includes the following steps: S1, finite element modeling and data extraction; S2, CM-PINN neural network construction and training; S3, surrogate evaluation and differential evolution optimization based on the CM-PINN solver; S4, result analysis and engineering verification output.

[0102] Specifically, in step S1, a finite element simulation model is established, the value range of optimization variables (4-dimensional geometric parameters and 6-dimensional load range) and the set of load conditions are set, and 1200 sets of training samples are generated.

[0103] The training samples include at least: (1) 4 geometric parameter vectors , , , (2) Load input vectors CF1, CF2, CF3, CM1, CM2, CM3; (3) Path strain responses S1-S16. The samples cover multiple single load conditions and representative points of the entire design space to ensure the generalization ability of the subsequent proxy model.

[0104] 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.

[0105] In one implementation, the sample set covers both symmetric load conditions and asymmetric representative points to improve the model's generalization ability.

[0106] Step S2: Construct and train a payload-specific CM-PINN network (e.g.) Figure 1 Module 2 Figure 2 )

[0107] The CM-PINN network includes: a load-dedicated branch modeling unit, a normalization unit, a geometric feature encoding unit, a core physical constraint layer, and an inverse normalization and output unit.

[0108] S2.1 Load-Specific Branch Modeling: The load-specific branch modeling unit constructs a four-branch structural model for six load conditions: CF1, CF2, CF3, CM1, CM2, and CM3.

[0109] CF1 and CF2 share branches and are trained jointly;

[0110] CM1 and CM2 share branches and are trained jointly;

[0111] CF3 uses an independent branch;

[0112] 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.

[0113] S2.2 Input / Output Normalization and Feature Encoding

[0114] 1. Standardized units are used to standardize both 4D geometric input and 6D load input.

[0115] 2. Standardized units are used to standardize the 16-dimensional strain output for training;

[0116] The standardized 4D geometric parameters are fed into the corresponding branch model according to the load category:

[0117] 3. The geometric feature encoding unit includes a CF encoder and a CM encoder, which are used to encode the standardized 4D geometric parameters into latent vectors according to the load type. The specific method is as follows:

[0118] The standardized 4D geometric input is fed into the corresponding encoder according to the load type:

[0119] CF encoder: 4D geometric features → 48D latent vectors;

[0120] CM encoder: 4D geometric features → 64D latent vectors.

[0121] S2.3 Core Physical Constraint Layer Processing

[0122] This layer comprises three sub-units: flexibility matrix generation, orthogonal projection, and physical calculation.

[0123] 1) The compliance matrix generation unit maps the latent vector output by the encoder to a 96-dimensional flattened vector and reconstructs it into the original compliance matrix:

[0124] This represents the original compliance matrix, which does not contain physical laws.

[0125] The output layer uses an unbiased linear mapping and can be enhanced with regularization terms.

[0126] 2) Orthogonal projection elements utilize constraint matrix B defined according to the structure (see...). Figure 2 (structural relationship) Performing L2 optimal orthogonal projection yields the projection compliance matrix that satisfies the hard constraints. :

[0127]

[0128] in Let B be the feasible subspace defined by matrix B. This process is a deterministic differentiable operation, does not introduce trainable parameters, and can participate in backpropagation.

[0129] This represents the projective compliance matrix, which contains physical laws.

[0130] Matrix B is:

[0131]

[0132] The size and elements of matrix B All are determined by the sensor structure (e.g.) Figure 2 In the figure, s1-s16 correspond to the strains collected by 16 strain gauges. Each row of the B matrix (CF1, CF2, CF3, CM1, CM2, CM3 from top to bottom) corresponds to the 16 strains (s1-s16 from left to right) of the sensors under 6 loads. 3) The physical calculation unit standardizes the load vector. and Multiply to obtain the standardized strain :

[0133] satisfy , where the dimension is (16×6)@ (6×1) -> (16×1).

[0134] in, This indicates the load after standardization.

