Excavator structure topology optimization method and system based on real-time stress field reconstruction

Abstract

This invention relates to the field of engineering machinery structural optimization technology, specifically to a method and system for topology optimization of excavator structures based on real-time stress field reconstruction. The method involves acquiring deformation and stress data of key parts of the excavator boom using a distributed fiber optic grating sensor array, and then modeling and simulating these data in finite element analysis software to obtain virtual data. A Kalman filter is designed to correct errors between the virtual and actual test data, and the corrected data is used to train the Kalman filter to predict the real-time stress field distribution. Furthermore, a topology optimization model of the excavator structure is established, encoding material properties into weight matrices in a neural network, and using stress constraint partial differential equations as constraints. This achieves high-precision reconstruction of the excavator boom stress field under actual working conditions, providing accurate boundary conditions for topology optimization.

Description

Technical Field

[0001] This invention relates to the field of engineering machinery structure optimization technology, specifically to a method and system for topology optimization of excavator structures based on real-time stress field reconstruction. Background Technology

[0002] Excavators, as crucial equipment in the construction machinery field, have structural performance that directly impacts work efficiency and service life. Traditional excavator structural design relies primarily on experience and finite element analysis, making it difficult to accurately capture stress distribution under actual working conditions. This leads to problems such as conservative redundancy or insufficient local strength in the structural design. While topology optimization is widely used in engineering structural optimization design, traditional topology optimization methods in the excavator field have the following limitations:

[0003] First, traditional topology optimization is mostly based on static loading assumptions, which makes it difficult to accurately reflect the actual stress state of excavators under complex dynamic working conditions. The optimization results often deviate significantly from the actual working conditions.

[0004] Secondly, conventional topology optimization algorithms are inefficient, struggle to handle complex constraints involving multi-physics coupling, and are difficult to simultaneously achieve the goals of structural lightweighting and fatigue life.

[0005] Third, traditional methods lack an effective mechanism for integrating real-time monitoring data with the optimization process, making it impossible to dynamically adjust optimization strategies based on actual working conditions.

[0006] Fourth, the optimization results lack a closed-loop verification and feedback mechanism, which cannot guarantee the reliability of the optimization scheme in actual working conditions.

[0007] Therefore, there is an urgent need to develop a new method that can perform efficient and accurate topology optimization based on real-time stress field data to meet the dual requirements of lightweight excavator structure and high reliability. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for topology optimization of excavator structures based on real-time stress field reconstruction. The method acquires excavator boom stress data in real time through distributed fiber optic grating sensors, reconstructs the stress field using a Kalman filter algorithm, and further optimizes the topology using a physical information neural network to achieve synergistic optimization of excavator structure lightweighting and fatigue life.

[0009] This invention proposes a topology optimization method for excavator structures based on real-time stress field reconstruction, including:

[0010] Based on a distributed fiber optic grating sensor array, deformation and stress test data of key parts of the excavator boom are acquired, and modeling and simulation are performed simultaneously in finite element analysis software to obtain corresponding virtual data.

[0011] A Kalman filter is designed to correct errors in the virtual data and the deformation and stress test data of the key parts. The Kalman filter is then trained. The corrected virtual data and the corrected deformation and stress test data of the key parts are input into the Kalman filter to obtain a prediction matrix of the fused state quantities. The optimal filter gain is obtained through the prediction matrix. The optimal filter gain is applied to the deformation and stress test data of the key parts to output the real-time stress field distribution during the excavator operation.

[0012] A topology optimization model is established for the excavator structure. When solving the topology optimization model, the material properties are encoded and used as the weight matrix between the input layer and the hidden layer in the neural network. Stress constraint partial differential equations are defined and embedded in the topology optimization model, and used as constraints in the neural network.

[0013] Preferably, the steps for obtaining deformation and stress test data of key parts of the excavator boom specifically include:

[0014] Define a data matrix, which includes: the virtual data and the corresponding time axis;

[0015] Acquire time-series data from a distributed fiber Bragg grating sensor array, including deformation and strain data;

[0016] By combining the data matrix, the deformation data and the strain data are subjected to dimensional transformation to obtain preprocessed data.

[0017] Preferably, in the step of designing the Kalman filter, the Kalman filter includes a measurement equation and a state equation. The measurement equation contains measurement noise, and the state equation contains system noise. The prediction output of the Kalman filter includes the excavator structural state measurement value, the predicted value, and the prediction variance. Based on Bayesian filtering theory, a recursive algorithm is used to obtain the predicted value and the observed value at the current time according to the initial state. The optimal state estimate under the minimum mean square error is obtained by the filtering algorithm. The optimal state estimate is the excavator structural state measurement value, and the optimal state estimate is obtained by the optimal filter gain.

[0018] Preferably, the steps for training the Kalman filter specifically include:

[0019] The preprocessed data and the virtual data are used as a training set, and the true values ​​of the fusion state variables and the prediction matrix of the fusion state variables are set in the training set.

[0020] The true value corresponding to the preprocessed data is determined based on the preprocessed data, and the prediction matrix corresponding to the virtual data is determined based on the virtual data. The true value represents the true error between the virtual data and the preprocessed data. The true value serves as the true value of the fused state quantity. The optimal filter gain is obtained based on the error between the prediction matrix and the true value. The optimal prediction matrix is ​​obtained based on the optimal filter gain.

