Conversion method, conversion device, and conversion program

Abstract

This disclosure enables evaluation while reducing the computational load by converting complex seismic motion into impulse seismic motion corresponding to the response of the target structural model. [Solution] In the conversion method, a computer takes the seismic motion as input and performs a time history response analysis of a structural model to identify the time at which a predetermined response index of the structural model reaches its maximum value, and determines the number of impulses corresponding to the repetition characteristics of the seismic motion. The computer identifies the time interval of the seismic motion that contributes to the response of the structural model and extracts the seismic motion in the specific interval. Based on the energy response of the structural model due to the seismic motion in the specific interval, the computer determines the input velocity of the impulse seismic motion, and converts the seismic motion into impulse seismic motion based on the number of impulses and the input velocity. The input velocity is determined so that the response of the structural model to the impulse seismic motion envelops the response of the structural model to the seismic motion.

Description

[Technical Field]

[0001] This disclosure relates to a conversion method, a conversion apparatus, and a conversion program for which a computer converts seismic motion into impulse seismic motion for use in seismic response analysis or seismic design of structures. [Background technology]

[0002] Conventionally, in structural design, including the design of base-isolated or vibration-damping structures, there is a technique for verifying the safety of a structure through seismic response analysis. In seismic response analysis, seismic motion is input into a structural model of the target structure, and the responses of the structural model, such as displacement, velocity, acceleration, inter-story drift angle, and strain energy, are evaluated. There is also a method that combines seismic response analysis with mathematical optimization techniques, modifying the structural model of the target structure while designing it so that the response of the structural model satisfies the design objectives. In such a design, the creation or modification of the model, seismic response analysis, and determination of the design objectives are repeatedly performed.

[0003] In designs combining seismic response analysis and mathematical optimization methods, multiple structural models, multiple seismic motions, and multiple iterative calculations may be involved. Therefore, the number of analyses increases in proportion to the product of the number of models created, the number of seismic motions handled, and the number of iterations, resulting in a significant computational load and time. Furthermore, techniques for evaluating structural responses using impulse seismic motions are known. For example, there is research that models seismic motion as impulse seismic motions and uses this for structural response evaluation or damper design. Since impulse seismic motions can be treated as simpler inputs compared to general seismic motions, they are useful for reducing the computational load in response evaluation and design optimization. Additionally, techniques for probabilistic robust optimization methods for variations in the phase characteristics of seismic motions using multiple impulse inputs have been disclosed (e.g., Patent Document 1). [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2025-82148 [Non-patent literature]

[0005] [Non-Patent Document 1] Kojima, K., and Takewaki, I. (2015). Critical earthquake response of elastic-plastic structures under near-fault ground motions (Part 1: Fling-step input). Frontiers in Built Environment, 1, 12. [Non-Patent Document 2] Akehashi, H., and Takewaki, I. (2022). Bounding of earthquake response via critical double impulse for efficient optimal design of viscous dampers for elastic-plastic moment frames. Japan Architectural Review, 5(2), 131-149. [Overview of the project] [Problems that the invention aims to solve]

[0006] One approach to design is to use only the dominant ground motion that maximizes the response of the structural model among the multiple ground motions used in seismic response analysis. However, if the vibration characteristics or strength of the structural model change during the design process, the dominant ground motion may also change. Therefore, it is not easy to appropriately select the dominant ground motion at each stage of the design process.

[0007] Another approach is to design using a shorter seismic motion waveform, discarding the weaker parts. However, seismic motion is a complex waveform in which various frequency components overlap at different intensities and phases. Therefore, simply shortening a portion of the waveform may result in a multi-peaked response surface due to the combination of the complexity of the external force waveform and the nonlinearity of the structural model, potentially causing mathematical optimization methods to stagnate at local optima.

[0008] Conventional techniques using double-impulse ground motion have a limited number of impulses, which may prevent them from adequately reflecting the repetition characteristics of ground motion. Furthermore, when dealing with long-period or long-duration ground motion, there is a risk of overestimation of the response.

[0009] Furthermore, even when using multiple impulse inputs, as in the technology described in Patent Document 1, the envelope of the response to an elastic single-degree-of-freedom system may only be statistically evaluated. In this case, it is not guaranteed that the response can be appropriately enveloped in an elastoplastic multi-degree-of-freedom system in which the responses of multiple vibration modes are coupled.

