Digital twin model dynamic correction method and system based on multi-objective optimization

Abstract

The application relates to the field of digital twinning and structural engineering, and discloses a dynamic correction method and system for a digital twinning model based on multi-objective optimization. The method comprises the following steps: collecting and standardizing the geometry, material, boundary and monitoring data of a structure to generate a data set; constructing an initial digital twinning model based on the data set; screening out key parameters to be corrected of local key cable-strut components by using global sensitivity analysis; taking the key parameters as decision variables to construct a multi-objective fidelity optimization model; solving the model by using a non-dominated sorting genetic algorithm II to obtain a Pareto optimal solution set and determine an optimal parameter combination; correcting the parameters of the local components based on the optimal combination and synchronously adjusting the surrounding components coupled mechanically to generate a corrected model; performing finite element simulation on the corrected model, verifying the consistency of the obtained virtual data and historical monitoring data, and obtaining a cable dome digital twinning model. The application effectively improves the precision and reliability of the digital twinning model.

Description

Technical Field

[0001] This application relates to the fields of digital twins and structural engineering, and in particular to a method and system for dynamic correction of digital twin models based on multi-objective optimization. Background Technology

[0002] Digital twin technology, by constructing virtual models that are mapped in real time to physical entities, has become a core supporting means for state monitoring, simulation prediction, and optimized control of complex engineering systems. The fidelity of the digital twin model directly determines the reliability of simulation analysis and decision-making control, while dynamic correction and iterative updates are crucial prerequisites for maintaining long-term fidelity and adapting to the evolution of physical entities and changes in operating conditions. For large-span spatial structures such as cable domes, their digital twin models typically involve multiple physical parameters, including the elastic modulus of the cables, cross-sectional properties, and boundary constraints. These parameters are highly dimensional and interconnected, making traditional correction methods that rely on empirical trial-and-error or individual parameter calibration insufficient for engineering applications.

[0003] Existing digital twin model correction methods have significant limitations at the optimization strategy level. Most methods adopt single-objective fidelity optimization, focusing solely on minimizing the deviation between the virtual response and measured data, neglecting constraints such as computational efficiency, parameter robustness, and hardware resource consumption. This leads to a surge in computational complexity of the corrected high-fidelity model, failing to meet the real-time requirements of scenarios such as structural health monitoring. While some methods introduce simplified models to improve efficiency, they sacrifice model structural accuracy for speed, resulting in excessive mapping deviations between the virtual model and the physical entity, making it difficult to support accurate decision-making. Furthermore, existing methods do not adequately consider multi-parameter collaborative optimization and local-global coordinated correction, lacking a systematic verification loop in the correction process, making it difficult to guarantee the spatial mapping reliability of the correction results.

[0004] Current technologies for correcting digital twin models of cable-stayed dome structures suffer from structural deficiencies in parameter selection and local correction. On one hand, the identification of key parameters in high-dimensional parameter space lacks quantitative methods, and blindly correcting all parameters leads to wasted computational resources and convergence difficulties. On the other hand, after correcting the parameters of local components, their mechanical effects are transmitted to surrounding related components through the structural stiffness matrix. If the parameters of coupled components are not adjusted synchronously, it will cause inconsistencies in the overall model's mechanical properties and even amplify simulation errors. Therefore, developing a method that can simultaneously address parameter selection, multi-objective optimization, accurate local correction, and overall coordinated verification has become a critical issue urgently needing to be solved in the field of digital twin modeling technology. Summary of the Invention

[0005] This application provides a method and system for dynamic correction of digital twin models based on multi-objective optimization, which can improve the accuracy and reliability of digital twin models.

[0006] Firstly, this application provides a method for dynamic correction of digital twin models based on multi-objective optimization, including: S1. Collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the solid cable dome structure through sensors, and generate a standardized modeling dataset through standardized processing; S2. Based on the standardized modeling dataset, construct an initial digital twin model through geometric modeling and finite element modeling; S3. Using a global sensitivity analysis algorithm, calculate the global sensitivity value of each physical parameter to be corrected related to the mechanical performance of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model, and screen out the key parameters to be corrected for the local key cable-stayed member based on the global sensitivity value. S4. Using the key parameters to be corrected as decision variables, and combining the standardized modeling dataset with preset constraints, construct a multi-objective fidelity optimization model. S5. The multi-objective fidelity optimization model is iteratively solved using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set, and the optimal combination of parameters to be corrected is determined according to the preset decision criteria. S6. Based on the optimal combination of parameters to be corrected, the physical parameters to be corrected for the corresponding local cable-stayed members are corrected. Combined with the correction results, the parameters of the surrounding mechanically coupled members are adjusted synchronously to generate a corrected digital twin model. S7. Perform finite element simulation on the corrected digital twin model to generate a virtual twin dataset. Verify the consistency between the virtual twin dataset and the historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

[0007] Secondly, this application provides a dynamic correction system for digital twin models based on multi-objective optimization, comprising: The data acquisition module is used to collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the physical cable dome structure through sensors, and generate a standardized modeling dataset after standardization processing. The initial model building module is used to construct an initial digital twin model based on the standardized modeling dataset through geometric modeling and finite element modeling. The parameter sensitivity analysis module is used to calculate the global sensitivity value of each physical parameter to be corrected related to the mechanical performance of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model using a global sensitivity analysis algorithm, and to screen out the key parameters to be corrected for local key cable-stayed members based on the global sensitivity value. The optimization modeling module is used to construct a multi-objective fidelity optimization model by taking the key parameters to be corrected as decision variables and combining them with the standardized modeling dataset and preset constraints. The optimization module is used to iteratively solve the multi-objective fidelity optimization model using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set, and to determine the optimal combination of parameters to be corrected according to the preset decision criteria. The model calibration module is used to correct the physical parameters of the corresponding local cable-stayed member based on the optimal combination of parameters to be corrected, and to adjust the parameters of the surrounding mechanically coupled members in conjunction with the correction results to generate a corrected digital twin model. The verification and finalization module is used to perform finite element simulation on the corrected digital twin model, generate a virtual twin dataset, and verify its consistency with the historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

[0008] Thirdly, this application provides a computer device comprising: a memory and at least one processor, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor communicates with the memory via a bus, and when the machine-readable instructions are executed by the processor, the steps of the above-described dynamic correction method for digital twin models based on multi-objective optimization are performed.

[0009] Compared with the prior art, the beneficial effects of this application are at least as follows: 1. By using global sensitivity analysis to identify key parameters that affect the mechanical response of the cable, the scope of correction is reduced from the entire model to local key components, reducing unnecessary computation, accelerating the optimization convergence speed, and improving the pertinence of model correction.

[0010] 2. By incorporating fidelity, computational efficiency, parameter robustness, and resource consumption into the optimization objective, a multi-objective fidelity optimization model is constructed, and the Pareto optimal solution set is solved using the non-dominated sorting genetic algorithm II. This achieves a balance between accuracy and real-time performance in the model correction results, avoiding the unintended consequences of single-objective optimization.

[0011] 3. By extracting the overall stiffness matrix after correcting the parameters of local components, analyzing and locating the affected surrounding coupled components, and adjusting their physical parameters synchronously, we can prevent local corrections from disrupting the overall mechanical coordination and ensure that the overall response of the model is consistent with the solid structure.

[0012] 4. By generating a virtual twin dataset through finite element simulation of the corrected model, the consistency of the model with historical operation monitoring data is verified in terms of spatial coordinates, mechanical quantities of key feature points, and data distribution. This confirms that the mapping deviation between the model and the physical entity is within a controllable range, ensuring the reliability of the correction results. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of the dynamic correction method for digital twin models based on multi-objective optimization proposed in this application; Figure 2 This is a convergence curve of the hypervolume index (HV) of this application; Figure 3 This is a verification diagram of the consistency of total strain energy under multiple working conditions in this application; Figure 4 This is a comparison diagram of the axial stress response of the cable in this application; Figure 5 This is a schematic diagram of the structure of the dynamic correction system for digital twin models based on multi-objective optimization in this application; Figure 6 This is a schematic block diagram of the structure of the dynamic correction device for digital twin models based on multi-objective optimization in this application. Detailed Implementation

[0015] This application provides a method and system for dynamic correction of digital twin models based on multi-objective optimization. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0016] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the dynamic correction method for digital twin models based on multi-objective optimization in this application includes: Step S1: Collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the physical cable dome structure through sensors, and generate a standardized modeling dataset through standardized processing.

