Building anti-seismic performance evaluation method based on entropy weight optimization shear wall building plane length-width ratio

Abstract

The invention relates to the technical field of shear wall structure building earthquake resistance, and discloses a building earthquake resistance evaluation method for optimizing the shear wall building plane length-width ratio based on an entropy weight method.The building earthquake resistance evaluation method comprises the following operation steps that S10, the length-width ratio of a shear wall building needing to be evaluated is selected, and each set of length-width ratio corresponds to a set of index parameters; s20, according to the anti-seismic performance requirement of the shear wall structure building, an index evaluation system of the shear wall structure building for the building plane length-width ratio is established; s30, according to an index evaluation system of the shear wall structure building for the building plane length-width ratio, an initial decision matrix is established, then standardization processing is performed on the matrix, according to scheme optimization, forward indexes are used for replacing original indexes, all the indexes are subjected to translation, zero in the indexes is removed, and a standardization matrix is obtained. The building anti-seismic performance evaluation method based on the entropy weight optimization building plane length-width ratio is used for comprehensively evaluating the building anti-seismic performance of the plane length-width ratios of different shear wall buildings so as to obtain the optimal length-width ratio of the building anti-seismic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic resistance of shear wall structure buildings, and specifically to a method for evaluating the seismic performance of buildings based on entropy weight optimization of the aspect ratio of the building plane of shear walls. Background Art

[0002] China is a country with frequent earthquakes. In the past 40 years, 10 major earthquakes with magnitudes ranging from 7.0 to 8.0 have occurred. The frequent and strong earthquakes have caused huge damage to the disaster areas, and the damage to buildings is particularly serious.

[0003] The impact of earthquakes on buildings is an important and complex issue. With the continuous development of building seismic performance evaluation technology, the indicators for evaluating the seismic performance of buildings are no longer limited to the lateral displacement of buildings during earthquakes. Among them, the torsional factor also plays a key role in the damage of buildings. Many scholars have conducted relevant statistics on the damage of buildings in many earthquakes at home and abroad and found that the torsional factor cannot be ignored in the impact of earthquakes on buildings. And it is statistically found that when the earthquake reaches the fortification intensity, the damage of buildings due to torsion is common, not a small probability event. As the most commonly used structure for civil high-rise residences, the safety performance of shear wall buildings is of utmost importance.

[0004] An important point in the design of the seismic performance of shear wall buildings lies in the aspect ratio of the building plane. The aspect ratio of the building plane is the ratio of the projected length of the shear wall plane in the long-axis direction to the projected length of the shear wall plane in the short-axis direction. Generally speaking, the closer the aspect ratio of the building is to 1, the more prominent its seismic performance will be. However, due to the characteristics of shear walls being commonly used in residences, issues such as ventilation and lighting need to be considered in the north-south direction, resulting in the unit lateral stiffness in the short-axis direction being greater than that in the long-axis direction. If the aspect ratio of the building plane is simply made closer to 1, it will instead affect the seismic performance of the building. If the length in the long-axis direction is lengthened to increase its lateral stiffness, it will lead to an increase in the torsional effect. If the long axis is too short, it will affect the lateral stiffness. Therefore, an appropriate aspect ratio of the building plane is crucial for the seismic performance of the building. Summary of the Invention

[0005] (1) Technical Problems to be Solved

[0006] The purpose of the present invention is to comprehensively evaluate the seismic performance of shear wall buildings with different aspect ratios of the building plane in order to obtain the aspect ratio of the building plane with the optimal seismic performance, and to propose a method for evaluating the seismic performance of buildings based on entropy weight optimization of the aspect ratio of the building plane of shear walls.

[0007] (2) Technical Solutions

[0008] The technical solutions for the present invention to solve the above technical problems are as follows:

[0009] An evaluation method for the seismic performance of a shear wall building based on optimizing the aspect ratio of the building plane by entropy weight, comprising the following operation steps:

[0010] S10. Select the aspect ratio of the plane of the shear wall building to be evaluated, and each group of aspect ratios corresponds to a group of index parameters;

[0011] S20. According to the requirements of the seismic performance of the building, establish an index evaluation system for the aspect ratio of the plane of the shear wall building to the seismic performance of the building;

[0012] S30. According to the index evaluation system for the aspect ratio of the plane of the shear wall building to the seismic performance of the building, establish an initial decision matrix, and then perform standardization processing on this matrix. For the optimal selection of the scheme, replace the original index with a positive index, perform translation on each index, and eliminate the 0 items in the index to obtain a standardized matrix;

