How to create simulated earthquake motion

Abstract

To obtain a simulated earthquake motion which conforms to an acceleration response spectrum being a target and in which input energy of the actual earthquake motion is properly expressed.SOLUTION: A simulated earthquake motion creation device 100 calculates an acceleration response spectrum vector of a simulated earthquake motion corresponding to a candidate input vector on the basis of the candidate input vector. The simulated earthquake motion creation device 100 calculates an energy vector of the simulated earthquake motion corresponding to the candidate input vector on the basis of the candidate input vector. The simulated earthquake motion creation device 100 sets a candidate output vector including the acceleration response spectrum vector and the energy vector. The simulated earthquake motion creation device 100 calculates an error vector between a target vector including a target acceleration response spectrum vector and a target energy vector and the candidate output vector. The simulated earthquake motion creation device 100 calculates a new candidate input vector such that an error vector becomes small.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for generating simulated earthquake motion. [Background technology]

[0002] A method for generating simulated seismic waves is known (see, for example, Patent Document 1). This method calculates, through an inversion analysis, incident seismic waves to be incident on the engineering bedrock of a target area in order to induce seismic motion indicated in analytical data prepared from ground vibrations at the ground surface of the target area, based on analysis parameters prepared from the ground characteristics of the surface ground of the target area. The method then amplifies or attenuates the amplitude of the incident seismic waves, adjusting the maximum value of this amplitude to be equal to the maximum amplitude of a preset simulated seismic wave, and outputs the simulated seismic wave.

[0003] Also, a method for estimating input earthquake motion that can estimate input earthquake motion simply and with high accuracy is known (see, for example, Patent Document 2). This estimation method uses publicly available earthquake waveform data on bedrock, creates earthquake motion waveforms at an appropriate depth on the ground surface or on the surface ground based on multiple analysis methods, and selects an appropriate earthquake motion waveform from the created earthquake motion waveforms.

[0004] Also, a method for more simply and appropriately calculating the acceleration amplification factor of the surface ground of a target area is known (see, for example, Patent Document 3). In this method, when calculating the acceleration amplification factor of the surface ground of a target area, a computer acquires AVS30, which indicates the average propagation velocity of seismic waves in the range from the surface to a predetermined depth in the ground, for the target area. Then, in this method, the basement depth of the target area, which indicates the depth from the surface to the basement in the ground, is estimated, and AVSs, which indicates the average propagation velocity of seismic waves in the surface ground of the target area, is calculated based on the AVS30 and the basement depth of the target area. Under the assumption that the surface ground of the target area is composed of two layers of uniform thickness, the acceleration amplification factor of the surface ground is calculated based on the calculated AVSs.

[0005] Furthermore, a method for generating simulated earthquake motion is known that obtains simulated earthquake motion that conforms to a target acceleration response spectrum and that appropriately expresses the time-dependent characteristics of actual earthquake motion (see, for example, Patent Document 4). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-006158 [Patent Document 2] Japanese Patent Application Laid-Open No. 2006-266940 [Patent Document 3] Japanese Patent Application Publication No. 2018-025516 [Patent Document 4] Japanese Patent Publication No. 2021-169977 Summary of the Invention [Problem to be solved by the invention]

[0007] When creating simulated earthquake motion that takes into account the characteristics of actual earthquake motion, it is preferable to also take into account the input energy of the earthquake motion.

[0008] The techniques disclosed in the above Patent Documents 1 to 3 create simulated earthquake motions taking into consideration the characteristics of the construction site, but do not take into consideration the input energy of the earthquake motions.

[0009] Furthermore, the technology disclosed in Patent Document 4 creates simulated earthquake motion by taking into account the time-dependent characteristics of actual earthquake motion, and the technology disclosed in Patent Document 4 also does not take into account the input energy of earthquake motion.

