Flexible photovoltaic support multi-objective optimization method and device for mountain environment

Abstract

The invention discloses a flexible photovoltaic support multi-objective optimization method and device for a mountain environment, and belongs to the technical field of structural engineering and renewable energy sources. A parameterized finite element model of the flexible photovoltaic support is established, and key design variable correlation material libraries such as the main cable sectional area and the stable cable sectional area are dynamically updated; generating dynamic wind load time-history data based on the mountain meteorological data, and applying the dynamic wind load time-history data to the model for time-history analysis after wind tunnel test verification to obtain structural response; performing normalized sensitivity analysis on the response data, and screening out key optimization variables which significantly influence the structural performance and cost; and adopting a genetic algorithm to perform multi-objective optimization search by taking the lowest total material cost as an objective in a solution space meeting the strength constraint, the rigidity constraint and the frequency constraint, outputting an optimal parameter combination, and verifying the safety and the standard conformity of the optimal parameter combination. The design optimization efficiency, the safety reliability and the economical efficiency of the support structure are improved.

Description

Technical Field

[0001] This invention relates to the fields of structural engineering and renewable energy technology, and in particular to a multi-objective optimization method, apparatus, equipment and storage medium for flexible photovoltaic supports for mountainous environments. Background Technology

[0002] Flexible photovoltaic (PV) supports are widely used in mountainous PV projects due to their advantages such as large span and strong adaptability to terrain. However, mountainous terrain is complex, and the wind field characteristics are significantly different from those in plains areas. There are significant wind vibration effects such as variable wind direction, uneven spatial distribution of wind speed, and susceptibility to vortices and flow around the wind. These pose serious challenges to the dynamic performance and safety of flexible supports.

[0003] Currently, conventional design methods in this field mainly rely on static calculations supplemented by empirical wind load coefficients, which have significant shortcomings: First, the design accuracy is low. Static calculations and rough empirical coefficients cannot realistically simulate the actual stress state of flexible supports in complex mountain wind fields, especially failing to accurately reflect their nonlinear dynamic response, resulting in a large deviation between the calculation model and the actual situation. Second, the economy is poor. To resist the wind vibration effect that is difficult to quantify precisely, the design usually tends to be conservative, resulting in generally high cross-sectional dimensions and material usage of major load-bearing components such as main cables and stabilizing cables, making it impossible to achieve precise control of project costs and violating the fundamental purpose of cost reduction and efficiency improvement in photovoltaic projects. Finally, there are hidden safety concerns. On the one hand, simplified calculation methods may ignore the dynamic fatigue and instantaneous overload risks of individual key components under the coupled action of specific wind directions and speeds, posing potential safety loopholes. On the other hand, overly conservative designs not only cause waste but may also affect the inherent dynamic characteristics by changing the overall stiffness and mass distribution of the structure, inducing new resonance or instability problems under specific working conditions.

[0004] Therefore, overcoming the problems of inaccurate safety assessment and high material consumption and cost in existing technologies due to their crude design methods, and achieving an optimal balance between safety and economy, has become a key technical challenge that urgently needs to be solved in this field. This invention aims to provide an effective solution to this problem. Summary of the Invention

[0005] The present invention aims to at least partially solve one of the technical problems in the related art.

[0006] To address this, this invention proposes a multi-objective optimization method for flexible photovoltaic supports in mountainous environments. By establishing a parameterized model and applying dynamic wind loads validated through wind tunnel testing for time history analysis, followed by sensitivity analysis to screen key variables, and then employing a genetic algorithm to automatically optimize the system under multiple performance constraints with the goal of minimizing total material cost, the method ultimately outputs the safe and economical optimal parameter combination.

[0007] Another objective of this invention is to provide a multi-objective optimization device for flexible photovoltaic supports in mountainous environments.

[0008] The third objective of this invention is to provide a computer device.

[0009] A fourth objective of this invention is to provide a non-transitory computer-readable storage medium.

[0010] To achieve the above objectives, this invention proposes a multi-objective optimization method for flexible photovoltaic supports in mountainous environments, comprising: S1. Establish a parametric finite element model of the flexible photovoltaic support system, and use the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stable cable, the moment of inertia of the support rod section and the volume of concrete of the side anchor foundation as adjustable design variables, and link the material library and the section library to achieve parametric updates. S2, Based on the meteorological data of the project site, dynamic wind load time history data that conforms to the characteristics of mountain winds is generated. After being verified by wind tunnel test, it is applied to the parameterized finite element model and time history analysis is performed to obtain structural response data. S3. Perform normalized sensitivity analysis on the structural response data to quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out the key optimization variables that significantly affect the response. S4. Using a genetic algorithm, within the solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, the algorithm performs a multi-objective optimization search on the key optimization variables with the goal of minimizing the total material cost, outputs the optimal parameter combination, and verifies its safety and compliance with specifications.

[0011] The multi-objective optimization method for flexible photovoltaic supports in mountainous environments according to an embodiment of the present invention may also have the following additional technical features: In one embodiment of the present invention, establishing a parametric finite element model of the flexible photovoltaic support system includes: S11, establish key nodes based on the span of the support and the position of the support column, and divide the nodes into end anchor system nodes, intermediate support system nodes, load-bearing main cable nodes and stabilizing cable nodes; S12, when defining the element type, set the load-bearing main cable and the stabilizing cable as cable elements that only bear axial tension, and set the supporting rods as beam elements that can bear bending moment and shear force, and dynamically associate the physical properties of the design variables through the material library.

[0012] In one embodiment of the present invention, dynamic wind load time history data conforming to the characteristics of mountain winds is generated based on meteorological data of the project location, including: S21 uses a ρ-order autoregressive model to simulate the time history of fluctuating wind speed, where ρ takes values ​​from 3 to 5, and solves for the autoregressive coefficients using the Yule-Walker equation. ; S22, Davenport spectrum based on mountain correction Calculate the standard deviation of a white noise sequence This is to control the variance of the output sequence.

[0013] In one embodiment of the present invention, normalized sensitivity analysis of structural response data includes: S31, using the normalized relative sensitivity coefficient formula The influence of quantization parameters, among which In response to changes, For parameter changes; S32, by plotting the response-parameter curve under single-parameter perturbation, key optimization variables with an absolute value of sensitivity coefficient greater than 0.1 are selected.

[0014] In one embodiment of the present invention, a genetic algorithm is used to optimize within a solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, including: S41 defines the total cost as: (Main cable material density × Main cable length × Main cable cross-sectional area × Main cable unit price) + (Stabilizing cable material density × Stabilizing cable length × Stabilizing cable cross-sectional area × Stabilizing cable unit price) + (Support rod weight × Support rod unit price) + (Concrete usage × Concrete unit price), and uses real number coding to parameterize the design variables. S42 uses the penalty function method to handle constraints. When the maximum equivalent stress of the structure exceeds the allowable stress of the material, an exponential penalty term is applied to the objective function.

[0015] In one embodiment of the present invention, it further includes: S5. A response surface model is constructed as an alternative model to finite element calculation. By selecting sample points, an approximate functional relationship between the structural response and design variables is generated, thereby reducing the number of calls to finite element calculation during the optimization process.

