Digital-twin-driven online optimization design method for fatigue constraint of major equipment

Abstract

The application provides a digital twin driven online optimization design method for fatigue constraint of major equipment, and belongs to the technical field of structural health monitoring and optimization design of major equipment. In view of the problems of low calculation efficiency, difficulty in realizing real-time evaluation and optimization of the traditional fatigue analysis method, firstly, a structure response rapid prediction model is constructed based on a model reduction method, and efficient calculation of key performance is realized; secondly, an online monitoring method for fatigue life is established by combining multi-source sensor data and fatigue damage evolution mechanism; an optimization design model with fatigue life as the constraint is constructed, and online optimization update of structure parameters is realized based on a digital twin model, thereby forming a closed-loop optimization mechanism. The application can realize real-time perception of the fatigue state of major equipment and dynamic optimization of structure performance, and improve the operation safety and design efficiency of the equipment.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring and digital twin technology for major equipment, and relates to a digital twin-driven online optimization design method for fatigue constraints of major equipment. Background Technology

[0002] Major equipment operates for extended periods in complex service environments, typically enduring the combined effects of alternating loads, impact loads, and temperature variations. Under the influence of multi-source uncertainties, the internal stress state of the structure exhibits significant time-varying and nonlinear characteristics, easily leading to the continuous accumulation and local evolution of fatigue damage. Traditional fatigue assessment and design methods based on offline simulation and empirical criteria struggle to cope with the real-time changes in structural state and performance evolution under complex service environments, exhibiting problems such as response lag, insufficient accuracy, and limited adaptability. Digital twin technology, by constructing a real-time mapping relationship between the physical system and a virtual model, can integrate multi-source monitoring data and mechanistic models to achieve online perception and high-precision prediction of structural state. Therefore, conducting digital twin-driven online optimization design for major equipment is of great significance for improving the adaptability, operational safety, and life-cycle performance of major equipment in complex environments.

[0003] Currently, digital twins for major equipment have been extensively studied and some solutions have been developed. Chinese invention patent (CN117408112A) provides a fatigue life monitoring system for complex equipment components based on digital twins, enabling real-time monitoring of the health status or fatigue life of components. However, while its invention method can monitor fatigue life, it is essentially a simple integration of traditional fatigue analysis and digital twin technology, lacking substantial breakthroughs in model innovation, real-time calculation, and bidirectional adaptive update mechanisms. Chinese invention patent (CN120046360B) provides a multi-objective optimization method for the structure of a high-pressure diaphragm pump check valve based on digital twins, enabling high-precision simulation of the check valve's operating state and solving for the optimal structural parameters for impact resistance. However, it still falls within the scope of traditional offline optimization design and struggles to achieve structural parameter optimization under sensor-driven, full-domain performance analysis.

[0004] Based on existing research, the current digital twin-driven optimization design of major equipment has the following significant drawbacks: (1) Insufficient computational efficiency and real-time performance. Existing methods mostly rely on high-fidelity models or offline proxy models, which are difficult to meet the needs of online optimization. At the same time, digital twins and optimization design are not tightly coupled and lack a closed-loop mechanism of "perception-prediction-optimization". (2) The model has insufficient adaptive and multi-source fusion capabilities, making it difficult to accurately reflect the dynamic evolution process under complex working conditions. Furthermore, it does not fully introduce fatigue constraints, making it difficult to achieve synergistic optimization of structural performance and lifespan.

[0005] Therefore, in order to overcome the shortcomings of existing technologies, it is necessary to propose a digital twin-driven online optimization design method for fatigue constraints of major equipment. Summary of the Invention

[0006] This invention aims to address the problems of low computational efficiency, difficulty in real-time evaluation, and lack of consideration for fatigue evolution during structural service in existing fatigue analysis methods for major equipment. It provides a digital twin-driven online optimization design method for fatigue constraints in major equipment. This method achieves rapid prediction of structural response by introducing a model order reduction method, realizes online evaluation of fatigue life by combining sensor data and fatigue damage mechanisms, and constructs an optimization design model constrained by fatigue life. It establishes an integrated closed-loop mechanism of "performance prediction - fatigue monitoring - optimization design" to achieve real-time evaluation of structural fatigue state and closed-loop updates of optimization design.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A digital twin-driven online optimization design method for fatigue constraints of major equipment, comprising the following steps: Step 1: Construct a high-fidelity dynamic model of the equipment structure and establish a digital twin reduced-order model; Based on structural modeling and performance analysis, a high-fidelity dynamic model is established to comprehensively describe the geometry, material properties, and connection constraints of each component of the equipment. Under typical operating loads, structural response data for key parts of the equipment, including physical quantities such as displacement, stress, and strain, are obtained. Subsequently, the intrinsic orthogonal decomposition method is used to extract features from the high-fidelity dynamic model, extracting the main modes and deformation patterns, and constructing a low-dimensional digital twin reduced-order model, thereby preserving the main dynamic characteristics of the structure and significantly reducing computational complexity. Specifically: Step 1.1: First, considering the nonlinear response behavior that major equipment may exhibit in complex service environments, a high-fidelity dynamic model of the equipment structure is established based on the finite element method. After discretizing the equipment structure into a finite element system composed of multiple nodes and elements, the high-fidelity dynamic model is expressed as: (1) in, The mass matrix represents the structure and is used to reflect the inertial characteristics of the structure in each degree of freedom. The structure represents the time... The acceleration response vector; The damping matrix is ​​used to characterize the energy dissipation characteristics of a structure during motion due to material energy consumption, connection friction, or the action of external media. Represents the velocity response vector; This represents the nonlinear stiffness matrix associated with the structural displacement vector, used to describe the nonlinear characteristics of structural stiffness as it changes with the degree of deformation. Represents the displacement response vector; This represents the external load vector, including static load, alternating load, and impact load.

[0008] Step 1.2: Solve the high-fidelity dynamic model from Step 1.1 under multiple typical working conditions to obtain displacement response samples corresponding to several times or several working conditions, and construct a response snapshot matrix: (2) in, This is a snapshot matrix, where each column of the matrix... Indicates the first The first sample working condition or the first The structural displacement response vector at each sampling time, with subscripts... This represents the total number of snapshot samples.

[0009] The response snapshot matrix is ​​used to centrally store high-dimensional structural response information, providing a data foundation for subsequent modality extraction and dimensionality reduction modeling.