[0135] S2.4 Inverse Normalization and Output

[0136] The signal is then inversely normalized by the inverse normalization unit to obtain 16 micro-strain predictions, which are then output by the output unit.

[0137] The specific training method for the CM-PINN solver is as follows:

[0138] First, the data foundation required for training and optimizing the CM-PINN solver is constructed, including: (1) establishing the sensor parameterized geometric model and finite element simulation model; (2) setting the range of design variables and load conditions; (3) extracting sample data, which includes at least geometric parameters, load input, and path strain response (4 geometric parameter vectors). , , , Load input vectors CF1, CF2, CF3, CM1, CM2, CM3; path strain response S1-S16).

[0139] 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.

[0140] Then, for the six load conditions, a four-branch structure is used for training, with each branch corresponding to one of the four load types. Symmetrical constraints are achieved through parameter sharing in symmetric channels, while independent modeling in asymmetric channels preserves the ability to express differences. Specifically, the branch models corresponding to symmetric load types (such as x / y force and x / y bending moment) use a parameter sharing mechanism to achieve structural symmetry constraints; the branch models corresponding to asymmetric load types (such as z-force and z-bending moment) use independent modeling to preserve the asymmetric differences in their mechanical responses. The geometric encoder, core physical constraint layer, and inverse normalized unit structure of each branch model are consistent. (Physical Constraints and Training) The physical constraint layer is used to map each latent vector to a compliance matrix that satisfies the physical constraints, and outputs 16-way normalized strain accordingly. During training, the Adam optimizer is used to iteratively update the model parameters, and an early stopping strategy is used to prevent overfitting, ensuring that the model has good generalization ability under unseen geometric and load conditions.

[0141] After training, the model's strain prediction accuracy under different geometric parameters and load conditions is verified through a test set to ensure that the model meets the preset error threshold. When the model's prediction error converges to the target range, the training is complete, and the trained CM-PINN solver is obtained.

[0142] S3 Six-dimensional force sensor optimization algorithm based on CM-PINN solver (e.g.) Figure 1 Steps 4 and 5 Figure 3 )

[0143] The CM-PINN neural network obtained in step S2 is used as a solver in the optimization process of this step.

[0144] S3.1 Uniaxial load prediction and surrogate evaluation of linear superposition

[0145] The surrogate evaluation module based on uniaxial load prediction and linear superposition is implemented. This module includes: an optimization variable construction unit, a uniaxial load prediction unit, a combined load case linear superposition unit, an objective function calculation unit, and a constraint violation calculation unit. This step is used to quickly evaluate candidate solutions, specifically including:

[0146] 1) Optimize variable construction

[0147] The optimization variables specifically include 10-dimensional variables such as the length, width, height, inner diameter of the central stage, and the range of the six loads of the sensor strain beam;

[0148] The optimization variable building block reduces the original 10-dimensional variables to an 8-dimensional design vector to be optimized:

[0149] This generates candidate solutions.

[0150] in, The load ranges of CF1 and CF2 are equal. The load ranges of CM1 and CM2 are equal. This indicates the load range of CF3. This indicates the load range of CM3. Indicates the sensor size, i=1-4 respectively correspond to , , , .

[0151] 2) Uniaxial load prediction: The uniaxial load prediction unit calls the CM-PINN solver for each candidate solution to obtain six types of uniaxial load strain responses, replacing the high-cost finite element combination calculation.

[0152] 3) Combined working condition linear superposition: Based on the principle of linear superposition, the combined working condition linear superposition element combines the prediction results of six types of uniaxial loads into a combined working condition response, which is used to replace the finite element combined solution.

[0153] 4) Objective Function Calculation: The objective function calculation unit constructs a multi-objective weighted function based on the combined operating condition response.

[0154]

[0155] This embodiment takes , representing the weights of the sensitivity consistency term, geometric deviation term, and range deviation term, respectively. For sensitivity consistency, For geometric deviation terms, This is the range deviation term.

