Earthquake economic loss optimization reinforcement inversion method

Abstract

The invention discloses an earthquake economic loss optimization reinforcement inversion method. The method comprises the following steps: extracting initial shear strength and rigidity of each floor of a target building from design software (such as PKPM); determining small, medium and large earthquake intensity and occurrence probability of the site; the economic loss of each intensity level is calculated based on a loss model, and an optimization design problem taking weighted annual loss minimization as a target is constructed in combination with the occurrence probability; designing variables and constraint conditions: taking the ratio (strength coefficient) of the shear strength of each floor to an initial value as a design variable, and keeping the total strength and the floor rigidity unchanged as constraints; carrying out efficient solution by adopting an artificial intelligence optimization algorithm and carrying a real-time online updated proxy model to obtain optimal strength coefficient distribution; and a result is fed back to original design software to automatically complete reinforcement correction and specification review. The method can be directly embedded into an existing design process, and real-time and dynamic post-earthquake loss minimization design is achieved on the premise that the manufacturing cost is hardly increased.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering and structural seismic design technology, specifically relating to a method for optimizing reinforcement inversion based on earthquake economic losses. Background Technology

[0002] Currently, architectural engineering design commonly employs specialized software such as PKPM for structural analysis and reinforcement design. This software primarily operates based on existing standards such as the "Code for Seismic Design of Buildings" (GB 50011-2010), with the design objective focusing on ensuring performance requirements of "no damage in minor earthquakes, repairability in moderate earthquakes, and no collapse in major earthquakes." However, this traditional design system does not explicitly consider direct economic losses from earthquakes as a design objective, making it difficult to proactively control post-earthquake repair costs and functional disruption losses during the design phase.

[0003] Existing earthquake damage surveys show that even if a structure meets code requirements and does not collapse, damage to numerous non-structural components (such as partition walls, ceilings, curtain walls, equipment pipelines, etc.) can still cause enormous economic losses, often accounting for more than 70% of total building losses. Therefore, merely meeting code safety requirements is insufficient to guarantee controllable post-earthquake economic losses. Under the premise of meeting current codes, how to further reduce future earthquake economic losses through reasonable adjustments to reinforcement distribution has significant practical engineering implications.

[0004] In recent years, performance-based seismic assessment methods have gradually developed. By constructing an analysis chain of "seismic motion—structural response—component damage—building performance," multiple performance indicators of buildings under different seismic levels can be quantitatively assessed. However, these methods are currently mostly used for post-earthquake performance assessment or scientific research and have not yet been effectively integrated into the routine design process in the early stages of engineering projects. Existing loss-based assessment and optimization often rely on large-scale nonlinear dynamic time history analysis, which is complex and time-consuming in modeling and calculation. Therefore, these methods are difficult to integrate with mainstream commercial design software such as PKPM, cannot complete rapid optimization within a limited design cycle, and have poor engineering applicability.

[0005] In summary, engineering practice urgently needs a solution: given the architectural design and preliminary structural reinforcement, based on conventional design results, this solution can help owners achieve the design that minimizes future economic losses from earthquakes without increasing costs through efficient reinforcement distribution inversion optimization. Furthermore, this method needs to be able to be embedded in existing design processes such as PKPM to ensure computational efficiency and engineering applicability. Summary of the Invention

[0006] The purpose of this invention is to address the problems in existing seismic design, such as the failure to explicitly incorporate seismic economic losses into structural design objectives and the difficulty in efficiently integrating with commonly used design software. This invention proposes a method for optimizing reinforcement distribution based on seismic economic losses. This method, while maintaining the initial construction cost, optimizes reinforcement distribution through swarm intelligence algorithms and surrogate models, thereby minimizing seismic economic losses. It features high computational efficiency and strong engineering applicability.

[0007] To achieve the above objectives, this invention provides a method for optimizing reinforcement inversion based on earthquake economic losses, comprising:

[0008] Obtain the target building structure model and the initial yield shear strength and stiffness of each floor from structural design software;

[0009] Divide earthquake intensity levels into multiple levels and their probability of occurrence;

[0010] Construct or invoke an earthquake economic loss assessment model to determine the expected direct economic loss at each earthquake intensity level, and combine it with the probability of occurrence to construct the annual economic loss as the optimization objective function;

[0011] Design variables and constraints: The variable is the ratio of the yield shear strength of each floor to be optimized to the initial yield shear strength of each floor, i.e., the strength coefficient; the constraint is that the sum of the yield shear strength of the total floors remains unchanged, and the stiffness of each floor remains unchanged.