[0010] Step 1.3, in order to more accurately characterize the nonlinear mechanical behavior of complex equipment, a nonlinear stiffness equivalent expression based on kernel function is introduced, as shown in formula (3): (3) in, This represents the initial stiffness matrix of the structure under linear small deformation conditions; This represents the kernel function term, used to characterize the current displacement response vector. With the Reference displacement vectors Similarity between them; The distance between two things is usually represented by the Euclidean norm; It can be configured with Gaussian kernels, polynomial kernels, or multiple quadratic kernels, etc. Indicates the first The weight coefficients corresponding to each kernel function; Indicates the number of reference samples. Indicates the first i Index of a reference displacement vector / kernel function.

[0011] Step 1.4: After obtaining the snapshot matrix, the dimensionality of the high-dimensional system is reduced using the intrinsic orthogonal decomposition method. Singular value decomposition is performed on the snapshot matrix: (4) in, The dominant mode matrix is ​​represented by column vectors that correspond to the dominant modes of the structural response. It is a singular value diagonal matrix. For its first i diagonal elements; is a right singular vector matrix used to describe the projection relationship of each snapshot in the modal space.

[0012] Singular value decomposition (SVD) enables the extraction of the most dominant deformation modes from large amounts of high-dimensional response data. To preserve the main dynamic characteristics, the preceding parameters are selected. The dominant mode as a reduced-order basis matrix And satisfy the energy retention criterion shown in formula (5): (5) in, Represents the singular valued diagonal matrix. One diagonal element; The numerator represents the total number of modes; the numerator in the formula represents the number of modes before the exponent. The total energy retained by the dominant mode; the denominator represents the total energy of all modes; This represents the energy retention threshold, typically set to 0.999.

[0013] Step 1.5: Construct a reduced-order basis matrix based on the dominant mode selected in Step 1.4. The high-fidelity dynamics model is then projected onto a low-dimensional subspace to obtain a digital twin reduced-order model: (6) in, This represents a reduced-order displacement coordinate vector, used to describe the dynamic response of the structure in low-dimensional space; This is a reduced-order velocity coordinate vector; This is a reduced-order acceleration coordinate vector; , and Let represent the projected reduced-order mass matrix, reduced-order damping matrix, and reduced-order nonlinear stiffness matrix, respectively; This represents the reduced-order load vector.

[0014] The predicted response of the digital twin reduced-order model for: (7) By using formula (6), the high-fidelity dynamic model with a high degree of freedom and a large amount of computation is transformed into a low-dimensional system with a dimension much lower than the original system but still retaining the main mechanical characteristics. This results in a digital twin reduced-order model that can meet the needs of real-time digital twin computation.

[0015] Step 2: Based on the digital twin reduced-order model obtained in Step 1, and combined with sensor data, realize the global response reconstruction of structural displacement.

[0016] During actual equipment operation, data acquisition devices such as strain sensors, acceleration sensors, and load sensors are deployed at key locations to acquire real-time structural operating status information. The collected measured data is fused with the prediction results of a digital twin reduced-order model. Through data correction and state update methods, the model prediction results are revised to obtain a structural response vector that more closely approximates the actual state. Based on the fused displacement response vector, the structural stress vector is further calculated, achieving an extended reconstruction from local measurement data to a global displacement response vector. Specifically: Step 2.1: During the actual operation of the equipment, strain sensors, acceleration sensors, and load sensors are deployed at key locations to collect real-time equipment service status information and construct observation vectors, as shown in formula (8): (8) in, Indicates time The comprehensive observation data vector; This represents measured strain data; This represents the measured acceleration data; Represents measured load data; symbols This indicates transpose, used to combine multiple observations into a column vector.

[0017] Step 2.2, in order to establish the mapping relationship between measured data and structural state, an observation model is constructed: (9) in, The observation matrix is ​​used to represent the global displacement response vector of the structure. Mapping to the sensor's observable space, for example, converting displacement into strain at the measuring point, acceleration at the measuring point, or local displacement; This is a measurement noise vector used to represent sensor error, external interference, and data acquisition uncertainty.

[0018] Based on the predicted response given by the digital twin reduced-order model in step 1.5 The least squares correction method is used to fuse and update the structural displacement vector, and the corrected displacement response vector is obtained, as shown in formula (10): (10) in, This represents the displacement response vector after fusion correction; This represents the observation residual, which is the difference between the measured value and the predicted observation value. This is the gain matrix, used to control the degree of influence of the observation residuals on the state correction.

[0019] When the prediction result has a large deviation, the gain matrix can increase the weight of the observation data; when the observation noise is large, the gain matrix can reduce the degree of observation intervention. The core idea of ​​formula (10) is to obtain a global response result that is closer to the real state by integrating "model prediction information" and "field measured information".

[0020] Step 2.3: Given the known structural displacement response, the internal stress vector of the structure is further obtained based on the finite element strain-displacement relationship and the material constitutive relation, achieving an extended reconstruction from the measured data to the global stress vector. After obtaining the corrected displacement response vector in Step 2.2, the structural stress vector is further calculated: (11) in, Indicates time The structural stress vector; This is the constitutive matrix of the material, used to describe the relationship between stress and strain in the material; This is the strain-displacement transformation matrix, used to obtain the element strain from the nodal displacements.

[0021] Step 3: Based on the structural stress vector obtained in Step 2, and combined with the fatigue damage calculation formula, construct a prediction model for the remaining service life of the equipment.

[0022] Based on the reconstructed structural stress vector, cyclic counting is performed to extract cyclic information under different stresses, and fatigue life is calculated in conjunction with material fatigue characteristics. Using a cumulative damage method, fatigue damage to the structure under complex loads is dynamically calculated to obtain fatigue damage values. Based on these fatigue damage values, a remaining service life prediction model is constructed, and the remaining service life of the structure is assessed according to the damage development trend. Simultaneously, high stress concentration areas and potential fatigue failure locations are identified based on stress distribution, providing a basis for subsequent optimization design. Specifically: Step 3.1, based on the structural stress vector obtained in step 2.3 The cyclic counting method is used to extract various load cyclic information, which is represented as follows: (12) in, Indicates the first Stress amplitude of stress cycles; This indicates the number of cycles at the corresponding stress amplitude; This indicates the total number of cyclic categories.

