Waveform generation method, waveform generation system, and waveform generation program

Abstract

To accurately evaluate building responses while reducing the computational cost of seismic response analysis. [Solution] The computer 10 receives seismic waveform data and a building model as input, derives multiple eigenmodes for the building model by performing eigenvalue analysis on the building model, creates multiple single-degree-of-freedom building models using the natural circular frequencies and damping constants of each of the multiple eigenmodes, derives the building response for a predetermined time point of the seismic waveform data by performing time history response analysis on a single-degree-of-freedom building model selected from the multiple single-degree-of-freedom building models, and executes a process to generate an input waveform that reproduces or approximates the building response at a predetermined time point by performing singular value decomposition on a matrix created based on the impulse response of the single-degree-of-freedom building model.

Description

[Technical Field]

[0001] This disclosure relates to a waveform generation method, a waveform generation system, and a waveform generation program. [Background technology]

[0002] In recent years, there has been an increase in the planning of high-rise buildings with complex vertical plane shapes. In the structural design process, full 3D models that model each member such as columns and beams are used to accurately evaluate the building's response. However, the computational load of seismic response analysis for full 3D models is extremely high, making it difficult to perform a vast number of seismic response analyses during the design phase.

[0003] In response to this, it is conceivable to trim, downsample, or decimate a portion of the seismic waveform to reduce the computational load. For example, Patent Document 1 describes a seismic waveform recording and compression device that can perform time-based decimation while maintaining the appearance of the seismic waveform. This seismic waveform recording and compression device is configured to receive a time series of measured seismic waveforms as input and to decimate the time series of seismic waveforms while maintaining the order of appearance times of the maximum and minimum values ​​of the time series of seismic waveforms. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2016-17869 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] However, with the conventional methods described above, changes in waveform can alter the building response, potentially compromising the accuracy of the response evaluation. Therefore, there is a need to accurately evaluate the building response while reducing the computational cost of seismic response analysis during the design phase.

[0006] This disclosure aims to provide a waveform generation method, a waveform generation system, and a waveform generation program that can accurately evaluate building responses while reducing the computational cost of seismic response analysis. [Means for solving the problem]

[0007] A waveform generation method according to a first aspect of this disclosure involves a computer performing the following steps: receiving seismic motion waveform data and a building model as input; deriving multiple eigenmodes for the building model by performing eigenvalue analysis on the building model; creating multiple single-degree-of-freedom building models using the natural circular frequencies and damping constants of each of the multiple eigenmodes; deriving the building response of the seismic motion waveform data for a predetermined time by performing time history response analysis on a single-degree-of-freedom building model selected from the multiple single-degree-of-freedom building models; and generating an input waveform that reproduces or approximates the building response at the predetermined time by performing singular value decomposition on a matrix created based on the impulse response of the single-degree-of-freedom building model.

[0008] A waveform generation method according to a second aspect of the present disclosure is a waveform generation method according to a first aspect, wherein the computer derives the building response of the seismic motion waveform data for a predetermined number of times by performing a time history response analysis on the one-degree-of-freedom building model, and generates an input waveform that reproduces or approximates the building response at the predetermined number of times by singular value decomposition of a matrix created based on the impulse response of the one-degree-of-freedom building model.

[0009] A waveform generation method according to a third aspect of this disclosure is a waveform generation method according to the first or second aspect, wherein the computer selects eigenmodes from the plurality of eigenmodes in descending order of mode mass until the sum of mode masses obtained by the eigenvalue analysis exceeds a predetermined value, and creates the plurality of 1-degree-of-freedom building models using the natural circular frequency and damping constant of each of the selected eigenmodes.

[0010] A waveform generation method according to a fourth aspect of this disclosure is a waveform generation method according to any one of the first to third aspects, wherein the computer performs the singular value decomposition on matrices that differ depending on whether the coordinate system representing the building response is a relative coordinate system or an absolute coordinate system.

[0011] A waveform generation system according to a fifth aspect of this disclosure includes: a reception unit that receives seismic motion waveform data and a building model as inputs; an eigenmode derivation unit that derives a plurality of eigenmodes for the building model by performing eigenvalue analysis on the building model; a creation unit that creates a plurality of single-degree-of-freedom building models using the natural circular frequencies and damping constants of each of the plurality of eigenmodes; a building response derivation unit that derives a building response for a predetermined time of the seismic motion waveform data by performing time history response analysis on a single-degree-of-freedom building model selected from the plurality of single-degree-of-freedom building models; and a generation unit that generates an input waveform that reproduces or approximates the building response at the predetermined time by singular value decomposition of a matrix created based on the impulse response of the single-degree-of-freedom building model.