[0010] This disclosure aims to provide a conversion method, a conversion device, and a conversion program that can perform evaluation while reducing the computational load by converting complex seismic motion into impulse seismic motion corresponding to the response of the target structural model, taking the above circumstances into consideration. [Means for solving the problem]

[0011] To achieve the above objective, the conversion method of this disclosure is a method by which a computer converts seismic motion into impulse seismic motion for use in seismic response analysis or seismic design of a structure. The conversion method includes the steps of: the computer performing a time history response analysis of a structural model with the seismic motion as input; identifying the time at which a predetermined response index of the structural model reaches its maximum value based on the results of the time history response analysis; determining the number of impulses corresponding to the repeatability characteristics of the seismic motion; identifying a time interval of the seismic motion that contributes to the response of the structural model based on the identified time and the number of impulses, and extracting the seismic motion corresponding to that time interval as seismic motion in a specific interval; determining the input velocity of the impulse seismic motion based on the energy response of the structural model due to the seismic motion in the specific interval; and converting the seismic motion into impulse seismic motion based on the number of impulses and the input velocity, wherein the input velocity is determined such that the response of the structural model to the impulse seismic motion encompasses the response of the structural model to the seismic motion. [Effects of the Invention]

[0012] According to this disclosure, by converting complex seismic motions into impulse seismic motions corresponding to the response of the target structural model, it is possible to perform evaluations while reducing the computational load. [Brief explanation of the drawing]

[0013] [Figure 1] Figure 1 is a block diagram showing the configuration of a conversion system including a conversion device according to this embodiment. [Figure 2] Figure 2 shows an example of the relationship between the number of impulses and the ratio of the maximum mechanical energy of a one-degree-of-freedom system model subjected to impulse seismic motion. [Figure 3] Figure 3 shows an example of the energy response time history for seismic motion and impulse seismic motion. [Figure 4] Figure 4 is a flowchart showing the process of converting seismic motion to impulse seismic motion. [Figure 5] Figure 5 shows a comparison of the response time histories of structural models to seismic motion and impulse seismic motion. [Figure 6] Figure 6 shows a comparative example of inter-story drift angle distribution for seismic motion and impulse seismic motion in a damper design example using converted impulse seismic motion. [Modes for carrying out the invention]

[0014] [Embodiments of this Disclosure] Embodiments of this disclosure will be described below with reference to the drawings. The embodiments described below are examples, and this disclosure is not limited to these embodiments. In the following description, the same or corresponding components will be denoted by the same reference numerals, and redundant descriptions may be omitted. This disclosure can be applied, for example, to time history response analysis, seismic performance evaluation, design of seismic isolation or damping members, and input ground motion conversion processing for damper design, targeting high-rise buildings, base isolation structures, vibration control structures, bridges, tower structures, plant equipment, and other structural models.

[0015] Figure 1 is a block diagram showing the configuration of a conversion system 100 including a conversion device 110 according to this embodiment. The conversion system 100 includes a user terminal 102 and a conversion device 110. The user terminal 102 and the conversion device 110 may be connected to each other via a network N for communication. The conversion device 110 includes an analysis unit 112, a specification unit 114, a first determination unit 116, an extraction unit 118, a second determination unit 120, a conversion unit 122, an evaluation unit 124, and a data storage unit 130.

[0016] The conversion device 110 is implemented as a computer including a CPU (Central Processing Unit), ROM (Read Only Memory) storing programs for implementing each processing routine, RAM (Random Access Memory) for temporarily storing data, memory as a storage means, and a network interface. Depending on the processing requirements, a GPGPU or accelerator may be used instead of the CPU, and an appropriate processing unit may be used. The functional parts of the conversion device 110 are implemented by the CPU, which is the processor, executing the conversion program. However, some or all of these functional parts may be implemented by hardware such as dedicated circuits, FPGAs, or ASICs.

[0017] The user terminal 102 is a terminal used by the designer or analyst. The user terminal 102 receives the specifications of the structural model, seismic motion data, analysis conditions, design objectives, types of response indicators, damping constants, setting conditions for the evaluation model, etc., and transmits them to the conversion device 110. The user terminal 102 may also display the conversion results from the conversion device 110, response analysis results, number of impulses, input velocity, start time and end time of seismic motion in a specific section, etc.