[0010] The present invention has been made in consideration of the above facts, and aims to obtain simulated earthquake motion that conforms to the target acceleration response spectrum and that appropriately represents the input energy of actual earthquake motion. [Means for solving the problem]

[0011] In order to achieve the above object, the simulated earthquake motion creation method of the present invention is a method for creating an acceleration time history vector that represents the acceleration time history of a simulated earthquake motion, the method comprising the steps of: setting an initial vector of the acceleration time history of the simulated earthquake motion as a candidate input vector that represents a candidate for the acceleration time history vector; calculating an acceleration response spectrum vector of the simulated earthquake motion that corresponds to the candidate input vector based on the candidate input vector; calculating an energy vector that represents the energy of the simulated earthquake motion that corresponds to the candidate input vector based on the candidate input vector; This is a simulated earthquake motion generation method in which a computer executes the following processing: setting a complementary output vector, calculating an error vector between the candidate output vector and a target vector including a target acceleration response spectrum vector and a target energy vector, calculating a new candidate input vector so as to reduce the error vector, repeating the calculation of the acceleration response spectrum vector, the calculation of the energy vector, setting the candidate output vector, the calculation of the error vector, and the calculation of the new candidate input vector, and when a predetermined condition is satisfied, acquiring the new candidate input vector as the acceleration time history vector of the simulated earthquake motion. This makes it possible to obtain simulated earthquake motion that conforms to the target acceleration response spectrum and that appropriately represents the input energy of actual earthquake motion.

[0012] The energy vector of the present invention may be an energy spectrum vector representing the energy spectrum of the simulated earthquake motion, thereby making it possible to obtain simulated earthquake motion that matches the target acceleration response spectrum and the target energy spectrum.

[0013] In the method for generating a simulated earthquake motion according to the present invention, when a new candidate input vector {x} is calculated, a partial differential matrix [K] of the error vector {r} with respect to the candidate input vector {x} is generated, and the partial differential matrix [K] is subjected to singular value decomposition to obtain a generalized inverse matrix [K] + Generate the generalized inverse matrix [K] + Submatrix [Σ] of-1 A first mode group having singular values ​​greater than a predetermined value is selected from a plurality of modes corresponding to singular values ​​of the matrix [K']. + and generate the modified generalized inverse matrix [K'] + and the error vector {r}, a first correction vector {Δx1} representing a first correction amount for the candidate input vector {x} is calculated, a second mode group whose singular values ​​are equal to or less than a predetermined value is selected from the submatrix [V] of the result of the singular value decomposition, and a submatrix [V R ] is generated, and the submatrix [V R ], a preset reduction rate λ, and the candidate input vector {x}, a second correction vector {Δx2} representing a second correction amount for the candidate input vector {x} is calculated, and a new candidate input vector {x} is generated based on the candidate input vector {x}, the first correction vector {Δx1}, and the second correction vector {Δx2}. This makes it possible to obtain simulated earthquake motion that conforms to a target acceleration response spectrum and that appropriately represents the input energy of actual earthquake motion. [Effects of the Invention]

[0014] According to the present invention, it is possible to obtain an effect that simulated earthquake motion that conforms to a target acceleration response spectrum and that appropriately represents the input energy of actual earthquake motion can be obtained. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a block diagram showing an example of the configuration of a simulated earthquake motion creation device according to an embodiment of the present invention. [Figure 2] FIG. 10 is a diagram for explaining generation of simulated seismic motion. [Figure 3] 10A and 10B are diagrams for explaining the difference between a conventional method and the method of this embodiment. [Figure 4] FIG. 10 is a diagram showing an example of a simulated earthquake motion creation processing routine according to the present embodiment. [Figure 5]FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment. [Figure 6] FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment. [Figure 7] FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[0017] <Configuration of the simulated earthquake motion creation device according to this embodiment>

[0018] Fig. 1 shows an example of the configuration of a simulated earthquake motion creation device 100 according to an embodiment of the present invention. Functionally, as shown in Fig. 1, the simulated earthquake motion creation device 100 can be represented as a configuration including a data receiving unit 10, a computer 20, and an output unit 50. The simulated earthquake motion creation device 100 of this embodiment creates an acceleration time history vector that represents the acceleration time history of simulated earthquake motion.

