A method for optimizing arrangement of pier-type energy dissipater based on genetic algorithm

Abstract

This invention relates to the field of structural design in building engineering, specifically to a method for optimizing the arrangement of pier-type energy dissipators based on genetic algorithms, including S1: establishing a non-vibration-damping structural model, calculating the frame node displacement results and the initial deformation [δ] of each span of each floor of the structure. 0 S2: Based on the genetic algorithm, a certain number of energy dissipator arrangement schemes are randomly generated, and each scheme is encoded to form a [sign] matrix; S3: Considering the additional damping ratio correction, the additional damping ratio of each energy dissipator arrangement scheme is calculated; S4: Genetic algorithm optimization is performed, different fitness functions are constructed for different optimal arrangements, individuals are selected for crossover and mutation, and genetic iteration is carried out to obtain the optimal energy dissipator arrangement scheme. This invention calculates based on the analysis results of the non-damping model, and uses a genetic algorithm to obtain the optimal energy dissipator arrangement scheme for each floor and each span of the structure based on the target additional damping ratio or the target number of energy dissipators.

Description

Technical Field

[0001] This invention relates to the field of structural design in building engineering, and in particular to a method for optimizing the layout of pier-type energy dissipators based on genetic algorithms. Background Technology

[0002] Energy dissipation and vibration reduction technology increases structural damping by installing energy dissipators at specific locations within a building structure. This effectively dissipates seismic energy, reduces the structure's response to earthquakes, and thus improves the building's seismic safety. The vibration reduction effect of energy dissipators can generally be assessed by measuring the additional damping ratio.

[0003] With the continuous development of vibration reduction structure theory, in order to determine the required parameters, quantity and arrangement of energy dissipators for the structure, various design methods for energy dissipation and vibration reduction structures have been proposed, such as design methods based on equivalent linearization theory, displacement-based energy dissipation and vibration reduction structure design methods, demand-capacity spectrum-based design methods, energy-based design methods, and genetic algorithm-based energy dissipation and vibration reduction structure design methods.

[0004] Existing energy dissipator design methods typically require converting the three-dimensional structural model into an equivalent multi-degree-of-freedom (MDOF) or even a single-degree-of-freedom (SDOF) model to determine the number of energy dissipators on each floor. The placement of energy dissipators on each floor plan can only be conceptually designed according to the principles of "uniformity, dispersion, and symmetry." However, even with the same number of energy dissipators on each floor, different placement locations result in significantly different vibration reduction effects. Therefore, the research on optimal energy dissipator placement should be extended to each floor and span of the structure to obtain the optimal placement, which has direct guiding significance for engineering applications. Summary of the Invention

[0005] The purpose of this invention is to provide an optimized arrangement method for pier-type energy dissipators based on a genetic algorithm for vibration reduction structures using pier-type energy dissipators.

[0006] In the first aspect,

[0007] This invention provides a method for optimizing the layout of pier-type energy dissipators based on genetic algorithms, comprising the following steps:

[0008] S1: Establish a non-damping structural model and perform calculations for the specified horizontal force conditions under the design waterproof level; extract the frame node displacement results and calculate the initial deformation [δ] of each span of each story of the structure according to the following formula. 0 ];

[0009] δ 0 =δ s +|θ E +θ F |×h zd

[0010]

[0011] In the formula, u and θ represent the horizontal displacement and angular displacement of the node, respectively, and h zd The heights of the upper and lower supports of the energy dissipator are given. A, B, C, and D are the four frame node numbers corresponding to the energy dissipator installation in this span, respectively. δ s θ represents the horizontal displacement difference between the energy dissipator layers. E θ F These are the corners of the frame beams at the corresponding positions of the upper and lower supports of the proposed energy dissipator;

[0012] S2: Based on the genetic algorithm, multiple energy dissipator layout schemes are randomly generated;

[0013] Depending on the different energy dissipator arrangement schemes, "1" indicates that an energy dissipator is installed in the span, and "0" indicates that no energy dissipator is installed in the span, forming different [sign] matrices;

[0014] S3: Considering the additional damping ratio correction, calculate the additional damping ratio for each energy dissipator arrangement scheme;

[0015] For each [sign] matrix, initialize the deformation [δ] caused by the energy dissipator reaction force. F ] = [0], [δ 0 ]、[δ F Both [sign] and [sign] are three-dimensional matrices, with dimensions equal to the number of axis numbers × the number of layers × the number of spans. The initial additional damping ratio is...

[0016] Calculate the deformation caused by the reaction force of the energy dissipator [δ] F ];

[0017] Based on geometric relationships and the constitutive mechanism of the energy dissipator, for a displacement-type energy dissipator, the deformation caused by the energy dissipator reaction force is calculated using the following formula:

[0018]

[0019] In the formula, The initial deformation is for the proposed energy dissipator position on the i-th layer and j-th span along the k-th axis. δ is the deformation caused by the reaction force F of the energy dissipator in the i-th layer and j-th span of the k-th axis, k2 is the stiffness of the energy dissipator after yielding, and δ y For yield displacement, F y For yield strength, h zd,i Let be the height of the energy dissipator support of the i-th layer. Let b be the stiffness of the frame beam along the k-th axis, the i-th floor, and the j-th span. Let F be the rotation angle of the frame beam pier position caused by the energy dissipator reaction force F of the (i-1)th floor, span of the k-th axis. k,i+1,j This represents the maximum output of the energy dissipator in the (i+1)th layer of the k-th axis, span j.