[0018] The data storage unit 130 stores seismic motion data, structural model data, evaluation model data, analysis conditions, conversion parameters, response analysis results, converted impulse seismic motion data, etc. The data storage unit 130 is not limited to being located inside the conversion device 110; it may also be an external server.

[0019] [Description of each processing unit] The analysis unit 112 takes seismic motion as input and performs a time history response analysis of the structural model. The analysis unit 112 receives seismic motion data and structural model data as input and calculates the displacement, velocity, acceleration, inter-story drift angle, restoring force, strain energy, mechanical energy, etc., of the structural model at each time point. The output of the analysis unit 112 is stored in the data storage unit 130 as the time history response analysis result.

[0020] The identification unit 114 identifies the time at which a predetermined response index of the structural model reaches its maximum value, based on the results of the time history response analysis. For example, the identification unit 114 compares the strain energy at each time point and identifies the time at which the strain energy is maximum as the terminal time t E The identification unit 114 may identify the time at which displacement, inter-story drift angle, mechanical energy, or other response indicators reach their maximum values, instead of strain energy.

[0021] The first determination unit 116 determines the number of impulses N corresponding to the repetition characteristics of seismic motion. I The first determination unit 116 calculates a first index when seismic motion acts on the evaluation model and a second index when candidate impulse seismic motion acts on the evaluation model, and determines the number of impulses N so that the first index and the second index are close together. I To decide.

[0022] The extraction unit 118 takes the time identified by the identification unit 114 and the number of impulses N determined by the first determination unit 116. I Based on this, the time intervals of the seismic motion that contribute to the response of the structural model are identified. The extraction unit 118 extracts the seismic motion corresponding to the said time interval as seismic motion in a specific interval. In this specification, seismic motion in a specific interval is also referred to as truncated seismic motion.

[0023] The second determination unit 120 determines the input velocity V of the impulse seismic motion based on the energy response of the structural model to the seismic motion in a specific section. The second determination unit 120 determines the input velocity V such that, for example, the maximum strain energy of the structural model for the impulse seismic motion corresponds to a value based on the input energy and energy consumption due to the seismic motion in a specific section.

[0024] The conversion unit 122 has an impulse number N. I Based on the input velocity V, the seismic motion is converted into impulse seismic motion. The conversion unit 122 converts, for example, input velocity V, number of impulses N I And generates impulse seismic motion data defined by the impulse time interval t0.

[0025] The evaluation unit 124 may evaluate whether the response of the structural model to the converted impulse seismic motion envelopes the response of the structural model to the original seismic motion. The evaluation unit 124 performs response analysis by inputting the generated impulse seismic motion into the structural model as necessary, and compares the maximum values of predetermined response indexes.

[0026] Next, a generation process of the impulse seismic motion will be described. The conversion unit 122 generates impulse seismic motion represented by, for example, the following formula (1). [Math.]] ...(1)

[0027] In formula (1), ¨u I (t) represents the ground acceleration of the impulse seismic motion, V represents the input velocity, δ(t) represents the delta function, N I represents the number of impulses, and t0 represents the impulse time interval. Formula (1) shows an example of impulse seismic motion, and the sign of the impulses, coefficients of the initial impulse, impulse time interval or action time of the impulses may be changed according to the structural model and the design purpose.

[0028] The impulse time interval t0 is not limited to being a main determination target in an independent claim. The impulse time interval t0 is determined based on, for example, half of the primary natural period of the structural model, half of the period of the evaluation model, or the timing when the input energy becomes large in the response to the impulse seismic motion.

[0029] [Determination of Number of Impulses] The first determination unit 116 determines the number of impulses N corresponding to the repeated characteristics of the seismic motion IThe repetitive characteristics of seismic motion refer to the property that seismic motion causes multiple energy inputs or multiple large responses to the structural model. In this embodiment, the first determination unit 116 uses a one-degree-of-freedom system model set based on the vibration characteristics of the structural model as an evaluation model, and determines the number of impulses N based on the mechanical energy of the one-degree-of-freedom system model. I Evaluate.

