A structural nonlinear dynamic analysis and optimization method based on hierarchical neural operator

Abstract

The application belongs to the technical field of structural nonlinear dynamic analysis and intelligent optimization, and specifically discloses a structural nonlinear dynamic analysis and optimization method based on a layered neural operator, which comprises the following steps: constructing a structural nonlinear dynamic analysis model; training a first neural operator based on first training samples generated by a reference nonlinear solver; embedding the first neural operator into a time integration framework to construct a hybrid operator solver, which obtains a local nonlinear state at each time step, determines an equivalent nonlinear action based on the local nonlinear state, and solves a global dynamic response of the structure; training a second neural operator based on second training samples generated by the hybrid operator solver; and performing hierarchical screening and multi-objective optimization on a candidate structure scheme based on preset constraints and the second neural operator. Through the application, the repeated calculation cost in structural nonlinear dynamic analysis and multi-objective optimization can be reduced while ensuring the physical consistency and calculation efficiency of nonlinear time-history analysis.

Description

Technical Field

[0001] This application belongs to the field of structural nonlinear dynamic analysis and intelligent optimization technology, and more specifically, relates to a structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators. Background Technology

[0002] Under the dynamic forces of earthquakes, wind, traffic, impact, waves, and mechanical vibration, engineering structures may exhibit complex responses, including material nonlinearity, geometric nonlinearity, contact nonlinearity, frictional nonlinearity, damage degradation, and nonlinearity of seismic isolation and energy dissipation devices. Nonlinear dynamic analysis of these responses is a crucial foundation for structural safety assessment, performance-based design, toughness assessment, and optimization design.

[0003] Structural nonlinear time history analysis is typically based on finite element models, lumped parameter models, or equivalent dynamic models, combined with time integration methods to solve for the structural dynamic response. During the analysis, local nonlinear states are usually updated based on material constitutive relations, component restoring force models, or equivalent nonlinear element models. Global dynamic equilibrium equations are then constructed using the structural mass matrix, damping matrix, reference stiffness matrix, and external dynamic excitations to obtain the structure's time history response under dynamic loads.

[0004] Building upon this, when comparing or optimizing multiple candidate structural schemes, it is typically necessary to repeatedly invoke nonlinear dynamic time history analysis for different structural design parameters and external dynamic excitations. During this process, updating local nonlinear states often requires solving constitutive evolution equations or performing substep integration, and this update is repeated throughout all time steps. Furthermore, structural optimization usually requires evaluating a large number of candidate structural schemes; when a complete nonlinear dynamic time history analysis is invoked for each candidate scheme, the overall computational load is substantial.

[0005] Therefore, how to reduce the cost of repetitive calculations in structural nonlinear dynamic analysis and multi-objective optimization while taking into account both physical consistency and computational efficiency in nonlinear time history analysis is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this application is to reduce the cost of repetitive calculations in structural nonlinear dynamic analysis and multi-objective optimization while taking into account both physical consistency and computational efficiency in nonlinear time history analysis.

[0007] To achieve the above objectives, in a first aspect, this application provides a structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators, comprising: Based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure, response evaluation coordinates are obtained, and a structural nonlinear dynamic analysis model including the effective stiffness matrix and local state extraction relationship is constructed. The first neural operator is trained based on the first training samples generated by the reference nonlinear solver. The first neural operator is used to predict the local nonlinear state based on the local state variables at the current time and historical time. The first neural operator is embedded into the time integration framework to construct a hybrid operator solver. In each time step, the hybrid operator solver calls the first neural operator based on the local state extraction relationship to obtain the local nonlinear state, thereby determining the equivalent nonlinear action, and solving the global dynamic response of the structure based on the effective stiffness matrix. The second neural operator is trained based on the second training samples generated by the hybrid operator solver. The second neural operator is used to predict the system-level structural response based on the response evaluation coordinates. Based on preset constraints and the second neural operator, candidate structural schemes are hierarchically screened and multi-objective optimized to obtain and output the Pareto design set.

[0008] Specifically, at the local level, the first neural operator learns the local nonlinear state evolution law of the target nonlinear part based on the first training sample generated by the reference nonlinear solver. After training, the first neural operator uses the local state variables of the current time and historical time as input, and can predict the local nonlinear state through a single forward inference, thereby replacing the constitutive evolution equation solving and substep integration repeatedly executed at each time step and each nonlinear part in the traditional method. On this basis, the first neural operator is embedded into the time integration framework to construct a hybrid operator solver: in each time step, the hybrid operator solver obtains the local state variables through the local state extraction relation and calls the first neural operator to obtain the local nonlinear state, thereby determining the equivalent nonlinear action, and then solving the global dynamic response of the structure based on the effective stiffness matrix. Since the effective stiffness matrix is ​​composed of the structural mass matrix, damping matrix and reference stiffness matrix, the matrix decomposition result can be reused in all time steps. Therefore, the hybrid operator solver reduces the repeated calculation of local nonlinear state updates while retaining the physical structure of the global dynamic equilibrium equation.

[0009] At the system level, the second neural operator, based on second training samples generated by the hybrid operator solver, learns the mapping relationship between structural design parameters, external dynamic excitation characteristics, and response evaluation coordinates to the system-level structural response. During multi-objective optimization, candidate structural schemes are hierarchically screened: first, design variable proportional constraints are checked through direct calculation; then, schemes satisfying linear or equivalent linear response constraints are screened through low-cost evaluation; finally, the second neural operator is invoked on the screened schemes to predict the system-level structural response under high-intensity dynamic action through a single forward inference. Through this hierarchical screening mechanism and the rapid evaluation capability of the second neural operator, while maintaining physical consistency and computational efficiency in nonlinear time-history analysis, the cost of repetitive calculations in structural nonlinear dynamic analysis and multi-objective optimization is reduced, ultimately obtaining and outputting the Pareto design set.