[0013] S40. Calculate the relative weights of each index, and then perform normalization processing on each index to obtain a normalized matrix of the original index data matrix. Calculate the entropy value of the matrix and determine its entropy weight ratio, and construct a weighted normalized matrix model based on entropy weight;

[0014] S50. Calculate the distances of each evaluation object from the positive ideal and the negative ideal according to the weighted normalized matrix model, and calculate the relative closeness of the influence of different aspect ratios of the building plane on the seismic performance to the distances of the positive and negative ideals;

[0015] S60. Rank according to the relative closeness, and then obtain the aspect ratio that is determined to have the best influence on the seismic performance of the building.

[0016] On the basis of the above technical solution, the present invention can also be improved as follows.

[0017] Further, the index parameters in step S10 are the maximum torsional displacement ratio of the building, the maximum torsional period ratio of the building, the maximum inter-story torsion of the building, the maximum inter-story displacement of the building, and the maximum eccentricity of the building.

[0018] Further, the initial decision matrix in step S30 is established according to the following formula:

[0019]

[0020] In the formula, m is the number of groups of aspect ratios of the shear wall building obtained, and n is the number of evaluation index parameters.

[0021] In step S30, for the standardization processing of each index in formula (1), when the value is a positive index, positive normalization processing is selected, and when the value is a negative index, reverse normalization processing is selected. The formula is as follows:

[0022]

[0023] In step S30, each index is translated to eliminate the zero items in the index. The formula is as follows:

[0024] Formula (2) + 0.0001 gives formula (3).

[0025] In step S30, the normalization matrix is established according to the following formula:

[0026]

[0027] Furthermore, the relative weights of each index in step S40 are established according to the following formula:

[0028]

[0029] In the formula, Yij is the value of the jth index parameter in the ith group of formulations, and pij is the relative weight of the ith aspect ratio in the jth index parameter;

[0030] The normalization matrix in step S40 is established according to the following formula:

[0031]

[0032] In the formula, m is the number of groups of aspect ratios of the plane of the shear wall buildings obtained, n is the number of index parameters selected in the index evaluation system, and pmn is the relative weight of the mth aspect ratio in the nth index parameter;

[0033] The calculation formulas for the entropy value Hj and the entropy weight ratio Wj in step S40 are as follows:

[0034]

[0035] The weighted normalization matrix is established according to the following formula in step S40:

[0036]

[0037] Furthermore, the distance between the aspect ratio of the plane of each group of shear wall buildings and the positive ideal in step S50 is calculated according to the following formula:

[0038]

[0039] The distance between the aspect ratio of the plane of each group of shear wall buildings and the negative ideal in step S50 is calculated according to the following formula;

[0040]

[0041] The relative closeness degree of the aspect ratio of the plane of each group of shear wall buildings to the optimal solution in step S50 is calculated according to the following formula;

[0042]

[0043] Further, rank according to the relative closeness degree to determine the optimal aspect ratio of the shear wall building.

[0044] (III) Beneficial effects

[0045] Compared with the prior art, the technical solution of the present application has the following beneficial technical effects:

[0046] In view of the randomness of the subjective evaluation of the influence of shear wall buildings with different aspect ratios on the seismic performance of buildings, the present invention establishes an evaluation method for the seismic performance of shear wall buildings with different aspect ratios based on the improved entropy weight method. This method is based on measured data and uses the entropy weight method for data analysis to determine the optimal aspect ratio value. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flowchart of an evaluation method for the seismic performance of a shear wall building with an aspect ratio optimized by entropy weight. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0049] Combined with Figure 1 As shown, an evaluation method for the seismic performance of a shear wall building with an aspect ratio optimized by entropy weight according to the present invention is characterized by including the following operation steps:

[0050] S10. Select the aspect ratio of the shear wall building to be evaluated, and each group of aspect ratios corresponds to a group of index parameters; in step S10, the index parameters are the maximum torsional displacement ratio of the building, the maximum torsional period ratio of the building, the maximum inter-story displacement of the building, the maximum inter-story torsion of the building, and the maximum eccentricity of the building.