[0012] The waveform generation program according to the sixth aspect of this disclosure receives seismic motion waveform data and a building model as inputs, derives a plurality of eigenmodes for the building model by performing eigenvalue analysis on the building model, creates a plurality of single-degree-of-freedom building models using the natural circular frequencies and damping constants of each of the plurality of eigenmodes, derives the building response of the seismic motion waveform data for a predetermined time by performing time history response analysis on a single-degree-of-freedom building model selected from the plurality of single-degree-of-freedom building models, and causes a computer to execute a process that generates an input waveform that reproduces or approximates the building response at the predetermined time by singular value decomposition of a matrix created based on the impulse response of the single-degree-of-freedom building model. [Effects of the Invention]

[0013] According to this disclosure, the effect is to reduce the computational cost of seismic response analysis while accurately evaluating the building response. [Brief explanation of the drawing]

[0014] [Figure 1] This figure shows an example of a schematic configuration of the waveform generation system according to the embodiment. [Figure 2] This block diagram shows an example of the functional configuration of a waveform generation system according to an embodiment. [Figure 3] Figure 3(A) is a schematic diagram illustrating the relationship between a pseudo-impulse input signal and a response signal. Figure 3(B) is a schematic diagram showing an example of a pseudo-impulse input signal. [Figure 4] This figure shows an example of ground acceleration waveform data. [Figure 5] Figure 5(A) shows an example of a seismic motion waveform generated for setting building response values. Figure 5(B) shows an example of a reduced input waveform generated by the proposed method. Figure 5(C) shows an example of the displacement response time history of a building model with a natural period of 8s and a damping constant of 0.05 for both waveforms in Figures 5(A) and 5(B). [Figure 6] This flowchart shows an example of the processing flow by the waveform generation program according to the embodiment. [Figure 7] Figure 7(A) shows an example of a seismic primordial wave. Figure 7(B) shows an example of a reduced input waveform generated by the proposed method using the seismic primordial wave shown in Figure 7(A). [Figure 8] Figures 8(A) to 8(D) show examples of displacement response time histories for seismic ground waves and reduced input waveforms. [Figure 9] Figure 9(A) shows a building with an 8-story, 20-span planar frame. Figure 9(B) shows the correspondence between each story and the second moment of area. Figure 9(C) shows the correspondence between each story and the cross-sectional area. [Figure 10] Figure 10(A) shows the ground displacement. Figure 10(B) shows the displacement spectrum. Figure 10(C) shows the velocity spectrum. Figure 10(D) shows the acceleration spectrum. [Figure 11]Figure 11(A) shows the time history of the acceleration response to the seismic ground wave and generated waveform (reduced input waveform) at the 5-layer floor. Figure 11(B) shows the time history of the acceleration response to the seismic ground wave and generated waveform (reduced input waveform) at the top floor. Figure 11(C) shows the ground displacement of the generated waveform (reduced input waveform). [Modes for carrying out the invention]

[0015] Hereinafter, an example of an embodiment for carrying out the technology of this disclosure will be described in detail with reference to the drawings. Components and processes that perform the same operation, action, or function are given the same reference numerals throughout the drawings, and redundant explanations may be omitted as appropriate. Each drawing is only a schematic representation to the extent that the technology of this disclosure can be fully understood. Therefore, the technology of this disclosure is not limited to the illustrated examples. Furthermore, in this embodiment, explanations of configurations not directly related to the technology of this disclosure or well-known configurations may be omitted.

[0016] Figure 1 is a diagram showing an example of the schematic configuration of the waveform generation system 1 according to this embodiment. As shown in Figure 1, the waveform generation system 1 according to this embodiment may include at least a computer 10 as an arithmetic unit. The computer 10 constituting the waveform generation system 1 may be a well-known computer, and specifically may include at least a processor 11, a ROM (Read Only Memory) 12 and RAM (Random Access Memory) 13 as an example of memory, storage 14, a communication interface 15, and an input / output interface 16. Furthermore, these components may be connected to each other so as to be able to communicate with one another via an internal bus.

[0017] The processor 11 may be composed of, for example, a CPU (Central Processing Unit) and capable of executing various programs and controlling various parts. Specifically, this processor 11 may be capable of reading various programs stored in ROM 12 or storage 14 and executing those programs using RAM 13 as a working area. The processor 11 may be capable of controlling each component of the waveform generation system 1 and performing various calculations according to the program.

[0018] ROM12 may be capable of storing various programs and various data. RAM13 may also be capable of temporarily storing programs or data as a working area.