[0010] Regarding the aforementioned "in each time step, the first neural operator is invoked based on the local state extraction relation to obtain the local nonlinear state," the following preferred implementation method can be adopted: in each time step, the first neural operator only provides the local nonlinear initial state. It is understandable that in long-term analysis, although the error predicted by the operator at each time step is extremely small, it accumulates into a global cumulative error as the number of time steps increases, affecting the final result. Therefore, the result of the first neural operator can be used as the local nonlinear initial state, and convergence can be achieved through several iterations, ensuring the same accuracy as the reference finite element solution while consuming fewer nonlinear iteration steps.

[0011] In one possible implementation, based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure, response evaluation coordinates are obtained, and a structural nonlinear dynamic analysis model including the effective stiffness matrix and local state extraction relationships is constructed, including: Based on the mass distribution, equivalent stiffness, damping characteristics, boundary conditions and connection relationships of the target engineering structure, an effective stiffness matrix and dynamic action mapping relationship are constructed. The effective stiffness matrix includes the structural mass matrix, damping matrix and reference stiffness matrix. Based on the relationship between the target nonlinear part and the global degrees of freedom, a local state extraction relation is constructed. The local state extraction relation is used to determine the local state variables related to the local nonlinear state from the global displacement, velocity or acceleration response.

[0012] In one possible implementation, the first neural operator includes a first branch network and a first backbone network: The first branch network is used to receive and encode the normalized structural design parameters and external dynamic excitation spectrum features, and output the first global feature vector; The first backbone network is used to receive and encode the current local deformation, historical local deformation, historical local nonlinear state and current local velocity, and output the first local state feature vector; Based on the inner product or feature fusion result of the first global feature vector and the first local state feature vector, the local nonlinear state at the current time is obtained; The first neural operator is obtained by training based on a first loss function, which includes the data loss between the predicted local nonlinear state and the reference local nonlinear state, as well as the initial condition regularization term that constrains the initial conditions of the local nonlinear state.

[0013] In one possible implementation, the hybrid operator solver solves the global dynamic response of the structure, including: The structural restoration action is decomposed into a linear restoration action corresponding to the reference stiffness matrix and a local nonlinear term provided by the first neural operator; and coupled to the global dynamic equilibrium equation of the structure under the time integration framework. An effective stiffness matrix is ​​formed based on the structural mass matrix, damping matrix, and reference stiffness matrix. The effective stiffness matrix is ​​decomposed at the beginning of the solution process, and the decomposition results are reused in subsequent time steps to obtain the global dynamic response of the structure at each time step.

[0014] In one possible implementation, the second neural operator includes a second branch network and a second backbone network: The second branch network is used to receive and encode the normalized structural design parameters and external dynamic excitation spectrum features, and output the second global feature vector. The second backbone network is used to receive and encode the response evaluation coordinates and output the response location feature vector; Based on the inner product or feature fusion result of the second global feature vector and the response location feature vector, the system-level structural response or performance index corresponding to the response evaluation coordinates is obtained. The second training sample is generated by the hybrid operator solver for multiple sets of structural design parameters and external dynamic excitations. The second training sample includes structural design parameters, external dynamic excitation characteristics, response evaluation coordinates, and the target peak response as the supervision target.

[0015] In one possible implementation, candidate structural schemes are subjected to hierarchical screening and multi-objective optimization, including: Check whether the candidate structural schemes meet the design variable ratio constraints; For candidate structural schemes that meet the proportional constraints of design variables, perform linear or equivalent linear response analysis under low-intensity dynamic action to obtain the response results of the candidate structural schemes under low-intensity dynamic action and check whether they meet the response constraints under low-intensity dynamic action. For candidate structural schemes that meet the response constraints under low-intensity dynamic action, the second neural operator is invoked to predict the target peak response under high-intensity dynamic action, and it is checked whether the response constraints under high-intensity dynamic action are met. Based on at least two optimization objectives, a multi-objective optimization algorithm is used to iteratively search the candidate structural schemes that have passed the screening to obtain the Pareto design set. Among them, low-intensity dynamic action is a dynamic action in which the intensity index of external dynamic excitation is not higher than the first preset threshold, and high-intensity dynamic action is a dynamic action in which the intensity index of external dynamic excitation is not lower than the second preset threshold, and the second preset threshold is not lower than the first preset threshold.

[0016] In one possible implementation, constitutive evolution equations are solved and substep integrations are performed at each time step and at each nonlinear part of the target, and the results of the analysis serve as the data source for generating the first training sample.

[0017] Secondly, this application provides a structural nonlinear dynamic analysis and optimization device based on hierarchical neural operators, comprising: The model building module is used to obtain response evaluation coordinates and construct a structural nonlinear dynamic analysis model that includes an effective stiffness matrix and local state extraction relationship based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure. The first operator training module is used to train the first neural operator based on the first training samples generated by the reference nonlinear solver. The first neural operator is used to predict the local nonlinear state based on the local state variables at the current time and historical time. The hybrid solver module is used to embed the first neural operator into the time integration framework to build a hybrid operator solver. At each time step, the hybrid operator solver calls the first neural operator based on the local state extraction relationship to obtain the local nonlinear state, thereby determining the equivalent nonlinear action and solving the global dynamic response of the structure based on the effective stiffness matrix. The second operator training module is used to train the second neural operator based on the second training samples generated by the hybrid operator solver. The second neural operator is used to predict the system-level structural response based on the response evaluation coordinates. The optimized output module is used to perform hierarchical screening and multi-objective optimization of candidate structural schemes based on preset constraints and the second neural operator, and to obtain and output the Pareto design set.