[0019] In the earthquake-resistant design of high-rise buildings and seismically isolated buildings, safety verification by time history response analysis is required. One of the simulated earthquake motions, which is the design input earthquake motion used in the earthquake-resistant design of these buildings, is the notification spectrum (Reference: Ministry of Construction Notification No. 1,461 "Establishing standards for structural calculations to verify the structural safety of high-rise buildings"<https: / / www.mlit.go.jp / notice / noticedata / pdf / 201703 / 00006505.pdf> ) earthquake motions that fit the earthquake are known.

[0020] This simulated earthquake motion is set to match the target acceleration response spectrum or pseudo-velocity response spectrum. Here, the target acceleration response spectrum is set in advance, taking into account the amplification characteristics of the ground relative to the notified spectrum. However, since the acceleration response spectrum is a plot of the maximum acceleration of a single-mass response analysis model, the above-mentioned "sufficient earthquake input" merely guarantees input in terms of the building's maximum response acceleration and maximum response shear force, and is not earthquake motion created in terms of input energy.

[0021] On the other hand, super high-rise buildings often use structures such as base isolation structures or vibration control structures, where the energy absorption of earthquake-resistant elements is an important indicator of earthquake resistance. In these structural types, in addition to the maximum response acceleration and maximum response shear force of the building, the input energy input to the building due to earthquake motion, such as the absorbed energy of vibration control elements, is important in design.

[0022] However, there are many unknowns regarding the level of input energy guaranteed by the earthquake motions created using the current method based on the notification spectrum.Furthermore, there are currently no methods or examples of creating earthquake motions that guarantee both the acceleration response spectrum and input energy.

[0023] Therefore, in this embodiment, we focus on the energy spectrum of earthquake motion as one of the indices for evaluating the input energy of earthquake motion, and propose a method for creating simulated earthquake motion that is compatible with the acceleration response spectrum and energy spectrum. Note that the energy spectrum is an example of information representing the energy of simulated earthquake motion.

[0024] An overview of this embodiment is shown in Figure 2. By creating simulated earthquake motion that matches both the target acceleration response spectrum ("Target acc. spectrum" in Figure 2) and the target energy spectrum ("Target energy spectrum" in Figure 2), it is believed possible to create a time history of simulated earthquake motion ("Time history of simulated earthquake motion" in Figure 2) that also guarantees input energy.

[0025] In this embodiment, simulated earthquake motion is created using a modal iterative error correction method (see, for example, references (Suzuki, T.: Generation of Simulated Earthquake Motions Considering Actual Earthquake Phase and Multi Target Response Spectrums, Journal of Structural and Construction Engineering (Transactions of AIJ), Vol. 84, No. 760, pp. 811-818, June 2019 (in Japanese)) and JP 2021-169977 A).

[0026] FIG. 3 is a diagram illustrating the difference between the conventional method and the method of this embodiment. In this embodiment, the target output vector includes an energy spectrum vector that represents the energy spectrum of the simulated earthquake motion. As shown in FIG. 3(a), in the conventional method ("Before improvement" in FIG. 3), the input vector {x} is converted into a Fourier amplitude spectrum vector {a f}, and an input / output system is assumed in which the output vector {o} is the acceleration response spectrum vector {Sa}, and an input vector is found by inverse analysis so that the output vector becomes the target spectrum.

[0027] On the other hand, in the method of this embodiment shown in FIG. 3(b) (“After improvement” in FIG. 3), the output vector is an energy spectrum vector {V E}. That is, the output vector in this embodiment is {o}={{Sa} T ,{V E} T} T In this way, in this embodiment, by correcting the output vector and adding the energy spectrum vector to the target value, it is possible to create a simulated earthquake motion that matches both the acceleration response spectrum and the energy spectrum.

[0028] The specific details will be explained below.

[0029] The variables used in this embodiment are as shown in Table 1 below.

