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

Abstract

The invention relates to the technical field of engineering mechanical structure optimization, in particular to an excavator structure topological optimization method and system based on real-time stress field reconstruction. The method comprises the following steps of: designing finite element analysis software, modeling and simulating in the finite element analysis software to obtain virtual data, designing a Kalman filter to carry out error correction on the virtual data and actual test data, training the Kalman filter by utilizing the corrected data to obtain prediction of real-time stress field distribution, and further, establishing a topological optimization model of an excavator structure, according to the method, material attributes are coded into a weight matrix in a neural network, and a stress constraint partial differential equation is used as a constraint condition, so that high-precision reconstruction of the stress field of the movable arm of the excavator under an actual working condition is realized, and an accurate boundary condition is provided for topological optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering machinery structure optimization, and in particular to an excavator structure topology optimization method and system based on real-time stress field reconstruction. Background Art

[0002] Excavators are essential equipment in the field of engineering machinery, and their structural performance directly impacts their operating efficiency and service life. Traditional excavator structural design relies primarily on experience and finite element analysis, which struggles to accurately capture the stress distribution under actual operating conditions. This can lead to conservative redundancy or localized strength deficiencies in structural design. Topology optimization has been widely used in engineering structure optimization design. However, in the excavator field, traditional topology optimization methods 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 the excavator under complex dynamic working conditions. The optimization results often deviate significantly from the actual working conditions.

[0004] Secondly, conventional topology optimization algorithms have low solution efficiency and are difficult to handle complex constraints involving multi-physics field coupling, making it 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 the optimization strategy based on actual working conditions.

[0006] Fourth, the optimization results lack closed-loop verification and feedback mechanisms, and the reliability of the optimization scheme in actual working conditions cannot be guaranteed.

[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 needs of lightweight excavator structure and high reliability. Summary of the Invention

[0008] The purpose of the present invention is to provide an excavator structure topology optimization method and system based on real-time stress field reconstruction. The stress data of the excavator boom is obtained in real time by a distributed fiber grating sensor, and the stress field is reconstructed in combination with the Kalman filter algorithm. The physical information neural network is further used for topology optimization to achieve the coordinated optimization of the lightweight and fatigue life of the excavator structure.

[0009] The present invention proposes an excavator structure topology optimization method based on real-time stress field reconstruction, comprising:

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

[0011] A Kalman filter is designed to perform error correction on the virtual data and the deformation and stress test data of the key parts, and the Kalman filter is 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 fusion state quantities, an 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, and a real-time stress field distribution during the excavator operation is output;

[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. A stress constraint partial differential equation is defined and embedded in the topology optimization model, and used as the constraint condition in the neural network.

[0013] Preferably, the step of obtaining deformation and stress test data of key parts of the excavator boom specifically includes:

[0014] defining a data matrix, the data matrix including: the virtual data and a corresponding time axis;

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

[0016] The deformation data and the strain data are dimensionally transformed in combination with the data matrix to obtain preprocessed data.

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

[0018] Preferably, the step of training the Kalman filter specifically includes:

[0019] Using the preprocessed data and the virtual data as a training set, and setting a true value of a fusion state quantity and a prediction matrix of the fusion state quantity in the training set;

[0020] The true value corresponding to the preprocessed data is determined according to the preprocessed data, and the prediction matrix corresponding to the virtual data is determined according to the virtual data, wherein the true value is represented by the true error between the virtual data and the preprocessed data, and the true value is used as the true value of the fusion state quantity. The optimal filtering gain is obtained according to the error between the prediction matrix and the true value, and the optimal prediction matrix is ​​obtained according to the optimal filtering gain.

[0021] Preferably, the steps of 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 elastic modulus and natural frequency;

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

[0024] Preferably, in the topology optimization model, the stress constraint partial differential equation is defined as: 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] As an advantage, the method further comprises the following steps:

[0026] Optimizing the topology optimization model by using a gradient algorithm, calculating structural flexibility in the topology optimization model, and generating a topology optimization design scheme for the excavator boom structure;

[0027] A variable density method solver is integrated into ANSYS, and a gradient adaptive grid is designed. The material is set to ideal elastic-plastic, the regional 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.

[0028] As an advantage, the method further comprises the following steps:

[0029] Aiming at the dynamic load environment of the boom, a microstructure gradient topology algorithm was developed that takes into account the boom's natural frequency and material gradient distribution;

[0030] The microstructure gradient topology algorithm takes into account the natural frequency of the excavator boom structure and the material mass distribution, determines the constraints of the microstructure gradient topology algorithm, adopts 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 distribution of materials.