[0020] The velocity-type energy dissipator is solved using an iterative method based on the following equations;

[0021]

[0022] In the formula, The initial deformation is for the proposed energy dissipator position on the i-th layer and j-th span along the k-th axis. Let F be the deformation caused by the reaction force F of the energy dissipator in the i-th layer and j-th span of the k-th axis, ω be the first frequency of the structure in the calculation direction, β be the correction factor for calculating the maximum output of the viscous energy dissipator, C be the damping coefficient of the viscous energy dissipator, α be the velocity exponent of the viscous energy dissipator, and h be the velocity index of the viscous energy dissipator. zd，i Let F be the height of the energy dissipator support of the i-th layer. k，i+1，j For the maximum output of the energy dissipator in the (i+1)th layer of the k-th axis, Let b be the stiffness of the frame beam along the k-th axis, the i-th floor, and the j-th span. The rotation angle of the frame beam support pier position caused by the energy dissipator reaction force F of the (i-1)th floor and j-th span on the k-th axis;

[0023] Consider additional damping ratio correction;

[0024] Calculate the energy dissipation of the energy dissipator and the total strain energy of the structure to obtain the additional damping ratio ξ under a given energy dissipator arrangement. a ;

[0025] Story shear force [F], inter-story displacement [u], and initial deformation of the energy dissipator [δ] 0 All results are obtained by multiplying the calculation results of the non-damping model by the structural response reduction factor η;

[0026] Update [δ] 0 ]、 [F], [u], repeat steps S2 to S3 until the additional damping ratio is reached. The error is less than the preset error convergence value. This indicates the calculation of the additional damping ratio after one iteration, and outputs the structural additional damping ratio corresponding to this energy dissipator arrangement scheme.

[0027] S4: Genetic Algorithm Optimization

[0028] For the first type of optimal arrangement: based on the target additional damping ratio, find the optimal arrangement position that minimizes the number of energy dissipators.

[0029] Calculate the additional damping ratio for each energy dissipator arrangement scheme, select the [sign] matrix that meets the target additional damping ratio requirement, and then use the following formula as the fitness function.

[0030] Fit(n)=ξ a / [n(1+ξ a )]

[0031] In the formula, n is the number of energy dissipators, i.e., the number of "1"s in the [sign] matrix, and ξ a To calculate the additional damping ratio;

[0032] For the second type of optimal arrangement: based on a fixed number of energy dissipators, find the optimal arrangement position that maximizes the calculated additional damping ratio.

[0033] Calculate the additional damping ratio for each energy dissipator arrangement scheme, select the [sign] matrix that meets the target additional damping ratio requirement, and then use the following formula as the fitness function.

[0034]

[0035] In the formula, This represents the expected maximum additional damping ratio;

[0036] Selection, crossover, and mutation: Select individuals for crossover and mutation to generate a new population. Perform g genetic iterations to obtain the [sign] with the highest fitness, which is the optimal arrangement scheme of the energy dissipator.

[0037] Preferably, in S1, θ E θ F It is calculated using the following formula:

[0038] Assume the distance from point E, where the support is located, to the end is xl, and the rotation angle is θ. E The bending moment at the pier location is M x According to the equation for the rotational displacement of a beam, we have:

[0039] M A =4iθ A +2iθ B -6iΔ v / l

[0040] M B =4iθ B +2iθ A -6iΔ v / l

[0041] M x =M A -x(M A +M B )

[0042] In the formula, i represents the beam stiffness considering the effect of floor slab stiffness, and Δ v =v A -v B Δ v Let θ be the vertical displacement difference between the two ends of the beam, l be the beam span, and θ be the vertical displacement difference between the two ends of the beam. A θ B These represent the end angular displacements, M and M respectively.A M B These are the end bending moments;

[0043] Then, by integrating the equation of the beam's deflection curve, we can obtain θ. E ;

[0044]

[0045] In the formula, EI is the bending stiffness;

[0046] The rotation angle at any point in the beam is a quadratic function of the distance xl from the end. The position with the maximum rotation angle is the inflection point, at which point we have:

[0047]

[0048] Maximum turning angle is

[0049] Preferably, for a general frame beam, the inflection point can be simplified to the mid-span, taking x = 1 / 2, then the mid-span rotation angle is given by the following formula.

[0050] θ E,x＝1 / 2 -(θ A +θ B -6Δ v / l) / 4

[0051]

[0052] In the formula, a negative value indicates that the direction of rotation of the support is opposite to the direction of rotation of the node.

[0053] Preferably, in step S3, the solution is... Depends on neighboring layers Solve the system of equations.

[0054] Preferably, in step S3, the following steps are performed: Initialize to zero, treat the deformation of non-i layer j span as known quantity, and solve for the unique unknown quantity.