[0030] [Table 1]

[0031] The data receiving unit 10 receives a target acceleration response spectrum vector, which is a target value of the acceleration response spectrum vector of the simulated earthquake motion. The data receiving unit 10 also receives a target energy spectrum vector, which is a target value of the input energy of the simulated earthquake motion. The data receiving unit 10 is realized by, for example, a keyboard, a mouse, or an input / output device that receives input from an external device. The target acceleration response spectrum vector and the target energy spectrum vector are set in advance by the designer in accordance with the ground characteristics, ground amplification, target building, etc. of the location where the simulated earthquake motion is to be created.

[0032] The computer 20 includes a CPU (Central Processing Unit), a ROM (Read Only Memory) storing programs for implementing each processing routine, a RAM (Random Access Memory) for temporarily storing data, a memory serving as a storage means, a network interface, etc. As shown in Fig. 1, the computer 20 functionally includes a data storage unit 21, a candidate input vector setting unit 22, a candidate output vector setting unit 24, an error vector calculation unit 26, a determination unit 28, a matrix generation unit 30, a matrix calculation unit 32, a correction vector calculation unit 34, an update unit 36, and a result acquisition unit 38.

[0033] The simulated earthquake motion creation device 100 of this embodiment creates simulated earthquake motion using the method disclosed in the reference (Suzuki, T.: Generation of Simulated Earthquake Motions Considering Actual Earthquake Phase and Multi Target Response Spectrums, Journal of Structural and Construction Engineering (Transactions of AIJ), Vol. 84, No. 760, pp. 811-818, June 2019 (in Japanese)) or JP 2021-169977 A.

[0034] The data storage unit 21 stores the target acceleration response spectrum vector and the target energy spectrum vector received by the data receiving unit 10.

[0035] The candidate input vector setting unit 22 sets the initial vector of the acceleration time history of the simulated earthquake motion as a candidate input vector representing a candidate of the acceleration time history vector. For example, the candidate input vector setting unit 22 sets the initial vector of the acceleration time history of the simulated earthquake motion {x init} as the candidate input vector {x}.

[0036]

number

[0037] Note that the initial vector {x init} may be 0. Alternatively, it is also possible to use earthquake motions fitted only to the response spectrum as initial vectors without considering energy.

[0038] The candidate output vector setting unit 24 calculates the acceleration response spectrum vector {Sa} of the simulated seismic motion corresponding to the candidate input vector {x} according to the following equation (2), based on the candidate input vector {x} obtained by the candidate input vector setting unit 22 or the update unit 36 ​​described later.

[0039] Further, the candidate output vector setting unit 24 calculates the energy spectrum vector {V E}.

[0040]

number

[0041] Here, f1 in the above formula (2) represents the process of calculating the acceleration response spectrum, and f2 in the above formula (3) represents the process of calculating the energy spectrum. f1 and f2 are realized by known methods.

[0042] Then, the candidate output vector setting unit 24 calculates the acceleration response spectrum vector {Sa} and the energy spectrum vector {V EA candidate output vector {o} including {x} and {o} is set. Note that it is also possible to express the calculation of the candidate output vector {o} from the candidate input vector {x} using a function F as shown in the following equation (4). F is realized by a known method.

[0043]

number

[0044] The error vector calculation unit 26 reads out the target acceleration response spectrum vector and the target energy spectrum vector stored in the data storage unit 21. Next, the error vector calculation unit 26 calculates a target vector {o tar Then, the error vector calculation unit 26 calculates the target vector {o tar} and the candidate output vector {o} set by the candidate output vector setting unit 24.

[0045]

number

[0046] The determination unit 28 determines whether the error vector {r} calculated by the error vector calculation unit 26 is within a preset allowable range according to the following equation (6). Specifically, the determination unit 28 determines whether the norm of the error vector {r} is less than a threshold value ε, as shown in the following equation (6). The norm of the error vector {r} being less than the threshold value ε is an example of the predetermined condition.