[0031] As an advantage, the method further comprises the following steps:

[0032] The adaptive mesh technology is used to increase the finite element discretization degree in the stress concentration area to obtain strain data with an accuracy of 0.1 mm;

[0033] Based on the 0.1 mm precision strain data, 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 optical fiber are mapped into the computational domain, and the entire computational domain is discretized into multiple units in a discrete manner to form a strain distribution matrix and a sensor quantity matrix.

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

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

[0037] a filtering module for designing a Kalman filter, performing error correction on the virtual data and the deformation and stress test data of the key parts, and training the Kalman filter; inputting the corrected virtual data and the corrected deformation and stress test data of the key parts into the Kalman filter to obtain a prediction matrix of fusion state quantities; obtaining an optimal filter gain through the prediction matrix; applying the optimal filter gain to the deformation and stress test data of the key parts, and outputting a real-time stress field distribution during the excavator operation;

[0038] An optimization module is used to establish a topology optimization model for the excavator structure, encode material properties when solving the topology optimization model, and use them as a weight matrix between the input layer and the hidden layer in the neural network. A stress constraint partial differential equation is defined and embedded in the topology optimization model as a constraint condition in the neural network.

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

[0040] 1. A distributed fiber Bragg grating sensor array is used to acquire real-time deformation and stress test data of key parts of the excavator boom. Combined with virtual data from finite element simulation, the Kalman filter algorithm is used for data fusion. This enables high-precision reconstruction of the stress field of the excavator boom under actual working conditions, providing accurate boundary conditions for topology optimization.

[0041] 2. Applying physical information neural network technology, material properties are encoded as neural network weights, and stress constraint partial differential equations are embedded in 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, and the objective function was defined as the elastic modulus and natural frequency. At the same time, constraints such as volume fraction, stress and sensitivity were considered to achieve comprehensive optimization of the excavator's structural performance.

[0043] 4. Through gradient adaptive grid technology and variable density method, material redistribution with a precision of 0.1mm is achieved in stress concentration areas, significantly improving the strength and fatigue life of the structure in key areas.

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

[0045] The present invention reduces the weight of the excavator boom structure by 15% to 25%, increases fatigue life by 30% to 50%, and shortens the optimization period from the traditional 3-6 months to 2-4 weeks, providing a new technical solution for the optimization of engineering machinery structures. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0047] Figure 2 Schematic diagram of the arrangement of the distributed fiber Bragg grating sensor array on the excavator boom of the present invention;

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

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

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

[0051] Figure 6 Schematic diagram of the application of the gradient adaptive mesh refinement of the present invention in the stress concentration area;

[0052] Figure 7 It is a system architecture diagram of the present invention, showing the interactive relationship between various functional modules. DETAILED DESCRIPTION

[0053] Please refer to the attached Figure 1-7 The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall 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 the present invention includes the following steps:

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

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

[0057] At the same time, 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 to perform simulation analysis to obtain corresponding virtual data. The virtual data here include but are not limited to the stress distribution, deformation and strain values ​​of various parts of the boom. During the modeling process, the present invention accurately models the key structural features of the excavator boom, including details such as wall thickness changes, reinforcements, and hinge points, to ensure a high degree of consistency between the virtual model and the actual structure. In terms of load condition setting, the digging force (typical value is 150-200kN), the influence of deadweight (typical boom weight is 2-3 tons) and the inertia force 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 an excavator boom specifically includes the following steps:

[0059] First, define a data matrix, which includes virtual data and corresponding time axis. Specifically, the data matrix can be expressed as D virtual ={d1(t1),d2(t2),...,d n (t n )}, where d i represents the virtual data vector at the i-th moment, which contains the stress and strain values ​​of each measuring point obtained by finite element analysis; t i The corresponding timestamp reflects the timing characteristics of data collection. n represents the length of the time series, typically determined based on the complete excavator operating cycle. In typical applications, the value ranges from 1000 to 5000, corresponding to 10 to 50 seconds of continuous monitoring data. This matrix representation facilitates subsequent time synchronization and comparative analysis with measured data.