[0019] Storage 14 refers to HDD (Hard Disk Drive) and SSD (Solid). It can be composed of recording media such as a State Drive or flash memory, and may store various programs including an operating system, as well as various data necessary to operate the waveform generation system 1. In this embodiment, the ROM 12 or storage 14 stores waveform generation programs for executing each function of the waveform generation system 1.

[0020] The communication interface (I / F) 15 can consist of an interface including a communication processor and an antenna. The communication interface 15 manages communication between multiple computers. Examples of communication standards applicable to the communication interface include wireless communication standards such as 5G (5th Generation Mobile Communication System), Wi-Fi (registered trademark), or Bluetooth (registered trademark). This communication interface 15 may be connected to a network NW. Examples of a network NW include a WAN (Wide Area Network) and / or a LAN (Local Area Network).

[0021] The input / output interface (I / F) 16 may be an interface for sending and receiving data, etc., between the waveform generation system 1 and various components. As shown in Figure 1, the input / output interface 16 of this embodiment can acquire or transmit predetermined data from, for example, the display 17 and the operation unit 18. Note that the components from which the input / output interface 16 acquires data or outputs data are not limited to those described above.

[0022] The display 17 may be a display device that shows the processing results performed by the computer 10, specifically the results of seismic response analysis, to the user. The display 17 can be a liquid crystal display (LCD) or an organic light-emitting diode (OLED).

[0023] The operation unit 18 may be a device for enabling user input operations. The operation unit 18 may employ a touch panel, a keyboard, a pointing device including a mouse, and a microphone, either individually or in combination.

[0024] Incidentally, as mentioned above, while it is conceivable to change the seismic waveform to reduce the computational load in seismic response analysis, the change in waveform may alter the building response, potentially impairing the accuracy of the response evaluation. Therefore, the waveform generation system 1 according to this embodiment generates an input waveform of arbitrary length that reproduces or approximates the building displacement and velocity response at any given time for arbitrary seismic waveform data and building model. According to this embodiment, by making the length of the generated waveform sufficiently shorter than the original wave, the overall length of the waveform can be shortened, thereby reducing the computational load. The following describes various functions for input waveform generation by the waveform generation system 1 according to this embodiment.

[0025] Figure 2 is a block diagram showing an example of the functional configuration of the waveform generation system 1 according to this embodiment. As shown in Figure 2, the waveform generation system 1 according to this embodiment includes at least a reception unit 101, a eigenmode derivation unit 102, a creation unit 103, a building response derivation unit 104, a generation unit 105, and an output unit 106. All of these components can be mainly implemented by the computer 10 described above. In other words, the processor 11 of the computer 10 functions as each of these units by executing a waveform generation program stored in the ROM 12 or storage 14.

[0026] The reception unit 101 accepts input of ground acceleration waveform data and a building model. Ground acceleration waveform data is an example of seismic motion waveform data. Ground acceleration waveform data may be acquired externally via the communication interface 15, or it may be stored in storage 14 or the like beforehand and read out as needed. The ground acceleration waveform data acquired here is used for seismic response analysis of buildings and may be original data measuring the ground acceleration of a specific seismic motion. Ground acceleration waveform data may be time-series data composed of multiple measurements taken at predetermined intervals. As such ground acceleration waveform data, well-known data such as El Centro waves, Taft waves, or Hachinohe waves can be used.

[0027] The building model is a full three-dimensional model that models each component such as columns and beams in order to accurately evaluate the building response of a given building, and there may be one or more such models. The building model may be acquired externally via the communication interface 15, similar to the ground acceleration waveform data, or it may be stored in advance in the storage 14, etc., and read out as needed for use.

[0028] The eigenmode derivation unit 102 derives multiple eigenmodes for the building model by performing eigenvalue analysis of the building model. For example, eigenmodes with large mode masses may be selected sequentially from the multiple eigenmodes until the sum of the mode masses obtained by the eigenvalue analysis exceeds a predetermined value (which is any value, but for example, 0.9 times the total building mass).

[0029] The creation unit 103 creates multiple single-degree-of-freedom building models using the natural circular frequencies and damping constants of each natural mode selected by the natural mode derivation unit 102.