[0012] An artificial intelligence optimization algorithm is used, combined with an online training and real-time updated surrogate model, to solve the problem and obtain the optimal strength coefficient for each floor, thereby determining the optimized yield shear strength of each floor.

[0013] Furthermore, the optimal strength coefficient of each floor is used as the reinforcement adjustment coefficient of each floor and fed back to the original structural design software, thereby adjusting the total amount of stirrups used in each floor and completing the reinforcement inversion and redesign.

[0014] Furthermore, the intensity levels of earthquakes and their probabilities of occurrence are classified, including:

[0015] earthquake level The earthquakes are classified into three intensity levels: minor, moderate, and major, based on the target site. The corresponding exceedance probabilities are obtained, and the annual occurrence probability used for weighted calculation of economic losses is then obtained.

[0016] Furthermore, the constructed or invoked earthquake economic loss assessment model is open-source and compatible with component-based (such as FEMA P-58 loss assessment) or floor-based loss assessment methods. It calculates damage probability and repair costs using engineering demand parameters, and then aggregates these to obtain the overall economic loss of the building. The general steps are as follows:

[0017] The building is divided into several performance groups g, namely the structural component group, the non-structural displacement-sensitive component group, and the non-structural acceleration-sensitive component group;

[0018] Using the engineering requirement parameter EDP as the independent variable, a vulnerability function in the form of a log-normal distribution is used to describe the exceedance probability of the performance group under different damage states;

[0019] The economic loss for all damage states is obtained by multiplying the probability of each damage state and the resulting loss.

[0020] Furthermore, the acquisition of the Engineering Requirements Parameters (EDP) includes:

[0021] For each earthquake level Select several actual ground motion records r that match the engineering site conditions;

[0022] Nonlinear dynamic time history analysis was performed on the target building structure model: for each seismic level For each record r and each floor i, the displacement time history of each floor is obtained. and floor acceleration time history This allows us to calculate the maximum inter-story drift angle and peak floor acceleration for each floor under different seismic levels, which can then be used as engineering requirement parameters.

[0023] Furthermore, during the optimization process, a proxy model is constructed and updated online in real time: the evaluated combinations of intensity coefficients and their corresponding true objective function values ​​are used as sample points to accumulate and form a training dataset, which is then used to train the regression model, establishing an intensity coefficient vector to EAL (Equal Algorithm). Nonlinear regression mapping;

[0024] In the optimization algorithm iteration, when the surrogate model prediction accuracy is ≥95% and R... 2 When the value is ≥0.9, the objective function value of the structure is quickly predicted by using a surrogate model.

[0025] Furthermore, the artificial intelligence optimization algorithm is a swarm intelligence optimization algorithm, such as particle swarm optimization or ant colony optimization; the regression algorithm used by the surrogate model includes neural networks, random forests, Bayesian networks, or support vector regression models.

[0026] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the above-described method for optimizing reinforcement inversion based on seismic economic losses.

[0027] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for optimizing reinforcement inversion of earthquake economic losses.

[0028] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for optimizing reinforcement inversion based on earthquake economic losses.

[0029] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0030] 1. It achieves efficient integration and closed-loop application with structural design software. Based on the conventional design results of software such as PKPM, the optimization results can be directly fed back to the initial design as reinforcement adjustment instructions, forming an automated process of "design-optimization-redesign". It is suitable for the reinforcement redesign of various types of engineering structures and has strong engineering applicability.

[0031] 2. Explicitly incorporate earthquake economic losses into the design phase. Using annual economic losses as the optimization target, and while ensuring the owner's construction cost remains essentially unchanged, intelligent optimization of floor shear strength achieves a design advancement from "ensuring safety" to "actively controlling economic losses," thus addressing the shortcomings of traditional designs in considering economic losses.

