JP7807974B2 - How to create simulated earthquake motion - Google Patents

Description

The present invention relates to a method for creating simulated earthquake motion.

A method for creating simulated seismic waves is known (see, for example, Patent Document 1). This method uses analysis parameters prepared from the ground characteristics of the surface ground in the target area to calculate incident seismic waves that should be incident on the engineering bedrock of the target area through inversion analysis in order to induce seismic motion indicated in the analysis data prepared from ground vibrations at the ground surface in 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 predetermined simulated seismic wave, and outputs the simulated seismic wave.

A method for estimating input earthquake motion is also known that can estimate input earthquake motion simply and with high accuracy (see, for example, Patent Document 2). This estimation method uses publicly available earthquake waveform data on bedrock surfaces to create earthquake motion waveforms at appropriate depths on the ground surface or in the surface layer based on multiple analysis methods, and then selects an appropriate earthquake motion waveform from the created earthquake motion waveforms.

A method for more simply and appropriately calculating the acceleration amplification factor of the surface ground of a target area is also 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 speed of seismic waves in the range from the surface to a specified depth in the ground. This method then estimates the basement depth of the target area, where the basement depth, which indicates the depth from the surface to the basement, is unknown. Based on AVS30 and the basement depth of the target area, AVSs, which indicates the average propagation speed of seismic waves in the surface ground of the target area, is calculated. 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.

In addition, a method for generating simulated earthquake motion is known that obtains simulated earthquake motion that conforms to the target acceleration response spectrum while appropriately representing the time-dependent characteristics of actual earthquake motion (see, for example, Patent Document 4).

Japanese Patent Application Laid-Open No. 2014-006158 Japanese Patent Application Laid-Open No. 2006-266940 Japanese Patent Application Publication No. 2018-025516 Japanese Patent Publication No. 2021-169977

By the way, 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.

The technologies disclosed in the above Patent Documents 1 to 3 create simulated earthquake motions by taking into account the characteristics of the construction site, but do not take into account the input energy of the earthquake motions.

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.

The present invention was made in light of the above facts, and aims to obtain simulated earthquake motion that conforms to the target acceleration response spectrum and appropriately represents the input energy of actual earthquake motion.

In order to achieve the above-mentioned objective, 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 simulated earthquake motion, and includes: 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 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; and generating a candidate vector including the acceleration response spectrum vector and the energy vector. This is a simulated earthquake motion generation method in which a computer executes the following processes: set a complementary output vector; calculate an error vector between the candidate output vector and a target vector, which includes a target acceleration response spectrum vector and a target energy vector; calculate a new candidate input vector so that the error vector is small; repeat the calculation of the acceleration response spectrum vector, the energy vector, the setting of the candidate output vector, the error vector, and the new candidate input vector; and, if a predetermined condition is met, obtain the new candidate input vector as the acceleration time history vector of the simulated earthquake motion. This allows for the generation of simulated earthquake motion that conforms to the target acceleration response spectrum and appropriately represents the input energy of actual earthquake motion.

The energy vector of the present invention may be an energy spectrum vector representing the energy spectrum of the simulated earthquake motion. This makes it possible to obtain simulated earthquake motion that matches the target acceleration response spectrum and the target energy spectrum.

The simulated earthquake motion generation method of the present invention, when calculating a new candidate input vector {x}, generates a partial differential matrix [K] of the error vector {r} with respect to the candidate input vector {x}, performs singular value decomposition on the partial differential matrix [K] to generate a generalized inverse matrix [K] ^{+ ,} selects a first group of modes whose singular values are greater than a predetermined value from a plurality of modes corresponding to singular values of a submatrix [Σ] ^-1 of the generalized inverse matrix [K] ⁺ , and generates a modified generalized inverse matrix [K']+ corresponding to the selected first group of modes, calculates a first correction vector {Δx ₁ } representing a first correction amount for the candidate input vector {x} based on the modified generalized inverse matrix [K'] ⁺ and the error vector {r}, selects a second group of modes whose singular values are less than a predetermined value from a submatrix [V] of the result of the singular value decomposition, and generates a submatrix [V _{R ]} corresponding to the selected second group of modes, and ], a preset reduction rate λ, and the candidate input vector {x}, a second correction vector {Δx ₂ } 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 {Δx ₁ }, and the second correction vector {Δx ₂ }. 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.