[0030] The building response derivation unit 104 derives the building response of ground acceleration waveform data for a predetermined time point by performing a time history response analysis on a single-degree-of-freedom building model selected from a plurality of single-degree-of-freedom building models. Here, "a predetermined time point" refers to, for example, the end time t of the waveform. e (See below)

[0031] The generation unit 105 generates an input waveform that reproduces or approximates the building response at a predetermined time by performing singular value decomposition on a matrix created based on the impulse response of a one-degree-of-freedom building model. Singular value decomposition is a method that decomposes one matrix into the product of three matrices and is used to compress the amount of data and reduce dimensionality. The input waveform generated by this singular value decomposition has a reduced amount of data (contracted) compared to the original ground acceleration waveform data without degrading the accuracy of the building response. Therefore, the computational cost of seismic response analysis can be reduced. Hereinafter, the input waveform generated by singular value decomposition will also be called the "contracted input waveform". Here, the generation unit 105 may perform singular value decomposition on different matrices depending on whether the coordinate system representing the building response is a relative coordinate system or an absolute coordinate system.

[0032] The output unit 106 outputs the reduced input waveform generated by the generation unit 105. The output destination may be, for example, the storage 14 or the display 17.

[0033] Next, a waveform generation method (proposed method) by the waveform generation system 1 according to the present embodiment will be specifically described with reference to FIGS. 3(A) and 3(B).

[0034] FIG. 3(A) is a schematic diagram for explaining the relationship between a pseudo impulse input signal and a response signal. FIG. 3(B) is a schematic diagram showing an example of a pseudo impulse input signal. Note that the "pseudo impulse input signal" can be rephrased as an input signal simulating an impulse input signal. As shown in FIG. 3(A), herein, at time t=(N dt +ΔN dt )dt, the problem of specifying a building response at )dt and obtaining an input ground motion acceleration u ·· (dt), ..., u ·· (N dt dt) that reproduces the specified building response is considered. However, the ·· of ·· u is immediately above u. Note that the values at time t=(N dt +1)dt, ..., (N dt +ΔN dt )dt are set to 0 (zero). Further, for t < 0, both the building response and the ground motion acceleration are set to 0 (zero).

[0035] Herein, N sets of single-degree-of-freedom building models are considered. Let the natural circular frequency of each model be ω1, ..., ω N and the damping constant be h1, ..., h N The building response and input ground motion are given in a discrete-time system, and the time step is dt. At time t=dt, ..., N dt dt, ground motion acceleration u g ·· (dt), ..., u g ·· (N dt dt), and the displacement response and velocity response (hereinafter also referred to as "displacement-velocity response") of the building model at t=(N dt +ΔN dt )dt satisfy the relationship of the following formula (1). However, the g ·· (dt) of ·· is immediately above u g .

[0036] JPEG0007923384000002.jpg2491 (1)

[0037] Furthermore, the following relationships (2) to (4) are satisfied.

[0038] JPEG0007923384000003.jpg8164(2)

[0039] JPEG0007923384000004.jpg9164 (3)

[0040] JPEG0007923384000005.jpg36147 (4)

[0041] H d (ω,h,Δt), H d· (ω,h,Δt)(however, d · The (directly above d) represents the displacement and velocity response after Δt seconds when a 1-degree-of-freedom system with natural circular frequency ω and damping constant h is subjected to a pseudo-impulse ground motion input. d (ω,h,Δt) shows the displacement response, H d· (ω,h,Δt) represents the velocity response. d(ω i ,h i ,(N dt +ΔN dt )dt), d · (ω i ,h i ,(N dt +ΔN dt )dt) is t=(N dt +ΔN dt This is the displacement-velocity response at dt. Note that d(ω i ,h i ,(N dt +ΔN dt )dt) shows the displacement response, d · (ω i ,h i ,(N dt +ΔN dt)dt) represents the velocity response. Here, a pseudo-impulse ground input is an input in which the acceleration value is 1 only at t=0 and 0 at all other times, and corresponds to a pseudo-impulse input signal. Also, the left side of equation (1) above is a 2N × 1 vector, and H is 2N × N dt This is the matrix. We perform singular value decomposition on H and express it as shown in equation (5) below.

[0042] JPEG0007923384000006.jpg1590 (5)

[0043] Here, U, V, and σ are diagonal matrices composed of left singular vectors, right singular vectors, and singular values, and the columns of U and V are orthogonal to each other. Also, n = min{2N,N} dt} Substitute equation (5) into equation (1) and Vσ -1 U T Raising the result to the left gives equation (6).

[0044] JPEG0007923384000007.jpg1992 (6)

[0045] VV T =v1v1 T +···+v n v n T is v1,···,v n This is the projection matrix onto the subspace formed by . From equation (6) above, (u g ·· (dt),···,u g ·· (N dt dt)) T We obtain it as shown in equation (7).