[0032] 3. A highly efficient hybrid optimization framework combining intelligent optimization algorithms and online surrogate models. This framework employs a swarm intelligence optimization algorithm for global exploration and introduces an online, real-time updated surrogate model for rapid prediction. By training a high-precision surrogate model with a small amount of real-world analytical data, and then leveraging the surrogate model to accelerate the optimization search, this framework significantly reduces the reliance of traditional optimization methods on massive nonlinear time-history analysis. It achieves a significant improvement in computational efficiency while maintaining accuracy, making it feasible for applications with complex structures. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This invention provides a flowchart of a structural seismic optimization design method based on earthquake economic losses.

[0035] Figure 2 This is a schematic diagram of a structural model provided for an embodiment of the present invention.

[0036] Figure 3This is a schematic diagram of component damage and loss assessment provided in an embodiment of the present invention.

[0037] Figure 4 The flowchart of the "swarm intelligence algorithm + online agent model" provided in the embodiment of the present invention.

[0038] Figure 5 This is a schematic diagram of an online proxy model provided in an embodiment of the present invention.

[0039] Figure 6 This is a comparison chart of economic losses before and after structural optimization under different earthquake intensities, provided as an embodiment of the present invention.

[0040] Figure 7 The distribution of inter-story drift angle and peak floor acceleration response under major earthquake intensity before and after structural optimization is provided in the embodiments of the present invention.

[0041] Figure 8 The normalized distribution diagram of floor shear strength before and after structural optimization is provided for an embodiment of the present invention. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features of the following embodiments and implementations can be combined with each other.

[0043] This invention discloses a seismic economic loss optimization reinforcement inversion method that can be integrated into structural design software. Its core lies in establishing an "analysis-optimization-feedback" closed loop that seamlessly integrates with existing design processes. It is applicable to various common building structure types, including reinforced concrete frames and shear wall structures. The method includes the following steps:

[0044] Step S1: Determine the earthquake intensity level and probability of occurrence based on Chinese seismic design code.

[0045] S1-1: Based on the engineering survey data and the "Code for Seismic Design of Buildings" (GB 50011-2010), determine the site category (e.g., Class I, Class II, Class III) and design seismic group of the building site. Determine the seismic design flood control levels for minor, moderate, and major earthquakes for this project.

[0046] Minor earthquakes (frequent earthquakes): 63% probability of occurrence within 50 years;

[0047] Moderate earthquake (design earthquake): 10% probability of exceeding the target in 50 years;

[0048] Major earthquake (rare earthquake): 2% probability of occurrence within 50 years.

[0049] S1-2: To facilitate the calculation of annual economic losses, this invention converts the above-mentioned 50-year exceedance probability into an annual exceedance probability: The formula is as follows:

[0050]

[0051] in, The probability of exceeding the target value in 50 years.

[0052] S1-3: After calculating the annual exceedance probability for small, moderate, and large earthquake intensity levels, further calculate the annual occurrence probability used for economic loss weighting:

[0053] Probability of a major earthquake:

[0054] Probability of a moderate earthquake:

[0055] Probability of minor earthquakes:

[0056] in, , , These are the annual exceedance probabilities for small, moderate, and large earthquakes, respectively. It serves as the weight of the three discrete earthquake intensity points in the subsequent annual economic loss calculation.

[0057] Step S2: Obtain initial structural design parameters from structural design software

[0058] S2-1: Create a target building structure model in commercial structural design software (such as PKPM), input the building layout, component cross-sectional dimensions, material strength, floor load and seismic fortification parameters, and complete conventional seismic design and reinforcement calculation according to current standards.

[0059] S2-2: Extract the following key parameters from PKPM via software interface or standard data exchange file as the input basis for this optimization method:

[0060] Quality of each floor: ;

[0061] Equivalent shear stiffness of each floor: (Mainly determined by the cross-sectional dimensions of beams and columns, which remain unchanged during the optimization process);

[0062] Initial yield shear strength of each floor: (Determined by the amount of reinforcement, used as an optimization variable);

[0063] S2-3: Define the sum of the initial layer shear strengths:

[0064]

[0065] Where N is the number of floors;

[0066] In subsequent optimizations, to ensure that the initial construction cost of the building structure does not increase, the core constraint is:

[0067]

[0068] Step S3: Structural nonlinear dynamic time history analysis (used to generate high-precision training samples)

[0069] This step involves obtaining the true structural response, providing data for accurate loss assessment and surrogate model training. Note that the structural nonlinear dynamic time history analysis can be obtained through a simplified model or based on structural design software.