[0030] First, the first decision unit 116 determines the index η based on the mechanical energy of the one-degree-of-freedom system model subjected to impulse seismic motion. I Defines the index η. I This can be expressed, for example, by equation (2). The first determination unit 116 determines the index η based on the mechanical energy of the one-degree-of-freedom system model subjected to seismic motion. GM Defines the index η. GM This can be expressed, for example, by equation (3).

number

number

[0031] In equation (2), E Mech,I (N I (V,ω,h,t) is the number of impulses N I This represents the mechanical energy at time t of a one-degree-of-freedom system model with natural circular frequency ω and damping constant h, subjected to impulse seismic motion defined by the input velocity V. h1 and h2 are different damping constants. Therefore, η I This represents the ratio of the maximum mechanical energy when the damping constant is h2 to the maximum mechanical energy when the damping constant is h1, for a one-degree-of-freedom system model subjected to impulse ground motion.

[0032] In equation (3), E Mech,GM(u¨g,ω,h,t) represents the mechanical energy at time t of a one-degree-of-freedom system model with natural circular frequency ω and damping constant h, subjected to ground acceleration u¨g. Therefore, η GM This represents the ratio of the maximum mechanical energy when the damping constant is h2 to the maximum mechanical energy when the damping constant is h1, for a one-degree-of-freedom system model subjected to seismic motion.

[0033] The first decision unit 116 determines the number of candidate impulses N I For η, equation (2) I Calculate and η calculated by formula (3) GM It is compared with the first decision unit 116, I and η GM The number of candidate impulses N that is closest to the given value. I The number of impulses N corresponds to the repeating characteristics of seismic motion. I It is decided as follows: η I and η GM For example, when the two are closest, η I and η GM This includes a decrease in the difference, ratio, relative difference, or evaluation value based thereon. The first decision unit 116 determines the number of candidate impulses N I From among them, η I and η GM The number of impulses N that best corresponds to this is I You may choose this option, provided the number of impulses is N. I The method for determining this is not limited to a specific optimization formula.

[0034] In this disclosure, “the first index” is η, which is the ratio of the maximum values ​​of the mechanical energy of the evaluation model when seismic motion is applied. GM Correspondingly, the "second index" is η, which is the ratio of the maximum value of the mechanical energy of the evaluation model when an impulse seismic motion is applied. I Corresponds to η represented by formula (3) in this disclosure. GM This corresponds to the first index, which is an index on the seismic motion side, and is expressed by equation (2) η I This corresponds to the second index, which is an index for impulse seismic motion.

[0035] Furthermore, the first determination unit 116 may set the natural circular frequency ω and damping constants h1 and h2 in equations (2) and (3) to reflect the vibration characteristics of the structural model to be designed. For example, the first determination unit 116 approximates the vibration characteristics of the structural model after design by equivalent linearization and sets the equivalent first natural circular frequency ω eq,1 , damping constant h corresponding to structural damping St , damping constant h corresponding to structural hysteresis deformation Hys , and damping constant h corresponding to the damper or additional damping Add The indicators of equations (2) and (3) may be made concrete using η. In this case, for example, equations (4a) and (4b) are used to express η I and η GM You may calculate this.

number

[0036] In equations (4a) and (4b), ω eq,1 This represents the first natural circular frequency based on the equivalent stiffness of the structural model being designed. St represents the damping constant corresponding to structural damping, h Hys This represents the damping constant corresponding to the structural hysteretic deformation or hysteretic damping, h Add ω represents the damping constant corresponding to the damper or additional damping. Equations (4a) and (4b) are specific examples in which the natural circular frequency ω and damping constants h1 and h2 in equations (2) and (3) are set based on the equivalent linearization of the structural model after design. Therefore, equations (4a) and (4b) apply the basic index definitions of equations (2) and (3) according to the vibration characteristics of the structural model under design.

[0037] Figure 2 shows η defined by equation (2). I This figure shows an example. The horizontal axis represents the number of impulses, N. I The vertical axis represents η IThis represents the number of impulses N, as shown in Figure 2. I When N changes, the ratio of the maximum mechanical energy values ​​corresponding to the combination of damping constants changes. The first determination unit 116 determines the number of such candidate impulses N I The evaluation value for each is obtained for a 1-degree-of-freedom system model subjected to seismic motion η GM By comparing it with the number of impulses N corresponding to the repetition characteristics of seismic motion, I It is possible to determine this.