[0047]

number

[0048] The matrix generation unit 30 generates a partial differential matrix [K] for the candidate input vector {x} of the error vector {r} calculated by the error vector calculation unit 26. The partial differential matrix [K] is a Jacobian matrix. Specifically, the matrix generation unit 30 generates the partial differential matrix [K] as shown in the following equation (7).

[0049]

number

[0050] The matrix calculation unit 32 performs singular value decomposition on the partial differential matrix [K] generated by the matrix generation unit 30 in accordance with the following equation (8), thereby deriving a generalized inverse matrix [K] of the partial differential matrix [K]: + Generate.

[0051]

number

[0052] The matrix calculation unit 32 calculates the generalized inverse matrix [K] + Submatrix [Σ] of -1 Next, the matrix calculation unit 32 calculates a modified generalized inverse matrix [K'] corresponding to the selected first mode group in accordance with the following equation (9): + Generate.

[0053]

number

[0054] Furthermore, the matrix calculation unit 32 selects a second mode group whose singular values ​​are equal to or less than a second predetermined value from the submatrix [V] of the singular value decomposition result. Then, the matrix calculation unit 32 calculates the submatrix [V] corresponding to the selected second mode group as shown in the following equation (10). RThe first predetermined value and the second predetermined value may be different values ​​or may be the same value.

[0055]

number

[0056] The correction vector calculation unit 34 calculates the corrected generalized inverse matrix [K'] generated by the matrix calculation unit 32. + and the error vector {r} calculated by the error vector calculation unit 26, a first correction vector {Δx1} representing a first correction amount for the candidate input vector {x} is calculated as shown in the following equation (11). The first correction vector {Δx1} is a vector that includes only components of the first mode group, which have large singular values ​​and a high degree of influence, and is therefore a correction vector in which the influence of noise is reduced.

[0057]

number

[0058] The correction vector calculation unit 34 calculates the submatrix [V R ], a preset reduction rate λ, and the candidate input vector {x} obtained by the candidate input vector setting unit 22 or the update unit 36 ​​described later, a second correction vector {Δx2} representing a second correction amount for the candidate input vector {x} is calculated as shown in the following equation (12). The reduction rate λ is, for example, a value between 0 and 1. The absolute value of the second correction vector {Δx2} is a vector containing components of a second mode group with small singular values ​​and small influence, and therefore is a correction vector containing noise. For this reason, as described below, the influence of noise can be reduced by adding the second correction vector {Δx2} multiplied by a negative number to the candidate input vector {x}.

[0059]

number

[0060] The update unit 36 ​​generates a new candidate input vector {x} according to the following equation (13) based on the candidate input vector {x} set by the candidate input vector setting unit 22 or the previous processing of the update unit 36 ​​and the first correction vector {Δx1} and the second correction vector {Δx2} calculated by the correction vector calculation unit 34. Specifically, as shown in the following equation (13), the update unit 36 ​​adds the first correction vector {Δx1} and the second correction vector {Δx2} to the candidate input vector {x} to generate a new candidate input vector {x}.

[0061]

number

[0062] Then, the acceleration response spectrum vector {Sa} is calculated and the energy spectrum vector {V E}, setting of candidate output vector {o}, calculation of error vector {r}, and calculation of new candidate input vector {x} are repeated.

[0063] When the norm |{r}| of the error vector {r} calculated by the error vector calculation unit 26 becomes less than the threshold value ε, the result acquisition unit 38 acquires the new candidate input vector {x} generated by the update unit 36 ​​as the acceleration time history vector corresponding to the target vector.

[0064] The output unit 50 outputs the acceleration time history vector obtained by the result obtaining unit 38. For example, the output unit 50 is realized by a display.

[0065] <Function of the earthquake motion simulation device 100>

[0066] Next, we will explain the operation of the simulated earthquake motion creation device 100. When the data receiving unit 10 of the simulated earthquake motion creation device 100 receives the input of the target acceleration response spectrum vector and the target energy spectrum vector, it stores them in the data storage unit 21. Then, when the computer 20 of the simulated earthquake motion creation device 100 receives an instruction signal to execute processing, it executes the simulated earthquake motion creation processing routine shown in Figure 4.