[0018] Thirdly, this application provides an electronic device, including: a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the electronic device to perform the method described in the first aspect or any possible implementation of the first aspect.

[0019] Fourthly, this application provides a computer-readable storage medium including instructions that, when executed on an electronic device, cause the electronic device to perform the method described in the first aspect or any possible implementation thereof.

[0020] It is understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0021] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application abstracts the local nonlinear state evolution into a learnable first neural operator mapping, which can reduce the repetitive cost of local constitutive integration, internal variable update and iterative computation.

[0022] (2) This application embeds the first neural operator into the time integration framework to form a hybrid operator solver, instead of performing black-box fitting only after time history analysis. Therefore, it can maintain the coupling relationship between local nonlinear state evolution and global dynamic equilibrium.

[0023] (3) This application directly predicts the system-level structural response or performance index through the second neural operator, so that optimization loop, scheme comparison and parameter analysis do not need to perform a complete nonlinear dynamic time history analysis for each candidate structural scheme.

[0024] (4) This application is not limited to a specific structural form, a specific nonlinear model or a specific dynamic action, and can be adapted according to the target engineering structure, the target nonlinear part and the target dynamic action.

[0025] (5) This application can be combined with preset constraint screening and multi-objective optimization algorithms to improve the search efficiency of Pareto design set while ensuring a clear evaluation hierarchy of candidate structural schemes. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators provided in the embodiments of this application; Figure 2 This is a schematic diagram of the overall process provided in the embodiments of this application; Figure 3 This is a schematic diagram of the hierarchical neural operator structure provided in the embodiments of this application; Figure 4 This is a schematic diagram of the equivalent model of the target engineering structure provided in the embodiments of this application; Figure 5 This is a schematic diagram of the hysteresis curve provided in the embodiments of this application; Figure 6 This is a schematic diagram of the full-time displacement distribution provided in the embodiments of this application; Figure 7 This is a schematic diagram of the Pareto front for multi-objective optimization provided in an embodiment of this application; Figure 8 This is a schematic diagram of the interlayer stiffness distribution on the Pareto front provided in an embodiment of this application; Figure 9 This is a schematic diagram illustrating the convergence history of the optimization algorithm provided in the embodiments of this application; Figure 10 This is a schematic diagram of the structure of the structural nonlinear dynamic analysis and optimization device based on hierarchical neural operators provided in the embodiments of this application; Figure 11 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0027] To facilitate a clearer understanding of the various embodiments of this application, some relevant background knowledge will be introduced as follows.

[0028] (I) Nonlinear dynamic time history analysis and time integration framework.

[0029] Nonlinear dynamic time-history analysis is used to solve for the time-varying response of a structure under dynamic excitation. Time-integration frameworks, such as the Newmark time-integration framework (or simply Newmark framework), are used to solve the global dynamic equilibrium equations step-by-step. In each time step, the restoring action needs to be updated based on the current structural state, and the global dynamic response of the structure needs to be solved. The structural restoring action can be decomposed into two parts: linear elastic terms and local nonlinear terms. The linear elastic terms are related to the structural reference stiffness matrix and can be directly handled by the time-integration framework; the local nonlinear terms are related to the local nonlinear state and require an additional update process.

[0030] Local nonlinear states are used to describe the internal evolution of a nonlinear part of a target during a dynamic process, including at least one of hysteretic displacement, plastic variables, damage variables, frictional slip, or internal variables of the damper. Local nonlinear states are usually obtained by solving constitutive evolution equations, and their common descriptive form is the Bouc-Wen hysteretic constitutive model (or Bouc-Wen model for short).

[0031] (ii) Reference nonlinear solvers and their computational costs.

[0032] The reference nonlinear solver is used for high-precision nonlinear dynamic time-history analysis of structures, and its analysis results can be used as a data source for generating training samples. As a specific example, the reference nonlinear solver can use the Bouc-Wen model to describe the hysteretic constitutive relations of the target nonlinear region. At each time step, it uses Newton-Raphson iteration (NR iteration) to solve the global dynamic equilibrium equations and employs fourth-order Runge-Kutta substep integration (RK4 substep integration) to update the local state of the Bouc-Wen model's hysteretic differential equations. Alternatively, the reference nonlinear solver can also be implemented using a general-purpose nonlinear solver in finite element analysis software. However, because the reference nonlinear solver needs to perform constitutive evolution equation solving and substep integration at each time step and at each nonlinear region, its computational cost is relatively high.

[0033] The reason why existing analysis methods are computationally expensive in multi-scheme comparison and optimization scenarios is as follows: On the one hand, within a single time history analysis, local nonlinear state updates require repeatedly solving constitutive evolution equations or performing substep integrations throughout all time steps, and the amount of repeated computation accumulates with the number of time steps; on the other hand, in the optimization loop, it is necessary to call complete nonlinear dynamic time history analyses for a large number of candidate structural schemes, and the amount of repeated computation is further amplified with the number of candidate structural schemes. The combination of these two aspects makes it computationally burdensome to directly support multi-objective optimization with complete nonlinear dynamic time history analysis.

[0034] (III) Multi-objective optimization and its evaluation bottleneck.