[0023] Step 3.2, simultaneously, based on the material fatigue characteristics, establish the SN curve relationship: (13) in, Indicates the stress amplitude The number of cycles that a material can withstand before fatigue failure under certain conditions; and These are material fatigue parameters, obtained through material testing. Indicates the fatigue strength coefficient of the material. Indicates the fatigue index of a material; The larger the stress amplitude, the smaller the allowable number of cycles. Formula (13) shows that there is an inverse power function relationship between the fatigue cycle number of a material and the stress amplitude, which is the basis for fatigue life estimation.

[0024] Step 3.3: Based on Miner's linear cumulative damage theory, calculate the fatigue damage value of the structure at the current stage, as shown in formula (14): (14) in, Indicates time Cumulative fatigue damage value; Indicates the first The damage contribution corresponding to the stress cycle; the total damage is obtained by summing the damage contributions of all cycles.

[0025] It is generally believed that when At that time, the structure reaches the critical state of fatigue failure.

[0026] Step 3.4, based on the cumulative fatigue damage value obtained in Step 3.3 A remaining useful life prediction model is constructed to obtain the remaining useful life, as shown in formula (15): (15) in, Indicates the remaining useful life; This indicates the remaining damage capacity before reaching the fatigue failure threshold. This represents the rate at which the current damage increases over time, expressed by the cumulative damage function. The time derivative is obtained.

[0027] Step 3.5, simultaneously, to identify hazardous areas, the high stress concentration area is defined as: (16) in, This represents the set of dangerous areas within the structure; Represents spatial coordinates, that is, it represents location; Indicates position Stress value at; This indicates the preset stress threshold, with a range of [value missing]. , This represents the fatigue limit of the material.

[0028] By using formula (16), all locations where stress exceeds the threshold are grouped together to determine high-risk fatigue zones or local failure sensitive zones, providing regional basis for subsequent optimization design.

[0029] Step 4: Based on the remaining service life and fatigue damage values ​​obtained in Step 3, and combined with the optimization design method, an online optimization design model under fatigue constraints is obtained.

[0030] Based on real-time updated fatigue damage values ​​and remaining service life, an online structural optimization model is constructed. The optimization objective is to minimize structural mass or increase stiffness, while introducing fatigue constraints to achieve performance improvement while meeting strength and service life requirements. During the optimization process, gradient optimization methods or intelligent optimization algorithms are used to solve for design variables, and a digital twin reduced-order model is combined to quickly evaluate the structural response, thereby significantly improving optimization computational efficiency and enabling online optimization design. Specifically: Step 4.1: Based on the fatigue damage values ​​and remaining service life obtained in steps 3.3 and 3.4, establish a structural optimization model. If lightweighting is the objective, the objective function is expressed as: (17) in, This represents the objective function to be optimized. Indicates position The material density design variable at the location typically takes a value between 0 and 1. The design area is represented; the integral result represents the total material usage or equivalent mass of the structure.

[0031] If the goal is to increase structural stiffness or decrease flexibility, the objective function is as follows: (18) in, Represents the external load vector; Represents the structural displacement response vector; It represents the structural flexibility; the smaller the value, the higher the overall stiffness of the structure.

[0032] Step 4.2: To ensure that the optimization results meet the actual structural response characteristics, equilibrium equation constraints are introduced under the objective function constraints of Step 4.1. By minimizing the work done by external forces, the structural resistance to deformation is improved.

[0033] (19) in, Representation and Design Variables The relevant structural stiffness matrix. The optimized structure must still satisfy the basic mechanical equilibrium conditions and cannot be designed without considering the actual structural response.

[0034] Simultaneously, fatigue damage constraints are introduced: (20) in, This represents the fatigue damage value calculated under the current design variable distribution; This indicates the maximum permissible damage threshold. A key feature of this invention is that it does not simply pursue lightweight or high stiffness, but rather requires that the optimization results meet fatigue life requirements.

[0035] Step 4.3: In addition to satisfying the objective function in Step 4.1 and the constraints in Step 4.2, the design variable for material density must also satisfy the following: (twenty one) in, The lower limit is the minimum density limit, used to avoid numerical singularity and retain minimum material connectivity; the upper limit of 1 represents the solid material state. The constraint shown in Equation (21) is used to limit the physical feasibility range of the design variables.

[0036] Step 4.4: Based on the structural optimization model constructed in steps 4.1 to 4.3 above, a gradient-based optimization method is used to solve the problem. Its sensitivity is expressed as: (twenty two) in, This represents the rate of change of the objective function with respect to the density variable; This represents the derivative of the stiffness matrix with respect to the density variable; Formula (22) is used to calculate the impact of stiffness changes on the overall structural performance. It provides a directional basis for optimization iteration, determining the degree of influence of increasing or decreasing the material in a certain region on the objective function.

[0037] Step 4.5: To improve the efficiency of online optimization calculation, a surrogate model is introduced in the optimization solution process of step 4.4 to quickly predict the structural displacement response, thereby reducing the number of calls to the high-fidelity model, as shown in formula (23): (twenty three) in, It is a reduced-order basis matrix; For parameters Mapping functions in low-dimensional space; It can represent load parameters, boundary condition parameters, geometric design parameters, or material parameters. Equation (23) indicates that by replacing the high-cost finite element solution process with proxy mapping, the structural displacement response can be predicted more quickly, thereby meeting the real-time calculation requirements of online optimization.

[0038] Step 5: Building upon Steps 1, 2, 3, and 4, implement a closed-loop update and online execution mechanism for the digital twin reduced-order model. Specifically, couple sensor data, the digital twin reduced-order model, fatigue analysis results, and optimization design to construct a closed-loop mechanism of "data acquisition - model prediction - fatigue assessment - optimization design - model update." During equipment operation, the system continuously updates model parameters and optimization variables based on real-time status, enabling dynamic adjustment of structural design or operating parameters according to changes in operating conditions. This achieves synergistic optimization of structural performance and fatigue life, improving equipment safety and operational reliability.

[0039] During equipment service, real-time sensor data (obtained in step two), the digital twin reduced-order model (obtained in steps one and two), the remaining service life prediction model (obtained in step three), and the structural optimization model (obtained in step four) are linked together to form a closed-loop process of "perception-prediction-evaluation-optimization-update". The monitoring information from the previous moment is used to correct the current twin state, the current twin state is used to update the fatigue damage and remaining service life results, and the fatigue damage results are further used as constraints input into the structural optimization model. The optimization results then adjust the structural or operational parameters in reverse for the state update at the next moment. Through this continuous iterative mechanism, the optimized design results are always consistent with the actual service state of the equipment, thereby realizing online fatigue constraint optimization design driven by digital twins.