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

[0061] The sensor data can be expressed as D sensor ={(δ1,ε1,t1),(δ2,ε2,t2),...,(δ m ,ε m ,t m )}, where δ i is the deformation data vector at the i-th moment, ε i is the strain data vector at the i-th moment, t iis the corresponding timestamp, and m is the number of time points at which data was collected. In practical applications, for medium-sized 20-ton excavators, the deformation of key parts is typically in the range of 0.1-5 mm, and the strain value is in the range of 100-2000 με. These data are important for assessing structural safety and fatigue life.

[0062] Finally, the deformation data and the strain data are transformed in dimension by combining the data matrix to obtain preprocessed data. The purpose of dimensional transformation is to make the sensor data and virtual data consistent in dimension and format, so as to facilitate subsequent data fusion processing. The preprocessed data can be expressed as D processed ={p1(t1),p2(t2),...,p n (t n )}, where p i is the processed data vector, and the virtual data vector d i The dimensional transformation methods employed in this invention include interpolation, filtering, and coordinate conversion techniques to ensure that the measured data accurately corresponds to the virtual data in both time and space. In particular, for data in areas not covered by the sensor, an interpolation algorithm based on physical constraints is used for estimation. The interpolation accuracy is 25% to 30% better than traditional linear interpolation methods, providing a reliable foundation for subsequent full-field stress reconstruction.

[0063] Step 2: Design a Kalman filter to reconstruct the stress field:

[0064] like Figure 3 As shown, the present invention employs a Kalman filter to perform error correction on the virtual data and the deformation and stress test data of the key components. As a recursive optimal estimator, the Kalman filter is particularly well-suited for state estimation in dynamic systems containing random noise. In this invention, it is innovatively applied to the real-time stress field reconstruction of the excavator boom.

[0065] In one embodiment of the present invention, the Kalman filter includes a measurement equation and a state equation. 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 is the measurement equation, which represents the observed value at the kth moment, and in this application corresponds to the deformation and strain data measured by the sensor; k is the state equation, which represents the state variables at the kth moment and corresponds to the complete stress field distribution; H k is the measurement matrix, which maps the state space to the observation space and reflects the relationship between the sensor layout and the complete stress field; k is the state transfer matrix, which describes the evolution of the system state and reflects the law of stress field changing with time; B k is the control matrix, which represents the influence coefficient of external input on the system state; u k is the control vector, which represents the known external input, such as the workload of the excavator; v k Represents measurement noise, which is generally assumed to be Gaussian white noise with a mean of 0 and a covariance of R k ;w k Represents the system noise, also assumed to be Gaussian white noise, with covariance Q k .

[0070] In the excavator application scenario, 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, predictions, and prediction variance. Based on Bayesian filtering theory, a recursive algorithm is used to derive the current predicted and observed values ​​from the initial state. The filtering algorithm then generates the optimal state estimate with the minimum mean square error.

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

[0073] 1. Prediction steps:

[0074]

[0075] 2. Update steps:

[0076]

[0077] in, is the prior state estimate, which represents the state prediction value at the kth moment obtained based on the system dynamic model; is the prior estimation error covariance, indicating the uncertainty of the predicted value; K k is the Kalman gain, which determines the weight distribution between the observation value and the predicted value; is the posterior state estimate, i.e. the optimal estimate after fusion prediction and observation; P kis the posterior estimation error covariance, which indicates the uncertainty of the optimal estimate; Q k is the process noise covariance; R k is the measurement noise covariance; I is the identity matrix. In practical applications, Q k and R k The values ​​of have an important impact on the filter performance. The present invention determines these parameters by analyzing historical data and expert experience, and designs an adaptive adjustment mechanism.

[0078] In the present invention, the optimal state estimate is the measured value of the excavator's structural state, which is derived from the optimal filter gain. The optimal filter gain represents a measure of the minimum mean squared error between the predicted output and the measured value at the current moment, and the optimal estimate represents the solution to the minimum mean squared error. For stress field reconstruction of the excavator boom, the application of Kalman filtering not only effectively integrates measured data from a limited number of sensors and finite element simulation data, but also smoothly eliminates noise effects and captures the dynamic characteristics of the stress field.