[0070] S3-1: Establish a simplified multi-degree-of-freedom model suitable for rapid iterative analysis

[0071] The building structure is simplified into an N-layer multi-degree-of-freedom model, with one horizontal degree of freedom set for the i-th layer;

[0072] The quality of the i-th layer is taken as The floors are connected by non-linear shear springs, and the elastic stiffness of the springs is a fixed value. Yield shear strength is the variable to be optimized. ;

[0073] By adopting the assumption of a rigid floor slab, the mass of the components in the floor plane is concentrated at the floor mass point.

[0074] S3-2: Selection and Amplitude Modulation of Seismic Ground Motion Records

[0075] For the three levels of minor, moderate and major earthquakes: select no fewer than 7 actual earthquake records that match the engineering site conditions and adjust the amplitude according to the target spectrum or peak ground acceleration (PGA).

[0076] S3-3: Nonlinear Dynamic Time History Analysis

[0077] For each earthquake level (Minor earthquakes, moderate earthquakes, major earthquakes) and each ground motion record r:

[0078] The amplitude-modulated seismic acceleration time history is applied to the bottom of the structural model;

[0079] The displacement time histories of each floor were calculated using open-source or commercial finite element platforms such as OpenSees. and floor acceleration time history .

[0080] S3-4: Extraction of Engineering Requirements Parameters (EDP)

[0081] For each level k, each record r, and each layer i, calculate:

[0082] Maximum inter-story drift angle

[0083]

[0084] Among them, h i Let be the floor height of the i-th floor;

[0085] Peak floor acceleration

[0086]

[0087] Then, statistical processing (such as taking the mean or median) is performed on multiple records at the same seismic level to obtain representative engineering requirement parameters for each floor at that level:

[0088] These EDPs will serve as the basis for subsequent damage and economic loss calculations, as well as for training surrogate models.

[0089] Step S4: Assessment of Direct Economic Losses from Earthquake

[0090] The loss assessment module in this invention is open-source; its core function is to map Engineering Requirements Parameters (EDP) to monetary losses. This embodiment demonstrates a general process (such as...). Figure 3 As shown in the figure, it can actually be equipped with standard evaluation systems such as FEMA P-58.

[0091] S4-1: Based on the selected evaluation criteria (such as FEMA P-58, HAZUS, floor loss function), determine the threshold values ​​of engineering requirement parameters and repair cost ratios for various structural and non-structural components under different damage states.

[0092] S4-2: Performance Group Division

[0093] The building is divided into several performance groups. including but not limited to:

[0094] Structural component groups: beams, columns, shear walls, etc.;

[0095] Non-structural displacement-sensitive component groups: infill walls, partition walls, exterior wall panels, etc.;

[0096] Non-structural acceleration-sensitive component groups: ceilings, electromechanical equipment, pipelines, etc.

[0097] S4-3: Calculate the probability of each damage state based on the vulnerability curve.

[0098] A vulnerability function in the form of a log-normal distribution is used to describe the exceedance probability of the performance group under different damage states. The EDPs obtained in step S3 for each floor are used as input to calculate the probability of various components reaching different damage states on each floor.

[0099]

[0100] in:

[0101] It is the standard normal distribution function;

[0102] The median required threshold for performance group g to reach the damage state ds;

[0103] is the logarithmic standard deviation.

[0104] The probability of the damaged state ds is:

[0105]

[0106] S4-4: Aggregated economic loss.

[0107] Repair cost ratio for each damage state (ds) This indicates the proportion of repair costs to replacement costs. Damage states are generally categorized as: no damage, minor damage, moderate damage, severe damage, and complete damage; specific repair costs can be determined based on the component damage database used (e.g., FEMA P58, HAZUS, floor loss function, etc.). Then, at the seismic level... Below, the expected direct economic loss of the i-th layer performance group g is:

[0108]

[0109] The entire building is at the level The expected direct loss is:

[0110]

[0111] Step S5: Calculation of Annual Economic Loss

[0112] The annual occurrence probabilities of small, moderate, and large earthquakes obtained in step S1 And the expected direct loss at the three levels obtained in step S4 , , Construct the expected annual economic loss:

[0113]

[0114] EAL is the objective function value used in this invention to evaluate the merits of a reinforcement scheme.