[0055] Preferably, in S3, the additional damping ratio ξ for a given energy dissipator arrangement scheme is... a The calculation method is as follows:

[0056]

[0057]

[0058] In the formula, F i，j For the maximum output of the energy dissipator across the i-th layer j, The energy dissipator arranged for the i-th layer and j-th span is subject to the expected deformation δ i，j The energy consumed in one cycle of repetition;

[0059] W s =(1 / 2)∑F i u i

[0060]

[0061] In the formula, W s To calculate the total strain energy of the structure under seismic loading, ξ a Add damping ratio F to the energy dissipator i Let u be the shear force of the i-th floor. i Let be the inter-story displacement of the i-th layer.

[0062] Preferably, in S3, the additional damping ratio ξ for a given energy dissipator arrangement scheme is... a The calculation method is as follows:

[0063]

[0064]

[0065] In the formula, For the maximum output of the energy dissipator across the i-th layer j, The energy dissipator arranged for the i-th layer and j-th span is subject to the expected deformation δ i,j The energy consumed in one cycle of the next reciprocating cycle, where λ1 is a function related to the damping exponent;

[0066] W s =(1 / 2)∑F i u i

[0067]

[0068] In the formula, W s To calculate the total strain energy of the structure under seismic loading, ξ a Add damping ratio F to the energy dissipator i Let u be the shear force of the i-th floor. i Let be the inter-story displacement of the i-th layer.

[0069] Preferably, in step S3, the expression for the structural response reduction coefficient η is:

[0070]

[0071] In the formula, ξ a The additional damping ratio is given by T, which is the first-order period of the structure in the direction of the energy dissipator arrangement. g The characteristic period is denoted as .

[0072] Secondly,

[0073] This invention provides a pier-type energy dissipator structure, which is arranged using any of the aforementioned pier-type energy dissipator optimization arrangement methods based on genetic algorithms.

[0074] Thirdly,

[0075] The present invention provides a computing device, including at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute any of the above-described genetic algorithm-based optimized arrangement method for pier-type energy dissipators.

[0076] In the fourth aspect,

[0077] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the above-described methods for optimizing the arrangement of a pier-type energy dissipator based on a genetic algorithm.

[0078] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0079] 1. The present invention discloses an optimal arrangement method for pier-type energy dissipators based on a genetic algorithm. By decomposing the deformation of the energy dissipator under seismic loading into the initial deformation without energy dissipators and the indirect deformation considering the reaction force of the energy dissipators, the actual deformation of the energy dissipators under a given arrangement scheme can be calculated based on the analysis results of the non-damping model. This allows for the calculation of the additional damping ratio generated by the energy dissipators under this arrangement scheme. Combined with the genetic algorithm, the optimal arrangement of energy dissipators for each floor and span of the structure can be obtained based on the target additional damping ratio or the target number of energy dissipators.

[0080] 2. The optimal arrangement method for pier-type energy dissipators based on genetic algorithms described in this invention does not require the establishment of a seismic analysis model based on the energy dissipator arrangement scheme, nor does it require the selection of seismic waves for dynamic time history analysis. Based on the parameters of the energy dissipator to be selected, the additional damping ratio corresponding to each energy dissipator arrangement scheme can be quickly calculated. Combined with the genetic algorithm, the optimal arrangement scheme of energy dissipators for each floor and each span of the structure can be obtained, which can greatly improve the efficiency of energy dissipator arrangement scheme comparison and selection, and has direct guiding significance for seismic engineering design. Attached image description:

[0081] Figure 1 This is a structural and mechanical analysis model diagram of a pier-type energy dissipator.

[0082] Figure 2 This is an exploded view of the deformation of a support-type energy dissipator.

[0083] Figure 3 The diagram shows the beam's deflection curve and bending moment.

[0084] Figure 4 Flowchart for calculating the additional damping ratio.

[0085] Figure 5 This is a schematic diagram of the genetic algorithm optimization process.

[0086] Figure 6 This is a floor plan of the building.

[0087] Figure 7 Schematic diagram of the optimization process for the B-axis energy dissipator placement. Figure 1 .

[0088] Figure 8 This is a diagram showing the optimal layout scheme for an X-axis velocity-type energy dissipator.

[0089] Figure 9 Schematic diagram of the optimization process for the B-axis energy dissipator placement. Figure 2 .

[0090] Figure 10 The optimal layout scheme for X-direction displacement type energy dissipator. Detailed Implementation

[0091] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0092] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0093] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," and "parallel" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it can be slightly tilted or have a deviation. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," not that the structure must be completely horizontal, but that it can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the present invention.

[0094] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing between identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0095] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as 2, 3, 4, 5, 6, 7, 8, or 9, and can even exceed nine.

[0096] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0097] Example 1

[0098] Pier-type energy dissipators are a common type of energy dissipator connection. The energy dissipator is connected to the main structural frame beams via upper and lower piers. It is widely used because it can be integrated with building walls, has minimal impact on building function, and provides good vibration damping. In a typical pier-type energy dissipator, the upper and lower piers are connected to the frame beams respectively. Since the piers have high stiffness in the deformation direction of the energy dissipator, the deformation of the piers themselves is generally ignored. Its structural and mechanical analysis model can be found in [reference needed]. Figure 1 .

[0099] A method for optimizing the layout of pier-type energy dissipators based on genetic algorithms includes the following steps:

[0100] S1: Establish a non-damping structural model and perform calculations for the specified horizontal force conditions under the design waterproof level.