[0038] [Evaluation of impulse input speed] The equations of motion for a structural model that approximates the post-design vibration characteristics using equivalent stiffness when subjected to seismic motion can be expressed, for example, as shown in equations (5a) and (5b).

number

[0039] In equation (5a), M represents the mass matrix, Keq represents the stiffness matrix based on equivalent stiffness, Ceq represents the equivalent damping matrix, u represents the relative displacement vector of the structural model, ·u represents the relative velocity vector, ¨u represents the relative acceleration vector, 1 represents the input direction vector, and ¨u g represents the ground acceleration of the seismic motion. Equation (5b) shows an example of reflecting the contributions of hysteretic deformation, structural damping, and additional damping in the equivalent damping matrix Ceq.

[0040] The second determination unit 120 calculates equation (5a) at time t S From time t E By integrating up to this point, we can obtain the energy relation shown in equation (6).

number

[0041] The integration range for equation (6) is time tS From time t E up to (t S ≦t≦t E ). Here, time t E In the main embodiment, this is the time when the strain energy is at its maximum, and time t S is, time t E This is the time obtained by going back the duration of the impulse ground motion. Also, t duration,I represents the duration of the impulse ground motion, T eq represents the equivalent period of the structural model or evaluation model. duration,I This is expressed as follows, with N being the number of impulses. I and equivalent period T eq It is determined based on the following. The extraction unit 118 determines the termination time t E from the said duration t duration,I The time that is set back by that amount is the start time t S It shall be defined as follows.

number

[0042] By expanding equation (6), the relationship between the terminal value of mechanical energy due to seismic motion, the damped energy consumed, and the input energy in a specific section can be summarized, for example, as shown in equations (7a) to (7e).

number

[0043] In equations (7c) to (7e), EMech,GM (t E ) represents the mechanical energy at the end time t of the time interval corresponding to the truncated ground motion E , and E Damp,GM (t S , t E ) represents the damped dissipated energy from the start time t S to the end time t E , and E Input,GM (t S , t E ) represents the input energy from the start time t S to the end time t E .

[0044] Note that although the integration range is from time t S to time t E , a new truncated ground motion is not input to the structural model in a stationary state. The energy relationship in formulas (7a) to (7e) is based on the results of time history response analysis performed on the entire time period of the original ground motion. E Input,GM (t S , t E ) may be treated as a concept including the initial value of mechanical energy at time t S . In this respect, the truncated ground motion is different from a shortened waveform for simply inputting a part of the original ground motion to a structural model in a stationary state.

[0045] Figure 3 is a diagram showing an example of energy response time history for ground motion and impulse ground motion. In FIG. 3, the energy response time history for ground motion and the energy response time history for impulse ground motion are schematically shown to explain the energy relationship shown in formulas (7a) to (7e).

[0046] The left side of Figure 3 shows a magnified time history of input energy, damped energy consumption, mechanical energy, and strain energy when seismic motion acts on a structural model. The right side of Figure 3 shows the time history of input energy, damped energy consumption, mechanical energy, and strain energy when impulse seismic motion acts on a structural model or evaluation model.

[0047] As shown in Figure 3, in the energy response time history to seismic motion, the time t is when the response index of the structural model reaches its maximum value. E Based on, time t E From the duration of the impulse seismic motion t duration,I The time t that goes back only that far S This is set. Time t S From time t E The seismic motion corresponding to the time interval up to that point is treated as seismic motion in a specific interval, i.e., truncated seismic motion.

[0048] In Figure 3, E Input,GM (t S ,t E ) is time t S From time t E This represents the input energy due to seismic motion corresponding to the section up to E. Damp,GM (t S ,t E ) is time t S From time t E This represents the decay energy consumed up to a certain point. Mech,GM (t E ) is the end time t E This represents the mechanical energy at time t. These energy quantities are given by equations (7a) to (7e), as shown in equations (7a) to (7e). S From time t E This represents the energy balance over the time interval up to that point.