[0035] Multi-objective optimization is used to search for compromise solutions between conflicting objectives such as economic efficiency and dynamic performance. The results are typically represented as a Pareto design set. Multi-objective optimization algorithms include multi-objective genetic algorithms (NSGA-II), particle swarm optimization (MOPSO), Pareto simulated annealing, and iterative greedy algorithms. During the optimization process, the dynamic response or performance index of each candidate structural scheme needs to be obtained for each evaluation. When the evaluation process directly relies on complete nonlinear dynamic time history analysis, the optimization efficiency is constrained by the evaluation cost.

[0036] (iv) Neural operators and operator learning.

[0037] Neural operators are used to learn function-to-function mappings. A common neural operator structure includes a branch network and a trunk network: the branch network receives and encodes the input function or input features, while the trunk network receives and encodes the query coordinates or state variables. The outputs of both are then fused through an inner product or feature fusion to obtain the target output. Using neural operators to characterize local nonlinear state evolution or system-level response mappings is beneficial for replacing repetitive numerical iterations with single forward inference. Based on this background knowledge, the structural nonlinear dynamic time history analysis and multi-objective optimization process can be hierarchically organized, thereby reducing the cost of repetitive computation. The specific implementation of this concept is described in the embodiments section below.

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0039] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0040] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0041] The embodiments of this application are described below with reference to the accompanying drawings.

[0042] like Figure 1As shown, the structural nonlinear dynamic time history analysis and multi-objective optimization method based on hierarchical neural operators (hereinafter referred to as "this method") provided in this embodiment includes steps S10 to S60. To facilitate understanding of the logical framework of this method, the functions of each level are first explained: the first neural operator is used to learn the local nonlinear state update law of the target nonlinear part; the hybrid operator solver is used to couple the prediction results of the first neural operator to the time integration framework and obtain the global dynamic response of the structure; the second neural operator is used to learn the mapping relationship between structural design parameters, external dynamic excitation characteristics, and response evaluation coordinates to the system-level structural response (including the target peak response) or performance indicators; the optimization evaluation stage calls the second neural operator to quickly evaluate candidate structural schemes. Thus, this method forms a hierarchical processing path from local nonlinear state, global dynamic response to system-level evaluation.

[0043] like Figure 2 As shown, this method does not replace full-time nonlinear dynamic analysis with a single neural network. Instead, it first learns the local nonlinear state update rules through a first neural operator, then preserves the global dynamic equilibrium solution process of the structure through a hybrid operator solver, and finally completes the system-level rapid evaluation of candidate structural schemes through a second neural operator. The three levels of the first neural operator, the hybrid operator solver, and the second neural operator are progressively connected according to the data generation and function call sequence, thereby improving the efficiency of optimization and evaluation while ensuring the physical consistency of the analysis process.

[0044] (1) Step S10: Establish a nonlinear dynamic analysis model of the structure.

[0045] Specifically, step S10 obtains response evaluation coordinates based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure, and constructs a structural dynamic analysis model of the target engineering structure.

[0046] In this embodiment, the target engineering structure can be represented as a finite element model, a lumped parameter model, or a reduced-order dynamic model, depending on the engineering requirements. Specifically, based on the mass distribution, equivalent stiffness, damping characteristics, boundary conditions, and connection relationships of the target engineering structure, a structural mass matrix, a damping matrix, a reference stiffness matrix, and a dynamic action mapping relationship can be constructed. It should be noted that the reference stiffness matrix can be the tangent stiffness matrix in the initial state; in the implementation using equivalent linearization, the equivalent linear stiffness matrix can replace the reference stiffness matrix in the construction of the global effective stiffness matrix. The equivalent linear stiffness matrix refers to the stiffness matrix obtained after equivalent linearization of the structure under a specific dynamic action level. In this embodiment, this term will be uniformly referred to as the reference stiffness matrix, and unless otherwise stated, it includes the aforementioned equivalent linear stiffness matrix. Simultaneously, a local state extraction relationship is constructed based on the relationship between the target nonlinear part and the global degrees of freedom to determine the local state variables related to the local nonlinear state from the global displacement, velocity, acceleration, or other generalized responses.

[0047] like Figure 3 As shown, both the first and second neural operators can employ a hierarchical neural operator structure including branch networks and backbone networks. Based on this structure, the first and second neural operators complete the corresponding mapping learning at the local and system levels, respectively.

[0048] like Figure 4 As shown, in one specific implementation, the target engineering structure is equivalent to a dynamic model with four horizontal degrees of freedom. The equivalent height of each control point is 3m, and the total structural height is 12m; the concentrated mass of each equivalent mass node is 30000kg; the damping matrix is ​​constructed using the Rayleigh damping model, and the target damping ratio is 0.05. The equivalent lateral stiffness between each control point is used as a structural design variable, i.e. , , , Its value range is set according to project requirements, for example, it can be set to the following range: ; Parameter explanation: : indicates the first The equivalent lateral stiffness corresponding to each control component, among which Take 1, 2, 3, 4, which correspond to... , , , ; : This represents the unit of equivalent lateral stiffness, i.e., Newtons per meter.

[0049] It is understood that the above equivalent model is only an exemplary model. In other implementations, different numbers of degrees of freedom, different discretization methods, or different reduced-order representations can be used depending on the target engineering structure.

[0050] (2) Step S20: Construct and train the first neural operator.

[0051] Specifically, step S20 generates a first training sample based on a reference nonlinear solver, constructs and trains a first neural operator, and enables the first neural operator to predict the local nonlinear state at the current moment based on structural design parameters, external dynamic excitation characteristics, and local state variables at the current and historical moments.