[0017] In one specific embodiment, the process of performing step S1 may specifically include the following steps: Sensors deployed on the solid cable dome structure collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data, and integrate them to obtain a multi-source heterogeneous raw dataset; Based on the sampling time series of historical operational monitoring data, time series alignment processing is performed on the multi-source heterogeneous original datasets, and a method combining the mechanical constraints of the cable dome structure is adopted. The principle is to remove outlier data, fill in missing time-series data with linear interpolation, fill in missing static data with cross-validation of design specification values ​​and measured values, normalize static parameters with minimum-maximum normalization, and standardize dynamic time-series data with zero mean to generate a standardized modeling dataset.

[0018] Specifically, sensors deployed at key stress-bearing components of the solid cable-stayed dome structure synchronously collect geometric data, material parameter data, boundary condition data, and historical operational monitoring data according to a preset sampling frequency. For example, strain sensors and displacement sensors are deployed at the end nodes of the circumferential cables, radial ridge cables, and central vertical compression members. Strain sensors are attached along the cable axis to capture changes in cable stress, while displacement sensors are deployed at core nodes to record spatial coordinate drift. Each sensor continuously records data through a data acquisition terminal. Geometric contour information, material factory inspection parameters, support constraint states, and stress and displacement time histories during the structure's service life are mapped and formatted uniformly. A data table structure is defined with timestamp as the primary key and sensor ID as the partition key, specifying the data type (floating-point / integer / character) for each field. Static attribute data is mapped to a time series table based on sensor ID and timestamp intervals, resulting in a multi-source heterogeneous raw dataset covering both static attributes and dynamic responses of the structure.

[0019] Based on the sampling time series of historical operation monitoring data, time series alignment processing is performed on the multi-source heterogeneous original dataset. The timestamp sequence of historical operation monitoring data is extracted as the main time axis. For static attribute data with low update frequency, such as geometric data and material parameter data, nearest neighbor interpolation is used to match to the nearest timestamp node. For dynamic data such as wind load and snow load in boundary condition data that change with the working conditions, linear resampling is used to align to a unified time step, so that all data sequences have a consistent time reference system.

[0020] In the time-aligned dataset, outliers were removed using the 3σ principle, which incorporates the mechanical constraints of the cable dome structure. Specifically, the sample mean was calculated for each type of monitoring indicator. with standard deviation It will exceed Data within a given interval is marked as statistical anomaly candidates. At the same time, the mechanical constraints of the cable dome structure are introduced as physical criteria. Based on the characteristic that cable members can only withstand axial tensile force, when the stress monitoring value of the cable body shows negative compressive stress or exceeds the design value of the tensile strength of the material, it is directly judged as abnormal data that violates the laws of mechanics and is removed, regardless of whether it is within three times the standard deviation interval. This avoids the omission of physical paradoxes by simple statistical criteria.

[0021] For time-series missing data resulting from outlier removal, linear interpolation is used for imputation. For example, if the stress of a cable rod is missing at time t, its adjacent valid sampled values ​​are respectively... and The corresponding time is and Then, the fill value σ at time t is calculated according to a linear proportional relationship as follows: To maintain the local continuity of the data curves, for missing static data such as elastic modulus and cross-sectional area in the material parameter data, cross-validation between design specification values ​​and measured values ​​is used to complete the data. Specifically, the design specification values ​​are first obtained by consulting the structural design standards. Then compare with the measured values ​​of the same batch of components on site. If the relative deviation is within the allowable range for engineering, then a weighted average will be used. As a supplementary value; if the deviation exceeds the limit, a retest process is triggered to re-collect and verify the data.

[0022] Considering the differences in physical dimensions and numerical ranges between static parameters and dynamic time-series data, directly mixing them would amplify the influence of higher-order parameters. Therefore, a differentiated standardization process is performed. For static parameters, a min-max normalization process is applied, iterating through the sample set of each parameter class to extract the maximum value. and minimum value , the original value Mapping to the [0,1] interval eliminates dimensional differences between different physical quantities. Zero-mean standardization is applied to dynamic time-series data, calculating the sample mean and standard deviation for each data category. This transforms the original sequence into a distribution with a mean of zero and a standard deviation of one, highlighting its relative characteristics over time rather than its absolute magnitude. After these processes, a standardized modeling dataset with consistent time series, unified dimensions, and a normalized distribution is generated. This dataset is then divided into a model training subset and a model validation subset according to a predetermined ratio, for subsequent model construction and verification, respectively.

[0023] Step S2: Based on the standardized modeling dataset, construct the initial digital twin model through geometric modeling and finite element modeling.

[0024] In one specific embodiment, the process of performing step S2 may specifically include the following steps: Geometric parameters from geometric data, material property parameters from material parameter data, boundary constraint parameters from boundary condition data, and working condition load parameters from boundary condition data are extracted from the standardized modeling dataset. Static parameters are de-standardized to their original dimensions based on the original maximum and minimum values ​​recorded before normalization. Dynamic time series data are de-standardized to their original dimensions based on the original mean and standard deviation recorded before normalization. A three-dimensional geometric model corresponding to the solid cable dome structure is constructed based on the geometric parameters, and the three-dimensional geometric model to be configured is output. Import the three-dimensional geometric model to be configured into the finite element modeling tool, and match the corresponding material properties for each component of the three-dimensional geometric model to be configured according to the material performance parameters. The cable component is defined using Link rod element, and the compression member is defined using Beam element, thus obtaining the initial finite element model with material properties. Based on the boundary constraint parameters and load parameters, nodal constraint conditions, dead load and live load conditions are configured for the initial finite element model to obtain the configured finite element model. The three-dimensional geometric model to be configured is associated and integrated with the configured finite element model to generate an initial digital twin model.

[0025] Specifically, geometric parameters from the geometric data, material property parameters from the material parameter data, boundary constraint parameters from the boundary condition data, and load parameters from the boundary condition data are extracted from the standardized modeling dataset. Geometric parameters include the spatial coordinates of the endpoints of each circumferential cable, radial ridge cable, diagonal cable, and central vertical compression member in the cable dome structure, the member axis length, cross-sectional dimensions, and the topological connection relationships between nodes. Material property parameters include the elastic modulus, Poisson's ratio, density, and coefficient of thermal expansion of the cables and compression members. Boundary constraint parameters include support node numbers, support types, and constraint degrees of freedom information. Load parameters include the location and magnitude of the dead load, the distribution pattern of the live load, and the combination coefficients. Based on the geometric parameters, a global Cartesian coordinate system is established in the geometric modeling platform. The spatial coordinates of the endpoints of each member are sequentially read to generate a set of node points. The nodes are connected according to the topological connection relationships between nodes to form the member axis. Then, cross-sectional dimensions are assigned along the axis to generate a wireframe entity, thereby constructing a 3D geometric model that is topologically consistent with and scale-matched to the actual cable dome structure. This model retains the spatial configuration and component relationships of the actual structure.

[0026] The 3D geometric model to be configured is imported into the finite element modeling tool using a standard interface format. The spatial vertices of the geometric model are mapped to finite element nodes, and the axes are mapped to element baselines. A mapping index between geometric node numbers and finite element node numbers is established. Material properties are matched to each component according to material performance parameters. Cable components are defined using Link rod elements, which are 2-node spatial rod elements. Each node has 3 translational degrees of freedom. The element can only bear axial tensile or compressive forces and cannot transmit bending moments or shear forces. This characteristic is consistent with the mechanical behavior of cables, which can only be subjected to tension. The cross-sectional area of ​​the element is taken from the equivalent cross-sectional area in the material performance parameters. The material constitutive relation adopts a linear elastic model. The elastic modulus and Poisson's ratio are directly taken from the measured values ​​in the standardized modeling dataset. The element stiffness matrix is ​​automatically assembled by the finite element kernel based on the material elastic modulus, cross-sectional area, and component length. The compression member is defined using Beam elements, which are 2-node spatial beam elements. Each node has 6 degrees of freedom, including 3 translational and 3 rotational degrees of freedom. The element can withstand the combined effects of axial force, shear force, bending moment, and torque. This characteristic matches the mechanical behavior of the compression member under axial compression, which may involve bending buckling. The moment of inertia and cross-sectional area of ​​the element section are calculated based on the cross-sectional profile dimensions in the geometric parameters. The material properties are also obtained by using the elastic modulus and Poisson's ratio from the dataset. The element stiffness matrix is ​​based on the cross-sectional moment of inertia, elastic modulus, and member length. During mesh generation, cable members are discretized with one element per cable length, while compression members are divided into at least three elements along their length to capture bending deformation, resulting in an initial finite element model with material properties.