[0046] JPEG0007923384000008.jpg18102 (7)

[0047] 2N ≤ N dt In this case, for the ground acceleration given by equation (7) above, t = (N dt +ΔN dtThe building response at dt is d,d · This matches. On the other hand, 2N > N dt In this case, the building response is d, d · It does not perfectly match, but gives an approximate solution. Note that N dt ,ΔN dt ,N,d,d · Depending on the combination of building models, waveforms with excessive amplitude may be generated. In this case, in equation (7) above, v1,···,v n Among these, those with relatively small corresponding singular values ​​may be excluded. Although the resulting waveform will be an approximation, it will have almost no effect on accuracy.

[0048] Next, we will explain numerical examples using the proposed method according to this embodiment, with reference to Figures 4, 5(A), 5(B), and 5(C).

[0049] Figure 4 shows an example of ground acceleration waveform data. In Figure 4, the vertical axis represents ground acceleration [m / s²]. 2 The horizontal axis shows [time], and the horizontal axis shows time [s].

[0050] As building models, we will use a total of four models, for example, with natural periods of 1, 2, 4, and 8 [s] and a damping constant of 0.05. Here, the building response values ​​and generated waveform parameters are set using the following procedure.

[0051] (Procedure 1) Prepare ground acceleration waveform data for a long-period, long-duration earthquake motion in a certain building (Figure 4) by changing the values ​​of steps 3001 to 32768 to 0, while leaving the values ​​of steps 1 to 3000 as they are in the original data.

[0052] (Step 2) Record the building response at step 3001 for the ground acceleration waveform data created in (Step 1) above.

[0053] (Step 3) Determine the input waveform of step 400 shown at step 401 of the building response value recorded in (Step 2) above (N dt =400,ΔN dt=1). Note that for the waveform created in the above (Procedure 1), the response of the building model from step 3001 to 32768 will be free vibration.

[0054] Figure 5(A) shows an example of a seismic motion waveform generated for setting building response values, Figure 5(B) shows an example of a reduced input waveform generated by the proposed method, and Figure 5(C) shows an example of the displacement response time history of a building model with a natural period of 8s and a damping constant of 0.05 for both waveforms in Figures 5(A) and 5(B). In Figures 5(A) and 5(B), the vertical axis represents ground acceleration [m / s²]. 2 The vertical axis represents the displacement response [m], and the horizontal axis represents time [s]. In Figure 5(C), the vertical axis represents the displacement response [m], and the horizontal axis represents time [s]. The solid line shows the displacement response to the seismic waveform shown in Figure 5(A), and the dotted line shows the displacement response to the reduced input waveform shown in Figure 5(B).

[0055] The reduced input waveform shown in Figure 5(B) has its start time delayed by 2600 steps, where time t = end time t e (For example, after 60 [s]) the acceleration values ​​of both waveforms become 0. As shown in Figure 5(C), t = end time t for both waveforms. e The displacement response at point t matches, and subsequent free vibrations also match. In other words, the end time of the seismic motion waveform and the reduced input waveform t e Specify that only responses should match (for example, 60[s]), and t = end time t e From this point onward, there is no input for either the seismic motion waveform or the reduced input waveform, and only free vibration occurs in the building. Therefore, t = end time t e If the responses match, then the subsequent free vibrations will naturally also match.

[0056] Next, we will describe an extension of the waveform generation method (proposed method) according to this embodiment to a form in which response analysis is performed by providing ground displacement and ground velocity.

[0057] The equations of motion for a one-degree-of-freedom system with natural circular frequency ω and damping constant h can be expressed in absolute coordinates as follows: (8) and (9).

[0058] JPEG0007923384000009.jpg987 (8)

[0059] JPEG0007923384000010.jpg733 (9)

[0060] Here, d a is the absolute displacement, d a · is the absolute velocity, and d a ·· is the absolute acceleration. Provided that the dot over d a · is placed directly above da, and the double dot over d a ·· over d a is placed directly above d a The absolute displacement d is expressed as the sum of the relative displacement from the building base and the ground motion displacement. When describing the building response in an absolute coordinate system, the above formula (1) can be rewritten as formula (10) below.

[0061] JPEG0007923384000011.jpg43155 (10)

[0062] Additionally, the relationships of the following formulas (11) to (15) are satisfied.

[0063] JPEG0007923384000012.jpg7164 (11)

[0064] JPEG0007923384000013.jpg9164 (12)

[0065] JPEG0007923384000014.jpg39131 (13)

[0066] JPEG0007923384000015.jpg21154 (14)

[0067] JPEG0007923384000016.jpg21156 (15)

[0068] H da (ω,h,Δt), H da· (ω,h,Δt) (where d a • of • is d a directly above) represent the absolute displacement response and absolute velocity response after Δt seconds when a single-degree-of-freedom system with natural circular frequency ω and damping constant h is subjected to a unit impulse horizontal external force (not ground motion). The left-hand side of the above formula (10) is a 2N×1 vector, and H a is a 2N×2N dt matrix, (P,PP) T is a 2N dt ×N dt matrix. In addition, P represents a matrix for time integration, and for example, in the case of trapezoidal integration, it is expressed by the following formula (16).