[0021] As a preferred option, the steps for establishing a topology optimization model for the excavator structure specifically include:

[0022] Multi-objective constrained topology optimization is performed on the excavator structure, and the objective function is defined as the elastic modulus and natural frequency;

[0023] The constraints of the topology optimization model are set as volume fraction constraints, stress constraints, and sensitivity constraints. The volume fraction constraints are used to limit the volume of the structure, the stress constraints are used to ensure that the stress value of the key parts is less than or equal to the maximum stress value of the material strength, and the sensitivity constraints are used to represent the sensitivity of the objective function and constraints to the design variables.

[0024] Preferably, in the topology optimization model, the stress constraint partial differential equation is defined as follows: the stress constraint partial differential equation represents the relationship between the maximum stress value and the stress value during the solution process, and is used to ensure that the stress value of the key part meets the stress constraint condition.

[0025] Preferably, the following steps are also included:

[0026] The topology optimization model is optimized using a gradient algorithm, the structural flexibility is calculated in the topology optimization model, and a topology optimization design scheme for the excavator boom structure is generated.

[0027] A variable density method solver is integrated into ANSYS, and a gradient adaptive mesh is designed. The material is set to ideal elastoplasticity, the region constraint state is defined, external forces and torques are applied, and a material redistribution map is obtained through finite element analysis. The material is then redistributed according to the material redistribution map.

[0028] Preferably, the following steps are also included:

[0029] For the dynamic load environment of the boom, a microstructure gradient topology algorithm that considers the boom's natural frequency and material gradient distribution was developed;

[0030] The microstructure gradient topology algorithm considers the natural frequency and material mass distribution of the excavator boom structure, determines the constraints of the microstructure gradient topology algorithm, uses a physical information neural network to solve the gradient weight function according to the constraints, and establishes a gradient topology optimization algorithm based on the gradient weight function in the physical information neural network to achieve the optimal material distribution.

[0031] Preferably, the following steps are also included:

[0032] The adaptive meshing technique is used to refine the finite element discretization in stress concentration regions, thereby obtaining strain data with an accuracy of 0.1 mm.

[0033] Based on the strain data with an accuracy of 0.1 mm, the stress field is reconstructed using the Kalman filter algorithm to obtain the stress distribution.

[0034] The reconstructed stress field data and the position information of the sensing fiber are mapped into the computational domain. The entire computational domain is discretized into multiple units using a discrete method to form a strain distribution matrix and a sensor number matrix.

[0035] The excavator structure topology optimization system based on real-time stress field reconstruction includes:

[0036] The acquisition module is used to acquire deformation and stress test data of key parts of the excavator boom based on a distributed fiber Bragg grating sensor array, and simultaneously model and simulate in finite element analysis software to obtain corresponding virtual data.

[0037] A filtering module is used to design a Kalman filter, correct errors in the virtual data and the deformation and stress test data of the key parts, train the Kalman filter, obtain a prediction matrix of fused state quantities based on the corrected virtual data and the corrected deformation and stress test data of the key parts, obtain the optimal filtering gain through the prediction matrix, apply the optimal filtering gain to the deformation and stress test data of the key parts, and output the real-time stress field distribution during the excavator operation.

[0038] The optimization module is used to establish a topology optimization model for the excavator structure. When solving the topology optimization model, the material properties are encoded and used as the weight matrix between the input layer and the hidden layer in the neural network. Stress constraint partial differential equations are defined and embedded in the topology optimization model, and used as constraints in the neural network.

[0039] The present invention has the following beneficial effects:

[0040] 1. By acquiring deformation and stress test data of key parts of the excavator boom in real time through a distributed fiber optic grating sensor array, and combining the virtual data from finite element simulation, the data was fused using a Kalman filter algorithm, achieving high-precision reconstruction of the stress field of the excavator boom under actual working conditions, and providing accurate boundary conditions for topology optimization.

[0041] 2. By applying physical information neural network technology, material properties are encoded as neural network weights, and stress constraint partial differential equations are embedded into the topology optimization model as constraints of the neural network. This significantly improves the computational efficiency and accuracy of topology optimization, enabling the topology optimization model to simultaneously consider multiple objectives such as structural lightweighting, stiffness, and fatigue life.

[0042] 3. A multi-objective constrained topology optimization model was established, defining the objective function as the elastic modulus and natural frequency, while considering constraints such as volume fraction, stress, and sensitivity, thus achieving comprehensive optimization of the excavator's structural performance.

[0043] 4. By using gradient adaptive meshing technology and variable density method, material redistribution with an accuracy of 0.1 mm was achieved in stress concentration areas, which greatly improved the strength and fatigue life of the structure in critical areas.

[0044] 5. A complete technical closed loop was constructed, from real-time data acquisition, stress field reconstruction, topology optimization to physical verification, which enabled the effectiveness verification and continuous improvement of optimization results.

[0045] This invention reduces the weight of the excavator boom structure by 15% to 25%, increases fatigue life by 30% to 50%, and shortens the optimization cycle from the traditional 3 to 6 months to 2 to 4 weeks, providing a new technical solution for the optimization of engineering machinery structures. Attached Figure Description

[0046] Figure 1 This is a flowchart of the excavator structure topology optimization method based on real-time stress field reconstruction of the present invention;

[0047] Figure 2 This is a schematic diagram of the arrangement of the distributed fiber optic grating sensor array of the present invention on the excavator boom;

[0048] Figure 3 This is a schematic diagram of the Kalman filter of the present invention applied to stress field reconstruction;

[0049] Figure 4 This is a schematic diagram of the physical information neural network structure of the present invention, illustrating the material property encoding and stress constraint embedding mechanism;

[0050] Figure 5 This is a diagram showing the relationship between the objective function and constraint conditions of the multi-objective constrained topology optimization model of this invention;

[0051] Figure 6 This is a schematic diagram illustrating the application of the gradient adaptive mesh refinement of this invention in stress concentration regions;