[0027] Based on the boundary constraint parameters, nodal constraint conditions are configured for the initial finite element model. Specifically, degree-of-freedom constraints are applied to corresponding nodes according to the support type. Fixed supports constrain all 6 degrees of freedom of the nodes; hinged supports release rotational degrees of freedom and constrain only 3 translational degrees of freedom; sliding supports release the corresponding translational degrees of freedom in the sliding direction and constrain the remaining degrees of freedom. The constraint information is bound by matching the node number with the support node number in the boundary constraint parameters. Based on the load conditions, dead load and live load conditions are configured. The dead load includes the structural self-weight and prestress. The structural self-weight is automatically calculated by the finite element software based on material density and element volume, and equivalent nodal forces are applied. Prestress is applied as initial strain or initial axial force to the nodes at both ends of the cable-stayed member. Live load includes wind load, snow load, and temperature load. Wind load is calculated as surface pressure according to the standard wind pressure formula and converted into nodal concentrated forces. Snow load is distributed as a uniform surface load based on the roof projection area and then equivalently converted into nodal loads. Temperature load is calculated based on the material's thermal expansion coefficient and temperature difference, and applied as a volume load. For example, thermal strain... According to the formula Calculation, where The coefficient of thermal expansion is a material property parameter. The difference between the ambient temperature and the reference temperature is used to superimpose the dead load and the live load according to the combination coefficients in the load parameters of the working condition, so as to obtain the configured finite element model.

[0028] The 3D geometric model to be configured is integrated with the configured finite element model to establish a one-to-one mapping table between geometric vertices and finite element nodes, a table for mapping geometric component numbers to finite element element numbers, and a binding table between material property libraries and component types. Through the mapping tables, geometric shape, material properties, constraint states, and load conditions are encapsulated into a unified data structure to generate an initial digital twin model. Within this model, a hierarchical relationship is established between the geometric layer, the physical layer, and the load layer. The geometric layer records spatial coordinates and topological relationships, the physical layer records material constitutive properties and element stiffness, and the load layer records boundary constraints and external loads. The three layers of data are mutually indexed through node numbers and element numbers, forming a multiphysics coupled model capable of simulation.

[0029] Step S3: Using a global sensitivity analysis algorithm, calculate the global sensitivity values ​​of each physical parameter to be corrected related to the mechanical properties of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model. Based on the global sensitivity values, select the key parameters to be corrected for the local key cable-stayed members.

[0030] In one specific embodiment, the process of performing step S3 may specifically include the following steps: Based on the historical operation monitoring data in the initial digital twin model and standardized modeling dataset, the set of physical parameters to be corrected and the mechanical output response indicators are determined. The mechanical output response indicators include cable stress and core node displacement. The Sobel global sensitivity analysis algorithm is used to construct Latin hypercube sampling samples for the set of physical parameters to be corrected. The Latin hypercube sampling samples are then input into the initial digital twin model for batch simulation to obtain the parameter-response corresponding dataset. Based on the parameter-response correspondence dataset, the global sensitivity value of each physical parameter to be corrected to the mechanical output response index is calculated, and a global sensitivity ranking table of parameters is obtained. The global sensitivity sorting table of parameters is filtered according to a preset sensitivity filtering threshold, and the filtered physical parameters to be corrected are output. The selected physical parameters to be corrected are mapped to the local cable members of the solid cable dome to determine the key parameters to be corrected.

[0031] Specifically, after constructing the initial digital twin model, to identify the core factors affecting the model's fidelity and avoid blind corrections in the high-dimensional parameter space, it is necessary to establish a set of physical parameters to be corrected and select mechanical output response indicators. Then, global sensitivity analysis is used to quantify the contribution of each parameter to the response. Based on the historical operational monitoring data in the initial digital twin model and the standardized modeling dataset, the set of physical parameters to be corrected and the mechanical output response indicators are determined. The set of physical parameters to be corrected includes material property parameters and geometric state parameters related to the mechanical properties of the cable-stayed member. For example, these include the elastic modulus of the cable, the cross-sectional area of ​​the cable, the elastic modulus of the compression member, the moment of inertia of the compression member section, the initial prestress value, and the support constraint stiffness. The mechanical output response indicators are selected as cable stress and core node displacement. Cable stress reflects the internal force state of the member, and core node displacement reflects the overall deformation pattern of the structure. Both together characterize the mapping consistency between the digital twin model and the physical structure at the mechanical behavior level.

[0032] Before calculating the global sensitivity value using the Sobel global sensitivity analysis algorithm, a Latin hypercube sampling sample needs to be constructed from the set of physical parameters to be corrected. Latin hypercube sampling is a hierarchical random sampling method that divides the probability distribution interval of each physical parameter to be corrected into several equally probable sub-intervals. A sample point is randomly selected from each sub-interval, and then the sample points of each parameter are randomly combined to form a uniformly distributed sample set covering the multidimensional parameter space. For example, suppose the number of physical parameters to be corrected is m, the distribution interval of each parameter is determined based on the measured statistical characteristics in the standardized modeling dataset or the allowable range of the design specifications, and the sampling size is set to n. Then, each parameter interval is divided into n equally probable sub-intervals. Through random permutation, the n sample points of each parameter are combined into n sets of m-dimensional parameter vectors, forming an n-m dimensional Latin hypercube sampling sample matrix. The Latin hypercube sampled samples are input into the initial digital twin model for batch simulation. Specifically, each row of parameter vectors in the sample matrix is ​​read sequentially, and the parameter values ​​are mapped to the corresponding material or geometric property fields in the initial digital twin model. After updating the model input, the finite element solver is called to perform static analysis and solve the problem. The stress values ​​of each cable and the displacement values ​​of the core node under the current parameter combination are extracted. The process is iterated row by row until all samples are calculated, resulting in a parameter-response correspondence dataset consisting of n sets of input parameter vectors and n sets of output response vectors.

[0033] Based on the parameter-response correspondence dataset, the Sobel global sensitivity analysis algorithm is used to calculate the global sensitivity values ​​of each physical parameter to be corrected to the mechanical output response index. The Sobel global sensitivity analysis algorithm is based on the principle of variance decomposition, which decomposes the total variance of the model output response into variance components contributed by each input parameter and their interactions. Specifically, let the cable stress or core node displacement be the output quantity y, and the i-th physical parameter to be corrected be the input quantity. The total variance V(y) is decomposed into variance components of various orders, including the variance of the one-parameter main effects. Second-order interaction variance (where j represents another parameter that interacts with the i-th parameter,) And higher-order interaction variances. First-order Sobel sensitivity index From the formula Calculate the total order Sobel sensitivity index. From the formula Calculation, where This is the sum of the variances contributed by the i-th physical parameter to be corrected itself and by all interactions with other physical parameters to be corrected. Using the Monte Carlo estimation method, based on the Latin hypercube sampling matrix and its contrast matrix, the outer loop iterates through the samples to calculate the unconditional variance, and the inner loop iterates through the parameters to calculate the conditional variance through the cross-combination matrix, thus estimating... and For example, Monte Carlo estimation uses two independent sample matrices A and B, each with a sample size of n, and constructs a cross-combination of A and B. Matrix, where The matrix inherits all columns of matrix A except for the i-th column, and the i-th column is replaced with the i-th column of matrix B. The expected value and variance of the output response corresponding to the three sets of samples are calculated to obtain... and Numerical estimation. The first-order sensitivity exponents and the total-order sensitivity exponents of all physical parameters to be corrected are arranged in descending order to form a global sensitivity ranking table for the parameters.

[0034] The global sensitivity ranking table of parameters is filtered according to a preset sensitivity screening threshold. The preset sensitivity screening threshold is determined as follows: the mean and standard deviation of the first-order sensitivity index of all physical parameters to be corrected are calculated, and the mean of the first-order sensitivity index plus one standard deviation is used as the first-order sensitivity screening threshold; at the same time, the mean and standard deviation of the total-order sensitivity index of all physical parameters to be corrected are calculated, and the mean of the total-order sensitivity index plus one standard deviation is used as the total-order sensitivity screening threshold. For example, if the first-order sensitivity screening threshold is 0.05 and the total-order sensitivity screening threshold is 0.1 calculated according to the above statistical method, parameters with a first-order sensitivity index greater than 0.05 and a total-order sensitivity index greater than 0.1 are judged to have a substantial impact on the model response and are retained; parameters with both the first-order sensitivity index and the total-order sensitivity index lower than the corresponding threshold are judged to have negligible impact on the current mechanical output response index and are discarded. After outputting the filtered physical parameters to be corrected, the filtered physical parameters to be corrected are mapped to the local cable-stayed members of the solid cable dome. Specifically, a mapping index is established between the physical parameters to be corrected and the component numbers. This index is constructed based on the association between the geometric and physical layers in the initial digital twin model. Each material property parameter or geometric state parameter is bound to a specific circumferential cable, radial ridge cable, diagonal cable, or compression member number. For example, if the elastic modulus of the cable is selected as a substantially sensitive parameter, the cable member number to which the elastic modulus attribute belongs is traced according to the mapping index, and the member is marked as a locally critical cable member. The corresponding elastic modulus of the cable is then determined as a critical parameter to be corrected. Through the above mapping, a subset of parameters whose influence on cable stress and core node displacement cannot be ignored is identified from all the physical parameters to be corrected, and these parameters are located to specific locally critical cable members, forming a list of critical parameters to be corrected.

