A building cluster reinforcement optimization method, apparatus, medium, and product

Abstract

This application discloses a method, equipment, medium, and product for optimizing the reinforcement of building complexes, relating to the fields of earthquake prevention and disaster reduction and urban planning. The method includes: estimating the probability of buildings reaching or exceeding various damage states under earthquake action based on the large-sample statistical characteristics of Monte Carlo simulations, obtaining the estimated exceedance probability; fitting earthquake vulnerability parameters using the least squares method and calculating the probability of buildings being in each damage state; calculating the expected functional loss by combining the post-earthquake functions of structural and non-structural components under different damage states; constructing a building reinforcement optimization model with the objective of minimizing the weighted sum of squared deviations between the expected functional loss of each type of building and the corresponding functional loss threshold, and solving it using a mixed integer programming algorithm to obtain the optimal reinforcement level for each building; and reinforcing the building complex based on the optimal reinforcement level for each building. This application can achieve differentiated improvement of the seismic toughness of buildings with different functions and balanced improvement of similar buildings.

Description

Technical Field

[0001] This application relates to the fields of earthquake prevention and disaster reduction and urban planning, and in particular to a method, equipment, medium and product for strengthening and optimizing building complexes. Background Technology

[0002] With the accelerating pace of urbanization, the scale of urban building complexes continues to expand, and the role of buildings with different functions in the urban system is becoming increasingly important. After an earthquake, structural damage to buildings not only causes direct economic losses but also leads to a decline in building functionality, thereby affecting the recovery of key urban functions such as medical treatment, traffic evacuation, emergency command, and material supply. Therefore, how to improve the seismic resilience of building complexes has become an important research issue in the field of disaster prevention and mitigation engineering.

[0003] In existing technologies, urban building seismic strengthening planning typically aims to minimize overall functional loss or total strengthening costs by implementing uniform or tiered strengthening strategies to improve overall seismic resistance. However, such methods often focus solely on minimizing overall loss, neglecting the differences in functional loss levels among different buildings. In reality, within building complexes, different functional types of buildings play significantly different roles in the urban system. For example, medical and health buildings and transportation hubs typically provide critical public service functions, and their functional loss directly impacts the city's overall emergency response capabilities; while residential and commercial buildings primarily serve residential and economic functions.

[0004] On the other hand, buildings of the same type should have similar functional levels after an earthquake because they perform similar functions. However, in actual building complexes, similar buildings often differ in construction date, structural type, and seismic design level, which often leads to varying degrees of damage and functional loss under earthquake action. This difference may cause some buildings to recover more slowly after an earthquake, thus affecting the overall recovery efficiency of similar buildings.

[0005] In summary, existing technologies have shortcomings such as a singular planning objective for seismic reinforcement of building complexes, neglect of differences in building functional attributes, and failure to consider the fairness of seismic resilience among similar buildings. Summary of the Invention

[0006] The purpose of this application is to provide a method, equipment, medium, and product for optimizing the reinforcement of building complexes, which can achieve differentiated seismic reinforcement of buildings with different functions, and make the seismic toughness of similar buildings after reinforcement more balanced and fair, thereby reducing the gap in functional loss of similar buildings after earthquakes, improving the overall seismic toughness of building complexes and the post-earthquake recovery efficiency of urban functions, and providing a scientific and reasonable optimization scheme for urban building complex seismic reinforcement planning and disaster prevention and mitigation decision-making.

[0007] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for strengthening and optimizing building complexes, including: Based on the large-sample statistical characteristics of Monte Carlo simulation, the probability of a building reaching or exceeding various damage states under seismic action is estimated, and the estimated exceedance probability is obtained. Based on the estimated exceedance probability, the least squares method is used to fit the seismic vulnerability parameters; the seismic vulnerability parameters include the median and logarithmic standard deviation of the ground peak ground acceleration when the building reaches each damage state; The probability of a building being in various damage states is calculated based on seismic vulnerability parameters, thus obtaining the probability of damage states. Based on the damage state probability, and combined with the post-earthquake functions of structural and non-structural components under different damage states, the expected functional loss is calculated. When the expected functional loss exceeds a set threshold, a building reinforcement optimization model is constructed with the objective of minimizing the weighted sum of squared deviations between the expected functional loss of various types of buildings and the corresponding functional loss threshold. The building reinforcement optimization model is solved using a mixed integer programming algorithm to obtain the optimal reinforcement level for each building; The building complex is reinforced based on the optimal reinforcement level for each building.