[0101] In specific implementation methods, common structural design software (PKPM / YJK / ETABS) can be used to establish a non-damping model of the structure, and the specified horizontal force conditions under the design waterproof level can be calculated according to the "Code for Seismic Design of Buildings" (GB50011-2010).

[0102] Extract the frame node displacement results and calculate the initial deformation of each span of each floor of the structure [δ] using the following formula. 0 ];

[0103] δ 0 =δ s +|θ E +θ F |×h zd

[0104]

[0105] In the formula, u and θ represent the horizontal displacement and angular displacement of the node, respectively, and h zd The heights of the upper and lower supports of the energy dissipator are given. A, B, C, and D are the four frame node numbers corresponding to the energy dissipator installation in this span, respectively. δ s θ represents the horizontal displacement difference between the energy dissipator layers. E θ F These are the corners of the frame beams at the corresponding positions of the upper and lower supports of the proposed energy dissipator.

[0106] S2: Based on the genetic algorithm, multiple energy dissipator layout schemes are randomly generated;

[0107] Depending on the different energy dissipator arrangement schemes, "1" indicates that an energy dissipator is installed in the span, and "0" indicates that no energy dissipator is installed in the span, forming different [sign] matrices;

[0108] S3: Considering the additional damping ratio correction, calculate the additional damping ratio for each energy dissipator arrangement scheme;

[0109] For each [sign] matrix, initialize the deformation [δ] caused by the energy dissipator reaction force. F ] = [0], [δ 0 ]、[δ F Both [sign] and [sign] are three-dimensional matrices, with dimensions of axis number × layer number × span number. The initial additional damping ratio is...

[0110] Calculate the deformation caused by the reaction force of the energy dissipator [δ] F ];

[0111] The deformation δ of the energy dissipator under seismic loading can be mainly divided into three parts: 1) Inter-story deformation δ caused by the difference in horizontal displacement between the upper and lower nodes. s ;2) The deflection δ of the frame beam caused by the vertical displacement difference and angular displacement at both ends. θ 3) Deflection δ of the frame beam caused by the reaction force of the energy dissipator F That is: δ = δ s +δ θ -δ F .

[0112] like Figure 2 As shown, the sum of the deformations of the first two parts is defined as the "initial deformation" δ. 0 The displacement can be calculated from the nodal displacements of the non-damping model under a specified horizontal force; the third part, deformation δ F The initial deformation δ generated by the reaction force of the energy dissipator 0 The reverse "indirect deformation" is related to the linear stiffness of the frame beams and the stiffness of the energy dissipator. The larger the deformation value of the energy dissipator, the better the energy dissipation effect, while δ... 0 The larger the value, the better the potential energy dissipation capacity after installing an energy dissipator at that location; δ F The larger the value, the smaller the ratio of the frame beam stiffness to the energy dissipator stiffness, the smaller the actual deformation of the energy dissipator, and the worse the energy dissipation capacity of the energy dissipator at that location.

[0113] In the specific implementation, the θ E θ F It can be calculated using the following methods:

[0114] The deflection curve and bending moment diagram of the beam with angular displacement and vertical deformation difference at both ends are shown in the figure. Figure 3 .

[0115] Assume the distance from point E, where the support is located, to the end is xl, and the rotation angle is θ. E The bending moment at the pier location is M x According to the equation for the rotational displacement of a beam, we have:

[0116] M A =4iθ A +2iθ B -6iΔ v / l

[0117] M B =4iθ B +2iθ A -6iΔ v / l

[0118] M x =M A -x(M A +M B )

[0119] In the formula, i represents the beam stiffness considering the effect of floor slab stiffness, and Δ v =v A -v B Δ v Let θ be the vertical displacement difference between the two ends of the beam, l be the beam span, and θ be the vertical displacement difference between the two ends of the beam. A θ B These represent the end angular displacements, M and M respectively. A M B These are the end bending moments;

[0120] Then, by integrating the equation of the beam's deflection curve, we can obtain θ. E ;

[0121]

[0122] In the formula, EI is the bending stiffness;

[0123] The rotation angle at any point in the beam is a quadratic function of the distance xl from the end. The position with the maximum rotation angle is the inflection point, at which point we have:

[0124]

[0125] Maximum turning angle is

[0126] For a typical frame beam, the inflection point can be simplified to mid-span, taking x = 1 / 2. The mid-span rotation angle is then given by the following formula.

[0127] θ E,x＝1 / 2 =-(θ) A +θ B -6Δ v / l) / 4

[0128] θ F,x＝1 / 2 -(θ C +θ D -6Δ v / l) / 4

[0129] In the formula, a negative value indicates that the rotation direction of the pier is opposite to that of the node. Therefore, the greater the inter-story drift difference and the beam end angular displacement, the greater the initial deformation; the smaller the vertical drift difference at the beam end (with a sign), the greater the initial deformation.

[0130] Based on the above formula, the initial deformation δ of the proposed energy dissipator in each floor and span can be obtained from the frame node displacements under a specified horizontal force condition using the non-damping model. 0 .