[0035] Step S4: Using the key parameters to be corrected as decision variables, and combining them with the standardized modeling dataset and preset constraints, construct a multi-objective fidelity optimization model.

[0036] In one specific embodiment, the process of performing step S4 may specifically include the following steps: The key parameters to be corrected are set as decision variables for multi-objective optimization, the reasonable range of numerical variation for each decision variable is defined, and the decision variable definition set is output. Based on the standardized modeling dataset, parameter value constraints and mechanical performance constraints of decision variables are set to form a set of preset constraints. Based on the requirements of structural health monitoring projects, multiple independent optimization objective functions are set to obtain a set of optimization objective functions; A multi-objective fidelity optimization model is constructed using the set of decision variable definitions as input, the set of preset constraints as the solution boundary, and the set of optimization objective functions as the optimization guide.

[0037] Specifically, the key parameters to be corrected are transformed into decision variables for multi-objective optimization, with each decision variable corresponding to the value to be optimized for a key parameter. Based on the measured statistical characteristics of each parameter in the standardized modeling dataset and the allowable range of the design specifications, the numerical variation range of each decision variable is defined. For example, the lower bound of the elastic modulus of the cable is set as the measured statistical mean minus 2 standard deviations, and the upper bound is set as the measured mean plus 2 standard deviations; the lower bound of the initial prestress is set as 0.9 times the tension control value, and the upper bound is set as 1.1 times the tension control value. The identifiers, physical meanings, dimensions, and numerical variation ranges of each decision variable are encapsulated into structured data objects, outputting a decision variable definition set. This definition set determines the independent variable space dimension and the optimization boundary of the optimization problem.

[0038] Based on the determination of decision variables and their optimization boundaries, it is necessary to further limit the feasible domain of optimization to avoid invalid solutions that violate physical laws or structural safety. Two types of constraints are set based on a standardized modeling dataset to form a pre-defined set of constraints. Parameter value constraints are directly derived from the numerical variation range of the decision variable definition set. The lower and upper bounds of each decision variable are encoded as inequality constraints to ensure that parameter values ​​remain within the physically feasible domain during the optimization process. Mechanical performance constraints are set according to the requirements of the cable dome structure health monitoring project. By comparing the mechanical response of the initial digital twin model under the baseline working condition with the limits of the structural design specifications, structural safety thresholds are extracted as constraint boundaries. For example, the tensile stress of the cable rods must not exceed the design value of the material's tensile strength, the compressive stress of the compression members must not exceed the Euler critical stability bearing capacity, and the vertical displacement of the core nodes must not exceed the allowable threshold for structural deformation. The parameter value constraints and mechanical performance constraints are uniformly encoded into a constraint function set. The parameter value constraints are expressed in the form of upper and lower bounds of the decision variables, while the mechanical performance constraints are expressed in the structural response output of the finite element simulation. Together, they constitute the pre-defined set of constraints, limiting the feasible solution domain of multi-objective optimization.

[0039] After defining the feasible region, multi-dimensional indicators for evaluating the quality of solutions need to be established to form a set of optimization objective functions. Based on the requirements of structural health monitoring engineering, four independent optimization objective functions are set. The fidelity objective quantifies the deviation between the virtual twin data and the historical operational monitoring data in the standardized modeling dataset. It is calculated using the root mean square error (RMSE) form, i.e., the square root of the mean of the squared difference between the finite element simulation output value and the corresponding historical operational monitoring data for each monitoring point. The smaller this objective function value, the higher the model fidelity. The computational efficiency objective is measured by the CPU time consumed in a single finite element simulation solution. The smaller this objective function value, the higher the iterative computational efficiency. The parameter robustness objective characterizes the output stability of key parameters to be corrected under disturbances. It is defined as follows: at the nominal value points of each parameter defined by the decision variable definition set, the forward difference method is used to calculate the approximate first-order partial derivatives of the model's key mechanical response with respect to each decision variable. The absolute values ​​of each partial derivative approximation are weighted and summed according to preset weight coefficients to obtain the parameter robustness objective function value. For example, let n be the number of key parameters to be corrected. Let i be the nominal value of the i-th decision variable. Take 1% of the nominal value. For key mechanical responses such as cable stress or core node displacement, the approximate value of the first-order partial derivative is [ Preset weighting coefficients for each parameter The sensitivity index is determined based on its proportion in the total order sensitivity index in the sensitivity ranking table. and After multiplying and summing, we obtain the parameter robustness objective function value; the smaller this objective function value, the lower the model's sensitivity to parameter perturbations and the stronger its parameter robustness. The resource consumption objective is measured by the peak memory usage in a single simulation process; the smaller this objective function value, the lower the hardware resource consumption.

[0040] Since the four objective functions are independent of each other and have different dimensions, there is an inherent conflict between the fidelity objective and the computational efficiency and resource consumption objectives. Improving fidelity usually comes at the cost of increasing simulation precision and computation time, while the parameter robustness objective requires parameter values ​​to avoid sensitive regions, which may deviate from the optimal fidelity solution. Therefore, it is necessary to normalize the values ​​of each objective function to eliminate the difference in dimensions and make objective functions of different orders of magnitude comparable. The normalization process employs a fixed-reference scheme: for each objective function, fixed upper and lower limits of the normalization benchmark are pre-defined based on the design specifications for structural health monitoring and the physical limits of hardware resources. The upper limit for fidelity is the maximum acceptable root mean square error in engineering, and the lower limit is 0. The upper limit for computational efficiency is the maximum acceptable time for a single simulation, and the lower limit is 0. The upper limit for parameter robustness is the maximum allowable sum of the weighted partial derivatives of each parameter, and the lower limit is 0. The upper limit for resource consumption is the peak available memory of the system, and the lower limit is 0. The original values ​​of each objective function are mapped to a dimensionless interval of 0 to 1 using the formula (x - lower limit) / (upper limit - lower limit). Values ​​exceeding the interval boundaries are truncated according to the boundary values. Since the normalization benchmark is pre-determined before the optimization solution is initiated, it remains unchanged during the iteration of the non-dominated sorting genetic algorithm II, ensuring the consistency of fitness evaluation among individuals in each generation and the stability of the non-dominated sorting.

[0041] Once the indices and boundaries are complete, the various components are integrated into a comprehensive multi-objective fidelity optimization model. Using the set of defined decision variables as input, the set of pre-defined constraints as the solution boundary, and the set of objective functions as the optimization guide, a multi-objective fidelity optimization model is constructed. Specifically, all decision variables in the set of defined decision variables are combined into a decision vector, the dimension of which equals the number of key parameters to be corrected, with each component corresponding to a physical parameter to be optimized. All constraint functions in the set of pre-defined constraints are encoded into a system of inequalities concerning the decision vector, covering upper and lower bound constraints on parameter values ​​and mechanical performance response constraints. All objective functions in the set of objective functions are combined into an objective vector, the dimension of which equals the number of objective functions, with each component corresponding to a normalized dimensionless optimization index. Mathematically, the multi-objective fidelity optimization model is expressed as finding a set of decision vectors that satisfies all constraints, such that the objective vector reaches Pareto optimality, meaning that no objective function can be further improved without worsening at least one other objective function. This model extends the parameter correction problem from single-objective extreme value search to multi-objective trade-off optimization through a vector optimization framework, providing a complete mathematical framework and evaluation criteria for the subsequent iterative solution of the non-dominated sorting genetic algorithm II.

[0042] Step S5: Use the non-dominated sorting genetic algorithm II to iteratively solve the multi-objective fidelity optimization model to obtain the Pareto optimal solution set, and determine the optimal combination of parameters to be corrected according to the preset decision criteria.

[0043] In one specific embodiment, the process of performing step S5 may specifically include the following steps: Based on a multi-objective fidelity optimization model, the population is initialized with key parameters to be corrected as the encoding objects to obtain the initial population set. The initial population set of individuals is input into the initial digital twin model for batch simulation, the objective function value corresponding to each individual is obtained, and the population objective function value matrix is ​​output. The non-dominated sorting genetic algorithm II is used to quickly sort the population objective function value matrix and calculate the crowding degree, and the elite retention is combined to select a set of high-quality parent individuals. Simulated binary crossover and polynomial mutation are performed on the set of high-quality parent individuals to generate crossover offspring and mutated offspring, which are then merged with the set of high-quality parent individuals to generate a new generation population. Using the next generation of population as the input for the next round, repeat batch simulation, fast non-dominated sorting, crowding calculation, elite retention screening, binary crossover and polynomial mutation until the preset maximum number of iterations is reached, and output the Pareto optimal solution set. Based on the preset engineering decision criteria, the optimal combination of parameters to be corrected is selected from the Pareto optimal solution set to adapt to the fidelity correction of local cable-stayed components and the overall mechanical coordination.