[0156] The calculation formula is:

[0157]

[0158] in, It is the mean of the representative values ​​after taking the logarithm; The mean strain value corresponding to the i-th load type; As the zero offset; n is the number of effective load types (the types of loads that can produce an actual response to the current strain gauge);

[0159] The calculation formula is:

[0160]

[0161] The geometric deviation term can bring optimized geometric parameters closer to preset engineering feasible values, avoiding extreme dimensions, wherein: The current geometric parameters for the i-th load type; These are the preset target geometric parameters for the i-th load type; i = 1-4, corresponding to load types CF1 and CF2, load types CM1 and CM2, load type CF3, and load type CM3, respectively.

[0162] The calculation formula is:

[0163]

[0164] The range deviation term ensures that the load range is close to the actual application requirements, avoiding being too large (wasting sensitivity) or too small (insufficient); among which: For the current load range of the i-th load type, The preset target load range for the i-th load type; i = 1-4, corresponding to load types CF1 and CF2, load types CM1 and CM2, load type CF3, and load type CM3, respectively.

[0165] 5) Constraint Violation Calculation: The constraint violation is defined as the sum of the degree of violation of seven types of constraints. The seven types of constraints include: minimum measurable strain, single load stress safety, dimensional boundary, beam length patch, inner flange geometric validity, combined load sensitive path strength, and channel-order hard constraint.

[0166] The seven types of constraints are as follows:

[0167] Constraint 1: Minimum measurable strain constraint

[0168] Ensure that the strain on the sensitive path is not lower than the measurement threshold under minimum rated load:

[0169]

[0170] Where: k represents the k-th type of load, specifically including CF1, CF2, CF3, CM1, CM2, and CM3 loads; This represents the minimum measurable strain under the k-th type of load; This represents the set of sensitive strain paths for the k-th type of load; For the maximum range; Minimum measurable load , This represents the strain value generated on the i-th strain path under the k-th load condition. .

[0171] Constraint 2, Single Load Stress Safety Constraint

[0172] Hot spot stress at the location of maximum stress under maximum load for all paths Not exceeding allowable stress

[0173] Where: K=2 represents the stress amplification factor, that is, the strain gauge stress obtained within the linear elastic range is amplified to the position of maximum stress of the elastic beam of the sensor; E is the Young's modulus of the sensor, specifically, if the sensor material is aluminum, E=69e9; , For yield strength, This is for the safety factor.

[0174] Constraint 3, Dimensional Boundary Constraints

[0175] Size upper and lower limits: sensor model greater than 100mm and less than 350mm

[0176]

[0177] in, and These represent the beam length and the outer diameter of the sensor's inner flange, respectively.

[0178] Constraint 4, Beam Length Patch Constraint

[0179] The beam length is greater than twice the strain gauge length to meet the patching requirements.

[0180]

[0181] For strain gauge dimensions

[0182] Constraint 5: Geometric validity constraint of the inner flange

[0183] Sensor inner flange dimensions inner diameter From outer diameter The wall thickness was reduced by 20mm to ensure geometric validity.

[0184]

[0185] Constraint 6, Combined Load Strength Constraint

[0186] For the sensitive path, the combined stress under simultaneous six-axis loads satisfies the strength constraint:

[0187]

[0188] This represents the combined strain on the i-th sensitive strain path under simultaneous six-axis loading. This represents the combined stress on the i-th sensitive strain path under simultaneous six-axis loading. This represents the strain value generated on the i-th sensitive strain path under the k-th load condition.

[0189] As shown in Table 1, the configuration and number of sensitive strain paths corresponding to each load component are as follows:

[0190] Load component CF1: Sensitive paths include paths {1, 2, 3, 4}, {9, 10, 11, 12} (group A), and paths {6, 16}, {8, 14} (group B), for a total of 12 paths;

[0191] Load component CF2: Sensitive paths include paths {5, 6, 7, 8}, {13, 14, 15, 16} (group A), and paths {4, 10}, {2, 12} (group B), for a total of 12 paths;

[0192] Load component CF3: The sensitive paths are paths {1, 3, 5, 7, 9, 11, 13, 15}, a total of 8 paths;

[0193] Load component CM1: The sensitive paths are paths {5,7,13,15}, a total of 4 paths;

[0194] Load component CM2: The sensitive paths are paths {1, 3, 9, 11}, a total of 4 paths;

[0195] Load component CM3: The sensitive paths are paths {2, 4, 6, 8, 10, 12, 14, 16}, a total of 8 paths.