[0016] To achieve the above objectives, another aspect of the present invention proposes a multi-objective optimization device for flexible photovoltaic supports in mountainous environments, comprising: The parametric modeling module is used to establish a parametric finite element model of the flexible photovoltaic support system. It uses the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, the moment of inertia of the support rod section, and the volume of concrete in the side anchor foundation as adjustable design variables, and links the material library and the section library to achieve parametric updates. The dynamic wind load generation module is used to generate dynamic wind load time history data that conforms to the characteristics of mountain winds based on meteorological data of the project location. After being verified by wind tunnel test, the data is applied to the parameterized finite element model and time history analysis is performed to obtain structural response data. The sensitivity analysis module is used to perform normalized sensitivity analysis on structural response data, quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out key optimization variables that significantly affect the response. The multi-objective optimization module is used to perform multi-objective optimization search on the key optimization variables within the solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, with the goal of minimizing the total material cost. It outputs the optimal parameter combination and verifies its safety and compliance with specifications.

[0017] In one embodiment of the present invention, it further includes: The response surface modeling module is used to construct a response surface model as an alternative model for finite element calculation. By selecting sample points, it generates an approximate functional relationship between the structural response and design variables, thereby reducing the number of calls to finite element calculation during the optimization process.

[0018] This invention discloses a multi-objective optimization method and device for flexible photovoltaic supports in mountainous environments. By constructing a parametric finite element model and incorporating dynamic wind loads validated through wind tunnel testing for time-history analysis, it achieves accurate simulation of the nonlinear dynamic response of the structure under complex wind fields in mountainous areas. Furthermore, it combines normalized sensitivity analysis to identify key design variables and employs a genetic algorithm to automatically optimize and verify the design with the goal of minimizing total material cost while strictly satisfying multiple performance constraints. This invention achieves a closed-loop process from accurate modeling, load simulation, variable selection to intelligent optimization, effectively overcoming the core defects of traditional design methods such as insufficient accuracy and poor economy. While significantly ensuring structural safety and compliance with regulations, it achieves refined control of material costs, improving the overall technical and economic efficiency of mountainous photovoltaic projects.

[0019] To achieve the above objectives, a third aspect of this application provides a computer device comprising a processor and a memory; wherein the processor runs a program corresponding to the executable program code by reading executable program code stored in the memory, for implementing a multi-objective optimization method for flexible photovoltaic supports in mountainous environments as described in the first aspect embodiment.

[0020] To achieve the above objectives, the fourth aspect of this application proposes a non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements a multi-objective optimization method for flexible photovoltaic supports in mountainous environments as described in the first aspect embodiment.

[0021] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a multi-objective optimization method for flexible photovoltaic supports in mountainous environments according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the specific steps of a multi-objective optimization method for flexible photovoltaic supports in mountainous environments according to an embodiment of the present invention. Figure 3 This is a schematic diagram of a multi-objective optimization device for a flexible photovoltaic support in a mountainous environment according to an embodiment of the present invention; Figure 4 It is a computer device according to an embodiment of the present invention. Detailed Implementation

[0023] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] The following description, with reference to the accompanying drawings, describes a multi-objective optimization method, apparatus, equipment, and storage medium for flexible photovoltaic supports in mountainous environments, according to embodiments of the present invention.

[0026] The core idea of ​​this invention is to accurately simulate the nonlinear dynamic response of flexible supports in complex wind fields by constructing a high-fidelity parametric finite element model and introducing a dynamic wind load time history verified by wind tunnel tests and conforming to the characteristics of mountain winds. Based on this model, time history analysis is performed to obtain the actual structural response, and further, normalized sensitivity analysis is used to quantify the influence of each design variable on structural performance and cost, thereby accurately selecting key optimization variables. Finally, a genetic algorithm is used to automatically search for multi-objective optimization of key variables within a solution space that strictly satisfies multiple constraints such as strength, stiffness, and frequency, with the core objective of minimizing total material cost. The optimal parameter combination is output after verification of safety and compliance with standards. This transforms the traditional extensive design process that relies on static estimation and empirical coefficients into a closed-loop optimization system that integrates accurate simulation, intelligent analysis, and automatic optimization, fundamentally solving the core problem of the difficulty in coordinating safety, economy, and accuracy in the design of flexible photovoltaic supports in mountainous environments.

[0027] Example 1 To achieve the above invention, embodiments of the present invention provide a multi-objective optimization method for flexible photovoltaic supports in mountainous environments, such as... Figure 1 As shown, it includes: S1. Establish a parametric finite element model of the flexible photovoltaic support system, and use the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, the moment of inertia of the support rod section, and the volume of concrete in the side anchor foundation as adjustable design variables, and link the material library and the section library to achieve parametric updates.

[0028] Specifically, in some implementations, the model is constructed using professional finite element software such as MIDAS GEN. Its core lies in abstracting the key components of the structural system (such as main cables, stabilizing cables, and support rods) into element types with adjustable parameters. For example, main cables and stabilizing cables can be defined as cable elements that are only subjected to tension, while support rods are modeled using beam elements.

[0029] Furthermore, the material properties of each element in the model (such as elastic modulus, density, and yield strength) are all called from a pre-defined material library, while the cross-sectional geometric parameters (such as diameter, moment of inertia, and cross-sectional area) are parameterized and assigned values ​​through a cross-section library. For example, the cross-sectional area of ​​the main cable... It can be set as a variable, and its value range is usually within... The spacing is adjusted to meet the strength and stiffness requirements under different spans and wind loads. The moment of inertia of the support rod section... Usually in Variations within a certain range are used to control the deflection and vibration characteristics of the structure.

[0030] Specifically, this parametric model is widely applicable to the preliminary design stage of mountainous photovoltaic power plants, especially in situations with significant terrain undulations and complex wind fields. It can quickly generate multiple design schemes and compare their performance. By directly binding design variables with material and cross-sectional properties, the model supports automated iteration and optimization, significantly improving design efficiency and accuracy.

[0031] Specifically, the technical effect of this step is that it provides a high-precision and repeatable simulation platform for subsequent wind load simulation and multi-objective optimization, avoiding the problem of repeated modeling caused by inflexible parameter adjustment in traditional empirical design, and laying the foundation for quantitative analysis of structural performance.

[0032] Furthermore, S1 includes: S11. Based on the span of the support and the position of the support column, key nodes are established and the nodes are divided into end anchor system nodes, intermediate support system nodes, load-bearing main cable nodes and stabilizing cable nodes.

[0033] Specifically, the core of this step lies in constructing a basic framework for a finite element model that can accurately reflect the actual stress state through structural topology analysis and functional partitioning.

[0034] Specifically, this step first determines the geometric layout of the support system, including the main cable span, based on design drawings or site survey data. Column spacing Column height Key geometric parameters are then determined. The structure is then discretized into several key nodes, the arrangement of which must meet the accuracy requirements of structural mechanics analysis. Typically, end anchor system nodes are set at both ends of the main cables to simulate the rigid connection with the foundation; intermediate support system nodes are set at the connection between the support column and the main cable to reflect the constraint and load transfer characteristics of the support structure; load-bearing main cable unit nodes are set along the length of the main cable to simulate the load distribution of the photovoltaic modules; stabilizing cables are arranged on both sides or at intersections of the main cables, and their connection points are defined as stabilizing cable nodes, used to enhance the structure's resistance to lateral wind vibration.