[0131] Calculate the deformation caused by the reaction force of the energy dissipator [δ] F ];

[0132] Based on geometric relationships and the constitutive mechanism of the energy dissipator, for a displacement-type energy dissipator, the deformation caused by the energy dissipator reaction force is calculated using the following formula:

[0133]

[0134] In the formula, The initial deformation is for the proposed energy dissipator position on the i-th layer and j-th span along the k-th axis. δ is the deformation caused by the reaction force F of the energy dissipator in the i-th layer and j-th span of the k-th axis, k2 is the stiffness of the energy dissipator after yielding, and δ y For yield displacement, F y For yield strength, h zd，i Let be the height of the energy dissipator support of the i-th layer. Let b be the stiffness of the frame beam along the k-th axis, the i-th floor, and the j-th span. Let F be the rotation angle of the frame beam pier position caused by the energy dissipator reaction force F of the (i-1)th floor, span of the k-th axis. k，i+1，j This represents the maximum output of the energy dissipator in the (i+1)th layer of the k-th axis, span j.

[0135] The velocity-type energy dissipator is solved using an iterative method based on the following equations;

[0136]

[0137] In the formula, The initial deformation is for the proposed energy dissipator position on the i-th layer and j-th span along the k-th axis. Let F be the deformation caused by the reaction force F of the energy dissipator in the i-th layer and j-th span of the k-th axis, ω be the first frequency of the structure in the calculation direction, β be the correction factor for calculating the maximum output of the viscous energy dissipator, C be the damping coefficient of the viscous energy dissipator, α be the velocity exponent of the viscous energy dissipator, and h be the velocity index of the viscous energy dissipator. zd，i Let F be the height of the energy dissipator support of the i-th layer. k，i+1，j For the maximum output of the energy dissipator in the (i+1)th layer of the k-th axis, Let b be the stiffness of the frame beam along the k-th axis, the i-th floor, and the j-th span. Let F be the rotation angle of the frame beam support pier position caused by the energy dissipator reaction force F of the (i-1)th floor and j-th span on the k-th axis.

[0138] Whether it is a displacement-type energy dissipator or a velocity-type energy dissipator, the solution... Depends on neighboring layers Therefore, a system of equations can be used to solve it. Alternatively, [the system can be...]. Initialize to zero, treat the deformation of non-i layer j span as known quantity, and solve for the unique unknown quantity.

[0139] Consider additional damping ratio correction;

[0140] Calculate the energy dissipation of the energy dissipator and the total strain energy of the structure to obtain the additional damping ratio ξ under a given energy dissipator arrangement.a .

[0141] In specific implementation methods, depending on the type of energy dissipator and given its actual deformation, the maximum output force can be calculated using the mechanical constitutive models of displacement-type and velocity-type energy dissipators, respectively. Then, the energy dissipation of the energy dissipator and the total structural strain energy can be calculated using standard formulas, thereby obtaining the additional damping ratio ξ under a given energy dissipator arrangement. a .

[0142] For a displacement-type energy dissipator, given an energy dissipator arrangement scheme, the additional damping ratio ξ is... a The calculation method is as follows:

[0143]

[0144]

[0145] In the formula, F i，j For the maximum output of the energy dissipator across the i-th layer j, The energy dissipator arranged for the i-th layer and j-th span is subject to the expected deformation δ i，j The energy consumed in one cycle of repetition;

[0146] W s =(1 / 2)∑F i u i

[0147]

[0148] In the formula, W s To calculate the total strain energy of the structure under seismic loading, ξ a Add damping ratio F to the energy dissipator i Let u be the shear force of the i-th floor. i Let be the inter-story displacement of the i-th layer.

[0149] For a velocity-type energy dissipator, given an energy dissipator arrangement scheme, the additional damping ratio ξ is... a The calculation method is as follows:

[0150]

[0151]

[0152] In the formula, For the maximum output of the energy dissipator across the i-th layer j, The energy dissipator arranged for the i-th layer and j-th span is subject to the expected deformation δ i，j The energy consumed in one cycle of the next reciprocating cycle, where λ1 is a function related to the damping exponent;

[0153] W s =(1 / 2)∑Fi u i

[0154]

[0155] In the formula, W s To calculate the total strain energy of the structure under seismic loading, ξ a Add damping ratio F to the energy dissipator i Let u be the shear force of the i-th floor. i Let be the inter-story displacement of the i-th layer.

[0156] After considering the additional damping ratio generated by the energy dissipator, the seismic response of the structure will decrease, as will the story shear force [F], inter-story displacement [u], and initial deformation of the energy dissipator [δ]. 0 All values ​​are obtained by multiplying the results of the non-damping model calculation by the structural response reduction factor η.

[0157] In a specific implementation, the expression for the structural response reduction coefficient η can be:

[0158]

[0159] In the formula, ξ a The additional damping ratio is given by T, which is the first-order period of the structure in the direction of the energy dissipator arrangement. g The characteristic period is denoted as .

[0160] Iterative calculation, such as Figure 4 As shown:

[0161] Update [δ] 0 ]、 [F], [u], repeat steps S2 to S3 until the additional damping ratio is reached. The error is less than the preset error convergence value. This indicates the calculated additional damping ratio after one iteration, and outputs the structural additional damping ratio corresponding to this energy dissipator arrangement. Typically, the preset error convergence value should be less than or equal to 0.01%.