The present invention has the advantage of being able to obtain simulated earthquake motion that conforms to the target acceleration response spectrum and appropriately represents the input energy of actual earthquake motion.

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. FIG. 10 is a diagram for explaining generation of simulated seismic motion. 10A and 10B are diagrams for explaining the difference between a conventional method and the method of this embodiment. FIG. 10 is a diagram showing an example of a simulated earthquake motion creation processing routine according to the present embodiment. FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment. FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment. FIG. 1 is an explanatory diagram for explaining the contents of a simulation experiment.

Embodiments of the present invention will be described in detail below with reference to the drawings.

<Configuration of the earthquake motion simulation device according to this embodiment>

Figure 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 Figure 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.

The earthquake-resistant design of high-rise buildings and seismically isolated buildings requires safety verification using time history response analysis. One of the simulated earthquake motions, which serves as the design input earthquake motion used in the earthquake-resistant design of these buildings, is known to conform to the public notice spectrum (Reference: Ministry of Construction Public Notice 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>).

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, because 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.

On the other hand, super-high-rise buildings often use structures such as base-isolated structures or vibration-damping structures, in which the energy absorption of earthquake-resistant elements is an important indicator of earthquake resistance. In these structural types, in addition to the building's maximum response acceleration and maximum response shear force, the input energy input to the building due to earthquake motion, such as the energy absorbed by vibration-damping elements, is also important in the design.

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

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 that represents the energy of simulated earthquake motion.

Figure 2 shows an overview of this embodiment. 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.

In this embodiment, simulated earthquake motions are created using the 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).

Figure 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 representing the energy spectrum of the simulated earthquake motion. As shown in Figure 3(a), the conventional method ("Before improvement" in Figure 3) assumes an input/output system in which the input vector {x} is the Fourier amplitude spectrum vector {a _f } and the output vector {o} is the acceleration response spectrum vector {Sa}, and uses inverse analysis to find an input vector that will result in a target spectrum output vector.

On the other hand, in the method of this embodiment shown in Figure 3(b) ("After improvement" in Figure 3), the energy spectrum vector {V _E } is combined with the conventional acceleration response spectrum vector {Sa} in the output vector. That is, the output vector of this embodiment is {o} = {{Sa} ^T , {V _E } ^T } ^T. In this way, in this embodiment, by modifying the output vector and adding the energy spectrum vector to the target value, it is possible to create simulated earthquake motion that is compatible with both the acceleration response spectrum and the energy spectrum.

The details are explained below.

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

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

The computer 20 is composed of a CPU (Central Processing Unit), ROM (Read Only Memory) that stores programs for implementing each processing routine, RAM (Random Access Memory) that temporarily stores data, memory as a storage means, a network interface, etc. As shown in FIG. 1, the computer 20 functionally comprises 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.

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.

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.

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 for the acceleration time history vector. For example, the candidate input vector setting unit 22 sets the initial vector {x _init } of the acceleration time history of the simulated earthquake motion as the candidate input vector {x}, as shown in the following equation (1).

(1)

The initial vector {x _init } may be 0. Alternatively, it is also possible to use, as the initial vector, earthquake motion or the like that is fitted only to the response spectrum without taking energy into consideration.

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 below.

Furthermore, the candidate output vector setting unit 24 calculates the energy spectrum vector {V E } of the simulated seismic motion corresponding to the candidate input vector {x} according to the following equation (3), based on the candidate input vector {x} obtained by the candidate input vector setting unit 22 or the update _{unit 36} described later.

(2)

(3)

Here, _f1 in the above formula (2) represents a process for calculating an acceleration response spectrum, and _f2 in the above formula (3) represents a process for calculating an energy spectrum. _f1 and _f2 are realized by known methods.