[0035] Furthermore, the node division must meet the following criteria: end anchor nodes should be located at both ends of the main cable, and their constraint condition should be fixed support; intermediate support nodes should be aligned with the top of the support column, and their constraint form can be hinged support or fixed support, depending on the foundation type; the spacing between main cable nodes is usually [missing information]. This ensures that the nonlinear behavior of the suspension structure can be effectively captured; stabilizing cable nodes are typically staggered with the main cable nodes, with a spacing of [missing information - likely a unit of measurement]. .

[0036] Specifically, this step is applicable to the design of flexible photovoltaic support systems in complex terrains such as mountains and hills. Because wind fields in such terrains exhibit significant pulsation and directionality, the proper division of structural nodes directly affects the accuracy of subsequent wind-induced vibration response analysis. By classifying nodes according to their function, clear physical boundary conditions and load transfer paths can be provided for subsequent application of dynamic wind loads, parameter sensitivity analysis, and multi-objective optimization.

[0037] Specifically, the refined modeling and functional classification of structural nodes provide a reliable geometric and mechanical foundation for subsequent finite element simulation and optimization calculations. The rationality of node division directly affects the calculation accuracy of structural response and is a prerequisite for the safe, economical, and efficient design of flexible photovoltaic supports in mountainous environments.

[0038] S12, when defining the element type, set the load-bearing main cable and the stabilizing cable as cable elements that only bear axial tension, and set the supporting rods as beam elements that can bear bending moment and shear force, and dynamically associate the physical properties of the design variables through the material library.

[0039] Specifically, the technical implementation of this step involves the mechanical modeling of structural elements and the dynamic correlation of material properties. In some implementations, the load-bearing main cables and stabilizing cables are modeled as cable elements that only bear axial tension, while the supporting members are modeled as beam elements that can withstand bending moments and shear forces, thereby enabling refined mechanical response analysis of flexible structures under complex mountain wind loads.

[0040] Specifically, cable elements (such as the Cable element in MIDAS GEN) employ a one-dimensional rod system model, with constitutive relations based on Hooke's law, considering only axial tensile deformation and neglecting bending and shear stiffness. This type of element is suitable for simulating the tensile response of flexible components such as steel cables and wire ropes under wind loads. Support members, on the other hand, utilize three-dimensional beam elements (such as the Frame element), whose section properties include the moment of inertia. Cross-sectional area Shear area These parameters can accurately reflect the bending moment of a component under wind pressure. Shear force and axial force The coupling effect. Furthermore, by adjusting design variables (such as the main cable cross-sectional area)... Moment of inertia of the support rod (and the elastic modulus in the material library) ,density Yield strength By dynamically binding physical properties as parameters, the model can be automatically updated and iterated during the optimization process.

[0041] Furthermore, the axial stiffness of the cable element is given by the formula Confirmed, among which The elastic modulus of the material. For the cross-sectional area, Let be the element length. The bending stiffness of the beam element is... The shear stiffness is ,in This refers to the shear modulus. The range of values ​​for the design variables must meet the requirements of relevant structural design codes, such as the requirements for wind load combinations and component bearing capacity in the "Code for Design of Building Structures" (GB 50009).

[0042] Specifically, this step is typically performed in finite element software such as MIDAS GEN, where parametric modeling tools (such as Design Variable Manager) map design variables to model geometry and material properties. For example, the cross-sectional area of ​​the main cable... It can be set as an optimization variable, and its changes will automatically update the stiffness and mass properties of all main cable elements in the model, thereby providing accurate input conditions for subsequent time history analysis and optimization calculations.

[0043] Specifically, by rationally defining structural unit types and establishing parametric models, the accuracy of finite element simulation in predicting the response of flexible photovoltaic support systems under mountainous wind loads can be significantly improved, providing a reliable foundation for subsequent optimization design. Simultaneously, dynamically linking the material library with design variables enables the optimization process to possess good scalability and adaptability, quickly responding to design requirements under different terrain and wind field conditions, thereby improving overall design efficiency and economy.

[0044] S2. Based on meteorological data of the project location, dynamic wind load time history data that conforms to the characteristics of mountain winds is generated. After being verified by wind tunnel test, it is applied to the parameterized finite element model, and time history analysis is performed to obtain structural response data.

[0045] Specifically, this process is a crucial step in achieving precise design of flexible photovoltaic (PV) supports in complex mountainous wind fields. The first step is to collect long-term meteorological data for the project area, including the basic design wind speed. Ground roughness category, wind profile index Based on this data, the average wind speed at different altitudes is calculated. and wind pressure height variation coefficient Subsequently, the following was adopted. An autoregressive model (AR(ρ)) simulates the time history of fluctuating wind speeds. Its recursive formula is: ; in, For the time step, it is usually taken as To satisfy the Nyquist sampling theorem; These are autoregressive coefficients, solved by the Yule-Walker equation, and depend on the target power spectrum. The mountain-corrected Davenport spectrum is typically used. White noise sequence The standard deviation of the target spectrum is used to control the variance of the fluctuating wind speed; its value is determined by the target spectrum and... To be determined jointly.

[0046] Furthermore, wind pressure time history The calculation formula is: ; in, air density (usually taken as) ), This is the structural shape coefficient, determined according to the "Code for Design of Building Structures" (GB 50009) or wind tunnel test results; This is the wind pressure height variation coefficient, reflecting the influence of terrain on wind speed distribution.

[0047] Specifically, this step typically involves generating the wind speed time history in a scientific computing environment such as MATLAB or Python, exporting it as a CSV or TXT file, and then importing it into MIDAS GEN via the "Time History Analysis Data" module, defining it as a "user-defined" type time history load function. The load can be applied as a nodal load or an element surface pressure load, and the load direction (such as the global coordinate X / Y direction or the normal direction) must be selected appropriately according to the structural form.

[0048] Specifically, by introducing dynamic wind load time history analysis, the nonlinear dynamic response of flexible photovoltaic supports in mountainous wind fields can be accurately captured, such as cable vibration frequency, nodal displacement, and stress concentration. This replaces the traditional static equivalent or empirical coefficient method, significantly improving design accuracy and safety. Simultaneously, it provides realistic and reliable input conditions for subsequent parameter sensitivity analysis and multi-objective optimization, forming the basis for achieving a balance between structural performance and economy.

[0049] Furthermore, S2 includes: S21 uses a ρ-order autoregressive model to simulate the time history of fluctuating wind speed, where ρ takes values ​​from 3 to 5, and solves for the autoregressive coefficients using the Yule-Walker equation. .

[0050] Specifically, in some implementations, ρ takes the order 3 to 5. This order is chosen based on the spectral analysis results of the wind field fluctuation characteristics in mountainous areas, ensuring that the model can effectively capture the main frequency components in the wind speed time history. The AR(ρ) model is essentially a linear filter, and its recursive formula is: ; in, The time step is typically set to 0.1 to 0.2 seconds to meet the Nyquist sampling theorem's requirement for capturing the highest frequency of the wind speed signal. These are the autoregressive coefficients, and their solution depends on the Yule-Walker equation, which is derived from the target power spectrum. The theoretical autocorrelation function corresponding to (e.g., the mountain-corrected Davenport spectrum) This allows for the establishment of a spectrum matching mechanism for the time history of fluctuating wind speeds. The standard deviation of the white noise sequence is determined by the target spectrum and the order of the AR model. It is used to control the variance of the output sequence and reflects the turbulence intensity of the wind field.