[0052] Figure 7 This is a system architecture diagram of the present invention, which shows the interaction relationships between the various functional modules. Detailed Implementation

[0053] Please refer to the attached document. Figure 1-7 The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, the excavator structure topology optimization method based on real-time stress field reconstruction provided by this invention includes the following steps:

[0055] Step 1: Acquiring data based on a distributed fiber Bragg grating sensor array:

[0056] like Figure 2 As shown, this invention first acquires deformation and stress test data of key parts of the excavator boom based on a distributed fiber Bragg grating sensor array. Preferably, the distributed fiber Bragg grating sensor array is attached to high-stress areas of the excavator boom, such as the boom root, the curved surface in the middle of the boom, and key connecting hinge points. In practical applications, the fiber Bragg grating sensor used in this invention has the characteristics of high sensitivity, resistance to electromagnetic interference, and small size, and can acquire accurate strain data without affecting the normal operation of the excavator. The preferred sensor acquisition frequency is 100Hz. This frequency selection is based on the frequency characteristics analysis of a typical excavator working cycle, which can effectively capture dynamic strain changes under digging, lifting, and unloading conditions, while avoiding excessive redundant data.

[0057] Simultaneously, an accurate model of the excavator boom is established in finite element analysis software (such as ANSYS), and corresponding boundary conditions and loads are applied for simulation analysis to obtain corresponding virtual data. This virtual data includes, but is not limited to, stress distribution, deformation, and strain values ​​of various parts of the boom. During the modeling process, this invention accurately models the key structural features of the excavator boom, including details such as wall thickness variations, stiffeners, and hinge points, ensuring a high degree of consistency between the virtual model and the actual structure. Regarding load conditions, the excavation force (typically 150-200 kN), the influence of self-weight (typical boom weight is 2-3 tons), and inertial forces under dynamic working conditions are comprehensively considered to simulate various working conditions that the excavator may encounter in actual operation.

[0058] In one embodiment of the present invention, obtaining deformation and stress test data of key parts of the excavator boom specifically includes the following steps:

[0059] First, a data matrix is ​​defined, which includes dummy data and the corresponding time axis. Specifically, the data matrix can be represented as D. virtual ={d1(t1),d2(t2),...,d n (t n )}, where d i This represents the virtual data vector at time i, containing the stress and strain values ​​at each measuring point obtained from the finite element analysis; t i The timestamp represents the corresponding data, reflecting the temporal characteristics of the data acquisition; n represents the length of the time series, which is usually determined based on the complete cycle of the excavator's work cycle, typically ranging from 1000 to 5000 in typical applications, corresponding to 10 to 50 seconds of continuous monitoring data. This matrix representation method is beneficial for subsequent time synchronization and comparative analysis with measured data.

[0060] Secondly, data from a time-series distributed fiber Bragg grating sensor array is acquired, including deformation and strain data. Preferably, the sensor array contains 30-50 measuring points distributed in the key areas of the boom, with each measuring point simultaneously acquiring deformation data δ. i (Unit: mm) and strain data ε i (Unit: με, microstrain).

[0061] Sensor data can be represented as D sensor ={(δ1,ε1,t1),(δ2,ε2,t2),...,(δ m ,ε m ,t m )}, where δ i Let ε be the deformed data vector at time i. i Let t be the strain data vector at time i. iHere is the corresponding timestamp, and m is the number of data collection points. In practical applications, for medium-sized excavators of the 20-ton class, the deformation of key parts is usually in the range of 0.1-5mm, and the strain value is in the range of 100-2000με. These data are of great significance for assessing structural safety and fatigue life.

[0062] Finally, the deformation data and strain data are subjected to dimensionality transformation using the data matrix to obtain preprocessed data. The purpose of dimensionality transformation is to ensure that the sensor data and virtual data are consistent in dimension and format, facilitating subsequent data fusion processing. The preprocessed data can be represented as D. processed ={p1(t1),p2(t2),...,p n (t n )}, where p i The processed data vector, and the virtual data vector d i They possess the same dimensions and structure. The dimensional transformation methods employed in this invention include interpolation, filtering, and coordinate transformation techniques to ensure that the measured data accurately corresponds to the virtual data in both time and space dimensions. In particular, for data in areas not covered by the sensor, a physically constrained interpolation algorithm is used for estimation, achieving an interpolation accuracy 25%–30% better than traditional linear interpolation methods, thus providing a reliable foundation for subsequent full-field stress reconstruction.

[0063] Step 2: Design a Kalman filter for stress field reconstruction:

[0064] like Figure 3 As shown, this invention designs a Kalman filter to correct errors in the virtual data and the deformation and stress test data of the key components. As a recursive optimal estimator, the Kalman filter is particularly suitable for handling the state estimation problem of dynamic systems containing random noise, and in this invention, it is innovatively applied to the real-time stress field reconstruction of an excavator boom.

[0065] In one embodiment of the present invention, the Kalman filter includes a measurement equation and a state equation, wherein the measurement equation can be expressed as:

[0066] z k =H k x k +v k ,

[0067] The state equation can be expressed as:

[0068] x k =F k x k-1 +B k u k +w k ,

[0069] Among them, z k The measurement equation represents the observed value at time k, which in this application corresponds to the deformation and strain data measured by the sensor; x k The state equation represents the state variables at time k, corresponding to the complete stress field distribution; H k The measurement matrix maps the state space to the observation space, reflecting the relationship between the sensor arrangement and the complete stress field; F k B is the state transition matrix, describing the evolution of the system state and reflecting the law of stress field change over time; k The control matrix represents the influence coefficients of external inputs on the system state; u k The control vector represents known external inputs, such as the excavator's working load; v k The measurement noise is typically assumed to be Gaussian white noise with a mean of 0 and a covariance of R. k ;w k This represents system noise, also assumed to be Gaussian white noise, with a covariance of Q. k .