[0040] The beneficial effects of this invention are as follows: (1) This invention establishes a digital twin reduced-order model that can be efficiently calculated by constructing a high-fidelity dynamic model and combining it with a reduced-order modeling method, which significantly reduces the computational complexity while ensuring that the main dynamic characteristics of the structure are not lost. On this basis, the data from strain sensors, acceleration sensors and load sensors are fused and updated with the model prediction results to achieve full-domain reconstruction of key responses such as structural displacement and stress, thereby obtaining more complete and accurate displacement and stress vectors under limited measurement points, which significantly improves the state perception capability of complex equipment in actual service.

[0041] (2) Based on the structural stress vector obtained in step two, this invention conducts fatigue damage assessment and remaining service life prediction. By processing and quantifying the stress vector under complex loads, a unified description of fatigue effects under multiple working conditions is achieved, enabling fatigue damage to be dynamically updated over time. Compared with traditional methods that rely solely on simulation or single measurement data, this invention can more realistically reflect the damage evolution process of structures under complex service environments, thereby significantly improving the accuracy and reliability of fatigue life prediction.

[0042] (3) Based on this, the present invention introduces fatigue damage value and remaining service life into the structural optimization design process, constructs a structural optimization model considering fatigue constraints, and realizes the synergistic optimization of structural performance and remaining service life. At the same time, through the coupling between the digital twin reduced-order model, real-time monitoring data and optimization algorithm, a closed-loop mechanism of "perception-prediction-evaluation-optimization-update" is formed, so that the structural parameters can be dynamically adjusted according to the actual operating state, thereby realizing online optimization design driven by digital twin, and significantly improving the safety, reliability and intelligent operation and maintenance level of major equipment under complex working conditions.

[0043] In summary, this invention constructs a closed-loop digital twin framework of "perception-prediction-evaluation-optimization-update" by integrating high-fidelity modeling, model reduction, multi-source data fusion, and fatigue assessment methods. While ensuring accuracy, it significantly improves computational efficiency and state perception capabilities, and realizes dynamic prediction and performance optimization of structural fatigue life. This has important engineering application value for improving the safety, reliability, and intelligent operation and maintenance level of major equipment. Attached Figure Description

[0044] Figure 1 Framework diagram of a digital twin-driven online optimization design method for fatigue constraints in major equipment; Figure 2 This is a schematic diagram of the bidirectional mapping and interaction mechanism; Figure 3 This is a diagram showing the main mechanical structure of a mining electric shovel. Figure 4 A schematic diagram for modeling digital twins; Figure 5 A flowchart for fatigue life assessment; Figure 6 This is a schematic diagram of the closed-loop verification of the twin model; Figure 6 (a) in the figure represents the physical model. Figure 6 (b) in the figure represents the twin model. Detailed Implementation

[0045] The following uses the boom structure of a mining electric shovel as an example to specifically illustrate the online optimization design method for fatigue constraints of major equipment driven by digital twins as described in this invention. The goal is to construct a digital twin of the mining electric shovel boom and realize its fatigue life prediction and online structural optimization design. The parameter settings and results in this embodiment are only used to illustrate the feasibility of this invention and do not constitute a limitation on the scope of protection of this invention.

[0046] This implementation provides a digital twin-driven online optimization design method for fatigue constraints in major equipment. The calculation process is as follows: Figure 1As shown, a digital twin model of the mining electric shovel boom is first constructed based on a high-fidelity model and multi-condition simulation. Then, sensor data is fused to reconstruct displacement and stress, and fatigue analysis and life assessment are performed. Based on this, an optimization design model under fatigue constraints is established to optimize and adjust the structure. Finally, a closed-loop iteration is formed through result feedback to achieve synergistic optimization of structural performance and lifespan. The specific steps are as follows: Step 1: Construct a high-fidelity dynamic model of the mining electric shovel boom and establish a digital twin reduced-order model. The calculation process is as follows: Figure 2 As shown. First, based on structural modeling and performance analysis, a high-fidelity dynamic model is established to comprehensively describe the geometry, material properties, and connection constraints of each component of the mining electric shovel boom. Under typical working condition loads, structural response data of the mining electric shovel boom, including physical quantities such as displacement, stress, and strain, are obtained. Subsequently, the intrinsic orthogonal decomposition method is used to extract features from the high-fidelity dynamic model, extracting the main modes and deformation modes, and constructing a low-dimensional digital twin reduced-order model, thereby preserving the main dynamic characteristics of the structure and significantly reducing computational complexity. Specifically: Step 1.1: First, considering the potential nonlinear response behavior of the mining electric shovel boom structure under complex service environments, a high-fidelity dynamic model of the mining electric shovel boom is established based on the finite element method. The boom material is selected as high-strength structural steel, with an elastic modulus of E = 210 GPa, a Poisson's ratio of 0.3, and a density of 7.85 × 10⁻⁶. 6 kg / mm 3 The model is discretized using three-dimensional solid elements, with a total of approximately 1.2 × 10⁻⁶ nodes. 5 The degrees of freedom are approximately 3.6 × 10⁻⁶. 5 The high-fidelity dynamics model is then expressed as: (1) in, The mass matrix represents the structure and is used to reflect the inertial characteristics of the structure in each degree of freedom. The structure represents the time... The acceleration response vector; The damping matrix is ​​used to characterize the energy dissipation characteristics of a structure during motion due to material energy consumption, connection friction, or the action of external media. Represents the velocity response vector; This represents the nonlinear stiffness matrix associated with the structural displacement vector, used to describe the nonlinear characteristics of structural stiffness as it changes with the degree of deformation. Represents the displacement response vector; This represents the external load vector, including static load, alternating load, and impact load.

[0047] Step 1.2: Under typical excavation conditions, apply periodic loads (range 0–300 kN) and impact loads (peak value approximately 500 kN) to the boom, solve the high-fidelity dynamic model from Step 1.1, obtain displacement response samples corresponding to several moments or conditions, and construct a response snapshot matrix: (2) in, This is a snapshot matrix, where each column of the matrix... Indicates the first The first sample working condition or the first The structural displacement response vector at each sampling time, with subscripts... This represents the total number of snapshot samples. The response snapshot matrix is ​​used to centrally store high-dimensional structural response information, providing a data foundation for subsequent modality extraction and dimensionality reduction modeling.