[0008] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described building complex reinforcement and optimization method.

[0009] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for strengthening and optimizing building complexes.

[0010] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described building complex reinforcement and optimization method.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: This application overcomes the shortcomings of existing technologies that only focus on minimizing overall loss while ignoring individual differences by constructing an optimization model with the goal of "minimizing the weighted sum of squared deviations between the expected functional loss of various types of buildings and the corresponding functional loss thresholds". It not only effectively reduces the overall post-earthquake functional loss of building complexes, but also significantly reduces the dispersion of functional loss within similar buildings, achieving a balanced and equitable allocation of seismic resilience of similar buildings. This ensures that buildings undertaking similar urban functions have similar service recovery capabilities after an earthquake, thereby improving the overall emergency response efficiency of key urban functional systems. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 A flowchart illustrating a method for strengthening and optimizing a building complex, provided as an embodiment of this application; Figure 2 This is a schematic diagram illustrating the expected functional loss after reinforcement. Figure 3 A schematic diagram showing the mean and standard deviation of the expected functional loss of similar buildings before and after reinforcement. Detailed Implementation

[0014] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] In one exemplary embodiment, such as Figure 1 As shown, a method for strengthening and optimizing building complexes is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is described using a server as an example, and includes the following steps S1 to S7.

[0017] S1: Based on the large sample statistical characteristics of Monte Carlo simulation, the probability of a building reaching or exceeding various damage states under seismic action is estimated, and the estimated exceedance probability is obtained.

[0018] For each building in the complex, a discrete set of peak ground accelerations (PGAs) S = {a1, a2, …, ah} is established. Based on the large-sample statistical properties of Monte Carlo simulations, the estimated exceedance probability of a building reaching or exceeding damage state m at a given ah is estimated. : In the formula, To estimate the exceedance probability of reaching or exceeding damage state m under the h-th peak ground acceleration, Here, E represents the predicted damage state of the building, and E represents the total number of simulations. For indicator functions, This represents the predicted damage state of the building in the e-th simulation. Damage states include basically intact, slightly damaged, moderately damaged, severely damaged, and completely damaged, with corresponding values ​​of 0, 1, 2, 3, and 4, respectively. By traversing the PGA set, the discrete exceedance probability point set for the building under different seismic intensity levels can be obtained.

[0019] S2: Based on the estimated exceedance probability, the seismic vulnerability parameters are fitted using the least squares method; the seismic vulnerability parameters include the median and logarithmic standard deviation of the ground peak ground acceleration when the building reaches each damage state.

[0020] Specifically, this includes: assuming that the building seismic vulnerability curve follows a log-normal distribution, constructing a theoretical model of building seismic vulnerability; based on the theoretical model of building seismic vulnerability, determining the theoretical exceedance probability of a building reaching or exceeding each damage state under seismic action; constructing an objective function with the goal of minimizing the sum of squares of the difference between the estimated exceedance probability and the theoretical exceedance probability; and solving the objective function using the least squares method to obtain the seismic vulnerability parameters.

[0021] Assuming that the building seismic vulnerability curve follows a log-normal distribution, the expression for the theoretical model of building seismic vulnerability is as follows: In the formula, Let m be the theoretical exceedance probability of a building reaching or exceeding damage state m under seismic loading. The median PGA value for a building reaching damage state m; The logarithmic standard deviation of the building reaching damage state m reflects the dispersion of the vulnerability curve; It is the standard normal distribution function.

[0022] The objective function is constructed with the goal of minimizing the sum of squares of the differences between the estimated transcendence probability and the theoretical transcendence probability. The objective function is as follows: The least squares method was used to perform regression analysis on the discrete exceedance probability point set to fit the seismic vulnerability parameters.

[0023] S3: Calculate the probability of a building being in various damage states based on seismic vulnerability parameters, and obtain the probability of damage states.

[0024] Based on the seismic vulnerability parameters calculated in step S2, the probability of a building being in various damage states under any PGA can be calculated, i.e., the probability of damage states. : S4: Based on the damage state probability, and combined with the post-earthquake functions of structural and non-structural components under different damage states, calculate the expected functional loss.