[0044] Specifically, after constructing the multi-objective fidelity optimization model, in order to search for the Pareto optimal parameter combination that takes into account multiple engineering requirements within the physically feasible domain, it is necessary to drive the iterative simulation of the digital twin model through an evolutionary algorithm, and select the optimal solution that adapts to the fidelity of local components and the overall mechanical coordination from the population evolution. The non-dominated sorting genetic algorithm II is used to iteratively solve the multi-objective fidelity optimization model. This algorithm is a multi-objective optimization method based on population evolution, which searches for multiple non-dominated solutions in parallel in the decision variable space by simulating the survival competition and genetic variation mechanism in natural selection. Based on the multi-objective fidelity optimization model, the population is initialized with key parameters to be corrected as encoding objects to obtain an initial population set of individuals. Specifically, each key parameter to be corrected is mapped to a real-number encoded gene locus, and all key parameters to be corrected are arranged in a predetermined order to form the chromosome string of the individual. The dimension of the chromosome string is equal to the number of key parameters to be corrected. Within the numerical variation range defined by the decision variable definition set, an initial population set is generated using a random uniform sampling method. Each gene locus of each individual is independently and randomly selected between the upper and lower bounds of its corresponding parameter. For example, the population size is set to 50, that is, the initial population contains 50 individuals. Each individual represents a complete combination of physical parameters of a local component of the cable dome, including a random combination of the elastic modulus of the cable, the moment of inertia of the compression member, and the prestress value.

[0045] The initial population set of individuals is input into the initial digital twin model for batch simulation to obtain the objective function value corresponding to each individual, and the population objective function value matrix is ​​output. Specifically, for each individual in the initial population set, its chromosome string is decoded into physical parameter values ​​and assigned to the corresponding local key cable-stayed member attribute fields in the initial digital twin model. After updating the model input, the finite element solver is called to perform static analysis, extracting the cable-stayed member stress response and core node displacement response under the current parameter combination, and then calculating the response values ​​of the fidelity objective, computational efficiency objective, parameter robustness objective, and resource consumption objective. The response values ​​of all individuals on each objective function are arranged by individual number and objective number to form the population objective function value matrix. The rows of this matrix correspond to individuals, the columns correspond to optimization objectives, and the matrix elements represent the fitness performance of a specific individual on a specific objective, providing a quantitative comparison basis for subsequent non-dominated ranking.

[0046] A non-dominated sorting genetic algorithm II is used to quickly sort the objective function value matrix of the population and calculate crowding, combined with elite retention to select a set of high-quality parent individuals. The fast non-dominated sorting divides the population into non-dominated levels based on the dominance relationship between individuals. If individual A's response value is not inferior to individual B on all objective functions, and is strictly superior to individual B on at least one objective, then individual A is said to dominate individual B. Individuals with zero dominance counts constitute the first non-dominated level. After removing individuals from the first level, those with zero dominance counts constitute the second level, and so on until all individuals are classified. Crowding calculation measures the distribution density of individuals within the same non-dominated level. Individuals within the same level are sorted in ascending order according to their objective function values. The sum of the Euclidean distances between each individual's two adjacent individuals in the objective space is calculated. The crowding of boundary individuals is set to infinity to ensure their priority retention. A higher crowding level indicates a sparser distribution of solutions in the region where the individual resides, which helps maintain population diversity. The elite retention strategy directly replicates individuals in the first non-dominant tier of the current population to the next generation to prevent the loss of superior genes during crossover mutation. For example, the elite retention ratio is set to 10% of the population size, that is, retaining 5 top individuals to directly enter subsequent genetic operations.

[0047] Simulated binary crossover and polynomial mutation are performed on a set of high-quality parent individuals to generate crossed and mutated offspring. These offspring are then merged with the set of high-quality parent individuals to generate a new generation population. Simulated binary crossover is a crossover operator suitable for real-number encoding. It simulates the probability distribution characteristics of binary single-point crossover. Two parents are randomly selected from the set of high-quality parent individuals. Whether to perform crossover is determined based on the crossover probability. If crossover is performed, two offspring gene values ​​are generated at each gene position according to a normal distribution. The offspring gene values ​​tend to be distributed near the parent gene values. For example, the crossover probability is set to 0.9, and the crossover distribution index is set to 20. The larger the distribution index, the closer the offspring are to the parent; the smaller the distribution index, the wider the search range. Polynomial mutation is a mutation operator that applies random perturbation to the gene positions of individuals. Based on the mutation probability, a portion of the gene positions of an individual are randomly selected, and new mutated values ​​are generated within the gene position value range according to a polynomial probability distribution. This enables the population to have local fine-grained search capabilities in the later stages of iteration. For example, the mutation probability is set to the reciprocal of the number of key parameters to be corrected, and the mutation distribution index is set to 20. Crossover offspring are generated by simulating binary crossover, and mutated offspring are generated by polynomial mutation. The crossover offspring and mutated offspring are then merged with the high-quality parent individuals retained by the elite to form a new generation population of the same size as the initial population.

[0048] Using the new generation of individuals as the input for the next round, the process involves repeated batch simulations, fast non-dominated sorting, crowding calculation, elite retention screening, binary crossover, and polynomial mutation until a preset maximum number of iterations is reached, outputting a Pareto optimal solution set. Specifically, each individual in the new generation of individuals is decoded into physical parameters and input into the initial digital twin model for finite element simulation. After updating the population objective function value matrix, fast non-dominated sorting and crowding calculation are re-executed to select a new set of high-quality parent individuals. Then, crossover and mutation are performed to generate the next generation of individuals, and this process is repeated. For example, the preset maximum number of iterations is set to 100. After each iteration, the trend of the objective function value change of the first non-dominated level individuals is recorded. When the number of iterations reaches a preset threshold, the evolution process is terminated. At this point, all the first-level individuals in the non-dominated levels together constitute a Pareto optimal solution set. Each solution in this set represents a set of key parameter combinations that achieve a trade-off between fidelity, computational efficiency, parameter robustness, and resource consumption, and there are no other solutions that can further improve any objective without worsening at least one objective.

[0049] Based on preset engineering decision criteria, the optimal combination of parameters to be corrected is selected from the Pareto optimal solution set to suit both the fidelity correction of local cable-stayed components and the overall mechanical compatibility. The preset engineering decision criteria are set according to engineering preferences for structural health monitoring, selecting solutions from the Pareto optimal solution set that perform best on the fidelity objective and meet the engineering acceptable thresholds for all other objectives as candidates. If multiple candidates exist, their parameter robustness objective values ​​are further compared, and the one with the largest fluctuation tolerance is selected. For example, when the fidelity objective value of a solution in the Pareto optimal solution set is lower than the maximum allowable root mean square error, and the computational efficiency objective value is lower than the maximum acceptable time for a single simulation, while the parameter robustness objective value is in the top 30% quantile among all solutions, this solution is determined as the optimal combination of parameters to be corrected. The parameter values ​​in this combination directly correspond to the physical property correction amounts of the key local cable-stayed components of the solid cable dome, providing quantitative input for subsequent model calibration.

[0050] refer to Figure 2The figure shows the convergence curve of the hypervolume index (HV), illustrating the convergence trend of the HV as the number of iterations changes during the solution of a multi-objective fidelity optimization model using the non-dominated sorting genetic algorithm II. The hypervolume index is a common evaluation metric in multi-objective optimization, used to quantify the volume of the region dominated by the current non-dominated solution set in the objective space. A larger index value indicates better convergence and distribution of the solution set. The figure includes two trajectories: the initial curve and the smoothed trend curve. As can be seen from the figure, the HV index rises rapidly in the initial stage, indicating that the population is quickly approaching the Pareto front. As the number of iterations increases, the curve gradually stabilizes and approaches the theoretical maximum value, indicating that the algorithm has converged to a stable Pareto optimal solution set. This verifies that the non-dominated sorting genetic algorithm II has good convergence and solution efficiency within the multi-objective optimization framework of this application.

[0051] Step S6: Based on the optimal combination of parameters to be corrected, correct the physical parameters of the corresponding local cable-stayed member to be corrected. Combine the correction results and simultaneously adjust the parameters of the surrounding mechanically coupled members to generate the corrected digital twin model.