[0048] Step 1.3, in order to more accurately characterize the nonlinear mechanical behavior of the mining electric shovel boom, a nonlinear stiffness equivalent expression based on kernel function is introduced, as shown in formula (3): (3) in, This represents the initial stiffness matrix of the structure under linear small deformation conditions; This represents the kernel function term, used to characterize the current displacement response vector. With the Reference displacement vectors Similarity between them; The distance between two things is usually represented by the Euclidean norm; It can be configured with Gaussian kernels, polynomial kernels, or multiple quadratic kernels, etc. Indicates the first The weight coefficients corresponding to each kernel function; Indicates the number of reference samples. This represents the index of the i-th reference displacement vector / kernel function.

[0049] Step 1.4: After obtaining the snapshot matrix, the dimensionality of the high-dimensional system is reduced using the intrinsic orthogonal decomposition method. Singular value decomposition is performed on the snapshot matrix: (4) in, The dominant mode matrix is ​​represented by column vectors that correspond to the dominant modes of the structural response. It is a singular value diagonal matrix. For its first i diagonal elements; The right singular vector matrix describes the projection relationship of each snapshot in modal space. This decomposition allows extraction of the most dominant deformation modes from a large amount of high-dimensional response data. To preserve the main dynamic characteristics, the first... The dominant mode as a reduced-order basis matrix And satisfy the following energy conservation criterion: (5) in, Represents the singular valued diagonal matrix. One diagonal element; The numerator represents the total number of modes; the numerator in the formula represents the number of modes before the exponent. The total energy retained by the dominant mode; the denominator represents the total energy of all modes; This represents the energy retention threshold, typically set to 0.999. After order reduction, the model's degrees of freedom decrease from the original 3.6 × 10⁻⁶. 5 It dropped to 8.

[0050] Step 1.5: Construct a reduced-order basis matrix based on the dominant mode selected in Step 1.4. The high-fidelity dynamics model is then projected onto a low-dimensional subspace to obtain a digital twin reduced-order model: (6) in, Represents a reduced-order coordinate vector, used to describe the dynamic response of the structure in a low-dimensional space; , and Let represent the projected reduced-order mass matrix, reduced-order damping matrix, and reduced-order nonlinear stiffness matrix, respectively; Let represent the reduced-order load vector. Then, the predicted response of the digital twin reduced-order model... for (7) The above equation transforms the original high-fidelity dynamic model, which had a high degree of freedom and high computational cost, into a low-dimensional system with a much lower dimension but still retaining the main mechanical characteristics. The number of degrees of freedom is reduced by about five orders of magnitude. The results show that the digital twin reduced-order model reduces the single computation time from about 120s to 0.02s while maintaining the main structural response characteristics, achieving efficient digital twin modeling.

[0051] Step Two: Based on the digital twin reduced-order model obtained in Step One, and combined with sensor data, reconstruct the global response of structural displacement. The calculation process is as follows: Figure 3As shown, during the actual operation of the mining electric shovel, data acquisition devices such as strain sensors, acceleration sensors, and load sensors are deployed at key locations to obtain real-time structural operating status information. The collected measured data is fused with the prediction results of the digital twin reduced-order model. Through data correction and state update methods, the model prediction results are corrected to obtain a structural response vector that more closely approximates the actual state. Based on the fused displacement response vector, the structural stress vector is further calculated, realizing the extended reconstruction from local measurement data to the global displacement response vector.

[0052] Step 2.1: During the actual operation of the mining electric shovel, strain sensors, acceleration sensors, and load sensors are arranged at key locations. There are 12 strain sensors (arranged at welds and roots) and 4 acceleration sensors with a sampling frequency of 100Hz. The service status information of the mining electric shovel boom is collected in real time, and an observation vector is constructed as shown in formula (8). (8) in, Indicates time The comprehensive observation data vector; This represents measured strain data; This represents the measured acceleration data; Represents measured load data; symbols This indicates transpose, used to combine multiple observations into a column vector.

[0053] Step 2.2, in order to establish the mapping relationship between measured data and structural state, an observation model is constructed: (9) in, The observation matrix is ​​used to represent the global displacement response vector of the structure. Mapping to the sensor's observable space, for example, converting displacement into strain at the measuring point, acceleration at the measuring point, or local displacement; This is a measurement noise vector used to represent sensor error, external interference, and data acquisition uncertainty.

[0054] Based on the predicted response given by the digital twin reduced-order model in step 1.5 The least squares correction method is used to fuse and update the structural displacement vector, and the corrected displacement response vector is obtained, as shown in formula (10): (10) in, This indicates that the digital twin reduced-order model is at time... The predicted displacement response vector; This represents the displacement response vector after fusion correction; This represents the observation residual, which is the difference between the measured value and the predicted observation value. This is the gain matrix, used to control the degree of influence of observation residuals on state correction. When the prediction result has a large deviation, the gain matrix can increase the weight of the observation data; when the observation noise is large, the gain matrix can reduce the degree of observation intervention.

[0055] Step 2.3: After obtaining the corrected displacement response vector in step 2.2, the stress vector is further calculated: (11) in, Indicates time The structural stress vector; This is the constitutive matrix of the material, used to describe the relationship between stress and strain in the material; This is the strain-displacement transformation matrix, used to calculate element strain from nodal displacements. Measured data is input into the digital twin reduced-order model, and the model's prediction results are corrected using a data fusion method to obtain the fused structural displacement and stress vectors. Taking a typical working condition as an example, the comparison of the maximum stress before and after fusion is as follows: the finite element result is 158.6 MPa, the prediction before fusion is 150.2 MPa, and the result after fusion is 156.9 MPa, with the error reduced from approximately 5.3% to 1.1%.

[0056] Step 3: Based on the structural stress vector obtained in Step 2, and combined with the fatigue damage calculation formula, construct a prediction model for the remaining service life of the mining electric shovel boom. The specific calculation process is as follows: Figure 4 As shown, based on the reconstructed structural stress vector, cyclic counting is performed to extract cyclic information under different stresses, and fatigue life is calculated in conjunction with material fatigue characteristics. The fatigue damage of the structure under complex loads is dynamically calculated using the cumulative damage method to obtain fatigue damage values. A remaining service life prediction model is then constructed based on these fatigue damage values, and the remaining service life of the structure is assessed according to the damage development trend. Simultaneously, high stress concentration areas and potential fatigue failure locations are identified based on the stress distribution, providing a basis for subsequent optimization design.