[0049] Furthermore, as shown in equation (7d), E Input,GM (t S ,t E ) is time t S Mechanical energy E Mech,GM (tS ) and time t S From time t E It is expressed based on the input work up to time t. Therefore, the energy relations of equations (7a) to (7e) are given by time t S From time t E This is not obtained by inputting only the section up to time t into a static structural model, but rather is based on the results of a time history response analysis of the structural model for the entire duration of the original seismic motion. Therefore, the energy response corresponding to the truncated seismic motion is obtained at time t S It can reflect state variables such as velocity, displacement, and mechanical energy in a given system.

[0050] The energy response time history for impulse seismic motion shown on the right side of Figure 3 is given by the number of impulses N. I This also represents the response when an impulse ground motion defined by the input velocity V acts. The second determination unit 120 determines the input velocity V of the impulse ground motion based on the relationship between the energy response on the ground motion side and the energy response on the impulse ground motion side shown in Figure 3. Specifically, the second determination unit 120 determines the input velocity V such that the maximum value of the strain energy for the impulse ground motion corresponds to the value obtained by subtracting the energy consumed due to structural damping from the input energy due to the truncated ground motion.

[0051] Figure 3 is a schematic diagram illustrating the energy relationships shown in equations (7a) to (7e) and the determination relationships for the input velocity V shown in equations (8) to (10), which will be described later. Therefore, the curve shapes of each energy response time history, the relative magnitudes of each energy quantity, the positions at each time, and the line types shown in Figure 3 are examples and may vary depending on the seismic motion, structural model, evaluation model, damping constant, and design conditions.

[0052] The input velocity V of the impulse seismic motion is determined, for example, such that equation (8) holds.

number

[0053] In equation (8), E Hys,I This represents the strain energy in response to impulse ground motion. Furthermore, the right-hand side of equation (8) can also be rewritten as shown in equation (9).

number

[0054] Equation (8) means that the maximum strain energy for impulse ground motion corresponds to the input energy due to truncated ground motion minus the energy consumed due to structural damping. St h Hys and h Add This is merely a damping constant or damping contribution used to approximate the vibration characteristics after design through equivalent linearization, and it is not necessary to strictly exhibit the same damping effect during elastoplastic response analysis.

[0055] Assuming that the input energy due to truncated ground motion is approximately constant with respect to fluctuations in hysteretic deformation or additional damping, the relationship in equation (10) can be obtained by applying the concept of the constant energy law to truncated ground motion.

number

[0056] From equations (8), (9), and (10), the strain energy for impulse ground motion is evaluated to be greater than or equal to the strain energy for ground motion. Therefore, the second determination unit 120 can determine the input velocity V of the impulse ground motion so as to encompass the response of the structural model to the original ground motion.

[0057] [Conversion to impulse seismic motion] The conversion unit 122 determines the number of impulses N determined by the first determination unit 116. IBased on the input velocity V determined by the second determination unit 120, the seismic motion is converted into impulse seismic motion. The conversion unit 122 generates impulse seismic motion as shown in equation (1), for example. The impulse seismic motion generated by the conversion unit 122 is an input with a shortened and simplified waveform compared to the original seismic motion. The impulse seismic motion is not intended to directly reproduce the full time waveform of the original seismic motion, but rather to represent the main influence on the response of the structural model by the number of impulses and the input velocity. The conversion unit 122 may output the generated impulse seismic motion as at least one of the ground acceleration time history, the impulse action time sequence, the input velocity sequence, the number of impulses, the impulse time interval, and metadata.

[0058] [Response Envelopment] In this disclosure, “enveloping” means that, for a given response index, the response value of the structural model to an impulse ground motion is set to be greater than or equal to the response value of the structural model to the original ground motion. The response values ​​subject to enveloping are, for example, maximum strain energy, maximum displacement, maximum inter-story drift angle, maximum mechanical energy, or design indexes based thereon. In the main embodiment, the input velocity V is determined such that the maximum strain energy of the structural model to the impulse ground motion envelops the strain energy of the structural model to the original ground motion. This is adjusted to prevent response evaluation or design using the converted impulse ground motion from underestimating the response to the original ground motion. The evaluation of the enveloping is not limited to always exceeding the response value at each time in the entire time history. The evaluation of the enveloping may be performed for a design-important maximum value, a maximum value within a given time interval, or a value of a given evaluation index.