[0070] In excavator applications, measurement noise mainly comes from sensor accuracy limitations, installation errors, and external interference, while system noise mainly comes from model simplification and parameter uncertainty.

[0071] The Kalman filter's prediction output includes the excavator's structural state measurements, predicted values, and prediction variance. Based on Bayesian filtering theory, a recursive algorithm is used to obtain the predicted and observed values ​​at the current time step from the initial state, and the optimal state estimate with minimum mean square error is obtained by the filtering algorithm.

[0072] Preferably, the Kalman filter model can be expressed as:

[0073] 1. Prediction steps:

[0074]

[0075] 2. Update steps:

[0076]

[0077] in, For prior state estimation, it represents the predicted state value at time k obtained from the system dynamic model; K represents the prior estimation error covariance, indicating the uncertainty of the predicted value; k The Kalman gain determines the weighting of the observed and predicted values. The posterior state estimate is the optimal estimate obtained by fusing predictions and observations; P kLet Q be the posterior estimation error covariance, representing the uncertainty of the optimal estimate; k R represents the process noise covariance. k To measure the noise covariance; I is the identity matrix. In practical applications, Q... k and R k The values ​​of these parameters have a significant impact on the filter performance. This invention determines these parameters by analyzing historical data and expert experience, and designs an adaptive adjustment mechanism.

[0078] In this invention, the optimal state estimate is the measured value of the excavator's structural state, which is obtained from the optimal filter gain. The optimal filter gain represents the measure of the minimum mean square error between the predicted output and the measured value at the current moment, and the optimal estimate represents the solution for the minimum mean square error. For the stress field reconstruction of the excavator boom, the application of Kalman filtering can not only effectively fuse measured data from a finite number of sensors and finite element simulation data, but also smoothly eliminate noise effects and capture the dynamic characteristics of the stress field.

[0079] The present invention further trains the Kalman filter, and the specific steps are as follows:

[0080] First, the preprocessed data and the virtual data are used as a training set, and the ground truth values ​​and prediction matrices of the fused state variables are set in the training set. Preferably, the training set includes data under multiple working conditions to improve the generalization ability of the filter. In practical applications, data are collected to construct training sets for typical excavator operating conditions, such as digging, lifting, slewing, and unloading, to ensure that the filter can adapt to various working conditions. The training set data volume is typically 10-15 complete work cycles for each working condition, totaling 500-1000 seconds of time-series data.

[0081] Secondly, the true value corresponding to the preprocessed data is determined based on the preprocessed data, and the prediction matrix corresponding to the virtual data is determined based on the virtual data. Specifically, the true value represents the actual error between the virtual data and the preprocessed data, and can be expressed as:

[0082] e k =d k -p k ,

[0083] Where, e k Let d be the error vector at time k. k Let p be the virtual data vector at time k. k Let be the preprocessed data vector at time k. The true value is used as the true value of the fused state variable, denoted as . In excavator applications, these error data reflect the differences between the theoretical model and the actual structure, and are of great value for identifying model uncertainties and improving reconstruction accuracy.

[0084] Then, the error between the prediction matrix and the true value is calculated:

[0085]

[0086] in, The prediction matrix for the fused state variables represents the stress field distribution predicted by the Kalman filter. For the true stress field distribution, ε k This refers to the prediction error. For excavating booms, the magnitude and distribution characteristics of the prediction error can be used to evaluate filter performance and adjust filter parameters.

[0087] Finally, by minimizing the mean square value of the error, the optimal filter gain is obtained as follows:

[0088]

[0089] in, For the optimal Kalman gain, E[·] represents the expectation operation. This represents the square of the prediction error. In actual calculations, this minimization problem is solved using an iterative optimization method, which typically requires 5-10 iterations to converge to satisfactory accuracy.

[0090] Based on the optimal filter gain Obtain the optimal prediction matrix:

[0091]

[0092] in, The optimal prediction matrix, Let z be the prior prediction matrix. k For the observed value, H k The measurement matrix is ​​denoted as . The optimal prediction matrix represents the best estimate of the stress field distribution of the excavator boom under given observation data.

[0093] The optimal filtering gain is applied to the deformation and stress test data of the key components to output the real-time stress field distribution during excavator operation. Preferably, the stress field distribution is represented in three-dimensional tensor form, including the stress components of each part of the excavator boom in the x, y, and z directions, as well as the principal stress values ​​and von Mises equivalent stresses. In practical applications, the accuracy of the reconstructed stress field can reach ±5% of the measured stress value, and ±10% for non-measurement areas, far superior to traditional methods based solely on finite element simulation. This high-precision real-time stress field distribution provides reliable load boundary conditions for subsequent topology optimization.

[0094] Step 3: Construct a topology optimization model based on a physical information neural network:

[0095] like Figure 4 As shown, this invention establishes a topology optimization model for excavator structures. During the solution process of this model, material properties are encoded and used as the weight matrix between the input and hidden layers of a neural network. Stress constraint partial differential equations are defined and embedded into the topology optimization model, serving as constraints within the neural network. This innovative method of applying physical information neural networks to excavator structure topology optimization overcomes the limitations of traditional topology optimization methods, such as low computational efficiency and difficulty in handling complex constraints.