[0052] In one specific embodiment, the process of performing step S6 may specifically include the following steps: Based on the optimal combination of parameters to be corrected, the corresponding local key cable-stayed members in the initial digital twin model are matched and located, and a list of the locations of the members to be corrected is output. Replace the physical parameters to be corrected of the corresponding components in the list of components to be corrected with the corresponding parameter values ​​in the optimal combination of parameters to be corrected to obtain the digital twin model after local correction. The overall stiffness matrix is ​​extracted based on the locally corrected digital twin model. The surrounding components affected are determined through stiffness matrix correlation analysis, and a list of the impacts on the surrounding components is output. Based on the impact list of surrounding components, the parameters of the mechanically coupled surrounding components are adjusted synchronously to obtain a coordinated and adjusted digital twin model; The overall mechanical logic verification of the coordinated and adjusted digital twin model is performed. After the verification is passed, the corrected digital twin model is generated.

[0053] Specifically, the identifier codes of each parameter in the optimal combination of parameters to be corrected are read. The component type to which the parameter belongs is identified based on the code prefix, and the component number is matched based on the code suffix. The result is then retrieved from the mapping table of geometric layer node numbers and physical layer unit numbers and written into the list of components to be corrected. This list records the component number, component type, and parameter field address. The physical parameters to be corrected for the corresponding components in the list of components to be corrected are replaced with the corresponding parameter values ​​in the optimal combination of parameters to be corrected. Specifically, the material property library of the initial digital twin model is accessed by addressing the parameter field addresses in the list. The elastic modulus field of the original Link rod element is replaced with the elastic modulus of the cable in the optimal combination of parameters to be corrected, the original initial strain field is replaced with the optimal prestress value, and the original geometric section field is replaced with the optimal cross-sectional area, resulting in the locally corrected digital twin model.

[0054] The overall stiffness matrix is ​​extracted based on the locally corrected digital twin model. Specifically, all finite element elements in the model are traversed. For each Link element, the axial stiffness is calculated based on its elastic modulus, cross-sectional area, and current length. For each Beam element, the bending and shear stiffness are calculated based on its elastic modulus, moment of inertia, and current length. The stiffness matrices of each element are assembled into the overall stiffness matrix in the global coordinate system according to the node degrees of freedom number. The order of the overall stiffness matrix is ​​equal to the total number of degrees of freedom of the model, and the matrix elements are formed by the sum of the stiffness contributions between corresponding node pairs. The affected peripheral components are determined through stiffness matrix correlation analysis. Specifically, the row and column of the node number corresponding to the locally corrected component in the overall stiffness matrix are retrieved, and the coupling stiffness coefficient between this node and all other nodes is extracted. The non-zero coupling stiffness coefficients are sorted in descending order of absolute value. The components connected by the coupling path with an absolute value greater than a preset stiffness threshold are identified as mechanically coupled peripheral components. A list of peripheral component influences is output, which records the peripheral component number, the magnitude of the coupling stiffness coefficient, and the suggested adjustment direction.

[0055] The parameters of the mechanically coupled peripheral components are adjusted synchronously based on the list of surrounding component influences. Specifically, for peripheral components in the list whose coupling stiffness coefficient is greater than a preset stiffness threshold, the parameter adjustment range is determined based on the mechanical coupling strength with the locally modified components; the greater the coupling strength, the larger the adjustment range. The adjustment amount is determined as follows: each component in the list of surrounding component influences is sequentially used as a parameter to be identified. With the goal of minimizing the mechanical response deviation between the virtual twin dataset and historical operation monitoring data at the corresponding measurement points, univariate local optimization is performed within the feasible domain of each parameter to obtain the optimal parameter value for each peripheral component, which is then used as the synchronously adjusted parameter. The adjusted parameter values ​​are written into the material property field of the peripheral components, their element stiffness matrix is ​​updated, and they are reassembled into the overall stiffness matrix to obtain the coordinated adjusted digital twin model.

[0056] The overall mechanical logic of the coordinated and adjusted digital twin model is verified. Specifically, the overall stiffness matrix is ​​reassembled under the baseline working condition, and dead and live loads are applied. The nodal equilibrium equations are solved to obtain the nodal displacement vectors. The internal forces of each element are calculated by substituting the displacement vectors back into the equations. The support nodal reactions are extracted and compared with the resultant force of the external loads. If the difference between the two is less than the preset force equilibrium threshold, the nodal force equilibrium is determined to be satisfied. The total strain energy of the structure is calculated and compared with the total strain energy before the correction. If the rate of change of strain energy is within a reasonable physical range, the energy conservation is determined to be satisfied. The positive definiteness of the reduced stiffness matrix after applying loads and boundary constraints is checked. Zero eigenvalues ​​corresponding to rigid body displacements are excluded. If all remaining eigenvalues ​​are positive, the structural stability constraints are determined to be satisfied. After the nodal force equilibrium, energy conservation, and structural stability checks are all passed, the corrected digital twin model is generated.

[0057] refer to Figure 3 This figure shows the consistency verification of total strain energy under multiple working conditions, illustrating the comparison of total strain energy of the solid cable-stayed dome structure under five typical working conditions: measured monitoring data, simulation data after only local correction, and simulation data after coordinated correction. The figure reveals that when only the parameters of key local components are corrected without simultaneously adjusting the mechanically coupled surrounding components, there is a significant deviation between the simulated total strain energy and the measured values ​​under each working condition. However, after coordinating the adjustment of the surrounding component parameters through stiffness matrix correlation analysis, the simulated total strain energy highly matches the measured values, verifying that the local-to-global coordinated correction mechanism can effectively ensure the consistency of the overall mechanical properties of the corrected model with the solid structure.

[0058] Step S7: Perform finite element simulation on the corrected digital twin model to generate a virtual twin dataset. Verify the consistency between the virtual twin dataset and the historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

[0059] In one specific embodiment, the process of performing step S7 may specifically include the following steps: Based on the modified digital twin model, boundary conditions and load conditions consistent with the actual working conditions of the physical cable dome are configured. The finite element solver is called through the collaborative simulation platform to perform simulation and solve the problem, extracting the stress and strain data of the cable rods and the displacement data of the core nodes to generate a virtual twin dataset. Historical operation monitoring data corresponding to the working conditions are extracted from the standardized modeling dataset. The virtual twin dataset is aligned with the historical operation monitoring data in terms of time series and working conditions to obtain the aligned twin data pair. Multi-dimensional consistency verification was carried out on the aligned twin data pairs. The multi-dimensional consistency verification included spatial coordinate deviation analysis, mechanical data verification of key feature points, and data distribution consistency test. When all verification items meet the preset qualification threshold, the corrected digital twin model will be identified as the cable dome digital twin model.

[0060] Specifically, the ambient temperature, wind load direction angle, and snow load thickness for the current verification period are extracted from the standardized modeling dataset. Based on the real-time condition identification results of the structural health monitoring system, the support constraints are set to a constraint mode consistent with the current support state of the physical structure. The dead load is applied according to the self-weight partial factor in the structural design code, and the live load is superimposed according to the current condition combination factor. The simulation is performed by calling the finite element solver through a collaborative simulation platform. The collaborative simulation platform establishes a data interface between the corrected digital twin model and the finite element solver, and the configured boundary conditions and load conditions are written into the solver input card to trigger the static analysis calculation process. After the simulation is completed, the axial stress and axial strain of each cable and the three-dimensional spatial coordinate displacement components of each core node are extracted from the finite element result file. The stress-strain data and displacement data are organized into structured arrays according to the component number and node number to generate a virtual twin dataset.

[0061] Historical operational monitoring data corresponding to the working conditions are extracted from the standardized modeling dataset. The virtual twin dataset is then aligned with the historical operational monitoring data in terms of time sequence and working conditions to obtain aligned twin data pairs. Specifically, based on the simulation working condition identifier code corresponding to the virtual twin dataset, monitoring records with the same ambient temperature range, load level, and time window are retrieved from the historical operational monitoring data subset of the standardized modeling dataset. The stress and displacement monitoring values ​​of each measuring point within that time period are then extracted. When performing time sequence and working condition alignment, the virtual data output by the simulation is matched to the closest monitoring time according to the nearest neighbor principle, using the timestamp of the monitoring data as a reference. Linear resampling correction is used to correct time misalignment caused by differences in simulation step size and monitoring sampling frequency, so that the virtual value and monitoring value in each aligned twin data pair represent the mechanical response state of the same component under the same working condition at the same time.