[0057] Step 3.1, based on the stress vector obtained in step 2.3 The cyclic counting method is used to extract various load cyclic information, which is represented as follows: (12) in, Indicates the first Stress amplitude of stress cycles; This indicates the number of cycles at the corresponding stress amplitude; This indicates the total number of cycle categories. Statistical analysis of the stress vectors yields a stress range of 60–120 MPa and a cycle count of 10. 5 class.

[0058] Step 3.2, simultaneously, based on the material fatigue characteristics, establish the SN curve relationship: (13) in, Indicates the stress amplitude The number of cycles that a material can withstand before fatigue failure under certain conditions; and These are material fatigue parameters, obtained through material testing. Indicates the fatigue strength coefficient of the material. The fatigue index of the material is represented by the following values: and ; The larger the stress amplitude, the smaller the allowable number of cycles. Formula (13) shows that there is an inverse power function relationship between the fatigue cycle number of a material and the stress amplitude, which is the basis for fatigue life estimation.

[0059] Step 3.3: Based on Miner's linear cumulative damage theory, calculate the fatigue damage value of the structure at the current stage, as shown in formula (14): (14) in, Indicates time The cumulative fatigue damage value; Indicates the first The damage contribution corresponding to the stress cycle; the total damage is obtained by summing the damage contributions of all cycles.

[0060] It is generally believed that when At that time, the structure reaches the critical state of fatigue failure.

[0061] Step 3.4, based on the cumulative fatigue damage value obtained in Step 3.3 A remaining useful life prediction model is constructed to obtain the remaining useful life, as shown in formula (15): (15) in, Indicates the remaining useful life; This indicates the remaining damage capacity before reaching the fatigue failure threshold. The rate at which the current damage increases over time can be represented by the cumulative damage function. The time derivative was calculated. The results show that the current cumulative fatigue damage value of the critical part of the boom is 0.42, with a damage margin of 0.58. This transforms the previously difficult-to-determine fatigue state into a quantifiable lifespan result, providing a direct basis for maintenance decisions and structural optimization.

[0062] Step 3.5, simultaneously, to identify hazardous areas, the high stress concentration area is defined as: (16) in, This represents the set of dangerous areas within the structure; Represents spatial location coordinates; Indicates position Stress value at; This indicates the preset stress threshold, with a range of [value missing]. , The material fatigue limit is defined by formula (16). All locations where stress exceeds the threshold are grouped together to identify high-risk fatigue zones or sensitive areas for local failure, providing a regional basis for subsequent optimization design.

[0063] Step 4: Based on the remaining service life and fatigue damage values ​​obtained in Step 3, and combined with the optimization design method, an online optimization design model under fatigue constraints can be obtained. The specific calculation process is as follows: Figure 5 As shown in Figure 3.3 and 3.4, based on the real-time updated fatigue damage and remaining service life information obtained, a structural optimization model is constructed. The optimization objective is to minimize structural mass or increase stiffness, while introducing fatigue constraints to ensure performance improvement while meeting strength and service life requirements. During the optimization process, gradient optimization methods or intelligent optimization algorithms are used to solve for the design variables, and a digital twin reduced-order model is combined to quickly evaluate the structural response, thereby significantly improving the optimization computation efficiency and achieving online optimization design.

[0064] Step 4.1: Based on fatigue damage values ​​and remaining service life, establish a structural optimization model. If lightweighting is the objective, the objective function is expressed as: (17) in, This represents the objective function to be optimized. Indicates position The material density design variable at the location typically takes a value between 0 and 1. The design area is represented; the integral result represents the total material usage or equivalent mass of the structure.

[0065] If the goal is to increase structural stiffness or decrease flexibility, the objective function is as follows: (18) in, Represents the external load vector; Represents the structural displacement response vector; It represents the structural flexibility; the smaller the value, the higher the overall stiffness of the structure.

[0066] Step 4.2: To ensure that the optimization results meet the actual structural response characteristics, equilibrium equation constraints are introduced under the objective function constraints of Step 4.1. By minimizing the work done by external forces, the structural resistance to deformation is improved.

[0067] (19) in, Representation and Design Variables The relevant structural stiffness matrix; This is the structural displacement response vector; This represents the external load vector. The optimized structure must still meet the basic mechanical equilibrium conditions and cannot be designed without considering the actual structural response.

[0068] Simultaneously, fatigue damage constraints are introduced: (20) in, This represents the fatigue damage value calculated under the current design variable distribution; This indicates the maximum permissible damage threshold. A key feature of this invention is that it does not simply pursue lightweight or high stiffness, but rather requires that the optimization results meet fatigue life requirements.

[0069] Step 4.3: In addition to satisfying the objective function in Step 4.1 and the constraints in Step 4.2, the design variable for material density must also satisfy the following: (twenty one) in, The lower limit is the minimum density limit, used to avoid numerical singularity and retain minimum material connectivity; the upper limit of 1 represents the solid material state. The constraint shown in Equation (21) is used to limit the physical feasibility range of the design variables.

[0070] Step 4.4: Based on the structural optimization model constructed in steps 4.1 to 4.3 above, a gradient-based optimization method is used to solve the problem. Its sensitivity is expressed as: (twenty two) in, This represents the rate of change of the objective function with respect to the density variable; This represents the derivative of the stiffness matrix with respect to the density variable; Formula (22) is used to calculate the impact of stiffness changes on the overall structural performance. It provides a directional basis for optimization iteration, determining the degree of influence of increasing or decreasing the material in a certain region on the objective function.

[0071] Step 4.5: To improve the efficiency of online optimization calculation, a surrogate model is introduced in the optimization solution process of step 4.4 to quickly predict the structural displacement response, thereby reducing the number of calls to the high-fidelity model, as shown in formula (23): (twenty three) in, It is a reduced-order basis matrix; For parameters Mapping functions in low-dimensional space; It can represent load parameters, boundary condition parameters, geometric design parameters, or material parameters. Equation (23) indicates that by replacing the high-cost finite element solution process with proxy mapping, the structural displacement response can be predicted more quickly, thereby meeting the real-time calculation requirements of online optimization. The optimization results show that, under the premise of meeting the fatigue damage threshold of 0.58, the mass of the boom structure is reduced by about 9.7% compared with that before optimization, and the maximum stress in the critical part is reduced from 156.9 MPa to 149.8 MPa, indicating that the structural optimization model can simultaneously achieve weight reduction and life improvement.