[0196] Constraint 7: Channel order of magnitude constraint

[0197] With the sensitivity of each channel on the same order of magnitude, this constraint is a hard constraint that must be met, compared to the order-of-magnitude objective in the objective function. The objective function then provides optimization space.

[0198]

[0199] Define the mean strain value of the k-th load channel, where max represents the maximum value and min represents the minimum value.

[0200] Table 1

[0201]

[0202] S3.2 Differential Evolution Optimization Module

[0203] 1) Parameter initialization: Population size 50, coefficient of variation (0.5, 1.0), crossover probability 0.7, maximum number of generations 200; 2) Generate initial population: Sample in 8-dimensional space to generate initial candidate population; 3) Iterative optimization: Call the differential evolution algorithm library to iteratively update the candidate population, generate new candidate solutions and complete population update in each iteration; During each iteration, call the surrogate evaluation module of uniaxial load prediction and linear superposition to calculate the multi-objective weighted function value and constraint violation amount corresponding to the candidate solution, and complete the selection and retention of candidate solutions according to the preset superiority and inferiority comparison rules.

[0204] In one implementation, a DE / best / 1 / bin strategy is used for global optimization.

[0205] S3.3 Convergence Determination Module

[0206] Set one of the following termination conditions:

[0207] The improvement in the optimal multi-objective weighted function value is less than the threshold 1e-7;

[0208] The maximum number of iterations was reached: 200.

[0209] The feasible optimal solution is stable for 20 consecutive generations.

[0210] Once the conditions are met, the optimal geometric parameters and range configuration, as well as the corresponding multi-objective weighted function value and constraint violation amount, are output.

[0211] The beneficial effects of this embodiment are:

[0212] Compared with schemes that rely solely on iterative finite element methods, this invention achieves the following through "CM-PINN proxy prediction + DE global optimization": 1) significantly reducing optimization computation costs while maintaining physical consistency; 2) ensuring that the compliance matrix satisfies structural constraints through hard constraint projection; 3) simultaneously outputting optimization parameters and interpretable mechanical characteristics, facilitating engineering applications and design verification.

Claims

1. An optimization method for a six-dimensional force sensor based on CM-PINN, characterized in that, It relies on a six-dimensional force sensor optimization model based on CM-PINN. The six-dimensional force sensor optimization model based on CM-PINN includes a surrogate evaluation module for uniaxial load prediction and linear superposition, a differential evolution optimization module, and a convergence determination and output module. The surrogate evaluation module for uniaxial load prediction and linear superposition is used to: first, construct optimization variables and generate candidate solutions based on the optimization variables, wherein the optimization variables include the length, width, height, inner diameter of the central platform, and six load ranges of the sensor strain beam; Then, for each candidate solution, the CM-PINN solver is invoked to calculate the strain response under six uniaxial load conditions. The strain responses under the six uniaxial load conditions are then combined into a combined load condition response. A multi-objective weighting function is calculated based on the combined load condition response. The multi-objective weighting function includes a sensitivity consistency term, a geometric deviation term, and a range deviation term. The sensitivity consistency term is related to the strain response. The geometric deviation term is related to the length, width, height, and inner diameter of the center platform of the sensor strain beam. The range deviation term is related to the six loads. Next, the degree of violation of the seven types of constraints corresponding to the multi-objective weighting function is calculated, and the constraint violation amount is calculated based on this. The seven types of constraints specifically include minimum measurable strain, single load stress safety, dimensional boundary, beam length patch, inner flange geometric validity, combined load strength, and channel order of magnitude constraint. The differential evolution optimization module is used to generate an initial candidate population, perform mutation and crossover operations within the current population, call the surrogate evaluation module of uniaxial load prediction and linear superposition for the candidate solution to calculate its corresponding multi-objective weighted function value and constraint violation, and perform optimization iteration globally based on the multi-objective weighted function value and constraint violation. The convergence determination module is used to calculate the improvement amount of the optimal multi-objective weighted function value, the stability of the feasible solution in successive iterations, and the current iteration number during the optimization iteration process, and outputs the optimal optimization variable when the termination condition is met.