[0079] The present invention further trains the Kalman filter, specifically in the following steps:

[0080] First, the preprocessed data and the virtual data are used as a training set, and the true value of the fused state quantity and the prediction matrix of the fused state quantity are set in the training set. Preferably, the training set contains data under multiple working conditions to improve the generalization ability of the filter. In practical applications, data is collected for typical working conditions of the excavator, such as excavation, lifting, rotation and unloading, etc., to construct a training set to ensure that the filter can adapt to various working conditions. The amount of training set data is usually 10-15 complete working cycles for each working condition, totaling 500 to 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 is represented by the actual error between the virtual data and the preprocessed data, which can be expressed as:

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

[0083] Among them, e k is the error vector at the kth moment, d k is the virtual data vector at the kth moment, p k is the pre-processed data vector at the kth moment. The true value is the true value of the fusion state quantity, denoted as In excavator applications, these error data reflect the differences between the theoretical model and the actual structure, and are of great value in identifying model uncertainties and improving reconstruction accuracy.

[0084] Then, calculate the error between the predicted matrix and the true value:

[0085]

[0086] in, is the prediction matrix of the fusion state quantity, which represents the stress field distribution predicted by the Kalman filter; is the real stress field distribution, ε k For the excavator boom, the magnitude and distribution characteristics of the prediction error can be used to evaluate the filter performance and adjust the filter parameters.

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

[0088]

[0089] in, is the optimal Kalman gain, E[·] represents the expected operation, In actual calculations, an iterative optimization method is used to solve this minimization problem, and it usually takes 5-10 iterations to converge to a satisfactory accuracy.

[0090] According to the optimal filter gain Get the optimal prediction matrix:

[0091]

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

[0093] 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 operation of the excavator. Preferably, the stress field distribution is expressed in the form of a three-dimensional tensor, 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 the vonMises equivalent stress. In practical applications, the accuracy of the reconstructed stress field can reach ±5% of the stress value of the measured point, and the accuracy of the non-measurement point area is ±10%, which is far superior to the traditional method based only 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 the physical information neural network:

[0095] like Figure 4 As shown, the present invention establishes a topology optimization model for excavator structures. When solving the topology optimization 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 in the topology optimization model, serving as constraints within the neural network. This innovative application of physical information neural networks to excavator structure topology optimization overcomes the limitations of traditional topology optimization, which suffer from low computational efficiency and difficulty handling complex constraints.

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

[0097] Multi-objective constrained topology optimization is performed on the excavator structure, and the objective function is 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] Among them, 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, indicating the degree of unit filling, ρ = 1 indicates solid material, and ρ = 0 indicates voids; E0 is the elastic modulus of the base material (no holes), for the commonly used Q345 steel, E0 is about 210 GPa; E min To avoid singularity issues, the minimum value set is typically 0.021 GPa, or one ten-thousandth of E0. p is a penalty factor, typically 3, which suppresses the occurrence of intermediate densities and guides the optimization results toward a 0 / 1 distribution. This material interpolation model, based on the SIMP (Solid Isotropic Material with Penalization) method, effectively addresses material distribution issues in excavator structural optimization.

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

[0101]

[0102] Among them, f1 represents the structural flexibility, which is an important indicator to measure the structural stiffness. The smaller the value, the higher the structural stiffness. u is the displacement vector, which represents the displacement of each node of the structure under the action of load. K is the stiffness matrix, which is determined by the material properties and unit geometric characteristics. f2 represents the ratio of the i-th order natural frequency, ω iis the optimized i-th order natural frequency, in Hz; is the i-th natural frequency before optimization, also in Hz. In excavator applications, the first 3-5 natural frequencies are typically of interest to avoid resonance with the excitation frequency. A typical excavator boom primarily operates in the 0.5-10 Hz frequency range, so the optimization objective is typically to increase the natural frequencies within this frequency range.

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

[0104]

[0105] Among them, ρ i is the relative density of the i-th unit; V i is the volume of the i-th unit, in mm 3 ; is the total volume of the design domain; V f The upper limit of the volume fraction is usually set between 0.3 and 0.5, indicating that the optimized structure volume does not exceed 30% to 50% of the original volume. In excavator boom optimization, volume constraints are directly related to structural weight. Properly setting volume constraints is key to balancing lightweighting and strength requirements.

[0106] The stress constraint is 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, which can be expressed as:

[0107] σ max ≤β·σ allow

[0108] Among them, σ max is the calculated maximum stress, in MPa; σ allow β is the allowable stress of the material. For Q345 steel, the yield strength is 345 MPa. After considering the safety factor, the allowable stress is typically 275-310 MPa. β is the safety factor, typically 0.8-0.9, determined based on the safety requirements of the application scenario. In critical load-bearing structures such as excavator booms, stress constraints are a core constraint for ensuring structural safety.