[0115] Step S6: Optimization solution based on the collaboration of swarm intelligence algorithm and online agent model

[0116] This step is the core of the invention's efficient global optimization. A swarm intelligence algorithm (e.g., particle swarm optimization) is used as the main optimizer, and an online, real-time updated surrogate model is embedded to drive the optimization search with minimal cost of expensive time-series analysis.

[0117] S6-1: Design variables and constraints: The adjustment coefficient of yield shear strength for each floor is used as the design variable.

[0118]

[0119] The constraints that need to be satisfied for optimization are:

[0120] The total layer shear strength remains unchanged:

[0121] The layer stiffness remains essentially unchanged: (Fixed value)

[0122] S6-2: Particle Swarm Optimization (PSO) Algorithm Parameter Settings

[0123] This invention preferably uses a particle swarm optimization algorithm for global search, and an example of its parameter settings is as follows:

[0124] Particle population size:

[0125] Maximum number of iterations:

[0126] Variable range: ,For example

[0127] Particle velocity and position update: using the standard PSO formula, cognitive factor Social factors The value is typically between 1.5 and 2.0, representing the inertia weight. A linear decreasing strategy can be adopted.

[0128] Constraint handling: For each newly generated particle position (i.e., a set of constraints) The system is scaled proportionally to ensure it strictly meets the total strength constraint, and variables that exceed the boundary are truncated.

[0129] S6-3: Online Construction, Update, and Collaborative Optimization Mechanism of the Agent Model

[0130] To overcome the bottleneck of computational complexity in optimization, a proxy model that works in conjunction with PSO is constructed.

[0131] (1) Proxy Model Role: Establishing a proxy model role based on design variables To the objective function Approximate mapping It is used for rapid prediction.

[0132] (2) Initial training set generation: Before the optimization loop begins, an initial training set covering the design space is generated using experimental design methods (such as Latin hypercube sampling). The sample is calculated using the complete S3-S5 process to determine its true value. This constitutes the initial high-precision training dataset. .

[0133] (3) Real-time online update of the agent model:

[0134] This invention preferably uses the Gaussian process regression model fitrgp, which is included in the MATLAB Statistics and Machine Learning Toolbox, as a surrogate model to establish... Nonlinear regression mapping;

[0135] Other regression models, such as neural networks, random forests, and Bayesian algorithms, can also be incorporated as needed. This invention is not limited to a specific model type.

[0136] (4) Collaborative Iterative Process of PSO and Proxy Model:

[0137] a. Rapid Prediction and Candidate Selection: In each PSO iteration, for all newly generated particle positions (candidate solutions), the current surrogate model is first used. Perform quickly Forecasting and uncertainty estimation.

[0138] b. Precise evaluation of high-value samples: Based on the prediction results (e.g., small predicted values) and model uncertainties (e.g., large variance), select a subset of the most promising or informative particles (e.g., 5-10 per generation) and perform an expensive but sophisticated S3-S5 full-process analysis on them to obtain accurate data. value.

[0139] c. Real-time incremental update of the proxy model: The new data obtained in step b... The sample pairs are immediately added to the training dataset and applied to the proxy model. Perform online incremental training or retraining to obtain an updated and more accurate model. .

[0140] d. Elite Preservation and Population Update: The accurate evaluated true fitness of particles is used for elite selection and global optimum update in PSO. The PSO algorithm guides the search direction of the next generation of particles based on both true fitness and surrogate model predictions.

[0141] S6-4: Optimization Termination and Output of Optimal Solution

[0142] When the maximum number of iterations is reached or global optimum for multiple consecutive generations The optimization process is terminated when the improvement is less than a preset threshold (e.g., 0.1%).

[0143] Output all precisely evaluated samples throughout the entire optimization history. The combination of strength coefficients with the smallest value As the final optimal solution.