[0162] S4: Genetic Algorithm Optimization

[0163] Genetic algorithms are adaptive probabilistic search algorithms that simulate the genetic and evolutionary processes of organisms in their natural environment. This method treats solutions in the search space as individuals, encoding them as chromosome sequences. The fitness of each individual is evaluated using a fitness function; individuals with higher fitness have a greater probability of being passed on to the next generation. By repeatedly performing selection, crossover, and mutation operations on the population of individuals, the method simulates the genetic and evolutionary processes of organisms to obtain the optimal solution to the problem. The computational process is described in [link to computation]. Figure 5 .

[0164] The optimal arrangement of energy dissipators can be divided into two categories. The first category: based on engineering experience or code requirements, the energy dissipation and damping structure needs to achieve a minimum additional damping ratio limit. Therefore, it is necessary to find the optimal arrangement position based on the target additional damping ratio to minimize the number of energy dissipators. The second category: based on engineering experience, the number of energy dissipators used in this structure is estimated. Therefore, it is necessary to find the optimal arrangement position based on a fixed number of energy dissipators to maximize the calculated additional damping ratio. The algorithm operation will be explained in detail below.

[0165] First type of optimal layout

[0166] Initial population generation: Generate 100 [sign] matrices. The larger the actual deformation value of the proposed energy dissipator at each position, the greater the probability that its value is "1". The maximum number of generations is 100.

[0167] Fitness function: Calculate the additional damping ratio corresponding to each [sign] matrix using the SHF-C method, select the [sign] matrices that meet the target additional damping ratio requirements, and then use the following formula as the fitness function.

[0168] Fit(n)=ξ a / [n(1+ξ a )]

[0169] In the formula, n is the number of energy dissipators, i.e., the number of "1"s in the [sign] matrix, and ξ... a To calculate the additional damping ratio.

[0170] Selection: Select individuals with high fitness to generate a new population. Use a roulette wheel selection method. The higher the fitness function, the greater the probability of being selected.

[0171] Crossover: Select a pair of individuals and perform a single-point crossover operation on their codes. That is, arbitrarily determine a crossover point in the codes and swap the [sign] matrices of the two individuals before and after the crossover point to obtain a pair of individuals containing new codes, thereby increasing the diversity of the population.

[0172] Mutation: Basic bit mutation is adopted, and each coding bit of an individual is mutated with a certain probability, that is, from "1" to "0" or from "0" to "1". The larger the actual deformation value of the proposed energy dissipator for each coding bit, the greater the probability that its value will become "1".

[0173] Individuals with high fitness are selected for crossover and mutation to generate a new population. This process is repeated g times to obtain the [sign] with the highest fitness, representing the optimal arrangement of the energy dissipators. The calculated optimal arrangement reflects whether energy dissipators are placed in each layer and span of the structure. Therefore, this invention extends the study of optimal energy dissipator arrangement to each layer and span of the structure.

[0174] Second type of optimal layout

[0175] Initial population generation: 100 [sign] matrices containing a fixed number of "1"s are randomly generated. The larger the actual deformation value of the proposed energy dissipator at each position, the greater the probability that its value is "1". The maximum number of generations is 100.

[0176] Fitness function: The additional damping ratio corresponding to each [sign] matrix is ​​calculated according to the SHF-C method, and the fitness function is calculated as follows.

[0177]

[0178] In the formula, The maximum expected additional damping ratio can be preset to around 5%.

[0179] Selection: Select individuals with high fitness to generate a new population.

[0180] Crossover: Select a pair of individuals, arbitrarily determine the crossover point, swap the positions of the "1"s in the two individuals, and ensure that the number of "1"s in the [sign] matrix remains unchanged.

[0181] Mutation: Basic bit mutation is used. The larger the initial transformation of each coded bit, the greater the probability that its value becomes "1". When the current coded bit is mutated, an opposite coded bit is randomly selected for mutation at the same time to ensure that the number of "1"s in the [sign] matrix remains unchanged.

[0182] Individuals with high fitness are selected for crossover and mutation to generate a new population. This process is repeated g times to obtain the [sign] with the highest fitness, representing the optimal arrangement of the energy dissipators. The calculated optimal arrangement reflects whether energy dissipators are placed in each layer and span of the structure. Therefore, this invention extends the study of optimal energy dissipator arrangement to each layer and span of the structure.

[0183] The genetic algorithm-based optimized arrangement method for pier-type energy dissipators described in this invention can obtain the optimal arrangement of energy dissipators for each floor and span of the structure based on the target additional damping ratio or the target number of energy dissipators. This can greatly improve the efficiency of energy dissipator arrangement scheme comparison and has strong guiding significance for seismic engineering design.

[0184] This invention provides a pier-type energy dissipator structure, which is arranged using any of the aforementioned pier-type energy dissipator optimization arrangement methods based on genetic algorithms.

[0185] The present invention provides a computing device, including at least one processor and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to execute any of the above-described genetic algorithm-based optimized arrangement method for pier-type energy dissipators.

[0186] The present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the above-described methods for optimizing the arrangement of a pier-type energy dissipator based on a genetic algorithm.