[0072] Step 5: Based on Steps 1, 2, 3, and 4, implement a closed-loop update and online execution mechanism for the digital twin order reduction model. The constructed digital twin order reduction model is as follows: Figure 6 As shown, where Figure 6 (a) in the figure represents the physical model. Figure 6 (b) in the diagram represents the twin model. During the service life of the mining electric shovel, the real-time sensor data (obtained in step two), the digital twin reduced-order model (obtained in steps one and two), the remaining service life prediction model (obtained in step three), and the structural optimization model (obtained in step four) are linked together to form a closed-loop process of "perception-prediction-evaluation-optimization-update". The monitoring information from the previous moment is used to correct the current twin state, the current twin state is used to update the fatigue damage and remaining service life results, the fatigue damage results are further used as constraints input into the structural optimization model, and the optimization results are then used to adjust the structural parameters or operating parameters for the state update at the next moment. Through this continuous iterative mechanism, the optimization design results are always consistent with the actual service state of the mining electric shovel boom, thereby realizing online optimization design driven by digital twin for fatigue constraints.

[0073] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A digital twin-driven online optimization design method for fatigue constraints of major equipment, characterized in that, The online optimization design method for fatigue constraints of critical equipment includes the following steps: Step 1: Construct a high-fidelity dynamic model of the equipment structure and establish a digital twin reduced-order model; Based on structural modeling and performance analysis, a high-fidelity dynamic model is established; under typical working condition loads, structural response data of key parts of the equipment are obtained; then, the intrinsic orthogonal decomposition method is used to extract features from the high-fidelity dynamic model, extract the main modes and deformation modes, and construct a low-dimensional digital twin reduced-order model. Step 2: Based on the digital twin reduced-order model obtained in Step 1, and combined with sensor data, realize the global response reconstruction of structural displacement; During actual equipment operation, the deployed strain sensors, acceleration sensors, and load sensors acquire structural operating status information in real time. The collected measured data is fused with the prediction results of the digital twin reduced-order model. Through data correction and state update methods, the model prediction results are corrected to obtain the corrected displacement response vector. Then, the structural stress vector is calculated to realize the extended reconstruction from local measurement data to global displacement response vector. Step 3: Based on the structural stress vector obtained in Step 2, and combined with the fatigue damage calculation formula, construct a prediction model for the remaining service life of the equipment. Based on the reconstructed structural stress vector, cyclic counting is performed to extract cyclic information under different stresses, and fatigue life is calculated in conjunction with material fatigue characteristics. The fatigue damage of the structure under complex loads is dynamically calculated using the cumulative damage method to obtain fatigue damage values. A remaining service life prediction model is constructed based on these fatigue damage values, and the remaining service life of the structure is assessed according to the damage development trend. Simultaneously, high stress concentration areas and potential fatigue failure locations are identified based on the stress distribution. Step four: Based on the remaining service life and fatigue damage values ​​obtained in step three, an online optimization design model under fatigue constraints is obtained using optimization design methods. Based on real-time updated fatigue damage values ​​and remaining service life, an online structural optimization model is constructed. The optimization objective is to minimize structural mass or improve stiffness, while fatigue constraints are introduced to improve performance while meeting strength and service life requirements. During the optimization process, gradient optimization methods or intelligent optimization algorithms are used to solve the design variables, and a digital twin reduced-order model is combined to quickly evaluate the structural response, thereby significantly improving the optimization calculation efficiency and realizing online optimization design. Step 5: Based on Step 1, Step 2, Step 3 and Step 4, implement a closed-loop update and online execution mechanism for the digital twin downgrade model.

2. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 1, characterized in that, Step one specifically includes: Step 1.1: First, a high-fidelity dynamic model of the equipment structure is established based on the finite element method. After discretizing the equipment structure into a finite element system composed of multiple nodes and elements, the high-fidelity dynamic model is expressed as: （1） in, The mass matrix represents the structure and is used to reflect the inertial characteristics of the structure in each degree of freedom. The structure represents the time... The acceleration response vector; The damping matrix is ​​used to characterize the energy dissipation characteristics of a structure during motion due to material energy consumption, connection friction, or the action of external media. Represents the velocity response vector; This represents the nonlinear stiffness matrix associated with the structural displacement vector, used to describe the nonlinear characteristics of structural stiffness as it changes with the degree of deformation. Represents the displacement response vector; This represents the external load vector, including static load, alternating load, and impact load; Step 1.2: Solve the high-fidelity dynamic model from Step 1.1 under multiple typical working conditions to obtain displacement response samples corresponding to several times or several working conditions, and construct a response snapshot matrix: （2） in, This is a snapshot matrix, where each column of the matrix... Indicates the first The first sample working condition or the first The structural displacement response vector at each sampling time, with subscripts... Indicates the total number of snapshot samples; Step 1.3 introduces the equivalent expression of nonlinear stiffness based on kernel function, as shown in formula (3): （3） in, This represents the initial stiffness matrix of the structure under linear small deformation conditions; This represents the kernel function term, used to characterize the current displacement response vector. With the Reference displacement vectors Similarity between them; The distance between two things is usually represented by the Euclidean norm; Choose a Gaussian kernel, a polynomial kernel, or a quadratic kernel; Indicates the first The weight coefficients corresponding to each kernel function; Indicates the number of reference samples. Indicates the first i Indexes of reference displacement vectors / kernel functions; Step 1.4: After obtaining the snapshot matrix, the dimensionality of the high-dimensional system is reduced using the intrinsic orthogonal decomposition method; singular value decomposition is then performed on the snapshot matrix. （4） in, The dominant mode matrix is ​​represented by column vectors that correspond to the dominant modes of the structural response. It is a singular value diagonal matrix. For its first i diagonal elements; It is a right singular vector matrix; Before selection The dominant mode as a reduced-order basis matrix And satisfy the energy retention criterion shown in formula (5): （5） in, Represents the singular valued diagonal matrix. One diagonal element; The numerator represents the total number of modes; the numerator in the formula represents the number of modes before the exponent. The total energy retained by the dominant mode; the denominator represents the total energy of all modes; Indicates the energy retention threshold; Step 1.5: Construct a reduced-order basis matrix based on the dominant mode selected in Step 1.