[0144] Step S7: Reinforcement Inversion and PKPM Redesign Closed Loop

[0145] S7-1: Engineering mapping of optimal strength coefficient and reinforcement adjustment

[0146] The optimal strength coefficient obtained through optimization It is directly used as an adjustment factor for the floor reinforcement level. Under the condition that the cross-sectional dimensions of the member remain unchanged, the floor yield shear strength can be approximated. The total cross-sectional area of ​​stirrups in the main shear-resistant members (such as frame beams and columns) of this floor They are directly proportional. Therefore, in engineering practice, the stirrups can be adjusted proportionally:

[0147]

[0148] in, This represents the total amount of stirrups used in the initial design. This represents the optimized amount of stirrups. The longitudinal reinforcement can be adjusted accordingly based on the principle of stress compatibility.

[0149] S7-2: Integration into commercial software for automated redesign

[0150] The optimal adjustment coefficient The rules for adjustment are then fed back to the original PKPM model file via scripts or a dedicated interface. In the PKPM environment:

[0151] In engineering implementation, it can be As an amplification (or reduction) factor for the reinforcement of the i-th layer, it is applied to the reinforcement design results of that layer in PKPM. PKPM automatically completes the reinforcement layout and adjustment of the component layer according to the new layer reinforcement level, without the need for fine inversion of individual beam and column reinforcement in this method.

[0152] S7-3: Automation Specification Review and Output

[0153] Automatically perform internal force analysis and reinforcement verification of the entire building after structural adjustments in PKPM, and verify the following key indicators:

[0154] The bending and shear bearing capacity of beams and columns meet the requirements of the specifications;

[0155] The inter-story drift angle of the structure meets the seismic deformation limit.

[0156] The longitudinal reinforcement and stirrup reinforcement ratios of beams and columns meet the minimum reinforcement ratio, maximum reinforcement ratio, and structural requirements.

[0157] When all the above checks meet the requirements, it is considered that the optimal strength coefficient has been used. The overall adjustment of the layered reinforcement driven by the system has been developed into an optimized reinforcement scheme based on minimizing the economic loss caused by earthquakes in PKPM, which can be directly used for engineering implementation.

[0158] The implementation process of the method of the present invention will be described in detail below with reference to a typical reinforced concrete frame structure example and accompanying drawings. This embodiment is only used to illustrate the present invention, and the parameter selection and calculation details can be adjusted according to the engineering project, and do not constitute a limitation on the scope of protection of the present invention.

[0159] Optimized reinforcement design for earthquake economic losses of an 8-story reinforced concrete frame structure

[0160] The implementation process of this method is as follows: Figure 1 .

[0161] 1. Project Overview and Initial Design

[0162] Structural type: reinforced concrete frame structure;

[0163] Number of floors and floor height: 8 floors above ground, with the first floor having a floor height of 3.6m and the standard floors having a floor height of 3.3m;

[0164] Seismic fortification intensity: 8 degrees, basic design seismic acceleration value: 0.20g;

[0165] Site category: Class II site, first design response spectrum;

[0166] Function and layout: Office building, with regular structural layout, floor plan and elevation.

[0167] Design software: PKPM was used for conventional seismic design to obtain the initial reinforcement scheme.

[0168] Step S1: Determine the earthquake intensity level and annual probability of occurrence.

[0169] According to current standards and seismic zoning results, the site in this embodiment is located in an 8-degree seismic intensity zone (0.20g), a Class II site, and three seismic fortification levels are adopted:

[0170] Minor earthquakes (frequent earthquakes): 50-year probability of exceeding [a certain level of occurrence] , ;

[0171] Moderate earthquake (design earthquake): 50-year exceedance probability , ;

[0172] Major earthquake (rare earthquake): 50-year probability of occurrence , .

[0173] To facilitate the calculation of expected annual economic losses, the 50-year exceedance probability is converted into an annual exceedance probability. :

[0174]

[0175] Furthermore, mutually exclusive "probabilities of occurrence of small / medium / large earthquakes" are constructed:

[0176]

[0177] The detailed calculation results are shown in Table 1.

[0178] Table 1: PGA and 50-year surpassing probability of a Class II small / medium / large earthquake of magnitude 8 (0.20g)

[0179] The above three It will be used as the weight in the subsequent step S5 for EAL calculation.