[0051] Specifically, scientific computing tools such as MATLAB or Python can be used, based on wind tunnel test data or recommended specifications. and The parameters are used to construct an AR(ρ) model and generate fluctuating wind speed time history samples that conform to the characteristics of mountain winds. This step provides the basic input for the subsequent generation of wind pressure time history, ensuring that the loads applied to the finite element model have realistic dynamic characteristics, thereby improving the accuracy of structural response analysis. This method can effectively replace the traditional empirical coefficient method, achieving accurate simulation of the dynamic behavior of flexible photovoltaic supports in complex wind fields, and providing a reliable basis for optimization design.

[0052] S22, Davenport spectrum based on mountain correction Calculate the standard deviation of a white noise sequence This is to control the variance of the output sequence.

[0053] Specifically, the technical implementation of this step is based on the method for generating pulsating wind speed time histories in structural wind engineering. Its core lies in performing an inverse transformation of the target spectrum using an autoregressive model (AR(ρ)) to generate a wind speed time histories with specific frequency characteristics. Specifically, the standard deviation of the white noise sequence... The calculation formula is: .

[0054] Furthermore, this formula represents the target spectrum The square root of the integral in the frequency domain is taken to obtain the root mean square value of the white noise sequence, thereby controlling the variance of the fluctuating wind speed time history output by the AR model. In practice, this integral is usually calculated within a finite frequency range using numerical integration methods (such as Simpson's method or trapezoidal method). The upper frequency limit is generally taken as 2 to 3 times the first-order natural frequency of the structure to ensure that the main dynamic response frequency band is captured.

[0055] Furthermore, The mountain-corrected Davenport spectrum is in the following form: ; in, The design average wind speed at the reference height. The frequency is denoted by . This spectrum is based on the plain Davenport spectrum and incorporates a topographic correction factor to reflect the high turbulence intensity and non-uniformity of the mountain wind field. Through calculation... This ensures that the pulsating wind speed sequence output by the AR model has a turbulent energy distribution consistent with the actual mountain wind field, thereby improving the accuracy of wind load simulation.

[0056] Specifically, this step is typically implemented in scientific computing environments such as MATLAB or Python. The user inputs wind speed statistics for the project location (e.g.,...). , ground roughness category, wind profile index α, etc., and determined according to the specifications (such as the Code for Design of Building Structures GB 50009). The corrected form. Then, numerical integration is used to calculate... And use it as the input parameter of the AR model to drive the Gaussian white noise sequence. Generate time histories of fluctuating wind speeds with mountain wind characteristics. .

[0057] Specifically, on the one hand, it ensures that the dynamic characteristics of wind loads are highly consistent with the actual mountain wind field, providing a realistic input for subsequent finite element time history analysis; on the other hand, by precisely controlling the variance of pulsating wind speed, it avoids the design redundancy brought about by the traditional empirical coefficient method, thereby improving the economy and safety of structural design.

[0058] S3. Normalize the structural response data and perform sensitivity analysis to quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out the key optimization variables that significantly affect the response.

[0059] Specifically, this step, based on finite element simulation results, uses a combination of the control variable method and normalized sensitivity coefficients to achieve a systematic evaluation of design parameters.

[0060] Specifically, the sensitivity analysis first uses a parametric finite element model to subject design variables such as the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, and the moment of inertia of the support rod section to single-variable perturbations. Specifically, each variable is perturbed at its baseline value. Based on this, discrete change points of ±10%, ±20%, and ±30% were selected, while other variables remained unchanged. Subsequently, dynamic time history analysis was performed to obtain the structural response values ​​under the corresponding working conditions. Including maximum equivalent stress Maximum nodal displacement , structural fundamental frequency and total material cost .

[0061] Furthermore, the normalized sensitivity coefficient is calculated. Its definition is: ; in, The response value is the value under the baseline operating condition. In response to changes, This represents the change in parameters. This coefficient reflects the design parameters. Response When the absolute value of the relative influence is greater than 0.1, it indicates that the parameter has a significant impact on the response and should be the focus of optimization.

[0062] Specifically, this step is typically performed in finite element software such as MIDAS GEN or ANSYS, followed by post-processing using MATLAB or Python to generate sensitivity matrices and response curves. Through this analysis, designers can identify variables that play a dominant role in structural performance. For example, the cross-sectional area of ​​the main cables may have a significantly greater impact on maximum stress and fundamental frequency than that of the stabilizing cables, allowing for priority adjustment in subsequent multi-objective optimization, thus improving optimization efficiency and design accuracy.

[0063] Specifically, the technical value of this step lies in replacing empirical judgment with quantitative analysis, thus providing a scientific basis for the optimization process, avoiding the waste of resources caused by blindly adjusting parameters, and providing a basis for variable selection for multi-objective optimization, significantly improving the economy and safety of the design.

[0064] Furthermore, S3 includes: S31, using the normalized relative sensitivity coefficient formula The influence of quantization parameters, among which In response to changes, This represents the change in parameters.

[0065] Specifically, this step quantifies the influence of each design parameter on the structural response, providing a scientific basis for subsequent multi-objective optimization. Specifically, the normalized relative sensitivity coefficient formula is used: ; in, Indicates the first Design parameters For the Structural response The sensitivity coefficient, In response to changes, For parameter changes, and These are the baseline values ​​for the response and the parameter, respectively. This formula eliminates the influence of dimensions by calculating the ratio of the relative rate of change of the response to the relative rate of change of the parameter, facilitating comparisons between different parameters.

[0066] Specifically, this step is typically performed using the parametric study function in finite element software (such as MIDAS GEN). First, several key design variables are selected, such as the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, and the moment of inertia of the support rod section, and their baseline values ​​are set. Then, using the univariate perturbation method, each parameter is varied by 10%, 20%, and 30% above and below its baseline value, while the remaining parameters remain unchanged. Through multiple finite element time history analyses, the variation data of the corresponding structural response (such as maximum equivalent stress, maximum nodal displacement, and structural fundamental frequency) are obtained.

[0067] Furthermore, sensitivity coefficient The absolute value of the parameter directly reflects the degree of its influence on the response. It is generally considered that when... When this parameter has a significant impact on structural performance, it should be given priority as an optimization variable; while when When the impact is relatively small, it can be appropriately ignored or simplified. This indicator provides a quantitative basis for selecting optimization variables.

[0068] Specifically, this step is widely applicable to the preliminary optimization design phase of flexible support structures in mountainous photovoltaic projects. By identifying key influencing parameters, designers can focus on variables that play a dominant role in structural performance, avoiding blindly adjusting all parameters, thereby improving optimization efficiency and design accuracy.

[0069] Specifically, this sensitivity analysis method effectively improves the scientific rigor and economy of the design. By accurately identifying key parameters, the optimization process can focus resources on the variables that have the greatest impact on the structural response, avoiding redundant calculations, while ensuring the safety and stability of the structure under complex wind loads. This step lays a solid foundation for achieving a balance between the dual objectives of "safety and economy."

[0070] S32, by plotting the response-parameter curve under single-parameter perturbation, key optimization variables with an absolute value of sensitivity coefficient greater than 0.1 are selected.

[0071] Specifically, this step is based on the parameterization of the finite element model, using the control variable method to independently perturb each design parameter, and recording the degree of influence of each parameter on the structural response (such as maximum stress, maximum displacement, fundamental frequency, etc.).