4. The high-fidelity dynamics model is then projected onto a low-dimensional subspace to obtain a digital twin reduced-order model: （6） in, This represents a reduced-order displacement coordinate vector, used to describe the dynamic response of the structure in low-dimensional space; This is a reduced-order velocity coordinate vector; This is a reduced-order acceleration coordinate vector; , and Let represent the projected reduced-order mass matrix, reduced-order damping matrix, and reduced-order nonlinear stiffness matrix, respectively; Represents a reduced-order load vector; The predicted response of the digital twin reduced-order model for: （7）。 3. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 2, characterized in that, Step two specifically includes: Step 2.1: During the actual operation of the equipment, based on the deployment of strain sensors, acceleration sensors, and load sensors, the service status information of the equipment is collected in real time, and an observation vector is constructed, as shown in formula (8): （8） in, Indicates time The comprehensive observation data vector; This represents measured strain data; This represents the measured acceleration data; Represents measured load data; symbols This indicates transpose, used to combine multiple observations into a column vector form; Step 2.2, in order to establish the mapping relationship between measured data and structural state, an observation model is constructed: （9） in, The observation matrix is ​​used to represent the global displacement response vector of the structure. Mapped to the sensor's observable measurement space; To measure the noise vector; Based on the predicted response given by the digital twin reduced-order model in step 1.5 The least squares correction method is used to fuse and update the structural displacement vector, and the corrected displacement response vector is obtained, as shown in formula (10): （10） in, This represents the displacement response vector after fusion correction; This represents the observation residual, which is the difference between the measured value and the predicted observation value. This is the gain matrix; Step 2.3: Given the structural displacement response, the internal stress vector of the structure is obtained based on the finite element strain-displacement relationship and the material constitutive relation, realizing the extended reconstruction from the measured data to the global stress vector; after obtaining the corrected displacement response vector in Step 2.2, the structural stress vector is calculated: （11） in, Indicates time The structural stress vector; The constitutive matrix of the material; This is the strain-displacement transformation matrix.

4. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 3, characterized in that, Step three specifically includes: Step 3.1, based on the structural stress vector obtained in step 2.3 The cyclic counting method is used to extract various load cyclic information, which is represented as follows: （12） in, Indicates the first Stress amplitude of stress cycles; This indicates the number of cycles at the corresponding stress amplitude; Indicates the total number of cyclic categories; Step 3.2, simultaneously, based on the material fatigue characteristics, establish the SN curve relationship: （13） in, Indicates the stress amplitude The number of cycles that a material can withstand before fatigue failure under certain conditions; and These are material fatigue parameters, obtained through material testing. Indicates the fatigue strength coefficient of the material. Indicates the fatigue index of a material; This indicates that the larger the stress amplitude, the smaller the allowable number of cycles; Step 3.3: Based on Miner's linear cumulative damage theory, calculate the fatigue damage value of the structure at the current stage, as shown in formula (14): （14） in, Indicates time Cumulative fatigue damage value; Indicates the first Damage contribution corresponding to stress cycle; total damage is obtained by summing the damage contributions of all cycles. when At that time, the structure reaches the critical state of fatigue failure; Step 3.4, based on the cumulative fatigue damage value obtained in Step 3.3 A remaining useful life prediction model is constructed to obtain the remaining useful life, as shown in formula (15): （15） in, Indicates the remaining useful life; This indicates the remaining damage capacity before reaching the fatigue failure threshold. This represents the rate at which the current damage increases over time, expressed by the cumulative damage function. Obtained by taking the time derivative; Step 3.5, simultaneously, to identify hazardous areas, the high stress concentration area is defined as: （16） in, This represents the set of dangerous areas within the structure; Represents spatial coordinates, that is, it represents location; Indicates position Stress value at; Indicates the preset stress threshold; By using formula (16), all locations where stress exceeds the threshold are grouped together to determine high-risk fatigue zones or sensitive areas for local failure.

5. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 4, characterized in that, In step 3.5, a preset stress threshold is established. The range is , This represents the fatigue limit of the material.

6. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 5, characterized in that, Step four specifically involves: Step 4.1: Based on the fatigue damage value and remaining service life obtained in Steps 3.3 and 3.4, establish a structural optimization model and determine the objective function; Step 4.2: To ensure that the optimization results meet the actual structural response law, equilibrium equation constraints are introduced under the constraints of the objective function in step 4.

1. （19） in, Representation and Design Variables The relevant structural stiffness matrix; Simultaneously, fatigue damage constraints are introduced: （20） in, This represents the fatigue damage value calculated under the current design variable distribution; Indicates the maximum permissible damage threshold; Step 4.3, based on satisfying the objective function in Step 4.1 and the equilibrium equation and fatigue damage constraints in Step 4.2, the material density design variable values ​​must satisfy: （21） in, The lower limit is the minimum density; the upper limit of 1 indicates the solid material state. Step 4.4: Based on the structural optimization model constructed in steps 4.1 to 4.3 above, a gradient-based optimization method is used to solve the problem and obtain the sensitivity. Step 4.5: In the optimization process of step 4.4, a surrogate model is introduced to predict the structural displacement response, as shown in formula (23): （23） in, It is a reduced-order basis matrix; For parameters Mapping functions in low-dimensional space; This indicates load parameters, boundary condition parameters, geometric design parameters, or material parameters.

7. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 6, characterized in that, In step four: In step 4.1: If the goal is lightweighting, then the objective function is expressed as: （17） in, This represents the objective function to be optimized. Indicates position The material density design variable at the location typically takes a value between 0 and 1. The design area is represented; the integral result represents the total material usage or equivalent mass of the structure. If the goal is to increase structural stiffness or decrease flexibility, the objective function is as follows: （18） in, Represents the external load vector; Represents the structural displacement response vector; It represents the structural flexibility; the smaller the value, the higher the overall stiffness of the structure. In step 4.4, sensitivity is expressed as: （22） in, This represents the rate of change of the objective function with respect to the density variable; This represents the derivative of the stiffness matrix with respect to the density variable; Used to calculate the impact of stiffness variations on the overall structural performance.

8. The digital twin-driven online optimization design method for fatigue constraints of major equipment according to claim 7, characterized in that, Step five specifically involves: During equipment service, the sensor data acquired in real time in step two, the digital twin reduced-order model obtained in steps one and two, the remaining service life prediction model obtained in step three, and the structural optimization model obtained in step four are linked together to form a closed-loop process of perception-prediction-evaluation-optimization-update. The monitoring information of the previous moment is used to correct the current twin state, the current twin state is used to update the fatigue damage and remaining service life results, the fatigue damage results are further used as constraints to input the structural optimization model, and the optimization results are then used to adjust the structural parameters or operating parameters in reverse for the state update of the next moment. Through a continuous iteration mechanism, the optimization design results are always kept consistent with the actual service status of the equipment, realizing online optimization design of fatigue constraints driven by digital twin.

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