[0180] Step S2: Extraction of initial structural design parameters

[0181] A three-dimensional frame model was established using PKPM, and conventional seismic design was completed according to the "Code for Seismic Design of Buildings" (GB 50011) and the "Code for Design of Concrete Structures" (GB 50010) to obtain an initial reinforcement scheme that meets the code requirements. The mass of each story was extracted based on the PKPM results. Equivalent stiffness equivalent yield shear strength of the layer The process diagram is as follows: Figure 2 The initial design parameters are summarized in Table 2.

[0182] Table 2: Initial structural floor design parameters (8-degree seismic zone, Class II site)

[0183] Note: The values ​​in the table can be replaced according to the actual engineering calculation results. This example provides a set of representative schematic parameters.

[0184] Let the initial total layer shear strength be:

[0185]

[0186] Subsequent optimization processes require that the total shear strength of the layers remain constant.

[0187] Step S3: Nonlinear dynamic time history analysis

[0188] This embodiment uses OpenSees to perform structural dynamic time history analysis and obtain EDP parameters.

[0189] 1. Model Establishment

[0190] The structure is simplified into a multi-degree-of-freedom layer model, where the mass of the i-th layer is... The results are given in Table 2;

[0191] Nonlinear shear springs are installed in the i-th and (i+1)-th layers, with elastic stiffness of... (Table 2), yield shear strength is ;

[0192] During initial response analysis, take .

[0193] 2. Seismic motion selection and amplitude modulation

[0194] For the minor, moderate and major earthquake PGA determined in step S1, select no less than 7 actual strong earthquake records under Class II site conditions, and adjust the response spectrum or PGA amplitude according to the target design.

[0195] 3. Nonlinear dynamic time history analysis and EDP extraction

[0196] For each seismic level k and each record r, nonlinear dynamic time history analysis was performed in OpenSees to obtain the displacement and acceleration time histories of each floor, and the following calculations were performed:

[0197]

[0198] For multiple records at the same level: the maximum value of inter-story displacement is taken, and the average value of floor acceleration is taken.

[0199]

[0200] Step S4: Calculation of Economic Loss

[0201] Figure 3 The diagram illustrates the calculation of component damage and loss. Following the detailed steps in S4-1 to S4-4 above, and combining the vulnerability function and loss consequence data, the economic loss of each performance group under each damage state is calculated:

[0202] Summing the values ​​for all floors and performance groups yields the expected direct economic losses under minor, moderate, and major earthquakes. .

[0203] Step S5: Calculation of Annual Economic Loss

[0204] The annual occurrence probability obtained in step S1 Combined with the loss results obtained in step S4, calculate the annual economic loss:

[0205]

[0206] Step S6: Co-optimization of Particle Swarm Optimization and Proxy Model

[0207] Following steps S6-1 to S6-4, perform an optimization solution for economic losses.

[0208] S6-1 Design Variables and Constraints

[0209] Design variables: Strength coefficient of each layer

[0210]

[0211] Constraints: The total layer shear strength remains essentially constant.

[0212]

[0213]

[0214] in, .

[0215] S6-3 MATLAB Training Agent Model

[0216] This embodiment introduces a built-in regression surrogate model into the PSO algorithm, specifically the fitrgp function from the Statistics and Machine Learning Toolbox, to establish a "..." See the mapping relationship between "-EAL" and "-EAL". Figure 4 The specific details are as follows:

[0217] In the initial generations of the genetic algorithm, all individuals are used as training samples by employing "real" time history analysis and loss calculation.

[0218] See Figure 5 Using MATLAB's built-in regression model to The surrogate model is trained using seismic motion parameters as input and EAL as output.

[0219] Once the surrogate model's prediction accuracy reaches 95%, subsequent generations primarily rely on the surrogate model to quickly provide EAL estimates, with only a small number of key individuals undergoing real time-history analysis for verification, thereby significantly reducing computational load.

[0220] Example of optimization results in S6-4

[0221] After optimization, a set of optimal strength coefficients satisfying the constraints was obtained. The corresponding optimized layer shear strength is The illustrative results are shown in Table 3.

[0222] Table 3: Comparison of initial and optimized layer shear strength and strength coefficient (illustrated)

[0223] Figure 6 The study presents a comparison of the losses of the structure before and after optimization in the range of 0.1g to 1.2g. The results show that the economic loss of the optimized structure is reduced by up to 38.96% and the average reduction is 26.7%.