[0052] In this embodiment, the first neural operator is used to learn the local nonlinear state evolution mapping of the target nonlinear region. The local state variables include at least one of the current local deformation, historical local deformation, historical local nonlinear state, and current local velocity; the output of the first neural operator is the local nonlinear state at the current moment, which includes at least one of the current internal variable, equivalent recovery effect, or state update amount.

[0053] The first neural operator comprises a first branch network and a first backbone network. The first branch network receives and encodes the normalized structural design parameters and external dynamic excitation spectrum features, outputting a first global feature vector. The first backbone network receives and encodes the current local deformation, historical local deformation, historical local nonlinear states, and current local velocity, outputting a first local state feature vector. To improve the expressive power for local nonlinear abrupt changes and high-frequency responses, the first backbone network can introduce Fourier feature encoding before the fully connected layer. Based on the inner product or feature fusion result of the first global feature vector and the first local state feature vector, the local nonlinear state at the current time step is obtained.

[0054] In one specific implementation, the first neural operator employs a hysteresis-deepONet deep operator network (also known as Hysteresis-DeepONet), with 64 basis functions. Both the first branch network and the first backbone network utilize Tanh-activated multilayer perceptrons and are initialized uniformly using Xavier. The first training samples of the first neural operator are generated by a reference nonlinear solver and include structural design parameters, external dynamic excitation spectrum features, current local deformation, historical local deformation, historical local nonlinear states, current local velocity, and target local nonlinear states. Based on the first training samples, the first loss function of the first neural operator is constructed using the following formula: ; Parameter explanation: : Represents the first loss function of the first neural operator; : Represents the data loss between the predicted local nonlinear state and the reference local nonlinear state; : Represents the initial condition regularization term used to constrain the initial conditions of the local nonlinear state; : Represents the weight coefficient of the initial condition regularization term.

[0055] The first neural operator is trained based on the first loss function until the first loss function converges or reaches the preset training conditions, thereby obtaining the first neural operator that can predict local nonlinear states.

[0056] (3) Step S30: Construct a hybrid operator solver.

[0057] Specifically, in step S30, the first neural operator is embedded into the time integration framework to construct a hybrid operator solver. The hybrid operator solver calls the first neural operator in each time step to obtain the local nonlinear state, determines the equivalent nonlinear action based on the local nonlinear state, and solves the global dynamic response of the structure based on the equivalent nonlinear action.

[0058] In this embodiment, the time integration framework can employ the Newmark framework or other structural dynamic time-progression methods. The hybrid operator solver calculates the predicted response at each time step based on the global response of the previous time step, obtains the local state variables of the target nonlinear region through local state extraction relationships, inputs the local state variables and global features into the first neural operator, and determines the equivalent nonlinear action based on the output of the first neural operator, thereby updating the global dynamic response at the current time step. The global dynamic equilibrium equation of the structure is expressed as follows: ; Parameter explanation: : Represents the structural mass matrix; : Represents the structural damping matrix; : Represents the structural reference stiffness matrix; : Represents the global displacement response vector of the structure; : Represents the global velocity response vector of the structure; : Represents the global acceleration response vector of the structure; : Represents the vector of external dynamic excitation; : Represents the equivalent nonlinear action determined by the local nonlinear state predicted by the first neural operator.

[0059] Specifically, the structural restoration effect is decomposed into a linear restoration effect corresponding to the reference stiffness matrix and a local nonlinear term provided by the first neural operator; and coupled to the global dynamic equilibrium equations of the structure under the time integration framework. The effective stiffness matrix is ​​formed by the structural mass matrix, damping matrix, and reference stiffness matrix. Since the effective stiffness matrix is ​​mainly composed of the above three matrices, it can be decomposed once at the beginning of the solution and the decomposition result can be reused in subsequent time steps. In this way, the hybrid operator solver retains the coupling relationship between local nonlinear state evolution and global dynamic equilibrium while reducing repeated substep integration of local nonlinear state equations and repeated solving of some matrices.

[0060] like Figure 5 As shown, Figure 5 This illustrates the shear force-local deformation relationship obtained by the reference nonlinear solver and the hybrid operator solver at the target nonlinear region. Figure 5 It can be seen that the hybrid operator solver can reproduce the hysteresis loop shape, amplitude, and energy consumption characteristics obtained from the reference nonlinear solver quite well. For example... Figure 6 As shown, Figure 6 The comparison of displacement response between the reference nonlinear solver and the hybrid operator solver over the entire time range is shown to verify the time-history tracking capability of the first neural operator after embedding it into the time integration framework.

[0061] In one specific implementation, the normalized root mean square error of the first neural operator for local nonlinear states is less than 0.004; under multiple external dynamic excitations, the global peak displacement ratio is between 0.972 and 0.995, and the normalized root mean square error of the global displacement time history is less than 0.024. These results demonstrate that the hybrid operator solver can maintain good consistency between the evolution of local nonlinear states and the global dynamic response.

[0062] (4) Step S40: Construct and train the second neural operator.

[0063] Specifically, step S40 generates a second training sample based on the hybrid operator solver, constructs and trains a second neural operator, and enables the second neural operator to predict the system-level structural response or performance index corresponding to the response evaluation coordinates based on structural design parameters, external dynamic excitation characteristics and response evaluation coordinates.

[0064] In this embodiment, the second neural operator is used to learn the mapping between structural design parameters, external dynamic excitation features, and response evaluation coordinates to system-level structural responses or performance indicators. The second neural operator includes a second branch network and a second backbone network: the second branch network receives and encodes the normalized structural design parameters and external dynamic excitation spectrum features, outputting a second global feature vector; the second backbone network receives and encodes the response evaluation coordinates, outputting a response position feature vector. Based on the inner product or feature fusion result of the second global feature vector and the response position feature vector, the system-level structural response or performance indicator corresponding to the response evaluation coordinates is obtained.