[0067] In step S100, the candidate input vector setting unit 22 calculates the initial vector {x init} as the candidate input vector {x}.

[0068] In step S102, the candidate output vector setting unit 24 calculates the acceleration response spectrum vector {Sa} corresponding to the candidate input vector {x} according to the above formula (2) based on the candidate input vector {x} obtained in the above step S100 or the previous step S120. Also in step S102, the candidate output vector setting unit 24 calculates the energy spectrum vector {V E}.

[0069] Then, in step S102, the candidate output vector setting unit 24 calculates the acceleration response spectrum vector {Sa} and the energy spectrum vector {V E} and set a candidate output vector {o} containing

[0070] In step S104, the error vector calculation unit 26 reads out the target acceleration response spectrum vector and the target energy spectrum vector stored in the data storage unit 21. Next, in step S104, the error vector calculation unit 26 calculates a target vector {o tarThen, in step S104, the error vector calculation unit 26 calculates the target vector {o tar} and the candidate output vector {o} set in step S102 above.

[0071] In step S106, the determination unit 28 determines whether the norm of the error vector {r} calculated in step S106 is less than the threshold ε according to the above formula (6). If the norm of the error vector {r} is less than the threshold ε, the process proceeds to step S122. If the norm of the error vector {r} is equal to or greater than the threshold ε, the process proceeds to step S108.

[0072] In step S108, the matrix generation unit 30 generates a partial differential matrix [K] of the error vector {r} calculated in step S104 with respect to the candidate input vector {x} as shown in the above equation (7).

[0073] In step S110, the matrix calculation unit 32 performs singular value decomposition on the partial differential matrix [K] generated in step S108, as shown in the above formula (8), to obtain the generalized inverse matrix [K] of the partial differential matrix [K]. + Generate.

[0074] In step S112, the matrix calculation unit 32 calculates the generalized inverse matrix [K] generated in step S110. + Submatrix [Σ] of -1 Next, in step S112, the matrix calculation unit 32 calculates a modified generalized inverse matrix [K'] corresponding to the selected first mode group in accordance with the above equation (9). + Generate.

[0075] In step S114, the matrix calculation unit 32 selects a second mode group having singular values ​​equal to or less than a predetermined value from the submatrix [V] of the singular value decomposition result obtained in step S110. Then, in step S114, the matrix calculation unit 32 calculates the submatrix [V R ] is generated.

[0076] In step S116, the correction vector calculation unit 34 calculates the corrected generalized inverse matrix [K'] generated in step S112. + and the error vector {r} calculated in step S104, as shown in the above equation (11), a first correction vector {Δx1} for the candidate input vector {x} is calculated.

[0077] In step S118, the correction vector calculation unit 34 calculates the submatrix [V R ], a preset reduction rate λ, and the candidate input vector {x} obtained in step S100 or the previous step S120, a second correction vector {Δx2} for the candidate input vector {x} is calculated as shown in equation (12) above.

[0078] In step S120, the update unit 36 ​​generates a new candidate input vector {x} in accordance with the above equation (13) based on the candidate input vector {x} obtained in the above step S100 or the previous step S120, the first correction vector {Δx1} calculated in step S116, and the second correction vector {Δx2} calculated in step S118.

[0079] The simulated earthquake motion creation routine calculates the acceleration response spectrum vector {Sa} and the energy spectrum vector {V E}, setting of candidate output vector {o}, calculation of error vector {r}, and calculation of new candidate input vector {x} are repeated.

[0080] If the norm of the error vector {r} is less than the threshold value ε, in step S122, the result acquisition unit 38 acquires a new candidate input vector {x} as the acceleration time history vector of the simulated earthquake motion.

[0081] The output unit 50 outputs the acceleration time history vector acquired by the result acquisition unit 38 as a result.