[0051] S20. Establish an index evaluation system for the seismic performance of the shear wall building according to the road use performance requirements;

[0052] S30. According to the index evaluation system for the seismic performance of the shear wall building based on the aspect ratio, establish an initial decision matrix, and then perform standardization processing on this matrix. For the optimal selection of the scheme, replace the original index with a positive index, and perform translation on each index to eliminate the 0 items in the index to obtain a standardized matrix;

[0053] The initial decision matrix in step S30 is established according to the following formula:

[0054]

[0055] Wherein, m is the number of groups of the aspect ratio of the length to the width of the plane of the obtained shear wall building, and n is the number of evaluation index parameters.

[0056] In step S30, each index of formula (1) is standardized. When the value is a positive index, positive normalization processing is selected. When the value is a negative index, reverse normalization processing is selected. The formula is as follows:

[0057]

[0058] In step S30, each index is translated to eliminate the 0 term in the index. The formula is as follows:

[0059] Formula (2) + 0.0001 gives formula (3).

[0060] In step S30, the standardization matrix is established according to the following formula:

[0061]

[0062] S40. Calculate the relative weight of each index, then normalize each index to obtain the normalized matrix of the original index data matrix, calculate the entropy value of the matrix and determine its entropy weight ratio, and construct a weighted normalized matrix model based on entropy weight;

[0063] In step S40, the relative weight of each index is established according to the following formula:

[0064]

[0065] Wherein, Yij is the value of the jth index parameter in the ith group of formulations, and pij is the relative weight of the ith aspect ratio in the jth index parameter;

[0066] The normalized matrix in step S40 is established according to the following formula:

[0067]

[0068] Wherein, m is the number of groups of the aspect ratio of the length to the width of the plane of the obtained shear wall building, n is the number of index parameters selected by the index evaluation system, and pmn is the relative weight of the mth aspect ratio in the nth index parameter;

[0069] In step S40, the calculation formulas for the entropy value Hj and the entropy weight ratio Wj are as follows:

[0070]

[0071] In step S40, the weighted normalized matrix is constructed according to the following formula:

[0072]

[0073] S50. Calculate the distances between each evaluation object and the positive ideal and negative ideal according to the weighted normalization matrix model, and calculate the relative closeness of the influence of different aspect ratios on the seismic performance of the building to the distances from the positive and negative ideals;

[0074] In step S50, the distance between the aspect ratio of the plane of each group of shear wall buildings and the positive ideal is calculated according to the following formula:

[0075]

[0076] In step S50, the distance between the aspect ratio of the plane of each group of shear wall buildings and the negative ideal is calculated according to the following formula;

[0077]

[0078] In step S50, the relative closeness of the aspect ratio of the plane of each group of shear wall buildings to the optimal solution is calculated according to the following formula;

[0079]

[0080] S60. Rank according to the relative closeness, and then obtain the aspect ratio that is determined to have the best influence on the seismic performance of the building. Rank according to the relative closeness to determine the optimal aspect ratio value of the shear wall building.

[0081] In this example, 5 groups of shear wall buildings with different aspect ratios of the plane are selected for evaluation, and the aspect ratio values and the index parameters used to evaluate the seismic performance of the building are shown in Table 1:

[0082] Table 1 Aspect ratio of the plane of the shear wall building and the index parameters used to evaluate the road performance.

[0083] The evaluation system in this paper selects five indicators: the maximum torsional displacement ratio, the maximum torsional period ratio of the building, the maximum inter-story displacement of the building, the maximum inter-story torsion of the building, and the maximum eccentricity of the building among the index parameters.

[0084] In this example, there are 5 aspect ratios of the plane of the selected shear wall buildings, and the evaluation system selects 5 index parameters; therefore, the initial decision matrix [M ij m×n has parameters m = 5 and n = 5. In the initial decision matrix, the row labels represent the performance indicators, and the column labels represent the aspect ratios. The initial decision matrix model is established as shown in Table 2 according to Equation (1):

[0085] Table 2 Initial decision matrix model of the seismic performance indicators of the shear wall building

[0086] ​

[0087] Construct a standardized matrix according to formulas (2), (3), and (4). The results are shown in Table 3 as follows:

[0088] Table 3 Standardized matrix of the building seismic performance indexes of shear wall buildings

[0089]

[0090] Calculate the proportion of 5 groups of data according to formula (5) and establish a normalized matrix according to formula (6). As shown in Table 4:

[0091] Table 4 Normalized matrix of the building seismic performance indexes of shear wall buildings

[0092]

[0093] Calculate the entropy value and entropy weight proportion of 5 index parameters according to formula (7), as shown in Table 5:

[0094] Table 5 Calculation results of entropy value and entropy weight proportion

[0095]

[0096] Establish a weighted decision matrix based on entropy weight according to formula (8), as shown in Table 6:

[0097] Table 6 Weighted matrix based on entropy weight

[0098]

[0099]

[0100] Calculate the positive ideal distance, negative ideal solution distance, and relative closeness degree of 5 groups of data according to formulas (9), (10), and (11)

[0101] Table 7 Calculation results of positive ideal distance, negative ideal solution distance, and relative closeness degree

[0102]

[0103] Sort according to the relative closeness degree. Project 4 > Project 2 > Project 1 > Project 5 > Project 3. The aspect ratio of the length to the width of the shear wall building in Project 4 is 2.26, which is the optimal solution with the best comprehensive performance of the building seismic performance among the 5 shear wall buildings.

[0104] The present invention excludes the subjective factors of human evaluation and adopts an objective mathematical method to evaluate the building seismic performance of shear wall buildings, and can accurately obtain the optimal solution.

[0105] It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising said element.

[0106] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio, characterized in that: The steps include: S10, selecting the plane aspect ratio of the shear wall building to be evaluated, each set of aspect ratios corresponding to a set of index parameters; S20. According to the requirements of building seismic performance, establish an index evaluation system for the effect of shear wall building plane length-width ratio on building seismic performance; S30, establishing an initial decision matrix based on the index evaluation system of the seismic performance of the building plane length-width ratio of the shear wall building, and then standardizing the matrix, replacing the original index with a positive index for the optimal solution, and translating each index to eliminate the 0 item in the index, and obtaining a standardized matrix; S40, calculating the relative weight of each indicator, then normalizing each indicator to obtain a normalized matrix of the original indicator data matrix, calculating the entropy value of the matrix and determining its entropy weight ratio, and constructing a weighted normalized matrix model based on entropy weight; S50, calculating the distance between each evaluation object and the positive ideal and the negative ideal according to the weighted normalized matrix model, and calculating the relative closeness of the influence of different aspect ratios on the seismic performance of the building and the positive and negative ideal distances; S60. Rank them according to relative proximity to obtain the best aspect ratio that has the best impact on the seismic performance of the building.

2. According to claim 1, a building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio is characterized in that: The index parameters in step S10 are the maximum torsional displacement ratio of the building, the maximum torsional period ratio of the building, the maximum inter-story torsion of the building, the maximum inter-story displacement of the building, and the maximum eccentricity of the building.

3. The building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio according to claim 1 is characterized in that: The initial decision matrix in step S30 is established according to the following formula: In the formula, m is the number of sets of the plane aspect ratio of the shear wall building obtained, n is the number of evaluation index parameters, In step S30, each index of formula (1) is normalized. When the value is a positive index, a positive normalization process is used. When the value is a negative index, a negative normalization process is used. The formula is as follows: In step S30, each index is shifted to eliminate the 0 item in the index. The formula is as follows: Formula (2) + 0.0001 to get formula (3) In step S30, the normalization matrix is ​​established as follows:

4. The building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio according to claim 1 is characterized in that: The relative weight of each index in step S40 is established according to the following formula: Where Yij is the value of the jth index parameter in the i-th group of formulas, and pij is the relative weight of the i-th aspect ratio in the j-th index parameter; The normalization matrix in step S40 is established according to the following formula: In the formula, m is the number of groups of the obtained plane aspect ratios of the shear wall building, n is the number of index parameters selected by the index evaluation system, and pmn is the relative proportion of the mth aspect ratio in the nth index parameter; The calculation formulas for the entropy value Hj and the entropy weight ratio Wj in step S40 are as follows: In step S40, the weighted normalization matrix is ​​constructed according to the following formula:

5. The building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio according to claim 1 is characterized in that: In step S50, the plane aspect ratio and the positive ideal distance of each group of shear wall buildings are calculated according to the following formula: In step S50, the plane aspect ratio of each group of shear wall buildings and the distance from the negative ideal are calculated according to the following formula; In step S50, the relative closeness between the plane aspect ratio of each group of shear wall buildings and the optimal solution is calculated according to the following formula:

6. The building seismic performance evaluation method based on entropy weight optimization of shear wall building plane aspect ratio according to claim 1 is characterized in that: The optimal plane length-to-width ratio of the shear wall structure building is determined by ranking according to relative proximity.

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