[0062] Multi-dimensional consistency verification was conducted on the aligned twin data pairs, including spatial coordinate deviation analysis, key feature point mechanical data verification, and data distribution consistency test. Specifically, spatial coordinate deviation analysis focused on the three-dimensional spatial coordinates of the core nodes. The Euclidean distance between the coordinate values ​​of each core node in the virtual twin dataset and its coordinate values ​​in the historical operational monitoring data was calculated, and this distance was used as the spatial coordinate deviation. This was repeated for all core nodes by node number to obtain a spatial coordinate deviation sequence. Key feature point mechanical data verification focused on the stress of the cable-stayed members and the displacement of the core nodes. Locations of extreme structural response values ​​and high-stress components were selected as key feature points. The relative differences between virtual stress values ​​and monitored stress values, as well as between virtual displacement values ​​and monitored displacement values, were compared at each key feature point, and these relative differences were used as mechanical data verification indicators. Data distribution consistency test examined the stress and displacement samples of all measuring points. The sample mean and sample standard deviation of the virtual twin dataset and the historical operational monitoring data were calculated, and empirical cumulative distribution curves were plotted. The maximum difference in the ordinate of the two curves at the same horizontal axis was taken as the distribution distance indicator.

[0063] Because the three verification dimensions have different dimensions and physical meanings, directly judging them side-by-side is insufficient to reflect the degree of difference in their impact on structural safety. Therefore, a weighted comprehensive judgment mechanism is established. Specifically, the spatial coordinate deviation in the spatial coordinate deviation analysis is divided by the maximum permissible spatial deviation to obtain the normalized spatial deviation index; the mechanical data verification index in the key feature point mechanical data verification is divided by the upper limit of the permissible error to obtain the normalized mechanical error index; and the distribution distance index in the data distribution consistency test is divided by the upper limit of the distribution distance to obtain the normalized distribution difference index. Weighting coefficients are set according to the engineering priority of the cable dome structure health monitoring: the spatial coordinate shape reflects the overall geometric configuration stability of the structure, and the weighting coefficient is set to 0.4; the mechanical data of key feature points directly relates to the load-bearing safety status of components, and the weighting coefficient is set to 0.4; and the data distribution consistency reflects the degree of consistency of overall statistical characteristics, and the weighting coefficient is set to 0.2. The comprehensive consistency index is obtained by multiplying each of the three normalized indices by its corresponding weighting coefficient and then summing the results. The overall qualification threshold is set to 0.1. When the overall consistency index is not greater than the overall qualification threshold, it is determined that the corrected digital twin model and the physical cable dome structure have sufficient consistency in mechanical response under actual working conditions, and the corrected digital twin model is determined as the cable dome digital twin model; if the overall consistency index is greater than the overall qualification threshold, the model calibration step is returned to be corrected again.

[0064] refer to Figure 4This figure shows a comparison of the axial stress response of the cable-stayed structure, illustrating the distribution and consistency of three sets of stress values ​​at various monitoring points: measured data, pre-correction simulation data, and post-correction simulation data. The figure uses broken lines to compare the trends of the three sets of data along each monitoring point. It can be seen from the figure that there is a significant deviation between the pre-correction simulated stress value and the measured monitoring data, and the overall direction of deviation is inconsistent; while the post-correction simulated stress value curve highly overlaps with the measured monitoring data curve, showing a consistent trend and a significantly reduced deviation. This comparison result intuitively verifies that the digital twin model corrected by the method of this application has a high degree of mapping consistency with the solid structure at the stress response level.

[0065] It is understood that the executing entity of this application can be a dynamic correction system for a digital twin model based on multi-objective optimization, or it can be a terminal or a server; the specific implementation is not limited here. This application's embodiments use a server as an example for illustration.

[0066] The above describes the dynamic correction method for digital twin models based on multi-objective optimization in the embodiments of this application. The following describes the dynamic correction system for digital twin models based on multi-objective optimization in the embodiments of this application. Please refer to [link / reference]. Figure 5 One embodiment of the dynamic correction system for digital twin models based on multi-objective optimization in this application includes: The data acquisition module is used to collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the physical cable dome structure through sensors, and generate a standardized modeling dataset after standardization processing. The initial model building module is used to construct an initial digital twin model based on a standardized modeling dataset through geometric modeling and finite element modeling. The parameter sensitivity analysis module is used to calculate the global sensitivity value of each physical parameter to be corrected related to the mechanical performance of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model using a global sensitivity analysis algorithm. Based on the global sensitivity value, the key parameters to be corrected for local key cable-stayed members are selected. The optimization modeling module is used to construct a multi-objective fidelity optimization model by taking key parameters to be corrected as decision variables and combining them with a standardized modeling dataset and preset constraints. The optimization module is used to iteratively solve the multi-objective fidelity optimization model using the non-dominated sorting genetic algorithm II, obtain the Pareto optimal solution set, and determine the optimal combination of parameters to be corrected according to the preset decision criteria. The model calibration module is used to correct the physical parameters of the corresponding local cable-stayed members based on the optimal combination of parameters to be corrected. Combined with the correction results, the parameters of the surrounding mechanically coupled members are adjusted simultaneously to generate the corrected digital twin model. The verification and finalization module is used to perform finite element simulation on the corrected digital twin model, generate a virtual twin dataset, and verify its consistency with historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

[0067] Through the collaborative efforts of the aforementioned components, the data acquisition module first performs time-series alignment, anomaly removal, and standardization on the geometric, material, boundary, and historical monitoring data collected by sensors, generating a unified standardized modeling dataset for the initial model building module to use. Based on this dataset, the initial model building module completes 3D geometric modeling and finite element modeling, building an initial digital twin model with realistic material properties, constraints, and load configurations, which is then transferred to the parameter sensitivity analysis module as the underlying simulation platform. The parameter sensitivity analysis module performs global sensitivity analysis, filtering out key parameters that significantly affect the stress of the cable and the displacement of the core nodes from numerous physical parameters to be corrected, narrowing the subsequent optimization scope to local key components. The optimization modeling module then... Key parameters are set as decision variables. A multi-objective fidelity optimization model is established based on actual engineering constraints. The optimization solution module drives a non-dominated sorting genetic algorithm II for background iteration. Batch finite element simulation is used to balance fidelity and efficiency, outputting a Pareto optimal solution set and determining the optimal parameter combination. The model calibration module corrects local cable-stayed members according to the optimal combination, while extracting the overall stiffness matrix to locate and adjust surrounding force-coupled members to prevent local modifications from disrupting the overall balance. Finally, the verification and finalization module re-simulates the corrected model, comparing the virtual twin data with historical monitoring data in multiple dimensions, including spatial coordinates, mechanical quantities of feature points, and distribution trends. If the deviation is confirmed to be within the allowable range, the final version is output; otherwise, it is returned to the front end for correction. The modules are interconnected, data is passed sequentially, and the final verification forms a feedback loop. Together, they build a complete technical system from data acquisition, model construction, parameter selection, multi-objective optimization, local-to-global coordinated correction to result verification. This ensures that the digital twin model accurately reflects the state of local components while maintaining the overall structural response coordination, achieving a continuous and reliable mapping with the physical cable dome.

[0068] above Figure 5 The dynamic correction system for digital twin models based on multi-objective optimization in this application embodiment is described in detail from the perspective of modular functional entities. The dynamic correction device for digital twin models based on multi-objective optimization in this application embodiment is described in detail from the perspective of hardware processing.

[0069] Figure 6This is a schematic diagram of a multi-objective optimization-based dynamic correction device for digital twin models, provided in an embodiment of this application. The multi-objective optimization-based dynamic correction device 300 can vary significantly due to different configurations or performance characteristics. It may include one or more central processing units (CPUs) 310 (e.g., one or more processors) and a memory 320, and one or more storage media 330 (e.g., one or more mass storage devices) for storing application programs 333 or data 332. The memory 320 and storage media 330 can be temporary or persistent storage. The program stored in the storage media 330 may include one or more modules (not shown in the diagram), each module including a series of instruction operations on the multi-objective optimization-based dynamic correction device 300. Furthermore, the processor 310 may be configured to communicate with the storage media 330, executing the series of instruction operations in the storage media 330 on the multi-objective optimization-based dynamic correction device 300 to implement the steps of the aforementioned multi-objective optimization-based dynamic correction method for digital twin models.