[0072] Specifically, first, select a certain design parameter (such as the cross-sectional area of ​​the main cable). (Keep the baseline values ​​for the remaining parameters) Under the premise of keeping the parameter constant, discretize and perturb it within a certain range (e.g., ±10%, ±20%, ±30%). For each perturbation value, perform a complete dynamic time history analysis to calculate the structure's response value under the change of the parameter. And record its change. Then, according to the normalized relative sensitivity coefficient formula: .

[0073] Furthermore, the sensitivity coefficient of this parameter to the response is calculated. .in, As the baseline response value, In response to changes, This represents the change in parameters. This coefficient reflects the relative sensitivity of the response value to parameter changes. When its absolute value is greater than 0.1, it indicates that the parameter has a significant impact on structural performance and should be listed as a key optimization variable.

[0074] Furthermore, to visually demonstrate the relationship between parameters and response, the calculation results can be plotted as a response-parameter curve. The horizontal axis represents the disturbance value of the parameter, and the vertical axis represents the corresponding structural response value. By observing the change in the slope of the curve, the sensitive range of the parameter can be determined. For example, if the maximum nodal displacement decreases significantly when the cross-sectional area of ​​the main cable increases, it indicates that the parameter has a high sensitivity to structural stiffness.

[0075] Specifically, this is typically achieved through the parameter study module in MIDAS GEN or other finite element software. Designers can set the parameter variation step size, response type, and output frequency, and the system will automatically perform multiple analyses and generate result tables and graphs. In the design of mountain photovoltaic support systems, this method can effectively identify the parameters that have the greatest impact on wind vibration response, such as the cross-sectional area of ​​the main cable and the moment of inertia of the support rod, thus providing a clear basis for variable selection for subsequent multi-objective optimization.

[0076] Specifically, this step, through quantitative analysis, avoids the inefficiency of indiscriminate optimization of all parameters in traditional empirical methods, thus improving the targeting and computational efficiency of the optimization process. Simultaneously, the sensitivity analysis results provide designers with a scientific basis, helping to achieve optimal control of material usage and cost while ensuring structural safety.

[0077] S4. Using a genetic algorithm, within the solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, the algorithm performs a multi-objective optimization search on the key optimization variables with the goal of minimizing the total material cost, outputs the optimal parameter combination, and verifies its safety and compliance with specifications.

[0078] Specifically, this step is the core link in achieving synergistic optimization of the economy and safety of flexible photovoltaic supports in mountainous environments.

[0079] In some implementations, the optimization process of the genetic algorithm is based on an iterative search using the output response of a parameterized finite element model. First, the objective function is defined as the total material cost. Its expression is: ; in, Indicates the density of the material. For the length of the cable or rod, For cross-sectional area, The weight of the support rod. For concrete volume, Let be the unit cost of the corresponding material. This objective function is minimized using a genetic algorithm.

[0080] Furthermore, the constraints include: the maximum equivalent stress of the structure. Maximum nodal displacement (usually span) ), and the first-order natural frequency of the structure. (Generally set as) To avoid coinciding with the vortex-induced vibration frequency of the mountain wind field.

[0081] Specifically, the genetic algorithm encodes design variables (such as the cross-sectional area of ​​the main cable and stabilizing cable, the moment of inertia of the support rod, etc.) and performs population initialization, crossover, mutation, and other operations within the feasible region that satisfies the above constraints, gradually approaching the optimal solution. During the algorithm iteration process, the fitness function of each generation is calculated based on the finite element simulation results, ensuring that the optimization process is closely related to the actual structural performance.

[0082] Specifically, the technical advantage of this step lies in its ability to achieve automatic optimization of multiple objectives under complex constraints, significantly reducing material costs while ensuring the safety and compliance of the structure under dynamic wind loads. Compared to traditional empirical design methods, this invention, through an algorithm-driven optimization process, improves the scientific rigor and economy of the design, providing an efficient and precise solution for the structural design of mountain photovoltaic projects.

[0083] Furthermore, S4 includes: S41 defines the total cost as: (Main cable material density × Main cable length × Main cable cross-sectional area × Main cable unit price) + (Stabilizing cable material density × Stabilizing cable length × Stabilizing cable cross-sectional area × Stabilizing cable unit price) + (Support rod weight × Support rod unit price) + (Concrete usage × Concrete unit price), and uses real number coding to parameterize the design variables.

[0084] Specifically, this step provides a calculable and comparable objective function for subsequent optimization algorithms by quantifying the relationship between design variables and costs, thereby minimizing material costs while meeting structural safety and performance constraints.

[0085] Furthermore, total cost The calculation model is based on the geometric and material properties of each structural component. Specifically, the material usage of key components such as main cables, stabilizing cables, and support rods is determined by their material density. ,length Cross-sectional area and the unit price of the corresponding materials These parameters are jointly determined. By incorporating them into the cost function, a precise assessment of the overall economic efficiency of the structure can be achieved. For example, the main cable cost can be expressed as... The same applies to other components. This model supports flexible combinations of different materials and cross-sectional shapes, demonstrating good versatility.

[0086] Specifically, this invention uses real-number encoding to represent design variables. Unlike traditional integer or discrete encoding, real-number encoding allows design variables to take values ​​in a continuous space, thereby improving the search accuracy and efficiency of the optimization algorithm. Design variables typically include the cross-sectional areas of the main cable and stabilizing cable, the moment of inertia of the support rod, and the prestress of the cable, etc., and their value range needs to be set according to engineering experience and specification requirements. For example, the cross-sectional area of ​​the main cable... Available The moment of inertia of the support rod varies within a certain range. Available Adjustments can be made within a given range. By mapping these variables to real-valued vectors, optimization methods such as genetic algorithms can directly perform crossover and mutation operations on them, thereby efficiently exploring the solution space.

[0087] Specifically, this step applies to the economic optimization design of flexible support systems in mountain photovoltaic projects. By combining the cost function with structural performance constraints (such as strength, stiffness, and frequency), the amount of material used can be minimized while meeting safety requirements. For example, in a flexible support system with a span of 80m, optimizing the cross-sectional area of ​​the main cable and stabilizing cable can reduce the total cost by more than 5%, while ensuring that the maximum stress of the structure under a 10-year return period wind speed does not exceed the allowable stress of the material.

[0088] Specifically, by establishing a precise cost model and parameterization mechanism, a mathematical foundation is provided for multi-objective optimization, significantly improving the economic efficiency and scientific rigor of the design. Simultaneously, the real-number encoding method enhances the adaptability of the optimization algorithm, enabling it to more effectively address design challenges under complex terrain and wind load conditions.

[0089] S42 uses the penalty function method to handle constraints. When the maximum equivalent stress of the structure exceeds the allowable stress of the material, an exponential penalty term is applied to the objective function.

[0090] Specifically, the core of this step lies in determining the maximum equivalent stress of the structure under dynamic wind loads. Exceeding the allowable stress of the material When, an exponential penalty term is introduced. This is done to modify the objective function, thereby guiding the optimization algorithm to avoid design schemes that do not meet the strength requirements.

[0091] Furthermore, this penalty term is embedded into the objective function as part of the fitness function of the optimization algorithm. Specifically, the objective function is typically the total material cost, expressed as: ; Specifically, when the structural response calculation results show At this time, the penalty term is activated and added to the objective function, forming a new fitness function: ; in, This is the penalty coefficient, and its value needs to be adjusted according to the sensitivity of the optimization problem, typically within a certain range. The range is selected to ensure that the penalty term has a significant impact on the objective function when the constraint is violated, while avoiding numerical instability.