Then, the candidate output vector setting unit 24 sets a candidate output vector {o} including the acceleration response spectrum vector {Sa} and the energy spectrum vector {V _E }. Note that the calculation of the candidate output vector {o} from the candidate input vector {x} can also be expressed by a function F as shown in the following equation (4). F is realized by a known method.

(4)

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 sets a target vector {o _tar } including the target acceleration response spectrum vector and the target energy spectrum vector. Then, the error vector calculation unit 26 calculates an error vector {r} between the target vector {o _tar } and the candidate output vector {o} set by the candidate output vector setting unit 24 according to the following equation (5).

(5)

The determination unit 28 determines whether the error vector {r} calculated by the error vector calculation unit 26 is within a preset tolerance range according to the following equation (6). Specifically, the determination unit 28 determines whether the norm of the error vector {r} is less than the 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 a predetermined condition.

(6)

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).

(7)

The matrix calculation unit 32 generates a generalized inverse matrix [K]+ of the partial differential matrix [K] by performing singular value decomposition on the partial differential matrix [K] generated by the matrix generation unit ³⁰ in accordance with the following equation (8).

(8)

The matrix operation unit 32 selects a first group of modes whose singular values are greater than a first predetermined value from a plurality of modes corresponding to the singular values of the submatrix [Σ] ⁻¹ of the generalized inverse matrix [K] ⁺ . Next, the matrix operation unit 32 generates a modified generalized inverse matrix [K′] ⁺ corresponding to the selected first group of modes according to the following equation (9):

(9)

Furthermore, the matrix operation unit 32 selects a second group of modes, the singular values of which are equal to or less than a second predetermined value, from the submatrix [V] of the singular value decomposition result. Then, the matrix operation unit 32 generates a submatrix [V _R ] corresponding to the selected second group of modes, as shown in the following equation (10). Note that the first predetermined value and the second predetermined value may be different values or the same value.

(10)

The correction vector calculation unit 34 calculates a first correction vector {Δx 1 } representing a first correction amount for the candidate input vector {x}, as shown in the following equation (11), based on the modified generalized inverse matrix [K'] ⁺ generated by the matrix calculation unit 32 and the error vector {r} calculated by the error vector calculation unit 26. The first correction vector {Δx ₁ } 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.

(11)

The correction vector calculation unit 34 calculates a second correction vector {Δx 2 } representing a second correction amount for the candidate input vector {x}, as shown in the following equation (12), based on the submatrix [V _R ] generated by the matrix calculation unit 32, 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. The reduction rate λ is, for example, a value between 0 and 1. The absolute value of the second correction vector {Δx ₂ } is a vector containing components of a second mode group having small singular values and little influence, and therefore is a correction vector containing noise. For this reason, as described later, the influence of noise can be reduced by adding the second correction vector {Δx ₂ } multiplied by a negative number to the candidate input vector {x}.

(12)

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 {Δx ₁ } and the second correction vector {Δx ₂ } 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 {Δx ₁ } and the second correction vector {Δx ₂ } to the candidate input vector {x} to generate a new candidate input vector {x}.

(13)

Then, the processes of calculating the acceleration response spectrum vector {Sa}, calculating the energy spectrum vector {V _E }, setting the candidate output vector {o}, calculating the error vector {r}, and calculating a new candidate input vector {x} are repeated so that the error vector {r} becomes smaller.

When the norm |{r}| of the error vector {r} calculated by the error vector calculation unit 26 is 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.

The output unit 50 outputs the acceleration time history vector acquired by the result acquisition unit 38 as a result. For example, the output unit 50 is realized by a display.

<Function of the earthquake motion simulation device 100>

Next, the operation of the earthquake motion simulation device 100 will be explained. When the data receiving unit 10 of the earthquake motion simulation device 100 receives input of a target acceleration response spectrum vector and a target energy spectrum vector, it stores them in the data storage unit 21. Then, when the computer 20 of the earthquake motion simulation device 100 receives a command signal to execute processing, it executes the earthquake motion simulation processing routine shown in Figure 4.