[0025] The expected functional loss of a building is calculated from the post-earthquake functions of structural and non-structural components. The difference in the impact of the post-earthquake functions of structural and non-structural components on building function is also considered for different building types. In the formula, For the expected functional loss, and These represent the post-earthquake functions of structural and non-structural components when the building is in a damaged state (m). This is the functional weighting coefficient for structural components, with a value ranging from 0 to 1, reflecting the differences in the contribution of structural and non-structural components to the building function in different types of buildings. for The correction coefficients are used. The post-earthquake functions of structural and non-structural components are quantified through a building damage state mapping, while assuming they follow a triangular probability distribution. When a building is in a certain damage state, the post-earthquake function of a component corresponds to a triangular distribution with a minimum value of p, a most likely value of r, and a maximum value of q, to ​​account for the uncertainty of the component's post-earthquake function under a given building damage state.

[0026] S5: When the expected functional loss exceeds the set threshold, construct a building reinforcement optimization model with the objective of minimizing the weighted sum of squared deviations between the expected functional loss of various types of buildings and the corresponding functional loss threshold.

[0027] When the expected functional loss exceeds a set threshold (e.g., the expected functional loss threshold for medical and health buildings is 0.2), it indicates that the post-earthquake functional level of the building cannot meet the established functional goals, and its seismic toughness needs to be improved through seismic reinforcement.

[0028] The role of building reinforcement is to improve the seismic resistance of the structure, which, from a probabilistic perspective, reduces the probability of the building reaching a severe damage state. The reinforcement level is characterized by adjusting the median value of the vulnerability curve, while keeping the logarithmic standard deviation constant. With K discrete reinforcement levels set up, after implementing the k-th reinforcement level, the median value of the vulnerability curve is adjusted to... The corresponding theoretical model of building seismic vulnerability is updated as follows: In the formula, Indicates the level of reinforcement of a building; This indicates that the building will not be reinforced.

[0029] Buildings are classified into I categories according to their function, such as single-family homes, medical and health facilities, and transportation hubs. The number of buildings in category i is... To minimize the weighted sum of squared deviations between the expected functional loss and the corresponding functional loss threshold of various building types under rare earthquakes (i.e., maximizing fairness), a building reinforcement optimization model is constructed: In the formula, The target value for the building reinforcement optimization model; For 0-1 decision variables, =1 indicates that the j-th building of the i-th type adopts the k-th reinforcement level. =0 indicates that it is not used; The expected functional loss when reinforcement level k is applied to the j-th building of type i; The threshold for functional loss of the i-th type of building; The importance weight coefficient for the j-th building in the i-th category; Let be the functional importance coefficient of the i-th type of building; This represents the maximum functional importance coefficient for all building categories. Let J be the building area of ​​the j-th building of the i-th type; This represents the maximum building area for all building categories. The number of reinforcement levels; and These are the weighting coefficients for the importance of building function and the building area, respectively.

[0030] The building reinforcement optimization model should meet the following constraints: (1) Reinforcement uniqueness constraint: Each building can only choose one reinforcement level: (2) Strengthen budget constraints: In the formula, The cost of reinforcement when reinforcement level k is adopted for building j of type i; Let $\frac{i}{j}$ be the replacement cost of the $i$-th building. C represents the reinforcement level coefficient; C represents the building complex reinforcement budget.

[0031] S6: The building reinforcement optimization model is solved using a mixed integer programming algorithm to obtain the optimal reinforcement level for each building.

[0032] A mixed-integer programming algorithm is used to iteratively solve the model, and the output is the globally optimal reinforcement scheme that minimizes the objective function Z.

[0033] S7: Reinforce the building complex based on the optimal reinforcement level for each building.

[0034] The beneficial effects of this application are as follows: (1) This application constructs a building reinforcement optimization model with the goal of minimizing the weighted sum of squares of the expected functional loss of various types of buildings and the corresponding functional loss threshold, so that similar buildings exhibit similar functional loss levels after the earthquake. This solves the problem of uneven and unfair configuration of seismic toughness of similar buildings in the existing building group reinforcement optimization technology, and improves the fairness of seismic toughness among similar buildings. (2) This application allows for the setting of different importance weight coefficients and different functional loss thresholds for different types of buildings according to the actual needs of urban planning, thereby realizing the refined control of functional loss thresholds for different types of buildings and providing a scientific basis for the efficient allocation of funds for seismic reinforcement of building complexes.