[0082] As described above in detail, the simulated earthquake motion creation device 100 of this embodiment sets the initial vector of the acceleration time history of the simulated earthquake motion as a candidate input vector representing a candidate for the acceleration time history vector. Based on the candidate input vector, the simulated earthquake motion creation device 100 calculates the acceleration response spectrum vector of the simulated earthquake motion corresponding to the candidate input vector. Based on the candidate input vector, the simulated earthquake motion creation device 100 calculates the energy spectrum vector of the simulated earthquake motion corresponding to the candidate input vector. The simulated earthquake motion creation device 100 sets a candidate output vector including an acceleration response spectrum vector and an energy spectrum vector. The simulated earthquake motion creation device 100 calculates an error vector between the target vector, including the target acceleration response spectrum vector and the target energy spectrum vector, and the candidate output vector. The simulated earthquake motion creation device 100 calculates a new candidate input vector so as to reduce the error vector. The simulated earthquake motion creation device 100 repeats the calculation of the acceleration response spectrum vector, the calculation of the energy spectrum vector, the setting of the candidate output vector, the calculation of the error vector, and the calculation of a new candidate input vector, and when a predetermined condition is satisfied, acquires the new candidate input vector as the acceleration time history vector of the simulated earthquake motion. In this way, it is possible to obtain simulated earthquake motion that conforms to the target acceleration response spectrum and that appropriately represents the input energy of the actual earthquake motion.

[0083] Specifically, the simulated earthquake motion creation device 100 of this embodiment sets the energy spectrum as a target value in addition to the acceleration response spectrum, thereby obtaining simulated earthquake motion that satisfies the target acceleration response spectrum and appropriately reflects the input energy of the actual earthquake motion.

[0084] In this embodiment, the input vector, which is a variable, is set to the acceleration time history instead of the amplitude spectrum, which makes it possible to uniquely determine the simulated earthquake motion to be created.

[0085] <Simulation experiment>

[0086] Next, the effect of the method for generating simulated earthquake motion according to this embodiment will be confirmed using an example problem.

[0087] FIG. 5(A) shows the target acceleration response spectrum. FIG. 5(B) shows the target energy spectrum. The α in FIG. 5(B) represents different energies. In the following, a simulated earthquake motion that matches the target acceleration response spectrum in FIG. 5(A) and the target energy spectrum (α=2.0) in FIG. 5(B) will be created using the method of this embodiment. The horizontal axis of the graphs in FIG. 5, FIG. 6, and FIG. 7 represents time (s), and the vertical axis represents acceleration (m / s 2 ) and speed conversion value (m / s).

[0088] FIG. 6 shows simulated earthquake motion created by the method of this embodiment. FIG. 6(A) shows the acceleration time history of the simulated earthquake motion created by the method of this embodiment. "Generated" in FIG. 6(B) is the acceleration response spectrum of the simulated earthquake motion created by the method of this embodiment. "Target" in FIG. 6(B) is the target acceleration response spectrum. "Generated" in FIG. 6(C) is the energy spectrum of the simulated earthquake motion created by the method of this embodiment. "Target" in FIG. 6(C) is the target energy spectrum. It can be seen that the simulated earthquake motion shown in FIG. 6 is a simulated earthquake motion that conforms to both the target acceleration response spectrum and the target energy spectrum. Therefore, it can be seen that this embodiment creates simulated earthquake motion that conforms to both the target acceleration response spectrum and the target energy spectrum.

[0089] For comparison, FIG. 7 shows simulated earthquake motions created using a method of adapting only the target acceleration response spectrum (hereinafter simply referred to as the conventional method). FIG. 7(A) shows the acceleration time history of the simulated earthquake motions created using the conventional method. FIG. 7(B) shows the energy spectrum of the simulated earthquake motions created using the conventional method. As shown in FIG. 7, although the simulated earthquake motions created using the conventional method conform to the target acceleration response spectrum, the energy spectrum varies, and it is difficult to say that the input energy conforms to the target energy spectrum. Therefore, comparing FIG. 6 and FIG. 7, it can be seen that the simulated earthquake motion creation method according to this embodiment can generate simulated earthquake motions that satisfy the target acceleration response spectrum and appropriately reflect the input energy of actual earthquake motions.