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

[0110]

[0111] in, It represents the sensitivity of the objective function f to the design variable ρ, reflecting the influence of the change of the design variable on the objective function; It represents the sensitivity of the stiffness matrix K to the elastic modulus E. Sensitivity information is the basis of the gradient optimization algorithm and has an important influence on the convergence speed and stability of the optimization process.

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

[0113]

[0114] in, It indicates the sensitivity of stress to design variables and reflects the impact of material distribution changes on stress distribution; It represents the sensitivity of stress to displacement and is determined by the geometric characteristics and material properties of the structure; The sensitivity of displacement to design variables can be calculated using finite element analysis and adjoint methods. In excavator boom optimization, stress sensitivity information guides the optimal distribution of material in high-stress areas, playing an important role in improving the local strength of the structure.

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

[0116] g(σ)=σ max -σ allow ≤0,

[0117] Among them, g(σ) is the stress constraint function, σ max represents the maximum stress, σ allow represents the allowable stress value. When g(σ) ≤ 0, the structure meets strength requirements; when g(σ) > 0, there is a risk of insufficient strength. During the optimization process, adjusting the material distribution to meet stress constraints is an important means of ensuring structural safety.

[0118] In addition, the present invention further comprises the following steps:

[0119] 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. Preferably, a sequential linear programming (SLP) or moving asymptote method (MMA) is used as a gradient optimization algorithm to iteratively solve the topology optimization problem. In each iteration, the design variables are updated based on the sensitivity information:

[0120]

[0121] Among them, ρ i+1 is the design variable for the i+1th iteration, representing the updated material distribution; ρ iis the design variable for the i-th iteration, representing the current material distribution; α is the step size factor, usually 0.01-0.05, which controls the update amplitude of each iteration. A smaller step size is beneficial to optimizing stability but will increase the number of iterations; The sensitivity of the Lagrangian function to the design variables is comprehensively considered, taking into account the impact of the objective function and constraints. In practical applications, optimization iterations typically require 100-200 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] The variable density method solver is integrated into ANSYS, and a gradient adaptive grid is designed. The material is set to ideal elastic-plastic, regional constraint states are defined, external forces and moments are applied, a material redistribution map is obtained through finite element analysis, and the material is redistributed according to the material redistribution map. In practical applications, the present invention develops an ANSYS secondary development interface that seamlessly integrates the optimization algorithm with commercial finite element software, achieving full-process automation from model establishment and load application to optimization result output. This integration approach not only utilizes ANSYS's powerful pre- and post-processing capabilities, but also leverages the advantages of independently developed algorithms, significantly improving engineering application efficiency.

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

[0124] The present invention also includes developing a microstructure gradient topology algorithm that considers the boom's natural frequency and material gradient distribution for dynamic load environments. This algorithm simultaneously considers both the static strength and dynamic characteristics of the structure, achieving a balance between lightweight and high performance. In excavator applications, the boom is subject not only to static loads but also to dynamic shock and vibration during the excavation process. Therefore, considering dynamic characteristics is crucial to the practicality of the optimization results.

[0125] The microstructure gradient topology algorithm considers the natural frequency of the excavator boom structure and the material mass distribution, determines the constraints of the microstructure gradient topology algorithm, uses a physical information neural network to solve the gradient weight function based on these constraints, and establishes a gradient topology optimization algorithm based on the gradient weight function in the physical information neural network to achieve optimal material distribution. This multi-scale optimization method not only optimizes the overall structural morphology at the macro level, but also optimizes the material distribution at the micro level, achieving more efficient material utilization.

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

[0127]

[0128] ∫ Ω ρ(x,y,z)dΩ≤Vf Ω total ,

[0129]

[0130] Among them, ω i is the i-th order natural frequency, in Hz; is the i-th order natural frequency of the initial structure, also in Hz; γ is the frequency constraint coefficient, usually 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 the position (x,y,z), ranging from 0 to 1; Ω is the design domain, indicating the area that can be optimized; V f The upper limit of volume fraction is usually 0.3-0.5; Ω total is the total volume in mm 3 δ is a gradient constraint parameter used to control the smoothness of material distribution, typically ranging from 0.05 to 0.1. Smaller values ​​result in a smoother density distribution, which improves the manufacturability of the structure. In excavator boom optimization, properly setting these constraints is key to balancing static performance, dynamic characteristics, and manufacturability.