[0059] [Overall processing] Next, the processing as a conversion method executed by the conversion device 110 will be described. Figure 4 is a flowchart of the conversion process from seismic motion to impulse seismic motion. The processing of the analysis unit 112, the identification unit 114, the first determination unit 116, the extraction unit 118, the second determination unit 120, the conversion unit 122, and the evaluation unit 124 is realized by the calculation unit 112, the identification unit 114, the first determination unit 116, the extraction unit 118, the second determination unit 120, the conversion unit 122, and the evaluation unit 124. These processes may be executed for a single seismic motion, or for multiple seismic motions, one wave at a time. When this process is executed for multiple seismic motions, the conversion device 110 may generate multiple impulse seismic motions corresponding to each seismic motion and select the impulse seismic motion that is dominant for a predetermined design index.

[0060] In step S100, the conversion device 110 acquires data to be processed. For example, the conversion device 110 acquires seismic motion data, structural model data, analysis conditions, response index type, evaluation model setting conditions, damping constant, design target, etc., from the user terminal 102. The acquired data is stored in the data storage unit 130. Seismic motion data is, for example, time history data of ground acceleration. Structural model data includes, for example, mass, stiffness, damping, number of floors, floor height, restoring force characteristics, characteristics of seismic isolation members or vibration control members, etc.

[0061] In step S102, the analysis unit 112 takes the seismic motion acquired in step S100 as input and performs a time history response analysis of the structural model. The analysis unit 112 calculates the response at each time point when the seismic motion acts on the structural model. The calculated response includes, for example, displacement, velocity, acceleration, inter-story drift angle, restoring force, strain energy, mechanical energy, damping energy consumption, and input energy. The analysis unit 112 stores the obtained time history response analysis results in the data storage unit 130.

[0062] In step S104, the identification unit 114 identifies the time at which a predetermined response index of the structural model reaches its maximum value, based on the time history response analysis results obtained in step S102. For example, the identification unit 114 compares the strain energy at each time point and identifies the time at which the strain energy is maximum as the terminal time t E This is specified as follows. Note that the specified response index is not limited to strain energy, but may also be displacement, inter-story drift angle, mechanical energy, or other response indexes.

[0063] In step S106, the first determination unit 116 determines the number of impulses N corresponding to the repetition characteristics of the seismic motion. I The first determination unit 116 determines an index η based on the mechanical energy of a one-degree-of-freedom system model subjected to impulse seismic motion. I And, an index η based on the mechanical energy of a one-degree-of-freedom system model subjected to seismic motion. GM The first decision unit 116 then compares the number of candidate impulses N I From among them, η I and η GM The number of candidate impulses N that is closest to the given value. I The number of impulses N corresponds to the repeating characteristics of seismic motion. I This will be decided.

[0064] In step S108, the extraction unit 118 takes the time identified in step S104 and the number of impulses N determined in step S106. I Based on this, the time intervals of the seismic motion that contribute to the response of the structural model are identified. For example, the extraction unit 118 determines the time at which a predetermined response index reaches its maximum value as the termination time t E Let the number of impulses be N. I The duration of the impulse seismic motion is determined according to the termination time t. E The time calculated by going back from the start time t S It is identified as such. Then, the extraction unit 118 determines the start time t S from end time t E The seismic motion corresponding to the time interval up to that point is extracted as seismic motion in a specific interval, i.e., truncated seismic motion.

[0065] In step S110, the second determination unit 120 determines the input velocity V of the impulse seismic motion based on the energy response of the structural model due to the seismic motion in the specific section extracted in step S108. For example, the second determination unit 120 determines the input velocity V of the impulse seismic motion at time t S From time t E Based on the relationship between input energy, damping energy consumption, mechanical energy, and strain energy over the time interval up to a certain point, the input velocity V is determined such that the maximum strain energy for the impulse ground motion envelops the response of the structural model to the original ground motion.

[0066] In step S112, the conversion unit 122 converts the number of impulses N determined in step S106. I Based on the input velocity V determined in step S110, the seismic motion is converted into impulse seismic motion. For example, the conversion unit 122 converts the number of impulses N I The system generates impulse seismic motion defined by the input velocity V and the impulse time interval t0. The generated impulse seismic motion may be stored in the data storage unit 130 or output to the user terminal 102.