[0035] (3) This application constructs a clear log-normal vulnerability curve (i.e., a theoretical model of building seismic vulnerability) for each building, and characterizes the building reinforcement level as the increase in the median value of the vulnerability curve. This method can describe the impact of reinforcement measures on the probability of building damage from the perspective of structural seismic performance, and provides a basis for establishing a quantitative relationship between reinforcement measures and the probability of seismic damage.

[0036] (4) This application introduces a reinforcement budget constraint in the building reinforcement optimization model. By limiting the reinforcement budget of the building group, the optimized reinforcement scheme is economically feasible. At the same time, it can realize the optimal allocation of limited funds in the building group, which is conducive to improving the economic efficiency of seismic reinforcement funds.

[0037] The following is a building complex example to verify the building complex reinforcement and optimization method proposed in this application: (1) A building complex containing 969 buildings was selected as the research object. The building complex is located in a seismic fortification intensity zone of 8 degrees, the site category is Class II, the basic design seismic acceleration is 0.20g, and the peak ground acceleration corresponding to a rare earthquake is 0.4g. The building structure types include masonry structure and reinforced concrete frame structure. According to the functional type, the buildings are divided into 7 categories: multi-family residential buildings, single-family residential buildings, administrative offices, medical and health facilities, transportation stations, shopping centers, and cultural and entertainment buildings. The functional loss thresholds of each type of building under a rare earthquake are 0.5, 0.5, 0.3, 0.2, 0.2, 0.5, and 0.7, respectively, and the corresponding functional importance coefficients are 0.7, 0.7, 0.9, 1.0, 1.0, 0.6, and 0.3, respectively. The weight coefficients for building functional importance and building area are set to 0.6 and 0.4, respectively. Thirteen discrete reinforcement levels are set, with reinforcement level values ​​ranging from 0 to 1.2, an interval of 0.1, and a reinforcement level coefficient of 0.3. The budget for the reinforcement of the building complex is 4% of the total replacement cost of the building complex, which is 381,351,162 yuan.

[0038] (2) Set up a set of PGAs from 0.02g to 1.0g with an interval of 0.02g, estimate the estimated exceedance probability of the building in each damage state, and then use the least squares method to fit a continuous vulnerability curve.

[0039] (3) Without seismic reinforcement, the mean expected functional losses of multi-family residential buildings, single-family residential buildings, administrative offices, medical and health facilities, transportation hubs, shopping centers, and cultural and entertainment buildings were 0.41, 0.17, 0.47, 0.49, 0.34, 0.36, and 0.40, respectively, with corresponding standard deviations of 0.23, 0.11, 0.22, 0.20, 0.23, 0.24, and 0.27. The results indicate that the functional losses within similar buildings exhibit significant dispersion and obvious imbalance.

[0040] (4) A mixed-integer programming algorithm is used to iteratively solve the building reinforcement optimization model to obtain the globally optimal reinforcement scheme. The total reinforcement cost of this scheme is 333,838,175 yuan, which is 87.5% of the reinforcement budget. At this time, the expected functional loss after reinforcement is as follows: Figure 2 As shown, the mean expected functional losses for the seven building types are 0.26, 0.17, 0.25, 0.18, 0.15, 0.32, and 0.40, respectively, with corresponding standard deviations of 0.18, 0.11, 0.09, 0.04, 0.08, 0.19, and 0.27. From... Figure 3It can be seen that for single-family residential buildings and cultural and entertainment buildings that were not reinforced, their mean and standard deviation of expected functional loss remained unchanged. For administrative offices, medical and health facilities, and transportation hubs, the mean of expected functional loss was effectively reduced to below the corresponding loss threshold, and the standard deviation within the same type of building also decreased significantly. This demonstrates that the building reinforcement optimization model effectively improves the seismic resilience of building complexes while reducing the differences in functional loss among similar buildings, achieving a fair allocation of seismic resilience among similar buildings, and possesses practical engineering value.

[0041] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments. The computer device can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores data to be processed. The I / O interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communicating with an external terminal via a network connection. When the computer program is executed by the processor, it implements the steps in the above-described method embodiments.