[0069] JPEG0007923384000017.jpg2667 (16)

[0070] In the above proposed method, the reduced input waveform is obtained by singular value decomposition of the coefficient matrix H on the right-hand side of the above formula (1), which is a formulation when the building response displacement is expressed in relative coordinates. On the other hand, when describing the building response in an absolute coordinate system, by setting the object of singular value decomposition as H a (P,PP) T , the reduced input waveform can be obtained through the same procedure. The formulation in the case of description in an absolute coordinate system is useful when the input ground motion varies depending on the planar position of the building or there is a time phase difference.

[0071] The formulation of the above formulas (1) to (16) is a method of generating a reduced input waveform by specifying only the response at one specific time, but it is also possible to generate a reduced input waveform by specifying responses for any plurality of times. That is, it is only required to create formula (1) or formula (10) for the number of times for which responses are specified, and rearrange them into a single formula.

[0072] In this case, the building response derivation unit 104 derives the building response of the ground acceleration waveform data for a predetermined number of time points by performing a time history response analysis on a one-degree-of-freedom building model. The generation unit 105 generates input waveforms that reproduce or approximate the building response at the predetermined number of time points by performing singular value decomposition on a matrix created based on the impulse response of the one-degree-of-freedom building model. The "determined number of time points" here refers to, for example, the start time t of the reduced input waveform. int From end time t e Any multiple time periods within that timeframe are acceptable.

[0073] Figure 6 is a flowchart showing an example of the processing flow by the waveform generation program according to this embodiment.

[0074] First, in step S101 of Figure 6, the processor 11 receives input of ground acceleration waveform data, which is an example of seismic motion waveform data, and a building model.

[0075] In step S102, the processor 11 performs eigenvalue analysis on the building model received in step S101. It selects eigenmodes in order from the largest to the smallest mode mass until the sum of the mode masses exceeds a specified value (which is arbitrary, but for example, 0.9 times the total building mass).

[0076] In step S103, the processor 11 creates multiple one-degree-of-freedom building models using the natural circular frequencies and damping constants of the eigenmodes selected in step S102.

[0077] In step S104, the processor 11 performs a time history response analysis on the 1-degree-of-freedom building model created in step S103. At a certain time t int From time t onward e The displacement response up to time t is stored. e It also memorizes the speed response.

[0078] In step S105, processor 11 determines time t ≤ t s At t, the acceleration is 0, int ≦t≦te A reduced input waveform whose response matches that of the seismic motion source wave is generated using the proposed method according to this embodiment (however, t s <t int ), and the series of processes by this waveform generation program is terminated. For example, if only one 1-degree-of-freedom building model (natural circular frequency ω, damping constant h) is used, the following equations (17) to (19) can be created, combined into a single equation, and used in place of the above equation (1).

[0079] JPEG0007923384000018.jpg10139 (17)

[0080] JPEG0007923384000019.jpg10138 (18)

[0081] JPEG0007923384000020.jpg8164 (19)

[0082] Here, n ts , n tint , n te This is time t in a discrete time system. s , t int , t e It is the number, t s =n ts dt, t int =n tint dt, t e =n te dt. Furthermore, even if the parameters of the building model fluctuate somewhat, the response to the original wave and the reduced input waveform is well-adjusted. Therefore, even if changes are made to member cross-sections, damper capacities, etc., during the structural design process, it is not necessary to regenerate the waveform each time, and the response can be evaluated with good accuracy using the waveform created initially.

[0083] Figure 7(A) shows an example of a seismic motion source wave, and Figure 7(B) shows an example of a reduced input waveform generated by the proposed method using the seismic motion source wave shown in Figure 7(A). In Figures 7(A) and 7(B), the vertical axis represents ground acceleration [m / s²].2 The horizontal axis represents time [s]. Here, time t s =52s, time t int Let = 60s, and time t e The end time of the seismic motion source wave is defined as . Furthermore, four models were used to generate the reduced input waveform, with natural periods of 1, 2, 4, and 8 s and a damping constant of 0.05. int From this point onward, the acceleration values ​​of the seismic ground wave and the reduced input waveform produced by the proposed method are almost identical.