2. The method for optimizing a six-dimensional force sensor based on CM-PINN according to claim 1, characterized in that, The CM-PINN solver includes a load-specific branch modeling unit, a normalized unit, a geometric feature encoding unit, a core physical constraint layer, an inverse normalized unit, and an output unit. The method for calling the CM-PINN solver for each candidate solution to calculate the strain response under six types of uniaxial load conditions is as follows: The load-specific branch modeling unit is used to construct branch models for six types of loads, and the same type of load shares the branch model. The 4D geometric parameters and the 6D load vector are standardized using standardized units respectively; The standardized 4D geometric parameters are fed into the corresponding branch model according to the load type; The geometric feature encoding unit encodes the standardized 4D geometric parameters into latent vectors according to the load type, and then enters the core physical constraint layer; The core physical constraint layer is used to map each hidden vector into a compliance matrix that satisfies the physical constraints, and outputs 16-way standardized strain accordingly. The 16 strains were inversely normalized using inverse normalization elements to obtain 16 strain responses under multiple loads. The output unit is used to output 16 strain responses; The workflow of each branch model is the same; the core physical constraint layer includes a compliance matrix generation unit, an orthogonal projection unit, and a physical calculation unit; the core physical constraint layer is used to map each latent vector into a compliance matrix that satisfies the physical constraints, and outputs 16-way standardized strain accordingly, specifically as follows: The implicit vector is mapped to a 96-dimensional flattened vector using the compliance matrix generation unit and reconstructed into the original compliance matrix. The original compliance matrix is ​​then subjected to L2 optimal orthogonal projection using the orthogonal projection unit based on the B matrix to obtain the projected compliance matrix. The physical calculation unit performs matrix multiplication on the projected compliance matrix and the standardized load vector to obtain the standardized strain.

3. The method for optimizing a six-dimensional force sensor based on CM-PINN according to claim 2, characterized in that, The training method for the CM-PINN solver is as follows: First, the range of values ​​for optimization variables and the set of load conditions are set to generate training samples. The training samples include the length, width, height, inner diameter of the central platform and six loads of the sensor strain beam, the length, width, height and outer diameter of the central platform of the sensor strain beam and 16 strain responses under multiple loads. Then, for the six load conditions, a four-branch structure is used for training, with each branch corresponding to one of the four load types. Symmetrical constraints are achieved through parameter sharing in symmetric channels, while the ability to express differences is preserved through independent modeling in asymmetric channels. Specifically, the branch models corresponding to symmetric load types use a parameter sharing mechanism to achieve structural symmetry constraints, while the branch models corresponding to asymmetric load types use independent modeling to preserve the asymmetric differences in their mechanical responses. The geometric encoder, core physical constraint layer, and inverse normalized unit structure of each branch model are consistent. The physical constraint layer is used to map each latent vector into a compliance matrix that satisfies the physical constraints, and outputs 16-way normalized strain accordingly. During training, the Adam optimizer is used to iteratively update the model parameters, while an early stopping strategy is used to prevent the model from overfitting. After training, the strain prediction accuracy of the CM-PINN solver under different geometric parameters and load conditions is verified through the test set to ensure that the CM-PINN solver meets the preset error threshold. When the prediction error converges to the target range, the training is completed and the trained CM-PINN solver is obtained.