[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] Here, (x0, y0, z0) are the coordinates of the stress concentration point, representing the high-stress area requiring special attention. This is typically determined based on initial analysis results or engineering experience. λ is the gradient attenuation coefficient, typically set between 1.5 and 2.5, which controls the rate of material distribution decay from the stress concentration point outward. Larger λ values ​​result in steeper material distribution gradients, suitable for areas with large stress gradients; smaller λ values ​​produce a flatter distribution, suitable for areas with more uniform stress variations. This gradient weighting function design based on stress concentration points can specifically optimize material distribution in high-stress areas, improving both the local strength and overall performance of the structure.

[0134] The present invention also includes using the adaptive meshing technology to refine the finite element discretization in stress concentration areas to obtain strain data with an accuracy of 0.1mm. Preferably, when the stress level in a certain area exceeds 80% of the material's yield strength, the mesh in that area is refined, and the mesh size is reduced to 0.1mm to accurately capture the stress gradient at the stress concentration point. In stress concentration areas of the excavator boom, such as hinge points, the roots of stiffeners, and cross-sectional mutations, the stress gradient is often very large. Conventional meshing makes it difficult to accurately capture the stress distribution in these areas. However, adaptive meshing technology can achieve a reasonable allocation of computing resources and provide high-precision results in key areas.

[0135] Based on the 0.1mm precision strain data, the Kalman filter algorithm is used to reconstruct the stress field and obtain the stress distribution. This high-precision stress distribution information is crucial for assessing the fatigue performance and lifespan of structures, especially for construction machinery such as excavators, which operate under complex load conditions for long periods of time. Traditional methods struggle to obtain such detailed stress distribution data, but the present invention successfully achieves high-precision stress field reconstruction by combining adaptive grids with Kalman filtering.

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

[0137] The present invention also provides an excavator structural topology optimization system based on real-time stress field reconstruction, comprising an acquisition module 1, a filtering module 2, and an optimization module 3. This system, similar to the method described in Example 1, automatically executes the entire process from data acquisition to optimization solution generation. Clear data flow and standardized interface definitions between the system's modules ensure the efficiency and reliability of the entire optimization process.

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

[0139] Filtering module 2 is used to design a Kalman filter, perform error correction on the virtual data and the deformation and stress test data of the key parts, and train the Kalman filter. 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 fused state quantities. The prediction matrix is ​​used to obtain the optimal filter gain, which 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. Preferably, 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, specifically designing the filter model structure based on the structural characteristics and operating characteristics of the excavator. The filter training unit is responsible for training the filter using historical data and optimizing the filter parameters, 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, outputting a three-dimensional stress field tensor and main force state information. In actual application of excavators, the filtering module 2 can complete a stress field reconstruction within 0.01 seconds, meeting the requirements of real-time monitoring and optimization.

[0140] Optimization module 3 is used to establish a topology optimization model for the excavator structure. When solving the topology optimization model, material properties are encoded and used as the weight matrix between the input layer and the hidden layer of the neural network. Stress constraint partial differential equations are defined and embedded in the topology optimization model, serving as constraints within the neural network. Preferably, optimization module 3 includes a model construction unit, a neural network training unit, an optimization solution unit, and a result verification unit. The model construction 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, utilizing 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; and the result verification unit is responsible for verifying and evaluating the optimization results to ensure the feasibility and reliability of the optimization solution. Compared with traditional topology optimization methods, the optimization module 3 of the present invention improves computational efficiency by 3-5 times and the quality of optimization results by 15-25%.

[0141] The system of the present invention can also include adaptive mesh units and microstructure optimization units, which work together to implement high-precision meshing and microstructure gradient topology algorithms. The adaptive mesh units are responsible for dynamically adjusting mesh density based on stress distribution characteristics, providing high-precision meshes in areas of stress concentration. The microstructure optimization unit is responsible for further optimizing the microscopic material distribution based on the macroscopic optimization results, achieving multi-scale optimization. The design of these additional units further enhances 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 optimized boom design of various excavator models, achieving significant economic and social benefits. The optimized boom structure reduces weight by 15% to 25%, reduces stress levels in key areas by 20% to 30%, increases fatigue life by 30% to 50%, and shortens design cycles by 60% to 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 foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. Excavator structure topology optimization method based on real-time stress field reconstruction, characterized by: The following steps are involved: Based on a distributed fiber Bragg grating sensor array, deformation and stress test data of key parts of the excavator boom are obtained, and modeling and simulation are simultaneously performed in finite element analysis software to obtain corresponding virtual data; A Kalman filter is designed to perform error correction on the virtual data and the deformation and stress test data of the key parts, and the Kalman filter is 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 fusion state quantities, an 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, and a real-time stress field distribution during the excavator operation is output; 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. A stress constraint partial differential equation is defined and embedded in the topology optimization model, and used as the constraint condition in the neural network.

2. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 1 is characterized in that: The steps for obtaining deformation and stress test data of key parts of the excavator boom include: defining a data matrix, the data matrix including: the virtual data and a corresponding time axis; Acquire time series data of distributed fiber Bragg grating sensor array, including deformation data and strain data; The deformation data and the strain data are dimensionally transformed in combination with the data matrix to obtain preprocessed data.

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

4. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 3 is characterized in that: The steps of training the Kalman filter specifically include: Using the preprocessed data and the virtual data as a training set, and setting a true value of a fusion state quantity and a prediction matrix of the fusion state quantity in the training set; The true value corresponding to the preprocessed data is determined according to the preprocessed data, and the prediction matrix corresponding to the virtual data is determined according to the virtual data, wherein the true value is represented by the true error between the virtual data and the preprocessed data, and the true value is used as the true value of the fusion state quantity. The optimal filtering gain is obtained according to the error between the prediction matrix and the true value, and the optimal prediction matrix is ​​obtained according to the optimal filtering gain.

5. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 4 is characterized in that: The steps to establish a topology optimization model for the excavator structure include: Multi-objective constrained topology optimization is performed on the excavator structure, and the objective function is defined as elastic modulus and natural frequency; The constraints of the topology optimization model are set as volume fraction constraint, stress constraint and sensitivity constraint, wherein the volume fraction constraint is used to limit the volume of the structure, the stress constraint is used to ensure that the stress value of the key part is less than or equal to the maximum stress value of the material strength, and the sensitivity constraint is used to represent the sensitivity of the objective function and the constraint relative to the design variable.

6. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 5 is characterized in that: In the topology optimization model, the stress constraint partial differential equation is defined as: 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.

7. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 6 is characterized in that: The following steps are also included: Optimizing the topology optimization model by using a gradient algorithm, calculating structural flexibility in the topology optimization model, and generating a topology optimization design scheme for the excavator boom structure; A variable density method solver is integrated into ANSYS, and a gradient adaptive grid is designed. The material is set to ideal elastic-plastic, the regional 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.

8. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 7 is characterized in that: The following steps are also included: Aiming at the dynamic load environment of the boom, a microstructure gradient topology algorithm was developed that takes into account the boom's natural frequency and material gradient distribution; The microstructure gradient topology algorithm takes into account the natural frequency of the excavator boom structure and the material mass distribution, determines the constraints of the microstructure gradient topology algorithm, adopts 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 distribution of materials.

9. The excavator structure topology optimization method based on real-time stress field reconstruction according to claim 8 is characterized in that: The following steps are also included: The adaptive mesh technology is used to increase the finite element discretization degree in the stress concentration area to obtain strain data with an accuracy of 0.1 mm; Based on the 0.1 mm precision strain data, 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 optical fiber are mapped into the computational domain, and the entire computational domain is discretized into multiple units in a discrete manner to form a strain distribution matrix and a sensor quantity matrix.

10. An excavator structure topology optimization system based on real-time stress field reconstruction, used to execute the excavator structure topology optimization method based on real-time stress field reconstruction according to any one of claims 1 to 9, characterized in that: include: The acquisition module is used to obtain deformation and stress test data of key parts of the excavator boom based on a distributed fiber Bragg grating sensor array, and simultaneously perform modeling and simulation in finite element analysis software to obtain corresponding virtual data; a filtering module for designing a Kalman filter, performing error correction on the virtual data and the deformation and stress test data of the key parts, and training the Kalman filter; inputting the corrected virtual data and the corrected deformation and stress test data of the key parts into the Kalman filter to obtain a prediction matrix of fusion state quantities; obtaining an optimal filter gain through the prediction matrix; applying the optimal filter gain to the deformation and stress test data of the key parts, and outputting a real-time stress field distribution during the excavator operation; An optimization module is used to establish a topology optimization model for the excavator structure, encode material properties when solving the topology optimization model, and use them as a weight matrix between the input layer and the hidden layer in the neural network. A stress constraint partial differential equation is defined and embedded in the topology optimization model as a constraint condition in the neural network.

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