[0084] Figures 8(A) to 8(D) show examples of displacement response time histories for seismic ground waves and reduced input waveforms. Figure 8(A) shows the displacement response time histories for a natural period of 1 s and a damping constant of 0.05, Figure 8(B) shows the displacement response time histories for a natural period of 2 s and a damping constant of 0.05, Figure 8(C) shows the displacement response time histories for a natural period of 4 s and a damping constant of 0.05, and Figure 8(D) shows the displacement response time histories for a natural period of 8 s and a damping constant of 0.05. The solid line represents the seismic ground wave, and the dotted line represents the reduced input waveform. As shown in Figures 8(A) to 8(D), the building response to the seismic ground wave and the generated reduced input waveform is shown at time t int From this point onward, it can be seen that the results match to such an extent that no error is detectable.

[0085] Figure 9(A) shows a building with an 8-story, 20-span planar frame, Figure 9(B) shows the correspondence between each story and the second moment of area, and Figure 9(C) shows the correspondence between each story and the cross-sectional area. In the examples in Figures 9(A) to 9(C), the height of each story is 4m (total story height is 4 × 8 = 32m), and the length of each span is 8m (total span length is 8 × 20 = 160m). The total mass of each story is 1280t (tons), the nodal mass at both ends of each story is 32t, and the nodal mass at the other ends is 64t. The column and beam cross-sections are common to each floor. For structural damping, stiffness-proportional damping corresponding to a first damping constant of 0.02 is assumed. In Figures 9(B) and 9(C), "column" refers to a column and "beam" refers to a beam. In Figure 9(B), the vertical axis represents the story (story), and the horizontal axis represents the second moment of area. In Figure 9(C), the vertical axis represents the number of floors, and the horizontal axis represents the cross-sectional area. The leftmost point of the horizontal axis corresponds to 0, and the vertical axis takes values ​​from 1 to 8.

[0086] Here, the input seismic ground motion source wave is a waveform based on the design response spectrum and phase characteristics set based on observational records from the 1968 Tokachi-oki earthquake. The time phase difference of the ground motion input to both ends of the building is set to 0.5 s. Since the duration of the ground motion at each input point is 120 s, the total analysis time is 120.5 s. s = 15s, t int =17s, t e Let's assume this is = 120.5s. Therefore, the number of time steps equivalent to 15s is reduced, and the total number of time steps is reduced by approximately 12.5%.

[0087] Figure 10(A) shows ground displacement, Figure 10(B) shows displacement spectrum, Figure 10(C) shows velocity spectrum, and Figure 10(D) shows acceleration spectrum.

[0088] When generating waveforms using the proposed method according to this embodiment, the responses of a total of six sets of one-degree-of-freedom building models are referenced: (ω1,···,ω6)=(6.01,16.0,28.6,44.6,64.5,87.1)[rad / s] and (h1,···,h6)=(0.02 / ω1)×(ω1,···,ω6). These correspond to the 1st to 6th order natural circular frequencies and damping constants when a rigid floor assumption is made. However, in time history response analysis, they are treated as non-rigid floor models. This setting has two purposes: (1) to significantly reduce the computational load of waveform generation by using a small number of simple one-degree-of-freedom building models without directly using a frame, and (2) to demonstrate that the response evaluation accuracy is good even for models other than the one used for waveform generation, even though the natural circular frequencies and damping constants differ between models with a rigid floor assumption and non-rigid floor models.

[0089] Figure 11(A) shows the time history of the acceleration response to the seismic ground wave and generated waveform (reduced input waveform) at the 5-layer floor, Figure 11(B) shows the time history of the acceleration response to the seismic ground wave and generated waveform (reduced input waveform) at the top floor, and Figure 11(C) shows the ground displacement of the generated waveform (reduced input waveform). In Figures 11(A) and 11(B), the vertical axis represents the acceleration response [m / s²]. 2 In Figure 11(C), the vertical axis represents ground displacement [m] and the horizontal axis represents time [s]. The solid line represents the seismic ground wave, and the dotted line represents the generated waveform (reduced input waveform). The circles indicate reference nodes.

[0090] The acceleration response for the seismic ground wave and generated waveform (reduced input waveform) shown in Figure 11(A) is given by time t int From this point onward, it can be seen that they are almost identical. Similarly, the acceleration response for the seismic motion source wave and generated waveform (reduced input waveform) shown in Figure 11(B) is given by time t int From this point onward, it can be seen that they are almost identical. The ground displacement for the seismic motion source wave and generated waveform (reduced input waveform) shown in Figure 11(C) is also shown for time t int From here on, you can see that they are almost identical.

[0091] Thus, according to this embodiment, it is possible to specify the response of a building at a certain time and generate a reduced input signal that realizes the specified response. By generating a reduced input signal, the computational cost of seismic response analysis can be reduced while accurately evaluating the building response.