[0092] Specifically, The design strength values ​​for steel are determined according to GB 50009-2012 "Load Code for Design of Building Structures" or GB / T 19963-2011 "Design Code for Photovoltaic Power Stations". For example, the allowable stress of Q345 steel is usually [value missing]. . The maximum equivalent stress response of key nodes or elements of the structure is then extracted through time history analysis using the MIDAS GEN finite element software.

[0093] Specifically, in practical applications, especially in complex wind field environments in mountainous areas, this step can effectively avoid the risk of structural failure caused by local stress concentration due to wind vibration. Through the nonlinear amplification characteristics of the exponential penalty term, the optimization algorithm can quickly identify and eliminate parameter combinations that do not meet the strength requirements, thereby focusing on the optimal solution within the feasible region in the solution space.

[0094] Specifically, this penalty mechanism significantly improves the convergence efficiency of the optimization process and the reliability of the design results. Compared with traditional linear penalty or no-penalty optimization strategies, the exponential penalty term is more sensitive to the degree of exceeding the limits, and can more effectively guide the optimization direction, ensuring that the final design scheme minimizes material costs while satisfying strength constraints. This step is one of the core control mechanisms of this invention for achieving the dual objective of "safety-economy" optimization.

[0095] S5. A response surface model is constructed as an alternative model to finite element calculation. By selecting sample points, an approximate functional relationship between the structural response and design variables is generated, thereby reducing the number of calls to finite element calculation during the optimization process.

[0096] Specifically, the core of this step lies in establishing an approximate functional relationship between the structural response and design variables by selecting representative sample points, thereby significantly reducing the number of calls to the finite element simulation model during the optimization process and improving computational efficiency.

[0097] Furthermore, response surface models (RSMs) typically employ multinomial regression methods, such as quadratic multinomial models, whose general form is: ; in, It represents the response of a structure (such as maximum stress, maximum displacement, or fundamental frequency). To design variable vectors, These are the regression coefficients. By selecting several sample points in the parameter space, finite element simulation is performed to obtain the corresponding structural response values. Then, the above polynomial model is fitted using the least squares method or other regression algorithms.

[0098] Specifically, regarding parameter selection, methods such as Latin hypercube sampling (LHS) or full factorial design can be selectively employed to ensure that the sample points have good distribution characteristics in the design variable space. The number of sample points is typically [number missing]. Between n^2, where This determines the number of design variables. For example, when there are 4 optimization variables, the number of sample points can be set to 9 to 16 to ensure the model's fitting accuracy.

[0099] Furthermore, the construction of the response surface model must meet certain fitting accuracy indicators, such as a coefficient of determination R^2 > 0.95 and a mean squared error (RMSE) less than a set threshold (e.g., 5% of the response mean), to ensure its reliability in the optimization process. This model can replace finite element simulation for iterative calculations of the optimization algorithm, thereby transforming the originally time-consuming simulation process into fast algebraic operations and significantly improving optimization efficiency.

[0100] Specifically, this step is particularly suitable for engineering problems such as mountain photovoltaic supports that require evaluation of multiple sets of parameters. By introducing a response surface model, efficient optimization of material costs can be achieved while ensuring that structural performance meets strength, stiffness, and frequency constraints, and at the same time reducing reliance on high-performance computing resources.

[0101] This invention discloses a multi-objective optimization method for flexible photovoltaic (PV) supports in mountainous environments. By constructing a parametric finite element model and incorporating dynamic wind loads validated through wind tunnel testing for time-history analysis, it achieves accurate simulation of the nonlinear dynamic response of the structure under complex mountain wind fields. This method further combines normalized sensitivity analysis to identify key design variables and employs a genetic algorithm to automatically optimize and verify the design while strictly satisfying multiple performance constraints, with the goal of minimizing total material cost. This achieves a closed-loop process from accurate modeling, load simulation, variable selection to intelligent optimization, effectively overcoming the core shortcomings of traditional design methods such as insufficient accuracy and poor economic efficiency. While significantly ensuring structural safety and compliance with regulations, it achieves refined control of material costs, improving the overall technical and economic efficiency of mountainous PV projects.

[0102] Example 2 To achieve the above invention, embodiments of the present invention also provide specific steps of a multi-objective optimization method for flexible photovoltaic supports in mountainous environments, such as... Figure 2 As shown, it includes: S101, Create a parametric finite element model.

[0103] Specifically, a parametric model of the flexible support system was established using finite element software such as MIDAS GEN. The core of the model includes: the end anchor system, the intermediate support system, the load-bearing main cable, and the stabilizing cable. The design variables to be optimized were set as model parameters, mainly including: the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, the moment of inertia of the intermediate support rod, and the concrete volume of the side anchor foundation.

[0104] Furthermore, establishing a parametric model for the flexible scaffold system specifically includes: First, key nodes are established based on the span and support column locations of the support structure. Then, elements are created based on these nodes, defining their material properties (e.g., high-strength steel cables, steel) and cross-sectional characteristics. For example, load-bearing cables and stabilizing cables can be defined as tension-only elements (e.g., truss elements or cable elements), while support members are defined as beam elements; accurately simulating the connection between the structure and the ground is crucial. End anchor points are typically defined as fixed supports, while the bottom of intermediate support columns can be defined as hinged or fixed depending on the actual foundation type. The aforementioned design variables (e.g., main cable cross-sectional area, stabilizing cable cross-sectional area, support rod cross-sectional moment of inertia) are associated with the model's material and section libraries. In this way, by simply changing the values ​​of these parameters, the software can automatically update the geometric and physical properties of the entire finite element model.

[0105] Specifically, this step digitizes the design object, providing a basis for accurate analysis.

[0106] S102, Apply mountain wind load.

[0107] Specifically, based on meteorological data from the project site, a wind pressure time-history curve conforming to the characteristics of mountain winds is generated and applied as a dynamic load to the finite element model. Wind tunnel test data is used to verify and correct the load model, ensuring the authenticity of the input conditions. This includes: Core Principles and Formulas: The generation of wind pressure time history ω(t) is based on fundamental formulas of structural wind engineering. The instantaneous wind speed V(t) acting on the structure can be decomposed into average wind speed. The sum of V and the fluctuating wind speed v(t), i.e., V(t) = V+v(t). Based on the wind pressure calculation formula derived from Bernoulli's equation, the wind pressure time history is: ω(t) = 1 / 2 × ρC d C e [ V+v(t)] 2 ; in, ρ Air density (standard value is approximately 1.25 kg / m³) 3 ), C d This is the shape coefficient of the structure or component, determined based on wind tunnel tests or specifications. C e This is the wind pressure height variation coefficient, reflecting the influence of terrain roughness and height on the mean wind. V represents the design average wind speed at the reference height. v(t) is the time history of fluctuating wind speed with statistical characteristics of mountain winds, which needs to be artificially simulated.