[0065] In one specific implementation, the second neural operator employs a system-response deep operator network (also known as Surrogate-DeepONet) with 64 basis functions. Both the second branch network and the second backbone network utilize Tanh-activated multilayer perceptrons. Response evaluation coordinates can be set to 0.25, 0.50, 0.75, and 1.00 to indicate the normalized positions corresponding to different control points. For each set of structural design parameters and each set of external dynamic excitations, a hybrid operator solver is invoked to obtain the nonlinear dynamic response. The target peak response is extracted from the nonlinear dynamic response as a supervision target, thus forming the second training sample. Based on the second training sample, the second neural operator is trained using structural design parameters, external dynamic excitation characteristics, and response evaluation coordinates as inputs, and the system-level structural response or performance index as the supervision target.

[0066] In one specific implementation, the second neural operator achieves a total normalized root mean square error of 0.0135 on a validation set including 600 samples, and a coefficient of determination of... It can achieve a value of 0.995. Therefore, the second neural operator can accurately reproduce the system-level response given by the hybrid operator solver within the structural design space, and can be used as a fast evaluation model in optimization loops.

[0067] (5) Step S50: Conduct evaluation of candidate structural schemes and multi-objective optimization.

[0068] Specifically, step S50 performs multi-objective optimization on candidate structural schemes based on preset constraints and the second neural operator to obtain the Pareto design set.

[0069] In this embodiment, candidate structural schemes are represented by design variables of the target engineering structure. Optimization objectives may include economic objectives and dynamic performance objectives; constraints may include proportional constraints on design variables, response constraints under low-intensity dynamic action, and response constraints under high-intensity dynamic action.

[0070] It should be noted that low-intensity and high-intensity dynamic actions can be classified based on the intensity indices of the external dynamic excitation. These indices include, but are not limited to, peak ground acceleration (PGA), peak velocity, response spectrum intensity, or a return period corresponding to the design flood level. As a specific example, dynamic actions can be divided into multiple intensity levels based on the design flood level. Dynamic actions not exceeding a first preset threshold are defined as low-intensity dynamic actions, and those not lower than a second preset threshold are defined as high-intensity dynamic actions, where the second preset threshold is not less than the first preset threshold. Under low-intensity dynamic actions, the target nonlinear component is mainly in a linear or approximately linear operating state, and the corresponding response constraint is a linear or equivalent linear response constraint. Under high-intensity dynamic actions, the target nonlinear component enters a significantly nonlinear operating state, and the corresponding response constraint is a nonlinear response constraint. It is understood that the above-mentioned intensity indices, thresholds, and return periods are illustrative examples and can be set and adjusted according to the specifications and engineering requirements of the region where the target engineering structure is located.

[0071] Further, step S50 may include steps S51 to S54.

[0072] Step S51: Check whether the candidate structural schemes meet the design variable ratio constraints by direct calculation.

[0073] Step S52 involves performing a dynamic evaluation on candidate structural schemes that satisfy the design variable proportionality constraints. It should be noted that using a hybrid operator solver makes the dynamic evaluation more efficient and convenient, effectively reducing computational resource consumption and achieving low-cost dynamic evaluation.

[0074] Step S53: For candidate structural schemes that pass the dynamic evaluation, call the second neural operator to predict the target peak response under high-intensity dynamic action, and check whether the candidate structural schemes meet the response constraints under high-intensity dynamic action.

[0075] Step S54: Based on at least two optimization objectives, a multi-objective optimization algorithm is used to iteratively search the candidate structural schemes that have passed the screening to obtain the Pareto design set.

[0076] In one specific implementation, the multi-objective optimization algorithm used is NSGA-II. The NSGA-II population size is 80, the number of iterations is 50, and the total number of evaluations is 4000. The crossover operator uses simulated binary crossover with a crossover probability of 0.9; the mutation operator uses polynomial mutation, with the mutation probability determined based on the number of design variables. It is understood that the above algorithm parameters are only an exemplary setting, and in other implementations, they can be adjusted according to the target engineering structure size, the number of design variables, and the required optimization accuracy.

[0077] (6) Step S60: Output the nonlinear dynamic analysis results and Pareto design set.

[0078] Specifically, step S60 outputs the nonlinear dynamic analysis results, target performance indicators, and Pareto design set of the target engineering structure.

[0079] In this embodiment, when the multi-objective optimization algorithm meets the preset termination conditions, it outputs the target response, target performance index, feasibility judgment result, and Pareto design set of the candidate structural scheme. The preset termination conditions may include at least one of the following: reaching the maximum number of iterations, convergence of the objective function, the proportion of feasible solutions meeting the requirements, the change of the Pareto front being less than a preset threshold, or other engineering-defined conditions.

[0080] like Figure 7 As shown, in one specific implementation, 51 feasible Pareto designs were obtained after 50 iterations. The Pareto design set reflects the trade-off between economic and dynamic performance objectives. At the low-cost end, the sum of structural parameters is approximately 4.45 × 10⁻⁶. 7 N / m corresponds to a target peak response of approximately 0.0108 rad; at the high-performance end, the sum of structural parameters is approximately 1.53 × 10⁻⁶. 8 N / m corresponds to a target peak response of approximately 0.0066 rad. Compared to the low-cost design, the high-performance design reduces the target peak response by approximately 39%, but the material usage or equivalent cost increases accordingly. Figure 7 The diagram also shows a compromise design point, located where the sum of structural parameters is approximately 7.86 × 10⁻⁶. 7 The location has a target peak response of approximately 0.0084 rad and a capacity of N / m.