[0092] According to this embodiment, the input seismic motion waveform used in structural design can be reconstructed from scratch without trimming or downsampling, and an almost identical response (result) can be reproduced.

[0093] This disclosure is not limited to the embodiments described above, and various modifications and applications are possible without departing from the gist of this disclosure.

[0094] The waveform generation systems according to each embodiment have been described as examples. Each embodiment may be in the form of a program that causes a computer to execute the functions of each part of the waveform generation system, or in the form of a program product containing such a program. The embodiments may also be in the form of a computer-readable non-temporary storage medium that stores these programs.

[0095] Furthermore, the configurations of the waveform generation systems described in each of the above embodiments are examples and may be modified as needed, without departing from the main purpose.

[0096] Furthermore, the program processing flow described in each of the above embodiments is merely an example, and unnecessary steps may be deleted, new steps added, or the processing order rearranged, as long as it does not deviate from the main purpose.

[0097] Furthermore, while the above embodiments describe cases in which the processes according to the embodiment are realized by a software configuration using a computer by executing a program, the embodiments are not limited to this. Embodiments may also be realized, for example, by a hardware configuration or a combination of a hardware configuration and a software configuration. [Explanation of Symbols]

[0098] 1. Waveform Generation System 10 Computers 11 processors 12 ROM 13 RAM 14 Storage 15 Communication I / F 16 Input / Output Interfaces 17 displays 18 Control section 101 Reception Department 102 Intrinsic Mode Derivation Unit 103 Creation Department 104 Building Response Derivation Section 105 Generation part 106 Output section

Claims

1. It accepts seismic waveform data and building model inputs. By performing eigenvalue analysis on the aforementioned building model, multiple eigenmodes for the building model are derived. Using the natural circular frequencies and damping constants of each of the aforementioned multiple natural modes, multiple one-degree-of-freedom building models are created. By performing a time history response analysis on a single-degree-of-freedom building model selected from the aforementioned plurality of single-degree-of-freedom building models, the building response for a predetermined time point in the seismic motion waveform data is derived. The process of generating an input waveform that reproduces or approximates the building response at a predetermined time by performing singular value decomposition on a matrix created based on the impulse response of the one-degree-of-freedom building model, A waveform generation method performed by a computer.

2. The aforementioned computer, By performing a time history response analysis on the aforementioned one-degree-of-freedom building model, the building response to the seismic motion waveform data for a predetermined number of time points is derived. Input waveforms that reproduce or approximate the building response at a predetermined number of time points are generated by singular value decomposition of a matrix created based on the impulse response of the one-degree-of-freedom building model. The waveform generation method according to claim 1.

3. The aforementioned computer, Until the sum of the mode masses obtained by the eigenvalue analysis exceeds a predetermined value, eigenmodes are selected from the plurality of eigenmodes in descending order of mode mass, Using the natural circular frequencies and damping constants of each of the selected natural modes, the multiple one-degree-of-freedom building models are created. Waveform generation method according to claim 1 or claim 2.

4. The aforementioned computer, The singular value decomposition is performed on different matrices depending on whether the coordinate system representing the building response is a relative coordinate system or an absolute coordinate system. Waveform generation method according to claim 1 or claim 2.

5. A reception unit that accepts seismic motion waveform data and building model inputs, An eigenmode derivation unit that derives multiple eigenmodes for the building model by performing eigenvalue analysis on the building model, A creation unit that creates multiple one-degree-of-freedom building models using the natural circular frequencies and damping constants of each of the aforementioned multiple natural modes, A building response derivation unit that derives the building response of the seismic motion waveform data for a predetermined time by performing a time history response analysis on a single-degree-of-freedom building model selected from the plurality of single-degree-of-freedom building models, A generation unit that generates an input waveform that reproduces or approximates the building response at a predetermined time by singular value decomposition of a matrix created based on the impulse response of the one-degree-of-freedom building model, A waveform generation system equipped with the following features.

6. It accepts seismic waveform data and building model inputs. By performing eigenvalue analysis on the aforementioned building model, multiple eigenmodes for the building model are derived. Using the natural circular frequencies and damping constants of each of the aforementioned multiple natural modes, multiple one-degree-of-freedom building models are created. By performing a time history response analysis on a single-degree-of-freedom building model selected from the aforementioned plurality of single-degree-of-freedom building models, the building response for a predetermined time point in the seismic motion waveform data is derived. The process of generating an input waveform that reproduces or approximates the building response at a predetermined time by performing singular value decomposition on a matrix created based on the impulse response of the one-degree-of-freedom building model, A waveform generation program to be run on a computer.

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