[0108] Specifically, the simulation of the fluctuating wind speed time history v(t): This invention uses a ρ-order autoregressive model (AR(ρ)) as the mathematical implementation of the linear filter, and its recursive formula is as follows: v(t) = ∑ i v ( t i Δ t )+ σ N ( t ); Where, Δ t The time step is determined according to the Nyquist sampling theorem and the highest frequency of interest, and is typically taken as 0.1. 0.2s. ρ is the model order, typically 2 to 4. i These are the autoregressive coefficients. This is the core of this method, determining the frequency characteristics (i.e., the shape of the power spectrum) of the output sequence v(t). These coefficients are obtained by solving the Yule-Walker equation, which depends on the target power spectrum S. v (f) The theoretical autocorrelation function R(τ) corresponding to the mountain-corrected Davenport spectrum. Σ The standard deviation of the white noise sequence is used to control the variance (turbulence energy) of the output sequence v(t), and its value is determined by the target spectrum S. v (f) and coefficients i The standard Gaussian white noise sequence with a mean of 0 and a variance of 1, N(t), is used as the driving signal.

[0109] Furthermore, the process is applied to the finite element model, specifically including: Step 1: Data preparation and environment setup: Input the basic design wind speed V0, ground roughness category, wind profile index α, etc. for the project location, and calculate the average wind speed at different heights. V and coefficients C e Determine the target fluctuating wind power spectral density function S. v (f) and the corresponding turbulence intensity I u Step 2: Generating wind pressure time history data in an external computing environment includes: using scientific computing software (such as MATLAB, Python), and based on the principles of the AR model described above, writing an algorithm to generate data that satisfies S... v (f) and I u The long-term fluctuating wind speed time history sample v(t); substitute v(t) into the wind pressure calculation formula ω(t)=1 / 2× ρC d Ce [ V+v(t)] 2 Step 1: Generate a wind pressure time history data file (such as TXT or CSV format, with columns for time and corresponding pressure values) acting on the windward side of the structural reference. Step 2: Apply the time history load to the MIDAS GEN finite element model, including: In MIDAS GEN's "Loads > Time History Analysis Data > Time History Load Functions", select the "User Defined" type and directly import or paste the ω(t) data generated in Step 2 in tabular form; Create a new time history analysis case, and the analysis type is usually selected as "Direct Integration Method"; In the load mode, select the load type (such as pressure in "Nodal Load" or "Element Load"), assign the defined time history load function to the corresponding structural nodes or element surfaces, and correctly specify the load direction (global coordinate X / Y direction or normal direction); Define the analysis duration (matching the length of ω(t)), time step, and damping ratio (Rayleigh damping or constant damping ratio, which can be 0.5%~1.5% for flexible steel structures).

[0110] Specifically, this step aims to realistically simulate the dynamic characteristics of mountain winds, replacing the crude static equivalence, which is a prerequisite for achieving precise design.

[0111] S103, Perform parameter sensitivity analysis.

[0112] Parameter studies are conducted using finite element method (FEM) software to analyze the influence of various design variables on the structural response (such as maximum stress, maximum displacement, and fundamental frequency). Specific analysis steps and methods are as follows: S1031, Select analysis variables and response objectives: Select the independent design parameters to be studied, which typically include: main cable cross-sectional area, stabilizing cable cross-sectional area, support rod section moment of inertia, initial prestress of the cable, etc.; Define the key performance indicators to be controlled, i.e. response objectives, which typically include: maximum equivalent stress (strength safety), maximum nodal displacement (stiffness and applicability), structural fundamental frequency (dynamic characteristics and wind vibration resonance risk), and total material cost (economic efficiency).

[0113] S1032, Univariate Disturbance Analysis: Using the "Control Variable Method", under the premise that all other design variables remain unchanged at the baseline value, the value of a certain variable to be analyzed (such as the cross-sectional area of ​​the main cable) is changed one by one. Usually, a series of discrete points are taken above and below the baseline value (such as ±10%, ±20%, ±30%).

[0114] S1033, Calculate the sensitivity coefficient: To quantify the degree of influence, a normalized relative sensitivity coefficient S is introduced. ij The calculation formula is as follows: ; Among them, S ij Represents the j-th design parameter Pj The response R of the i-th structure i The sensitivity coefficient. P j0 With R i0 They are parameters P j and R i The baseline value (initial design value). ΔP j and ΔR i These represent the change in the parameter and the resulting change in the response, respectively. This coefficient is essentially the ratio of the relative rate of change of the response value to the relative rate of change of the parameter value. Its absolute value directly reflects the significance of the influence (similar to a sensitivity coefficient). A value greater than 0.1 indicates that the parameter P... j For response R i It has a significant impact and is a key optimization variable. If it is approximately equal to 0, it means that the impact is negligible.

[0115] S1034, Results Analysis and Decision Making: Plot the curves of each response target as a function of a single parameter; form a sensitivity coefficient matrix table, where row i represents the response and column j represents the parameter.

[0116] Specifically, this step aims to identify the key variables that have the greatest impact on structural performance so that they can be addressed in subsequent optimizations.

[0117] S104, implement multi-objective optimization design.

[0118] Specifically, the optimized mathematical model is as follows: Total cost = (Main cable material density × Main cable length × Main cable cross-sectional area × Main cable unit price) + (Stabilizing cable material density × Stabilizing cable length × Stabilizing cable cross-sectional area × Stabilizing cable unit price) + (Support rod weight × Support rod unit price) + (Concrete usage × Concrete unit price); Constraints: Strength constraint: Maximum equivalent stress of the structure ≤ Allowable stress of the material; Stiffness constraint: Maximum displacement of the structure ≤ One percent of the span; Frequency constraint: First-order natural frequency of the structure ≥ Frequency limit set to avoid resonance; Using optimization algorithms such as genetic algorithms, the system automatically searches for the combination of design parameters that minimizes the total material cost within the "solution space" that satisfies all constraints.

[0119] Specifically, the purpose of this step is to find the optimal balance point through calculation in the complex "safety-economy" dilemma. S105, Output and Verification.

[0120] Specifically, the optimal combination of cross-sectional parameters is output to form the final, optimized flexible support design scheme; this scheme is then subjected to final verification calculations to ensure that it meets all specifications and safety requirements.

[0121] This invention provides specific steps for a multi-objective optimization method for flexible photovoltaic supports in mountainous environments. By constructing a high-fidelity parametric model and introducing dynamic wind loads verified through wind tunnel testing, accurate simulation of the structure's nonlinear dynamic response is achieved. Based on normalized sensitivity analysis, key design variables are identified, and an intelligent optimization algorithm is used to automatically find the optimal solution with the goal of minimizing total material cost while strictly satisfying multiple performance constraints. This transforms the traditional design process, which relies on experience and static calculations, into a closed-loop optimization system integrating accurate simulation, quantitative analysis, and automatic optimization. It fundamentally solves the core technical challenge of balancing safety, economy, and design accuracy in the design of flexible photovoltaic supports in mountainous areas, significantly improving the reliability and overall technical and economic efficiency of the design scheme.

[0122] Example 3 To achieve the above invention, such as Figure 3 As shown, this embodiment also provides a multi-objective optimization device 10 for flexible photovoltaic supports in mountainous environments. The device 10 includes: The parametric modeling module 100 is used to establish a parametric finite element model of the flexible photovoltaic support system. It uses the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, the moment of inertia of the support rod section, and the volume of concrete in the side anchor foundation as adjustable design variables, and links the material library and the section library to achieve parametric updates.

[0123] The dynamic wind load generation module 200 is used to generate dynamic wind load time history data that conforms to the characteristics of mountain winds based on meteorological data of the project location. After verification by wind tunnel test, the data is applied to the parameterized finite element model to perform time history analysis to obtain structural response data.