[0042] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0043] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0044] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0045] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0046] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0047] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0048] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method of building cluster reinforcement optimization, characterized in that, include: Based on the large-sample statistical characteristics of Monte Carlo simulation, the probability of a building reaching or exceeding various damage states under seismic action is estimated, and the estimated exceedance probability is obtained. Based on the estimated exceedance probability, the least squares method is used to fit the seismic vulnerability parameters; the seismic vulnerability parameters include the median and logarithmic standard deviation of the ground peak ground acceleration when the building reaches each damage state; The probability of a building being in various damage states is calculated based on seismic vulnerability parameters, thus obtaining the probability of damage states. Based on the damage state probability, and combined with the post-earthquake functions of structural and non-structural components under different damage states, the expected functional loss is calculated. When the expected functional loss exceeds a set threshold, a building reinforcement optimization model is constructed with the objective of minimizing the weighted sum of squared deviations between the expected functional loss of various types of buildings and the corresponding functional loss threshold. The building reinforcement optimization model is solved using a mixed integer programming algorithm to obtain the optimal reinforcement level for each building; The building complex is reinforced based on the optimal reinforcement level for each building.

2. The building cluster reinforcement optimization method of claim 1, wherein, The formula for calculating the estimated exceedance probability is as follows: wherein, is the estimated exceedance probability of reaching or exceeding the damage state at the hth ground peak acceleration, is the damage state prediction for the building, E is the total number of simulations, is the indicator function, is the damage state prediction for the building at the e th simulation.​ 3. The building cluster reinforcement optimization method of claim 1, wherein, Based on the estimated exceedance probability, the seismic vulnerability parameters are fitted using the least squares method, specifically including: Assuming that the seismic vulnerability curve of a building follows a log-normal distribution, a theoretical model of seismic vulnerability of a building is constructed. Based on the aforementioned theoretical model of building seismic vulnerability, the theoretical exceedance probability of a building reaching or exceeding various damage states under seismic action is determined. The objective function is constructed with the goal of minimizing the sum of squares of the difference between the estimated exceedance probability and the theoretical exceedance probability; The objective function is solved using the least squares method to obtain the seismic vulnerability parameters.

4. The method for strengthening and optimizing building complexes according to claim 3, characterized in that, The expression for the theoretical model of building seismic vulnerability is as follows: in, This represents the theoretical exceedance probability of a building reaching or exceeding each damage state m under seismic loading. For the predicted damage state of the building, It is the standard normal distribution function. The median peak ground acceleration is the value of the ground velocity at which the building reaches the damage state m. Let m be the logarithmic standard deviation of the building reaching the damaged state.

5. The method for strengthening and optimizing building complexes according to claim 1, characterized in that, The formula for calculating the expected functional loss is as follows: in, For the expected functional loss, Let the probability of the damaged state be denoted as . The functional weight coefficient of the structural components. for Correction factor, The post-earthquake function of structural components when the building is in a damaged state m. This refers to the post-earthquake function of non-structural components when a building is in a damaged state (m).

6. The method for strengthening and optimizing building complexes according to claim 1, characterized in that, The expression for the building reinforcement optimization model is: in, The target value for the building reinforcement optimization model. Let be the importance weight coefficient of the j-th building in the i-th category. As decision variables, =1 indicates that the j-th building of the i-th type adopts the k-th reinforcement level. =0 indicates that the j-th building of the i-th type does not adopt the k-th reinforcement level. The expected functional loss when the j-th building of type i is reinforced with reinforcement level k is given. Let be the functional loss threshold for the i-th type of building. Let be the functional importance coefficient of the i-th type of building. This represents the maximum functional importance coefficient for all building categories. Let be the building area of ​​the j-th building in the i-th category. This represents the maximum building area for all building categories. For the number of building categories, Let i be the number of buildings of type i. To reinforce the number of levels, and These are the weighting coefficients for the importance of building function and the building area, respectively.

7. The method for strengthening and optimizing building complexes according to claim 1, characterized in that, The constraints of the building reinforcement optimization model include reinforcement uniqueness constraints and reinforcement budget constraints; The expression for the reinforcement uniqueness constraint is: The expression for the reinforcement budget constraint is: in, As decision variables, =1 indicates that the j-th building of the i-th type adopts the k-th reinforcement level. =0 indicates that the j-th building of the i-th type does not adopt the k-th reinforcement level. The cost of reinforcement when reinforcement level k is applied to building j of type i. Budget for reinforcing the building complex, To reinforce the horizontal coefficient, Let the replacement cost be the cost of the j-th building of the i-th type. To reinforce the number of levels, For the number of building categories, Let be the number of buildings of type i.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the building complex reinforcement and optimization 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 executed by a processor, the computer program implements the building complex reinforcement and optimization method according to 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 building complex reinforcement and optimization method according to any one of claims 1-7.

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