[0081] like Figure 8 As shown, Figure 8 This shows the distribution of design variables corresponding to different Pareto designs, used to reflect the adjustment law of design variables in different control parts of the target engineering structure when economic and dynamic performance targets change. For example... Figure 9 As shown, Figure 9 The diagram illustrates the changes in the objective function and the proportion of feasible individuals with each iteration. In one specific implementation, the proportion of feasible individuals increases from 13.8% in the first generation to 100% in the sixth generation. The peak response of the objective stabilizes around the 33rd generation, and the economic objective continues to improve in subsequent iterations. This demonstrates that hierarchical screening and rapid evaluation of the second neural operator can effectively guide the search into the feasible region.

[0082] In one specific implementation, the Pareto design set is input into a reference nonlinear solver, a hybrid operator solver, and a second neural operator for comparison. A total of 153 nonlinear analysis tasks are performed for 51 Pareto designs and 3 sets of external dynamic stimuli. The prediction results of the second neural operator are close to those of the reference nonlinear solver, with an average prediction ratio of 1.001, a normalized root mean square error of 0.0168, a mean absolute percentage error of 1.80%, and 100% of the prediction ratios falling within the range of 0.8 to 1.2. The hybrid operator solver has a normalized root mean square error of 0.0036, a mean absolute percentage error of 0.41%, and an average prediction ratio of 1.003.

[0083] In terms of efficiency, for the aforementioned 153 nonlinear analysis tasks, the reference nonlinear solver took 36.1 seconds, and the second neural operator took 0.3 seconds, representing an acceleration of approximately 116.7 times. For the optimization task involving 4000 evaluations of candidate structural schemes, the overall optimization process was completed in approximately 1 second using hierarchical screening and a single forward inference iteration of the second neural operator. Therefore, this embodiment can reduce the repetitive computation costs in the nonlinear dynamic analysis and multi-objective optimization of the target engineering structure while maintaining acceptable engineering accuracy.

[0084] This embodiment, through steps S10 to S60, unifies the construction of the dynamic model of the target engineering structure, the local nonlinear state neural operator, the hybrid operator solver, the system response neural operator, and the multi-objective optimization process within the same analytical framework. Compared to the method that requires repeatedly calling the complete nonlinear dynamic time history analysis for each candidate structural scheme, this embodiment can reduce the redundant calculations of local nonlinear state updates and system-level response evaluations, and can quickly provide the nonlinear dynamic performance and Pareto optimization results of candidate structural schemes during engineering design iterations.

[0085] It is understood that the number of model degrees of freedom, structural parameter range, number of external dynamic excitation groups, neural network hyperparameters, optimization algorithm parameters and performance indicators in the above specific implementation methods are all illustrative examples, and those skilled in the art can replace, adjust or combine them according to the target engineering structure and engineering requirements.

[0086] The following describes the structural nonlinear dynamic analysis and optimization device based on hierarchical neural operators provided in this application. The structural nonlinear dynamic analysis and optimization device based on hierarchical neural operators described below can be referred to in correspondence with the structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators described above.

[0087] like Figure 10As shown, the device includes: a model building module T10, a first operator training module T20, a hybrid solution module T30, a second operator training module T40, and an optimization output module T50.

[0088] The model building module T10 is used to obtain response evaluation coordinates and build a structural nonlinear dynamic analysis model containing the effective stiffness matrix and local state extraction relationship based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure. The first operator training module T20 is used to train the first neural operator based on the first training samples generated by the reference nonlinear solver. The first neural operator is used to predict the local nonlinear state based on the local state variables at the current time and historical time. The hybrid solver module T30 is used to embed the first neural operator into the time integration framework to build a hybrid operator solver. At each time step, the hybrid operator solver calls the first neural operator based on the local state extraction relationship to obtain the local nonlinear state, determines the equivalent nonlinear action, and solves the global dynamic response of the structure based on the effective stiffness matrix. The second operator training module T40 is used to train the second neural operator based on the second training samples generated by the hybrid operator solver. The second neural operator is used to predict the system-level structural response based on the response evaluation coordinates. The optimized output module T50 is used to perform hierarchical screening and multi-objective optimization of candidate structural schemes based on preset constraints and the second neural operator, and to obtain and output the Pareto design set.

[0089] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0090] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0091] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 11 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0092] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0093] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0094] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0095] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0096] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0097] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0098] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0099] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators, characterized in that, include: Based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure, response evaluation coordinates are obtained, and a structural nonlinear dynamic analysis model containing the effective stiffness matrix and local state extraction relationship is constructed. The first neural operator is trained based on the first training samples generated by the reference nonlinear solver. The first neural operator is used to predict the local nonlinear state based on the local state variables at the current time and historical time. The first neural operator is embedded into the time integration framework to construct a hybrid operator solver. At each time step, the hybrid operator solver calls the first neural operator based on the local state extraction relationship to obtain the local nonlinear state, determines the equivalent nonlinear action, and solves the global dynamic response of the structure based on the effective stiffness matrix. The second neural operator is trained based on the second training samples generated by the hybrid operator solver. The second neural operator is used to predict the system-level structural response based on the response evaluation coordinates. Based on preset constraints and the second neural operator, candidate structural schemes are hierarchically screened and multi-objective optimized to obtain and output the Pareto design set.

2. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that, The nonlinear dynamic analysis model of the structure, which is based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure, obtains response evaluation coordinates and constructs a model including the effective stiffness matrix and local state extraction relationships, including: Based on the mass distribution, equivalent stiffness, damping characteristics, boundary conditions and connection relationships of the target engineering structure, an effective stiffness matrix and dynamic action mapping relationship are constructed. The effective stiffness matrix includes the structural mass matrix, damping matrix and reference stiffness matrix. Based on the relationship between the target nonlinear part and the global degrees of freedom, a local state extraction relation is constructed. The local state extraction relation is used to determine the local state variables related to the local nonlinear state from the global displacement, velocity or acceleration response.

3. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that, The first neural operator includes a first branch network and a first backbone network: The first branch network is used to receive and encode the normalized structural design parameters and external dynamic excitation spectrum features, and output the first global feature vector; The first backbone network is used to receive and encode the current local deformation, historical local deformation, historical local nonlinear state and current local velocity, and output the first local state feature vector; Based on the inner product or feature fusion result of the first global feature vector and the first local state feature vector, the local nonlinear state at the current time is obtained; The first neural operator is obtained by training based on a first loss function, which includes the data loss between the predicted local nonlinear state and the reference local nonlinear state, as well as the initial condition regularization term that constrains the initial conditions of the local nonlinear state.

4. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that, Hybrid operator solvers solve for the global dynamic response of structures, including: The structural restoration action is decomposed into a linear restoration action corresponding to the reference stiffness matrix and a local nonlinear term provided by the first neural operator; and coupled to the global dynamic equilibrium equation of the structure under the time integration framework. An effective stiffness matrix is ​​formed based on the structural mass matrix, damping matrix, and reference stiffness matrix. The effective stiffness matrix is ​​decomposed at the beginning of the solution process, and the decomposition results are reused in subsequent time steps to obtain the global dynamic response of the structure at each time step.

5. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that, The second neural operator includes a second branch network and a second backbone network: The second branch network is used to receive and encode the normalized structural design parameters and external dynamic excitation spectrum features, and output the second global feature vector. The second backbone network is used to receive and encode the response evaluation coordinates and output the response location feature vector; Based on the inner product or feature fusion result of the second global feature vector and the response location feature vector, the system-level structural response or performance index corresponding to the response evaluation coordinates is obtained. The second training sample is generated by the hybrid operator solver for multiple sets of structural design parameters and external dynamic excitations. The second training sample includes structural design parameters, external dynamic excitation characteristics, response evaluation coordinates, and the target peak response as the supervision target.

6. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that, The hierarchical screening and multi-objective optimization of candidate structural schemes includes: Check whether the candidate structural schemes meet the design variable ratio constraints; For candidate structural schemes that meet the proportional constraints of design variables, perform linear or equivalent linear response analysis under low-intensity dynamic action to obtain the response results of the candidate structural schemes under low-intensity dynamic action and check whether they meet the response constraints under low-intensity dynamic action. For candidate structural schemes that meet the response constraints under low-intensity dynamic action, the second neural operator is invoked to predict the target peak response under high-intensity dynamic action, and it is checked whether the response constraints under high-intensity dynamic action are met. Based on at least two optimization objectives, a multi-objective optimization algorithm is used to iteratively search the candidate structural schemes that have passed the screening to obtain the Pareto design set. Among them, low-intensity dynamic action is a dynamic action in which the intensity index of external dynamic excitation is not higher than the first preset threshold, and high-intensity dynamic action is a dynamic action in which the intensity index of external dynamic excitation is not lower than the second preset threshold, and the second preset threshold is not lower than the first preset threshold.

7. The structural nonlinear dynamic analysis and optimization method based on hierarchical neural operators according to claim 1, characterized in that: Local nonlinear states include at least one of the following: hysteretic displacement, plastic variables, damage variables, frictional slip, and internal variables of the damper; Local state variables include at least one of the following: current local deformation, historical local deformation, historical local nonlinear state, and current local velocity; The time integration framework is a time-progressive framework for solving the global dynamic equilibrium equations of a structure by advancing the time steps. The reference nonlinear solver is used to perform nonlinear dynamic time history analysis on the target engineering structure. It performs constitutive evolution equation solving and substep integration at each time step and at each nonlinear part of the target, and the analysis results serve as the data source for generating the first training sample.

8. A structural nonlinear dynamic analysis and optimization device based on hierarchical neural operators, characterized in that, include: The model building module is used to obtain response evaluation coordinates and construct a structural nonlinear dynamic analysis model that includes an effective stiffness matrix and local state extraction relationship based on the structural design parameters and external dynamic excitation characteristics of the target engineering structure. The first operator training module is used to train the first neural operator based on the first training samples generated by the reference nonlinear solver. The first neural operator is used to predict the local nonlinear state based on the local state variables at the current time and historical time. The hybrid solver module is used to embed the first neural operator into the time integration framework to build a hybrid operator solver. At each time step, the hybrid operator solver calls the first neural operator based on the local state extraction relationship to obtain the local nonlinear state, determines the equivalent nonlinear action, and solves the global dynamic response of the structure based on the effective stiffness matrix. The second operator training module is used to train the second neural operator based on the second training samples generated by the hybrid operator solver. The second neural operator is used to predict the system-level structural response based on the response evaluation coordinates. The optimized output module is used to perform hierarchical screening and multi-objective optimization of candidate structural schemes based on preset constraints and the second neural operator, and to obtain and output the Pareto design set.

9. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium comprising instructions, characterized in that: When the instructions are executed on an electronic device, the electronic device causes the electronic device to perform the method as described in any one of claims 1-7.

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