[0224] Step S7: Reinforcement Inversion and Closed-Loop Verification

[0225] Will Input the floor stirrup adjustment factor into PKPM, and the software will automatically modify the reinforcement.

[0226] PKPM's automatic verification shows that all bearing capacity and deformation indicators of the optimized scheme meet the requirements of GB 50010 and GB 50011 standards.

[0227] Performance comparison: Figure 7 Figures (A) and (B) show that the optimized structure exhibits significantly higher and more uniform inter-story drift angles and floor accelerations under a major earthquake, with the maximum inter-story drift angle reduced by approximately 60%. This effectively eliminates the weak story in the original design, which is the structural performance root cause of the reduced economic losses. Figure 8 The changes in floor strength distribution and the proportion of lateral force in each floor are presented. It can be seen that the lateral strength is further improved without increasing the construction cost, which intuitively reflects the comprehensive improvement effect of the method of the present invention in terms of earthquake economic loss control and stress rationality.

[0228] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for optimizing reinforcement inversion based on earthquake economic losses, characterized in that, Includes the following steps: S1. Obtain the target structural model that has completed conventional seismic design from the structural design software, and extract the initial yield shear strength and story stiffness of each floor. S2. Determine the multiple earthquake intensity levels at the site of the building and their corresponding annual probability of occurrence; S3. Construct an earthquake direct economic loss assessment model, determine the economic loss for each intensity level, and construct the annual economic loss as the optimization objective function by combining the probability of earthquake occurrence at each intensity level. S4. Design variables and constraints: The variable is the ratio of the yield shear strength of each floor to be optimized to the initial yield shear strength of each floor, i.e., the strength coefficient; the constraint is that the total floor yield shear strength and the stiffness of each floor remain unchanged. S5. Using an artificial intelligence optimization algorithm, combined with an online training and real-time updated surrogate model, the optimal strength coefficient that minimizes annual economic loss is obtained, thereby determining the optimized yield shear strength of each floor. S6. Based on the optimal strength coefficient, adjust and verify the reinforcement scheme of each floor in the structural design software to generate the optimized reinforcement design results.

2. The method according to claim 1, characterized in that, In step S3, the earthquake economic loss assessment model includes: A component-based loss assessment method is adopted to calculate the probability of structural and non-structural components under different damage states and the corresponding repair costs based on the engineering requirement parameters of structural and non-structural components. A floor-based loss function method is used to establish a functional relationship between the engineering demand parameters of a floor and the economic loss of that floor.

3. The method according to claim 1, characterized in that, In step S5, the artificial intelligence optimization algorithm is a swarm intelligence optimization algorithm.

4. The method according to claim 3, characterized in that, The swarm intelligence optimization algorithm includes any one of particle swarm optimization, ant colony optimization, and genetic algorithm.

5. The method according to claim 1, characterized in that, In step S5, the surrogate model is a prediction model built based on a machine learning regression algorithm, used to establish the mapping relationship between the intensity coefficient vector and the annual economic loss; the solution is obtained by combining the online trained and updated surrogate model, including: S5.

1. Using the sample points generated during the initial optimization process, perform initial training on the surrogate model; S5.2 During the optimization iteration process, the current surrogate model is used to quickly predict and filter the performance of candidate solutions; S5.3 Perform precise nonlinear time history analysis and loss calculation on some of the selected candidate solutions to obtain their true annual economic loss values. S5.4 Add the new sample points obtained in step S5.3 to the training set and update the proxy model in real time; S5.5 Repeat steps S5.2 to S5.4 until the optimization termination condition is met.

6. The method according to claim 5, characterized in that, The prediction model includes neural networks, random forests, Bayesian networks, or support vector regression models.

7. The method according to claim 1, characterized in that, In step S6, adjusting the reinforcement scheme of each floor according to the optimal strength coefficient specifically involves: using the optimal strength coefficient of each floor as the adjustment coefficient for the total shear reinforcement of that floor, and proportionally adjusting the amount of stirrups used in the beams and columns of that floor.

8. An electronic device comprising a memory and a processor, characterized in that, The memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the earthquake economic loss optimization reinforcement inversion method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements a method for optimizing reinforcement inversion based on earthquake economic losses as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the earthquake economic loss optimization reinforcement inversion method as described in any one of claims 1-7.

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