[0187] Example 2

[0188] This embodiment is a specific application of Embodiment 1. Specifically, a 10-story frame structure is built in the ETABS software, and the floor plan is shown below. Figure 6 Located in a seismic intensity zone of 7 degrees (0.1g), the first floor has a height of 6m, and the other floors have a height of 3.9m. The beam cross-section is 300mm×700mm, all using C30 concrete; the column cross-section is 800mm×800mm~500mm×500mm, using C50~C30 concrete. Taking the X direction as an example, it is planned to arrange pier-type energy dissipators along the B-axis to D-axis of the structure. However, due to the functional limitations of the building, energy dissipators cannot be arranged around the perimeter of the structure. Therefore, displacement-type and velocity-type energy dissipators are used for vibration reduction design.

[0189] The parameters of the energy dissipator are shown in Tables 1 and 2.

[0190] Table 1 Mechanical parameters of displacement type energy dissipator

[0191] Yield strength / kN Yield displacement / mm Stiffness before yielding / (kN / mm) Post-yield stiffness (kN / mm) 100 1.0 100 2.5

[0192] Table 2 Mechanical parameters of velocity-type energy dissipators

[0193] <![CDATA[Damping coefficient C / (kN / (mm) / s α )]]> Speed ​​index α <![CDATA[λ1]]> 30 0.3 3.66

[0194] The first three periods of the non-damped model are T1 = 1.74s (Y), T2 = 1.63s (X), and T3 = 1.54s (T).

[0195] For the first type of optimal arrangement

[0196] The vibration reduction design will utilize the viscous energy dissipator parameters shown in Table 2, with a target additional damping ratio of 3%. Following the aforementioned genetic algorithm-based optimized arrangement method for pier-type energy dissipators, taking the B-axis as an example, the [sign] matrix represents the energy dissipator placement locations, initial randomly generated locations, and optimal locations (see [sign]). Figure 7 Therefore, the optimal number of X-direction energy dissipators is 15. See the facade layout for details. Figure 8 .

[0197] For the second type of optimal arrangement

[0198] The displacement-type energy dissipator parameters in Table 1 are proposed for vibration reduction design. Based on engineering experience, the estimated number of energy dissipators in the X-direction is 24, calculated according to the building area. Following the aforementioned genetic algorithm-based optimized layout method for pier-type energy dissipators, taking the B-axis as an example, the [sign] matrix expresses the possible energy dissipator locations, the initial randomly generated locations, and the optimal locations (see [sign]). Figure 9 The X-direction energy dissipator facade layout is then obtained as shown in the figure. Figure 10 At this point, the additional damping ratio is 3.03%.

[0199] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimal arrangement of pier-type energy dissipater based on genetic algorithm, characterized in that, The method comprises the following steps: S1: Establish a non-damping model of structure, and calculate the prescribed horizontal force under the fortification level; extract the frame node displacement results, and calculate the initial deformation of each span of each layer of the structure according to the following formula [delta 0 ] delta 0 = delta s + theta E + theta F | x h zd where u and θ are the horizontal displacement and rotation displacement of the node, respectively, h zd is the height of the upper and lower piers of the damper, A, B, C, and D are the four frame node numbers corresponding to the span provided with the damper, respectively, δ s is the inter-story horizontal displacement difference of the damper, θ E , θ F are the frame beam rotation angles corresponding to the positions of the upper and lower piers of the damper, respectively. S2: randomly generating multiple energy dissipation device arrangement schemes according to a genetic algorithm; According to different energy dissipation device arrangement schemes, "1" represents that the span is provided with an energy dissipation device, and "0" represents that the span is not provided with an energy dissipation device, thereby forming different [sign] matrices; S3: considering additional damping ratio correction, calculating an additional damping ratio of each energy dissipation device arrangement scheme; For each [sign] matrix, initialize the deformation [delta F ] caused by the damper counterforce to [0], where [delta 0 ], [delta F ] and [sign] are three-dimensional matrices with dimensions axis number x layer number x span number, and the initial additional damping ratio is calculating the deformation [delta F ] caused by the energy absorber counterforce; According to geometric relations and energy dissipation device mechanics constitutive relation, for a displacement type energy dissipation device, deformation caused by an energy dissipation device counterforce is calculated according to the following formula: wherein, is the initial deformation of the kth axis, ith story, jth span of the proposed damper location, is the deformation of the kth axis, ith story, jth span of the damper due to the damper reaction force F, k2 is the post-yield stiffness of the damper, δ y is the yield displacement, F y is the yield force, h zd，i is the height of the ith story damper pier, is the b-line stiffness of the kth axis, ith story, jth span of the frame beam, is the rotation angle of the kth axis, ith story, jth span of the frame beam pier location due to the damper reaction force F, F k，i+1，j is the maximum output of the kth axis, ith story, jth span of the damper; For a velocity type energy dissipation device, an iterative method is used to solve according to the following equation; In the formula, is the initial deformation of the kth axis, the ith layer, and the jth span of the proposed energy dissipation position, is the deformation caused by the energy dissipation force F of the kth axis, the ith layer, and the jth span, ω is the calculated first frequency of the structure, β is the correction coefficient of the maximum output of the viscous energy dissipation, C is the damping coefficient of the viscous energy dissipation, α is the speed index of the viscous energy dissipation, h zd,i is the height of the energy dissipation pier of the ith layer, F k,i+1,j is the maximum output of the energy dissipation of the kth axis, the ith layer, and the jth span, is the linear stiffness of the frame beam b of the kth axis, the ith layer, and the jth span, is the corner of the frame beam pier position caused by the energy dissipation force F of the kth axis, the ith layer, and the jth span; Considering additional damping ratio correction; The energy dissipation of the energy dissipation device and the total strain energy of the structure are calculated to obtain the additional damping ratio ξ under the given energy dissipation device arrangement scheme a ; Floor shear force [F], inter-story drift [u] and initial deformation of damper [δ 0 ] are obtained by multiplying the results of non-dissipative model by the reduction factor η of structural response. update [delta 0 ], [F], [u], repeat steps S2-S3 until the additional damping ratio error is less than the preset error convergence value, representing the calculation of the additional damping ratio for one iteration, outputting the structural additional damping ratio corresponding to the energy absorber arrangement scheme; S4: genetic algorithm optimization For a first type of optimal arrangement: based on a target additional damping ratio, an optimal arrangement position is found, so that the number of energy dissipation devices is the least, An additional damping ratio of each energy dissipation device arrangement scheme is calculated, [sign] matrices meeting a target additional damping ratio requirement are screened, and the following formula is used as a fitness function Fit(n) = ξ a / [n(1+ξ a )] In the formula, n is the number of energy absorbers, i.e. the number of "1"s in the [sign] matrix, ξ a is the additional damping ratio; For a second type of optimal arrangement: based on a fixed number of energy dissipation devices, an optimal arrangement position is found, so that a calculated additional damping ratio is the largest, An additional damping ratio of each energy dissipation device arrangement scheme is calculated, [sign] matrices meeting a target additional damping ratio requirement are screened, and the following formula is used as a fitness function wherein is the expected maximum additional damping ratio; Selection, crossover and mutation: individuals are selected for crossover and mutation to generate a new population, g times of genetic iteration is performed, thereby obtaining a [sign] with the highest fitness, that is, an optimal energy dissipation device arrangement scheme.