[0096] In a preferred embodiment of the present invention, the step of establishing a topology optimization model for the excavator structure specifically includes:

[0097] Multi-objective constrained topology optimization is performed on the excavator structure, with the objective function defined as the elastic modulus and natural frequency. Preferably, the elastic modulus can be expressed as:

[0098] E(ρ)=E min +(E0-E min )ρ p ,

[0099] Where E(ρ) is the elastic modulus of the structure, in GPa, reflecting the stiffness characteristics of the material; ρ is the relative density of the material, ranging from 0 to 1, representing the degree of unit filling, ρ = 1 represents solid material, ρ = 0 represents voids; E0 is the elastic modulus of the matrix material (without voids), for commonly used Q345 steel, E0 is approximately 210 GPa; E min To avoid singularity issues, a minimum value is typically set to one ten-thousandth of E0, i.e., 0.021GP a; p is a penalty factor, usually set to 3, used to suppress the occurrence of intermediate densities and guide the optimization results to approach a 0 / 1 distribution. This material interpolation model based on the SIMP (Solid Isotropic Material with Penalization) method can effectively handle the material distribution problem in excavator structure optimization.

[0100] The objective function for topology optimization can be expressed as:

[0101]

[0102] Where f1 represents structural flexibility, an important indicator of structural stiffness; the smaller the value, the higher the structural stiffness; u is the displacement vector, representing the displacement of each node of the structure under load; K is the stiffness matrix, determined by material properties and element geometry; f2 represents the ratio of the i-th natural frequencies, ω iThe optimized i-th natural frequency, in Hz; This refers to the i-th natural frequency before optimization, also in Hz. In excavator applications, the first 3-5 natural frequencies are typically considered to avoid resonance with the excitation frequency. A typical excavator boom operates primarily in the 0.5-10Hz frequency range, therefore the optimization objective is usually set to increase the natural frequencies within this range.

[0103] The constraints of the topology optimization model are set as volume fraction constraints, stress constraints, and sensitivity constraints. The volume fraction constraints, used to limit the volume of the structure, can be expressed as:

[0104]

[0105] Where, ρ i V represents the relative density of the i-th unit; i Let represent the volume of the i-th unit, in mm. 3 ; V represents the total volume of the design domain. f This represents the upper limit of the volume fraction, typically set to 0.3-0.5, indicating that the optimized structure volume does not exceed 30% to 50% of the original volume. In the optimization of excavator booms, volume constraints are directly related to structural weight, and setting reasonable volume constraints is key to balancing lightweighting and strength requirements.

[0106] The stress constraint is used to ensure that the stress value at critical locations is less than or equal to the maximum stress value of the material strength, and can be expressed as:

[0107] σ max ≤β·σ allow

[0108] Where, σ max The maximum stress calculated is given in MPa; σ allow β represents the allowable stress of the material. For Q345 steel, its yield strength is 345 MPa. Considering the safety factor, the allowable stress is usually taken as 275-310 MPa. β is the safety factor, usually taken as 0.8-0.9, determined according to the safety requirements of the application scenario. In critical load-bearing structures such as excavator booms, stress constraint is the core constraint condition to ensure structural safety.

[0109] The sensitivity constraint is used to represent the sensitivity of the objective function and the constraint relative to the design variables, and can be expressed as:

[0110]

[0111] in, It represents the sensitivity of the objective function f to the design variable ρ, reflecting the degree of influence of changes in the design variable on the objective function; This represents the sensitivity of the stiffness matrix K to the elastic modulus E. Sensitivity information is fundamental to gradient optimization algorithms and has a significant impact on the convergence speed and stability of the optimization process.

[0112] In the topology optimization model, the stress-constrained partial differential equation is defined as:

[0113]

[0114] in, It represents the sensitivity of stress to design variables, reflecting the influence of changes in material distribution on stress distribution; It represents the sensitivity of stress to displacement, which is determined by the geometric characteristics and material properties of the structure; The sensitivity of displacement to design variables can be obtained through finite element analysis and adjoint methods. In the optimization of excavator booms, stress sensitivity information guides the optimal distribution of materials in high-stress regions, playing a crucial role in improving the local strength of the structure.

[0115] The stress constraint condition can be further expressed as:

[0116] g(σ)=σ max -σ allow ≤0,

[0117] Where g(σ) is the stress constraint function, σ max σ represents the maximum stress value. allow This represents the allowable stress value. When g(σ) ≤ 0, the structure meets the strength requirements; when g(σ) > 0, there is a risk of insufficient strength. Adjusting the material distribution to satisfy stress constraints during optimization is a crucial means of ensuring structural safety.

[0118] In addition, the present invention also includes the following steps:

[0119] The topology optimization model is optimized using a gradient algorithm. Structural flexibility is calculated within the topology optimization model, and a topology optimization design scheme for the excavator boom structure is generated. Preferably, sequential linear programming (SLP) or moving asymptote method (MMA) is used as the gradient optimization algorithm to iteratively solve the topology optimization problem. In each iteration, the design variables are updated based on sensitivity information.

[0120]

[0121] Where, ρ i+1 Let ρ be the design variable for the (i+1)th iteration, representing the updated material distribution; iLet be the design variable for the i-th iteration, representing the current material distribution; α is the step size factor, usually taken as 0.01-0.05, which controls the update magnitude of each iteration. A smaller step size is beneficial for optimization stability, but will increase the number of iterations. To assess the sensitivity of the Lagrangian function to design variables, the influence of the objective function and constraints is comprehensively considered. In practical applications, optimization iterations typically require 100-200 iterations to converge to a satisfactory result. However, using the physical information neural network method of this invention, the number of iterations can be reduced to 30-50, significantly improving computational efficiency.