In step S100, the candidate input vector setting unit 22 sets the initial vector {x _init } of the acceleration time history of the simulated earthquake motion as the candidate input vector {x}, as shown in the above formula (1).

In step S102, the candidate output vector setting unit 24 calculates an 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 an energy spectrum vector {V _E } corresponding to the candidate input vector {x} according to the above formula (3) based on the candidate input vector {x} obtained in the above step S100 or the previous step S120.

Then, in step S102, the candidate output vector setting unit 24 sets a candidate output vector {o} including the acceleration response spectrum vector {Sa} and the energy spectrum vector {V _E } as shown in the above formula (4).

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 sets a target vector {o _tar } including the target acceleration response spectrum vector and the target energy spectrum vector. Then, in step S104, the error vector calculation unit 26 calculates the error vector {r} between the target vector {o _tar } and the candidate output vector {o} set in step S102 in accordance with the above equation (5).

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 value ε, according to the above formula (6). If the norm of the error vector {r} is less than the threshold value ε, the process proceeds to step S122. If the norm of the error vector {r} is equal to or greater than the threshold value ε, the process proceeds to step S108.

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).

In step S110, the matrix operation unit 32 generates a generalized inverse matrix [K]+ of the partial differential matrix [K] by performing singular value decomposition on the partial differential matrix [K] generated in step ^S108 , as shown in the above equation (8).

In step S112, the matrix operation unit 32 selects a first group of modes whose singular values are greater than a predetermined value from the plurality of modes corresponding to the singular values of the submatrix [Σ] ⁻¹ of the generalized inverse matrix [K] ⁺ generated in step S110. Next, in step S112, the matrix operation unit 32 generates a modified generalized inverse matrix [K′] ⁺ corresponding to the selected first group of modes in accordance with the above equation (9).

In step S114, the matrix operation 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 operation unit 32 generates a submatrix [V _R ] corresponding to the selected second mode group, as shown in the above equation (10).

In step S116, the correction vector calculation unit 34 calculates a first correction vector {Δx 1 } for the candidate input vector {x}, as shown in the above equation (11), based on the modified generalized inverse matrix [K'] ⁺ generated in step S112 and the error vector {r} calculated in step _S104 .

In step S118, the correction vector calculation unit 34 calculates a second correction vector {Δx 2 } for the candidate input vector {x}, as shown in the above formula (12), based on the submatrix [V _R ] generated in step S114, the preset reduction rate λ, and the candidate input vector {x} obtained in the above step S100 or the previous step _S120 .

In step S120, the update unit 36 generates a new candidate input vector {x} in accordance with the above formula (13) based on the candidate input vector {x} obtained in the above step S100 or the previous step S120, the first correction vector {Δx ₁ } calculated in step S116, and the second correction vector {Δx ₂ } calculated in step S118.

In the simulated earthquake motion creation processing routine, the following processes are repeated: calculation of the acceleration response spectrum vector {Sa}, calculation of the energy spectrum vector {V _E }, setting of the candidate output vector {o}, calculation of the error vector {r}, and calculation of a new candidate input vector {x}.

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.

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

As described in detail above, 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 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 that the error vector is smaller. The simulated earthquake motion creation device 100 repeatedly calculates the acceleration response spectrum vector, calculates the energy spectrum vector, sets the candidate output vector, calculates the error vector, and calculates a new candidate input vector, and when certain conditions are met, acquires 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 while appropriately representing the input energy of the actual earthquake motion.

Specifically, the simulated earthquake motion creation device 100 of this embodiment sets target values for the energy spectrum in addition to the acceleration response spectrum, thereby generating simulated earthquake motion that satisfies the target acceleration response spectrum and appropriately reflects the input energy of actual earthquake motion.

Furthermore, in this embodiment, the input vector, which is a variable, is an acceleration time history rather than an amplitude spectrum. This makes it possible to uniquely determine the simulated seismic motion to be created.

<Simulation Experiment>

Next, we will use an example problem to confirm the effectiveness of the method for creating simulated earthquake motion according to this embodiment.