2. The method for optimization of arrangement of pier-type energy dissipator based on genetic algorithm as claimed in claim 1 wherein, θ E θ F is calculated from the following equation: Assume that the position of the support pier E is xl away from the end, and the rotation angle is θ E , the bending moment at the position of the support pier is M x , according to the rotation displacement equation of the beam, there is: M A = 4iθ A + 2iθ B - 6iΔ v / l M B = 4iθ B + 2iθ A - 6iΔ v / 1 M x = M A - x(M A + M B ) where i is the beam linear stiffness considering the effect of floor stiffness, Δ v = v A -v B , Δ v is the vertical displacement difference of the beam end nodes, l is the beam span, θ A , θ B are the end rotation displacement, M A , M B are the end moment, respectively. Then, according to the deflection equation of the beam, the integral of θ is obtained E ; In the formula, EI is bending stiffness; The rotation angle value of any point in the beam is a quadratic function of the distance xl from the end, and the maximum position of the rotation angle is the inflection point, at which time: maximum rotation angle is 3. The method of claim 1, wherein the method is characterized by: In the S3, solving Dependence on neighboring layers Solving the system of equations simultaneously.

4. The method of claim 1, wherein the method is characterized by: In S3, we have Initialize to zero, and solve for the unique unknown quantity 5. The method of claim 1, wherein the method is characterized by: In S3, for a given energy dissipator arrangement scheme, the additional damping ratio ξ is... a The calculation method is as follows: where F i，j is the maximum output of the i-th layer j-span absorber, is the i-th layer j-span absorber arranged in the expected deformation δ i，j energy consumed in one downward and upward cycle; W s = (1 / 2)∑F i u i wherein W s is the total strain energy of the structure under seismic action, ξ a is the additional damping ratio of the damper, F i is the shear force of the i-th floor, u i is the inter-story drift of the i-th floor.

6. The method of claim 1, wherein the method is characterized by: In S3, for a velocity-type energy dissipator, the additional damping ratio ξ under a given energy dissipator arrangement scheme is... a The calculation method is as follows: wherein is the maximum output of the i-th layer j-span absorber, is the i-th layer j-span absorber arranged in the expected deformation δ i,j the energy consumed in the downstroke cycle, λ1is a function related to the damping exponent; W s = (1 / 2)∑F i u i wherein W s is the total strain energy of the structure under seismic action, ξ a is the additional damping ratio of the damper, F i is the shear force of the i-th floor, u i is the inter-story drift of the i-th floor.

7. The method of claim 1, wherein the method is characterized by: In the S3, the expression of the structure response reduction coefficient η is: In the formula, ξ a The additional damping ratio is given by T, which is the first-order period of the structure in the direction of the energy dissipator arrangement. g The characteristic period is denoted as .

8. A pier-type energy dissipator structure characterized by The method is arranged by using the method for optimal arrangement of a support pier type energy dissipation device based on a genetic algorithm according to any one of claims 1-7.

9. A computing device, comprising: The method comprises at least one processor, and a memory connected in communication with the at least one processor; the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method for optimal arrangement of a support pier type energy dissipation device based on a genetic algorithm according to any one of claims 1-7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the method for optimal arrangement of a support pier type energy dissipation device based on a genetic algorithm according to any one of claims 1-7.

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