[0122] This invention integrates a variable density method solver into ANSYS, designs a gradient adaptive mesh, sets the material to ideal elastoplastic properties, defines region constraints, applies external forces and moments, obtains a material redistribution map through finite element analysis, and redistributes the material based on this map. In practical applications, this invention develops an ANSYS secondary development interface, seamlessly integrating the optimization algorithm with commercial finite element software, achieving fully automated processing from model creation and load application to optimization result output. This integration method leverages both ANSYS's powerful pre- and post-processing capabilities and the advantages of independently developed algorithms, significantly improving engineering application efficiency.

[0123] Step 4: Microstructure gradient topology algorithm and adaptive mesh technique:

[0124] This invention also includes a microstructure gradient topology algorithm developed for dynamic load environments of the boom, considering the boom's natural frequency and material gradient distribution. This algorithm can simultaneously consider the static strength and dynamic characteristics of the structure, achieving a balance between lightweight design and high performance. In excavator applications, the boom not only bears static loads but is also affected by dynamic impacts and vibrations during the excavation process; therefore, considering dynamic characteristics is crucial for the practicality of the optimization results.

[0125] The described microstructure gradient topology algorithm considers the natural frequency and material mass distribution of the excavating boom structure, determines the constraints of the algorithm, and uses a physical information neural network to solve for the gradient weight function based on these constraints. A gradient topology optimization algorithm is then established based on the gradient weight function in the physical information neural network to achieve the optimal material distribution. This multi-scale optimization method not only optimizes the overall structural morphology macroscopically but also optimizes the material distribution microscopically, achieving more efficient material utilization.

[0126] Preferably, the constraint conditions of the microstructure gradient topology algorithm can be expressed as:

[0127]

[0128] ∫ Ω ρ(x,y,z)dΩ≤Vf ·Ω total ,

[0129]

[0130] Where, ω i Let be the i-th natural frequency, in Hz; γ is the i-th natural frequency of the initial structure, also in Hz; γ is the frequency constraint coefficient, usually taken as 0.9-1.1, used to control the dynamic characteristics of the optimized structure; ρ(x,y,z) is the relative density of the material at position (x,y,z), with a value range of 0-1; Ω is the design domain, representing the optimizable region; V f This is the upper limit for volume fraction, typically taken as 0.3-0.5; Ω total Total volume, in mm 3 δ is the gradient constraint parameter, used to control the smoothness of material distribution. It is usually taken as 0.05-0.1. Smaller values ​​lead to a smoother density distribution, which is beneficial to improving the manufacturability of the structure. In the optimization of excavator booms, the reasonable setting of these constraints is the key to balancing static performance, dynamic characteristics and manufacturing feasibility.

[0131] The gradient weight function can be expressed as:

[0132] h(x,y,z)=[(x-x0) 2 +(y-y0) 2 +(z-z0) 2 ] -λ / 2 ,

[0133] Where (x0, y0, z0) are the coordinates of the stress concentration point, representing the high-stress area requiring special attention, typically determined based on initial analysis results or engineering experience; λ is the gradient attenuation coefficient, usually taken as 1.5-2.5, controlling the attenuation rate of material distribution from the stress concentration point outwards. A larger λ value results in a steeper material distribution gradient, suitable for areas with large stress gradients; a smaller λ value produces a gentler distribution, suitable for areas with more uniform stress changes. This gradient weight function design based on stress concentration points can specifically optimize the material distribution in high-stress areas, improving the local strength and overall performance of the structure.

[0134] This invention also includes refining the finite element discretization in stress concentration regions using the adaptive meshing technique to obtain strain data with an accuracy of 0.1 mm. Preferably, when the stress level in a certain region exceeds 80% of the material's yield strength, the mesh in that region is refined, with the mesh size reduced to 0.1 mm, to accurately capture the stress gradient at stress concentration points. In stress concentration areas of excavator booms, such as hinge points, stiffener roots, and abrupt changes in cross-section, the stress gradient is often large. Conventional meshing is difficult to accurately capture the stress distribution in these areas, while adaptive meshing technology can achieve reasonable allocation of computational resources and provide high-precision results in critical areas.

[0135] Based on the 0.1mm precision strain data, the stress field is reconstructed using the Kalman filter algorithm to obtain the stress distribution. This high-precision stress distribution information is crucial for evaluating the fatigue performance and lifespan of structures, especially for engineering machinery such as excavators that operate under complex load conditions for extended periods. Traditional methods struggle to obtain such detailed stress distribution data, but this invention successfully achieves high-precision stress field reconstruction by combining adaptive meshing and Kalman filtering.

[0136] The reconstructed stress field data and the position information of the sensing fiber are mapped into the computational domain. The entire computational domain is discretized into multiple elements to form a strain distribution matrix and a sensor number matrix. Preferably, the computational domain is discretized into a 100×100×50 grid, with each grid cell measuring 2mm×2mm×2mm, and locally refined to 0.1mm×0.1mm×0.1mm in stress concentration regions. This multi-resolution meshing strategy balances computational accuracy and efficiency, providing precise boundary conditions for subsequent topology optimization. In practical applications, for the boom structure of a 20-ton excavator, the global grid size is approximately 500,000, and the number of grid cells in locally refined regions is approximately 100,000-200,000. The total computation time is within an acceptable range for engineering applications (typically 2-4 hours).

[0137] This invention also provides an excavator structure topology optimization system based on real-time stress field reconstruction, including an acquisition module 1, a filtering module 2, and an optimization module 3. This system corresponds to the method described in Embodiment 1 and can automatically execute the entire process from data acquisition to optimization scheme generation. The data flow between the various modules of the system is clear, and the interface definitions are standardized, ensuring the efficiency and reliability of the entire optimization process.