[0070] The digital twin model dynamic correction device 300 based on multi-objective optimization may also include one or more power supplies 340, one or more wired or wireless network interfaces 350, one or more input / output interfaces 360, and / or one or more operating systems 331, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 6 The illustrated structure of the dynamic correction device for the digital twin model based on multi-objective optimization does not constitute a limitation on the dynamic correction device for the digital twin model based on multi-objective optimization provided in this application. It may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0071] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A dynamic correction method for digital twin models based on multi-objective optimization, characterized in that, include: S1. Collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the solid cable dome structure through sensors, and generate a standardized modeling dataset through standardized processing; S2. Based on the standardized modeling dataset, construct an initial digital twin model through geometric modeling and finite element modeling; S3. Using a global sensitivity analysis algorithm, calculate the global sensitivity value of each physical parameter to be corrected related to the mechanical performance of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model, and screen out the key parameters to be corrected for the local key cable-stayed member based on the global sensitivity value. S4. Using the key parameters to be corrected as decision variables, and combining the standardized modeling dataset with preset constraints, construct a multi-objective fidelity optimization model. S5. The multi-objective fidelity optimization model is iteratively solved using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set, and the optimal combination of parameters to be corrected is determined according to the preset decision criteria. S6. Based on the optimal combination of parameters to be corrected, the physical parameters to be corrected for the corresponding local cable-stayed members are corrected. Combined with the correction results, the parameters of the surrounding mechanically coupled members are adjusted synchronously to generate a corrected digital twin model. S7. Perform finite element simulation on the corrected digital twin model to generate a virtual twin dataset. Verify the consistency between the virtual twin dataset and the historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

2. The method according to claim 1, characterized in that, S1 includes: Sensors deployed on the solid cable dome structure collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data, and integrate them to obtain a multi-source heterogeneous raw dataset; Based on the sampling time series of historical operational monitoring data, the multi-source heterogeneous original dataset is time-series aligned, and a method combining the mechanical constraints of the cable dome structure is adopted. The principle is to remove outlier data, fill in missing time-series data with linear interpolation, fill in missing static data with cross-validation of design specification values ​​and measured values, normalize static parameters with minimum-maximum normalization, and standardize dynamic time-series data with zero mean to generate a standardized modeling dataset.

3. The method according to claim 1, characterized in that, S2 includes: Extract geometric parameters from the geometric data, material property parameters from the material parameter data, boundary constraint parameters from the boundary condition data, and working load parameters from the boundary condition data from the standardized modeling dataset. Construct a three-dimensional geometric model corresponding to the solid cable dome structure based on the geometric parameters, and output the three-dimensional geometric model to be configured. The three-dimensional geometric model to be configured is imported into the finite element modeling tool. According to the material performance parameters, the corresponding material properties are matched for each component of the three-dimensional geometric model to be configured. The cable component is defined using Link rod elements, and the compression member is defined using Beam elements, thus obtaining the initial finite element model with material properties. Based on the boundary constraint parameters and load parameters, nodal constraint conditions, dead load and live load conditions are configured for the initial finite element model to obtain the configured finite element model. The three-dimensional geometric model to be configured is associated and integrated with the configured finite element model to generate the initial digital twin model.

4. The method according to claim 1, characterized in that, S3 includes: Based on the initial digital twin model and the historical operation monitoring data in the standardized modeling dataset, the set of physical parameters to be corrected and the mechanical output response indicators are determined. The mechanical output response indicators include cable stress and core node displacement. The Sobel global sensitivity analysis algorithm is used to construct Latin hypercube sampling samples for the set of physical parameters to be corrected. The Latin hypercube sampling samples are then input into the initial digital twin model for batch simulation to obtain the parameter-response corresponding dataset. Based on the parameter-response correspondence dataset, the global sensitivity value of each physical parameter to be corrected to the mechanical output response index is calculated, and a global sensitivity ranking table of parameters is obtained. The global sensitivity sorting table of the parameters is filtered according to a preset sensitivity filtering threshold, and the filtered physical parameters to be corrected are output. The selected physical parameters to be corrected are mapped to the local cable members of the solid cable dome to determine the key parameters to be corrected.

5. The method according to claim 1, characterized in that, S4 includes: The key parameters to be corrected are set as decision variables for multi-objective optimization, the reasonable range of numerical variation for each decision variable is defined, and the decision variable definition set is output. Based on the standardized modeling dataset, parameter value constraints and mechanical performance constraints for decision variables are set to form a preset set of constraints. Based on the requirements of structural health monitoring projects, multiple independent optimization objective functions are set to obtain a set of optimization objective functions; Using the set of defined decision variables as input, the set of preset constraints as solution boundaries, and the set of objective functions as optimization guides, a multi-objective fidelity optimization model is constructed.

6. The method according to claim 1, characterized in that, S5 includes: Based on the multi-objective fidelity optimization model, the population is initialized with the key parameters to be corrected as the encoding objects to obtain the initial population set; The initial population set of individuals is input into the initial digital twin model for batch simulation, the objective function value corresponding to each individual is obtained, and the population objective function value matrix is ​​output. The non-dominated sorting genetic algorithm II is used to perform fast non-dominated sorting and crowding calculation on the objective function value matrix of the population, and combined with elite retention to select a set of high-quality parent individuals; Simulated binary crossover and polynomial mutation are performed on the set of high-quality parent individuals to generate crossover offspring and mutated offspring, which are then merged with the set of high-quality parent individuals to generate a new generation population. Using the next generation of population as the input for the next round, repeat batch simulation, fast non-dominated sorting, crowding calculation, elite retention screening, binary crossover and polynomial mutation until the preset maximum number of iterations is reached, and output the Pareto optimal solution set. Based on the preset engineering decision criteria, the optimal combination of parameters to be corrected is selected from the Pareto optimal solution set to adapt to the fidelity correction of local cable-stayed components and the overall mechanical coordination.

7. The method according to claim 1, characterized in that, S6 includes: Based on the optimal combination of parameters to be corrected, the corresponding local key cable-stayed members in the initial digital twin model are matched and located, and a list of the locations of the members to be corrected is output. Replace the physical parameters to be corrected of the corresponding components in the list of components to be corrected with the corresponding parameter values ​​in the optimal combination of parameters to be corrected to obtain the locally corrected digital twin model. Based on the locally corrected digital twin model, the overall stiffness matrix is ​​extracted, and the affected surrounding components are determined through stiffness matrix correlation analysis, and a list of the surrounding components affected is output. Based on the surrounding component influence list, the parameters of the mechanically coupled surrounding components are adjusted synchronously to obtain a coordinated and adjusted digital twin model; The coordinated and adjusted digital twin model is subjected to overall mechanical logic verification. After the verification is passed, a corrected digital twin model is generated.

8. The method according to claim 1, characterized in that, S7 includes: Based on the modified digital twin model, boundary conditions and load conditions consistent with the actual working conditions of the physical cable dome are configured. The finite element solver is called through the collaborative simulation platform to perform simulation and solve the problem, extracting the stress and strain data of the cable rods and the displacement data of the core nodes to generate a virtual twin dataset. Historical operation monitoring data corresponding to the working conditions are extracted from the standardized modeling dataset. The virtual twin dataset is aligned with the historical operation monitoring data in terms of time series and working conditions to obtain the aligned twin data pair. A multi-dimensional consistency verification is performed on the aligned twin data pair, which includes spatial coordinate deviation analysis, key feature point mechanical data verification, and data distribution consistency test. When all verification items meet the preset qualification threshold, the modified digital twin model is determined as the cable dome digital twin model.

9. A dynamic correction system for a digital twin model based on multi-objective optimization, used to implement the method as described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to collect geometric data, material parameter data, boundary condition data, and historical operation monitoring data of the physical cable dome structure through sensors, and generate a standardized modeling dataset after standardization processing. The initial model building module is used to construct an initial digital twin model based on the standardized modeling dataset through geometric modeling and finite element modeling. The parameter sensitivity analysis module is used to calculate the global sensitivity value of each physical parameter to be corrected related to the mechanical performance of the cable-stayed member in the initial digital twin model to the mechanical output response index of the model using a global sensitivity analysis algorithm, and to screen out the key parameters to be corrected for local key cable-stayed members based on the global sensitivity value. The optimization modeling module is used to construct a multi-objective fidelity optimization model by taking the key parameters to be corrected as decision variables and combining them with the standardized modeling dataset and preset constraints. The optimization module is used to iteratively solve the multi-objective fidelity optimization model using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set, and to determine the optimal combination of parameters to be corrected according to the preset decision criteria. The model calibration module is used to correct the physical parameters of the corresponding local cable-stayed member based on the optimal combination of parameters to be corrected, and to adjust the parameters of the surrounding mechanically coupled members in conjunction with the correction results to generate a corrected digital twin model. The verification and finalization module is used to perform finite element simulation on the corrected digital twin model, generate a virtual twin dataset, and verify its consistency with the historical operation monitoring data in the standardized modeling dataset to obtain the digital twin model of the cable dome.

10. A dynamic correction device for a digital twin model based on multi-objective optimization, characterized in that, The device includes: a memory and at least one processor, wherein the memory stores instructions; The processor invokes the instructions in the memory to cause the multi-objective optimization-based digital twin model dynamic correction device to execute the multi-objective optimization-based digital twin model dynamic correction method as described in any one of claims 1-8.

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