[0090] The present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the spirit and scope of the present invention.

[0091] For example, in the above embodiment, an example has been described in which an energy spectrum vector is used as a vector representing the energy of simulated earthquake motion, but the present invention is not limited to this. Any information representing the energy of simulated earthquake motion may be used.

[0092] Furthermore, in the above embodiment, a case has been described in which simulated earthquake motions are created by repeatedly calculating new candidate input vectors to reduce the error vector using the method disclosed in the reference document (Suzuki, T.: Generation of Simulated Earthquake Motions Considering Actual Earthquake Phase and Multi Target Response Spectrums, Journal of Structural and Construction Engineering (Transactions of AIJ), Vol. 84, No. 760, pp. 811-818, June 2019 (in Japanese)) or the method disclosed in Japanese Patent Application Laid-Open No. 2021-169977, but the present invention is not limited to this. For example, simulated earthquake motions may be created by repeatedly calculating new candidate input vectors to reduce the error vector using a nonlinear least squares method, Newton's method, steepest descent method, or genetic algorithm.

[0093] Furthermore, although the above describes a case in which the program is pre-stored (installed) in a storage unit (not shown), the program can also be provided in a form in which it is recorded on any of the recording media such as a CD-ROM, DVD-ROM, or microSD card. [Explanation of symbols]

[0094] 20 Computer 21 Data storage unit 22 Candidate input vector setting unit 24 Candidate output vector setting unit 26 Error vector calculation unit 28 Judgment section 30 Matrix generator 32 Matrix operation section 34 Correction vector calculation unit 36 Update section 38 Result acquisition part

Claims

1. A method for creating a simulated earthquake motion by generating an acceleration time history vector representing the acceleration time history of a simulated earthquake motion, comprising the steps of: setting an initial vector of the acceleration time history of the simulated earthquake motion as a candidate input vector representing a candidate of the acceleration time history vector; calculating an acceleration response spectrum vector of the simulated earthquake motion corresponding to the candidate input vector based on the candidate input vector; calculating an energy vector representing the energy of the simulated earthquake motion corresponding to the candidate input vector based on the candidate input vector; a candidate output vector including the acceleration response spectrum vector and the energy vector is set; calculating an error vector between a target vector including a target acceleration response spectrum vector and a target energy vector and the candidate output vector; Calculating new candidate input vectors so that the error vector is smaller; repeating the calculation of the acceleration response spectrum vector, the calculation of the energy vector, the setting of the candidate output vector, the calculation of the error vector, and the calculation of a new candidate input vector; If a predetermined condition is satisfied, the new candidate input vector is acquired as the acceleration time history vector of the simulated earthquake motion. A method for generating simulated earthquake motion in which processing is performed by a computer.

2. The energy vector is an energy spectrum vector representing the energy spectrum of the simulated seismic motion. The method for generating simulated earthquake motion according to claim 1.

3. When computing the new candidate input vector {x}, Generate a partial differential matrix [K] of the error vector {r} with respect to the candidate input vector {x}; The partial differential matrix [K] is subjected to singular value decomposition to obtain a generalized inverse matrix [K] ＋ Generate The generalized inverse matrix [K] ＋ Submatrix of [Σ] －１ selecting a first group of modes from a plurality of modes corresponding to singular values ​​of the [K'] is the modified generalized inverse matrix corresponding to the selected first mode group. ＋ Generate The modified generalized inverse matrix [K'] ＋ and the error vector {r}, a first correction vector {Δx １ }, selecting a second mode group, in which the singular values ​​are equal to or less than a second predetermined value, from the submatrix [V] of the result of the singular value decomposition; The submatrix [V Ｒ ], The submatrix [V Ｒ ], a preset reduction rate λ, and the candidate input vector {x}, a second correction vector {Δx ２ }, The candidate input vector {x} and the first correction vector {Δx １ } and the second correction vector {Δx ２ }, and generate a new candidate input vector {x}. The method for generating simulated earthquake motion according to claim 1 or 2.

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