Figure 5(A) shows the target acceleration response spectrum. Figure 5(B) shows the target energy spectrum. Each α in Figure 5(B) represents a different energy. Below, simulated earthquake motion that matches the target acceleration response spectrum in Figure 5(A) and the target energy spectrum (α = 2.0) in Figure 5(B) is created using the method of this embodiment. Note that the horizontal axis of the graphs in Figures 5, 6, and 7 represents time (s), and the vertical axis represents acceleration (m/ ^s2 ) and velocity conversion value (m/s).

Figure 6 shows simulated earthquake motion created using the method of this embodiment. Figure 6(A) shows the acceleration time history of the simulated earthquake motion created using the method of this embodiment. "Generated" in Figure 6(B) is the acceleration response spectrum of the simulated earthquake motion created using the method of this embodiment. "Target" in Figure 6(B) is the target acceleration response spectrum. "Generated" in Figure 6(C) is the energy spectrum of the simulated earthquake motion created using the method of this embodiment. "Target" in Figure 6(C) is the target energy spectrum. It can be seen that the simulated earthquake motion shown in Figure 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.

For comparison, Figure 7 shows simulated earthquake motion created using a method that adapts only to the target acceleration response spectrum (hereinafter simply referred to as the conventional method). Figure 7(A) shows the acceleration time history of simulated earthquake motion created using the conventional method. Figure 7(B) shows the energy spectrum of simulated earthquake motion created using the conventional method. As shown in Figure 7, although the simulated earthquake motion created using the conventional method adapts to the target acceleration response spectrum, the energy spectrum varies, and it is difficult to say that the input energy adapts to the target energy spectrum. Therefore, comparing Figures 6 and 7, it can be seen that the simulated earthquake motion creation method of this embodiment can obtain simulated earthquake motion that satisfies the target acceleration response spectrum and appropriately reflects the input energy of actual earthquake motion.

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

For example, in the above embodiment, an example was described in which an energy spectrum vector was used as a vector representing the energy of simulated earthquake motion, but this is not limited to this. Any information may be used as long as it represents the energy of simulated earthquake motion.

In addition, in the above embodiment, simulated earthquake motions are created by repeatedly calculating new candidate input vectors to reduce the error vector 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 the method disclosed in Japanese Patent Application Laid-Open No. 2021-169977. However, 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 the nonlinear least squares method, Newton's method, steepest descent method, or genetic algorithm.

In addition, while the above describes a configuration in which the program is pre-stored (installed) in a storage unit (not shown), the program can also be provided in a format in which it is recorded on a recording medium such as a CD-ROM, DVD-ROM, or microSD card.

20 Computer 21 Data storage unit 22 Candidate input vector setting unit 24 Candidate output vector setting unit 26 Error vector calculation unit 28 Determination unit 30 Matrix generation unit 32 Matrix calculation unit 34 Correction vector calculation unit 36 Update unit 38 Result acquisition unit

Claims (3)

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. 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. 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};
generating a generalized inverse matrix [K] ⁺ by singular value decomposition of the partial differential matrix [K];
selecting a first group of modes, the first group having singular values greater than a first predetermined value, from a plurality of modes corresponding to singular values of the generalized inverse matrix [K] ⁺ submatrix [Σ] ^−1;
generating a modified generalized inverse matrix [K′] ⁺ corresponding to the selected first set of modes;
calculating a first correction vector {Δx ₁ } representing a first correction amount for the candidate input vector {x} based on the modified generalized inverse matrix [K′] ⁺ and the error vector {r};
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;
generating a submatrix [V _R ] corresponding to the selected second mode group;
calculating a second correction vector {Δx 2 } representing a second correction amount for the candidate input vector {x} based on the submatrix [V _R ], a preset reduction rate λ, and the candidate input vector { _x };
The simulated earthquake motion generating method according to claim 1 or claim 2, further comprising generating a new candidate input vector { _x } based on the candidate input vector {x}, the first correction vector {Δx ₁ }, and the second correction vector {Δx 2 }.