4. The optimization method for a six-dimensional force sensor based on CM-PINN according to claim 1, characterized in that, The multi-objective weighting function is specifically expressed as follows: in, For sensitivity consistency, For geometric deviation terms, For the range deviation term, w1, w2, and w3 represent the weights of the sensitivity consistency term, geometric deviation term, and range deviation term, respectively. The calculation formula is: in, It is the mean of the representative values ​​after taking the logarithm; The mean strain value corresponding to the i-th load type; As the zero offset; n is the number of payload types; The calculation formula is: in: The current geometric parameters for the i-th load type; The preset target geometric parameters are for the i-th load type; i =1 corresponds to CF 1 and CF 2. Load type i =2 corresponds to CM 1 and CM 2. Load type i =3 corresponds to CF 3. Load type i =4 corresponds to CM 3. Load type; The calculation formula is: in: The current load range for the i-th load type; The preset target load range is for the i-th load type.

5. The optimization method for a six-dimensional force sensor based on CM-PINN according to claim 1, characterized in that, The seven types of constraints are as follows: Constraint 1: Minimum measurable strain constraint in, This represents the minimum measurable strain under the k-th type of load. This represents the set of sensitive strain paths for the k-th type of load. For the maximum range of the k-th type of load, The minimum measurable load for the k-th type of load. This represents the strain value generated on the i-th strain path under the k-th load condition; ; Constraint 2, Single Load Stress Safety Constraint Where: K represents the stress amplification factor. For hot spot stress; E is the Young's modulus of the sensor; For allowable stress, , For yield strength, For safety factor; Constraint 3, Dimensional Boundary Constraints in, and These represent the beam length and the outer diameter of the sensor's inner flange, respectively. These represent the beam length and the outer diameter of the sensor's inner flange, respectively. Constraint 4, Beam Length Patch Constraint For strain gauge dimensions; Constraint 5: Geometric validity constraint of the inner flange in, This refers to the inner diameter of the sensor's inner flange. Constraint 6, Combined Load Strength Constraint For the sensitive path, the combined stress under simultaneous six-axis loads satisfies the strength constraint. This represents the combined strain on the i-th sensitive strain path under simultaneous six-axis loading. This represents the combined stress on the i-th sensitive strain path under simultaneous six-axis loading. This represents the strain value generated on the i-th sensitive strain path under the k-th load condition; Constraint 7: Channel order of magnitude constraint Define the mean strain value of the k-th load channel, where max represents the maximum value and min represents the minimum value. .

6. The optimization method for a six-dimensional force sensor based on CM-PINN according to claim 1, characterized in that, The differential evolution optimization module specifically includes a parameter initialization unit, a population generation unit, and an iterative optimization unit. The parameter initialization unit is used to set the boundary of optimization variables, the weights of different objectives in the multi-objective weighting function, constraint rules, and differential evolution parameters, including population size, mutation factor, crossover probability, and maximum number of iterations. The population generation unit is used to generate an initial candidate population within the design space; The iterative optimization unit is used to call the differential evolution algorithm library to iteratively update the current candidate population. In each iteration, the surrogate evaluation module of single-axis load prediction and linear superposition is called for the candidate solution to calculate its corresponding multi-objective weighted function value and constraint violation amount, and the candidate population is updated according to the preset superiority and inferiority comparison rules, thereby gradually approaching the global optimal solution.

7. The method for optimizing a six-dimensional force sensor based on CM-PINN according to claim 1, characterized in that, The convergence determination module includes a convergence determination unit and a result output unit; The convergence determination unit is responsible for calculating the improvement amount of the optimal multi-objective weighted function value, the stability of the feasible solution in successive iterations and the current iteration number during the iteration process, and determining whether the convergence condition is met. The convergence conditions include: the improvement of the optimal multi-objective weighted function value is lower than a preset threshold, the maximum number of iterations is reached, and the feasible optimal solution remains stable for several consecutive generations. The result output unit is used to output the optimal geometric parameters and range configuration when at least one convergence condition is met, and to perform sensitivity, stress, size and order of magnitude verification.

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