[0138] Acquisition module 1 is used to acquire deformation and stress test data of key parts of the excavator boom based on a distributed fiber Bragg grating sensor array, and simultaneously model and simulate the data in finite element analysis software to obtain corresponding virtual data. Preferably, acquisition module 1 includes a sensor interface unit, a data preprocessing unit, and a data storage unit. The sensor interface unit is responsible for communicating with the distributed fiber Bragg grating sensor array, acquiring raw data, and supporting a high-frequency sampling rate of 100Hz to ensure the real-time performance and integrity of the data under dynamic working conditions. The data preprocessing unit is responsible for data cleaning, noise filtering, and format conversion, using digital filtering and outlier detection algorithms to improve data quality. The data storage unit is responsible for storing the preprocessed data and virtual simulation data, using efficient data structures and compression algorithms to optimize storage space utilization. In practical applications, the design of acquisition module 1 fully considers the complex environment of the engineering site and the reliability requirements of data transmission, and has strong anti-interference capabilities and adaptability.

[0139] The filtering module 2 is used to design a Kalman filter, correct errors in the virtual data and the deformation and stress test data of the key parts, and train the Kalman filter. Based on the corrected virtual data and the corrected deformation and stress test data of the key parts, the Kalman filter is input to obtain a prediction matrix of the fused state quantities. The optimal filtering gain is obtained through the prediction matrix, and the optimal filtering gain is applied to the deformation and stress test data of the key parts to output the real-time stress field distribution during excavator operation. Preferably, the filtering module 2 includes a Kalman filter design unit, a filter training unit, and a stress field reconstruction unit. The Kalman filter design unit is responsible for constructing the filter model and setting initial parameters, and designing the filter model structure specifically based on the excavator's structural characteristics and working characteristics. The filter training unit is responsible for training the filter using historical data, optimizing the filter parameters, and using a combination of batch learning and online learning to improve the filter's adaptability. The stress field reconstruction unit is responsible for reconstructing the complete stress field distribution based on the optimized filter parameters, and outputting the three-dimensional stress field tensor and main stress state information. In practical applications of excavators, filter module 2 can complete a stress field reconstruction within 0.01 seconds, meeting the requirements for real-time monitoring and optimization.

[0140] Optimization module 3 is used to establish a topology optimization model for the excavator structure. During the solution process of the topology optimization model, material properties are encoded and used as the weight matrix between the input and hidden layers of the neural network. Stress constraint partial differential equations are defined and embedded into the topology optimization model, serving as constraints in the neural network. Preferably, optimization module 3 includes a model building unit, a neural network training unit, an optimization solution unit, and a result verification unit. The model building unit is responsible for establishing a multi-objective constrained topology optimization model, defining the design domain, objective function, and constraints. The neural network training unit is responsible for training the physical information neural network, employing a deep learning framework and GPU acceleration technology to improve network training efficiency. The optimization solution unit is responsible for solving the topology optimization problem based on the trained neural network, achieving rapid convergence. The result verification unit is responsible for verifying and evaluating the optimization results to ensure the feasibility and reliability of the optimization scheme. Compared with traditional topology optimization methods, the optimization module 3 of this invention improves computational efficiency by 3 to 5 times and enhances the quality of optimization results by 15% to 25%.

[0141] The system of this invention may further include adaptive meshing units and microstructure optimization units, working together to achieve high-precision mesh generation and microstructure gradient topology algorithms. The adaptive meshing units are responsible for dynamically adjusting the mesh density based on stress distribution characteristics, providing a high-precision mesh in stress concentration regions; the microstructure optimization units are responsible for further optimizing the microscopic material distribution based on macroscopic optimization results, achieving multi-scale optimization. The design of these additional units further improves the system's flexibility and optimization performance, enabling it to adapt to engineering optimization problems of varying complexity.

[0142] In practical engineering applications, the system of this invention has been successfully applied to the boom optimization design of various excavator models, achieving significant economic and social benefits. The optimized excavator boom structure reduces weight by 15%–25%, stress levels in key components by 20%–30%, fatigue life by 30%–50%, and design cycle time by 60%–70%. These achievements not only enhance product competitiveness but also reduce resource consumption and environmental impact, contributing to the sustainable development of the construction machinery industry.

[0143] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for topology optimization of excavator structures based on real-time stress field reconstruction, characterized in that, Includes the following steps: Based on a distributed fiber optic grating sensor array, deformation and stress test data of key parts of the excavator boom are acquired, and modeling and simulation are performed simultaneously in finite element analysis software to obtain corresponding virtual data. A Kalman filter is designed to correct errors in the virtual data and the deformation and stress test data of the key parts. The Kalman filter is then trained. The corrected virtual data and the corrected deformation and stress test data of the key parts are input into the Kalman filter to obtain a prediction matrix of the fused state quantities. The optimal filter gain is obtained through the prediction matrix. The optimal filter gain is applied to the deformation and stress test data of the key parts to output the real-time stress field distribution during the excavator operation. A topology optimization model is established for the excavator structure. When solving the topology optimization model, the material properties are encoded and used as the weight matrix between the input layer and the hidden layer in the neural network. Stress constraint partial differential equations are defined and embedded in the topology optimization model, and used as the constraint conditions in the neural network. Multi-objective constrained topology optimization is performed on the excavator structure, and the objective function is defined as the elastic modulus and natural frequency; The constraints of the topology optimization model are set as volume fraction constraints, stress constraints, and sensitivity constraints. The volume fraction constraints are used to limit the volume of the structure, the stress constraints are used to ensure that the stress value of the key parts is less than or equal to the maximum stress value of the material strength, and the sensitivity constraints are used to represent the sensitivity of the objective function and constraints to the design variables. The topology optimization model is optimized using a gradient algorithm. The structural flexibility is calculated in the topology optimization model, and a topology optimization design scheme for the excavator boom structure is generated. A variable density method solver is integrated into ANSYS, and a gradient adaptive mesh is designed. The material is set to ideal elastic-plasticity, the region constraint state is defined, external forces and external moments are applied, and a material redistribution map is obtained through finite element analysis. The material is then redistributed according to the material redistribution map.

2. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 1, characterized in that, The specific steps for obtaining deformation and stress test data for key components of an excavator boom include: Define a data matrix, which includes: the virtual data and the corresponding time axis; Acquire time-series data from a distributed fiber Bragg grating sensor array, including deformation and strain data; By combining the data matrix, the deformation data and the strain data are subjected to dimensional transformation to obtain preprocessed data.

3. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 2, characterized in that, In the design of the Kalman filter, the Kalman filter includes a measurement equation and a state equation. The measurement equation contains measurement noise, and the state equation contains system noise. The predicted output of the Kalman filter includes the excavator structural state measurement value, the predicted value, and the prediction variance. Based on Bayesian filtering theory, a recursive algorithm is used to obtain the predicted value and the observed value at the current time according to the initial state. The optimal state estimate under the minimum mean square error is obtained by the filtering algorithm. The optimal state estimate is the excavator structural state measurement value, and the optimal state estimate is obtained by the optimal filter gain.

4. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 3, characterized in that, The specific steps for training the Kalman filter include: The preprocessed data and the virtual data are used as a training set, and the true values ​​of the fusion state variables and the prediction matrix of the fusion state variables are set in the training set. The true value corresponding to the preprocessed data is determined based on the preprocessed data, and the prediction matrix corresponding to the virtual data is determined based on the virtual data. The true value represents the true error between the virtual data and the preprocessed data. The true value serves as the true value of the fused state quantity. The optimal filter gain is obtained based on the error between the prediction matrix and the true value. The optimal prediction matrix is ​​obtained based on the optimal filter gain.

5. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 1, characterized in that, In the topology optimization model, the stress constraint partial differential equation is defined as follows: the stress constraint partial differential equation represents the relationship between the maximum stress value and the stress value during the solution process, and is used to ensure that the stress value of the key part meets the stress constraint condition.

6. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 1, characterized in that, It also includes the following steps: For the dynamic load environment of the boom, a microstructure gradient topology algorithm that considers the boom's natural frequency and material gradient distribution was developed; The microstructure gradient topology algorithm considers the natural frequency and material mass distribution of the excavator boom structure, determines the constraints of the microstructure gradient topology algorithm, uses a physical information neural network to solve the gradient weight function according to the constraints, and establishes a gradient topology optimization algorithm based on the gradient weight function in the physical information neural network to achieve the optimal material distribution.

7. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 6, characterized in that, It also includes the following steps: The adaptive meshing technique is used to refine the finite element discretization in stress concentration regions, thereby obtaining strain data with an accuracy of 0.1 mm. Based on the strain data with an accuracy of 0.1 mm, the stress field is reconstructed using the Kalman filter algorithm to obtain the stress distribution. The reconstructed stress field data and the position information of the sensing fiber are mapped into the computational domain. The entire computational domain is discretized into multiple units using a discrete method to form a strain distribution matrix and a sensor number matrix.

8. A topology optimization system for excavator structures based on real-time stress field reconstruction, used to execute the topology optimization method for excavator structures based on real-time stress field reconstruction as described in any one of claims 1-7, characterized in that, include: The acquisition module is used to acquire deformation and stress test data of key parts of the excavator boom based on a distributed fiber Bragg grating sensor array, and simultaneously model and simulate in finite element analysis software to obtain corresponding virtual data. A filtering module is used to design a Kalman filter, correct errors in the virtual data and the deformation and stress test data of the key parts, train the Kalman filter, obtain a prediction matrix of fused state quantities based on the corrected virtual data and the corrected deformation and stress test data of the key parts, obtain the optimal filtering gain through the prediction matrix, apply the optimal filtering gain to the deformation and stress test data of the key parts, and output the real-time stress field distribution during the excavator operation. An optimization module is used to establish a topology optimization model for the excavator structure. When solving the topology optimization model, the material properties are encoded and used as the weight matrix between the input layer and the hidden layer in the neural network. Stress constraint partial differential equations are defined and embedded in the topology optimization model and used as constraints in the neural network. Multi-objective constrained topology optimization is performed on the excavator structure, and the objective function is defined as the elastic modulus and natural frequency; The constraints of the topology optimization model are set as volume fraction constraints, stress constraints, and sensitivity constraints. The volume fraction constraints are used to limit the volume of the structure, the stress constraints are used to ensure that the stress value of the key parts is less than or equal to the maximum stress value of the material strength, and the sensitivity constraints are used to represent the sensitivity of the objective function and constraints to the design variables. The topology optimization model is optimized using a gradient algorithm. The structural flexibility is calculated in the topology optimization model, and a topology optimization design scheme for the excavator boom structure is generated. A variable density method solver is integrated into ANSYS, and a gradient adaptive mesh is designed. The material is set to ideal elastic-plasticity, the region constraint state is defined, external forces and external moments are applied, and a material redistribution map is obtained through finite element analysis. The material is then redistributed according to the material redistribution map.

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