[0124] The sensitivity analysis module 300 is used to perform normalized sensitivity analysis on structural response data, quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out key optimization variables that significantly affect the response.

[0125] The multi-objective optimization module 400 is used to perform multi-objective optimization search on the key optimization variables within the solution space that satisfies strength constraints, stiffness constraints and frequency constraints, with the goal of minimizing the total material cost, and outputs the optimal parameter combination and verifies its safety and compliance with specifications.

[0126] The joint prediction and loss optimization module 400 is used to set up a health status prediction head and a lifetime prediction head based on a shared global representation, construct a joint loss function that includes a health error term, a lifetime error term, a consistency constraint term, and a monotonicity constraint term, and train the model by combining a sliding time window and a dynamic edge weight update mechanism to simultaneously optimize the health status and lifetime prediction results.

[0127] In one embodiment of the present invention, it further includes: a response surface modeling module, used to construct a response surface model as an alternative model for finite element calculation, and to generate an approximate functional relationship between the structural response and design variables by selecting sample points, so as to reduce the number of calls to finite element calculation during the optimization process.

[0128] This invention provides a multi-objective optimization device for flexible photovoltaic supports in mountainous environments. Through the synergistic effect of parametric modeling, dynamic wind load generation, sensitivity analysis, and intelligent optimization modules, a closed-loop optimization system integrating accurate simulation, quantitative evaluation, and automatic optimization is constructed. This device achieves accurate simulation of the nonlinear dynamic response of structures under complex mountain wind fields and, based on quantitative analysis, locks in key variables for cost-optimal design, effectively overcoming the shortcomings of traditional methods that rely on static calculations and empirical coefficients. This invention significantly improves the level of refined control over material usage and the overall technical and economic efficiency of the design scheme while ensuring structural safety and compliance with regulations.

[0129] To implement the methods of the above embodiments, the present invention also provides a computer device, such as... Figure 4 As shown, the computer device 600 includes a memory 601 and a processor 602; wherein, the processor 602 reads the executable program code stored in the memory 601 to run a program corresponding to the executable program code, so as to implement the various steps of the multi-objective optimization method for flexible photovoltaic support in mountainous environments described above.

[0130] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a multi-objective optimization method for flexible photovoltaic supports in mountainous environments as described in the foregoing embodiments.

[0131] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0132] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A multi-objective optimization method for flexible photovoltaic supports in mountainous environments, characterized in that, include: S1. Establish a parametric finite element model of the flexible photovoltaic support system, and use the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stable cable, the moment of inertia of the support rod section and the volume of concrete of the side anchor foundation as adjustable design variables, and link the material library and the section library to achieve parametric updates. S2, Based on the meteorological data of the project site, dynamic wind load time history data that conforms to the characteristics of mountain winds is generated. After being verified by wind tunnel test, it is applied to the parameterized finite element model and time history analysis is performed to obtain structural response data. S3. Perform normalized sensitivity analysis on the structural response data to quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out the key optimization variables that significantly affect the response. S4. Using a genetic algorithm, within the solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, the algorithm performs a multi-objective optimization search on the key optimization variables with the goal of minimizing the total material cost. The algorithm outputs the optimal parameter combination and verifies its safety and compliance with specifications.

2. The method as described in claim 1, characterized in that, Establish a parametric finite element model of the flexible photovoltaic support system, including: S11, establish key nodes based on the span of the support and the position of the support column, and divide the nodes into end anchor system nodes, intermediate support system nodes, load-bearing main cable nodes and stabilizing cable nodes; S12, when defining the element type, set the load-bearing main cable and the stabilizing cable as cable elements that only bear axial tension, and set the supporting rods as beam elements that can bear bending moment and shear force, and dynamically associate the physical properties of the design variables through the material library.

3. The method as described in claim 1, characterized in that, Dynamic wind load time history data conforming to mountain wind characteristics is generated based on meteorological data of the project site, including: S21 uses a ρ-order autoregressive model to simulate the time history of fluctuating wind speed, where ρ takes values ​​from 3 to 5, and solves for the autoregressive coefficients using the Yule-Walker equation. ; S22, Davenport spectrum based on mountain correction Calculate the standard deviation of a white noise sequence This is to control the variance of the output sequence.

4. The method as described in claim 1, characterized in that, Normalized sensitivity analysis of structural response data was performed, including: S31, using the normalized relative sensitivity coefficient formula The influence of quantization parameters, among which In response to changes, For parameter changes; S32, by plotting the response-parameter curve under single-parameter perturbation, key optimization variables with an absolute value of sensitivity coefficient greater than 0.1 are selected.

5. The method as described in claim 1, characterized in that, The genetic algorithm is used to optimize within the solution space that satisfies strength, stiffness, and frequency constraints, including: S41 defines the total cost as: (Main cable material density × Main cable length × Main cable cross-sectional area × Main cable unit price) + (Stabilizing cable material density × Stabilizing cable length × Stabilizing cable cross-sectional area × Stabilizing cable unit price) + (Support rod weight × Support rod unit price) + (Concrete usage × Concrete unit price), and uses real number coding to parameterize the design variables. S42 uses the penalty function method to handle constraints. When the maximum equivalent stress of the structure exceeds the allowable stress of the material, an exponential penalty term is applied to the objective function.

6. The method as described in claim 1, characterized in that, Also includes: S5. A response surface model is constructed as an alternative model to finite element calculation. By selecting sample points, an approximate functional relationship between the structural response and design variables is generated, thereby reducing the number of calls to finite element calculation during the optimization process.

7. A multi-objective optimization device for flexible photovoltaic supports in mountainous environments, characterized in that, include: The parametric modeling module is used to establish a parametric finite element model of the flexible photovoltaic support system. It uses the cross-sectional area of ​​the main cable, the cross-sectional area of ​​the stabilizing cable, the moment of inertia of the support rod section, and the volume of concrete in the side anchor foundation as adjustable design variables, and links the material library and the section library to achieve parametric updates. The dynamic wind load generation module is used to generate dynamic wind load time history data that conforms to the characteristics of mountain winds based on meteorological data of the project location. After being verified by wind tunnel test, the data is applied to the parameterized finite element model and time history analysis is performed to obtain structural response data. The sensitivity analysis module is used to perform normalized sensitivity analysis on structural response data, quantify the influence of each design variable on the maximum equivalent stress, maximum nodal displacement, structural fundamental frequency and total material cost, and screen out key optimization variables that significantly affect the response. The multi-objective optimization module is used to perform multi-objective optimization search on the key optimization variables within the solution space that satisfies strength constraints, stiffness constraints, and frequency constraints, with the goal of minimizing the total material cost. It outputs the optimal parameter combination and verifies its safety and compliance with specifications.

8. The apparatus as claimed in claim 7, characterized in that, Also includes: The response surface modeling module is used to construct a response surface model as an alternative model for finite element calculation. By selecting sample points, it generates an approximate functional relationship between the structural response and design variables, thereby reducing the number of calls to finite element calculation during the optimization process.

9. An electronic device, comprising: processor; The memory stores executable instructions; when the processor executes the instructions, it implements the multi-objective optimization method for flexible photovoltaic supports in mountainous environments as described in any one of claims 1-6.

10. A computer-readable storage medium storing a computer program, which, when executed by a processor, implements a multi-objective optimization method for flexible photovoltaic supports in mountainous environments as claimed in any one of claims 1-6.

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