[0067] In step S114, the evaluation unit 124 evaluates the response of the structural model to the impulse ground motion generated in step S112, if necessary. For example, the evaluation unit 124 performs a response analysis of the structural model to the impulse ground motion and compares it with the response of the structural model to the original ground motion. The evaluation unit 124 may also evaluate whether the response to the impulse ground motion encompasses the response to the original ground motion with respect to a predetermined response index.

[0068] Note that the process shown in Figure 4 is just one example, and the order of each step may be changed as long as it does not contradict the processing content. For example, the number of impulses N in step S106. IPart of the decision process may be performed before the time-specification process in step S104. Also, the evaluation process in step S114 may be omitted and may be incorporated into seismic performance evaluation, design of base isolation members or vibration control members, or damper design using the converted impulse seismic motion. Furthermore, when this process is performed for multiple seismic motions, the conversion device 110 may perform the processes from step S100 to step S112 for each seismic motion to generate multiple impulse seismic motions.

[0069] As described above, according to the conversion device 110 of this embodiment, the number of impulses N corresponding to the repetition characteristics of seismic motion I By using an input velocity V based on the energy response in the time interval that contributes to the response of the structural model, the ground motion can be converted into impulse ground motion. This shortens and simplifies the input in seismic response analysis or seismic design compared to using the original ground motion as is. Furthermore, by determining the input velocity V such that the response to impulse ground motion envelops the response to the original ground motion, it is possible to perform response evaluation that reduces the computational load while suppressing underestimation of the response.

[0070] [Comparison of structural model responses to seismic ground motion and impulse ground motion] To verify the above method, the responses of structural models to ground motion and impulse ground motion were compared. Figure 5 shows a comparison of the response time histories of structural models to ground motion and impulse ground motion. In Figure 5, three artificially generated waves simulating random phase ground motion, long-period long-duration ground motion, and pulsed ground motion were used as input ground motions, and an example is shown in which impulse ground motions corresponding to each ground motion were generated. For example, a 20-story building model may be used as the structural model.

[0071] In Figure 5, the upper panel shows the time history of ground acceleration for each seismic motion, and the middle panel compares the time history of the structural model's top displacement response for each seismic motion with the time history of the structural model's top displacement response for the corresponding impulse seismic motion. The lower panel shows an example of the arrangement of impulse inputs included in each impulse seismic motion. The time intervals corresponding to the truncated seismic motions shown in Figure 5 are examples of time intervals from the original seismic motion that contribute to the structural model's response. In the example shown in Figure 5, the time history of the top displacement response for each seismic motion and the time history of the top displacement response for the impulse seismic motion are compared for random phase seismic motion, long-period long-duration seismic motion, and pulsed seismic motion. This confirms that although the converted impulse seismic motion does not directly reproduce the entire time history waveform of the original seismic motion, it can represent the response trend in the time intervals that contribute to the structural model's response.

[0072] As an example, the elastic first-order natural period of a 20-story building model is 2.68 seconds. The equivalent first-order periods corresponding to the design targets for random phase ground motion, long-period, long-duration ground motion, and pulsed ground motion may be 2.68 seconds, 3.13 seconds, and 3.70 seconds, respectively. The maximum displacement response to impulse ground motion may be set to be greater than the maximum displacement response to the original ground motion. This ensures that the response to impulse ground motion encompasses the response to the original ground motion.

[0073] The similarity of the response waveforms may also be evaluated by the cosine similarity between the time history of the top displacement response for the original ground motion and the time history of the top displacement response for the impulse ground motion in a predetermined interval. If the two waveforms are similar in shape, the absolute value of the cosine similarity will be 1. In one example, the cosine similarities for random phase ground motion, long-period long-duration ground motion, and pulsed ground motion are 0.932, 0.876, and 0.962, respectively, confirming that the converted impulse ground motion accurately captures the properties of the time interval that contributes to the response of the structural model among the corresponding ground motions.

[0074] [Examples of application to seismic design or damper design] Figure 6 shows a comparison of inter-story drift angle distributions for seismic motions and impulse seismic motions in damper design examples using converted impulse seismic motions for groups A to C. The conversion device 110 can use the converted impulse seismic motions for seismic design or damper design. For example, the conversion device 110 or design device converts multiple seismic motions into impulse seismic motions and selects the impulse seismic motion that is dominant for a predetermined design index from among the multiple converted impulse seismic motions. The conversion device 110 or design device may use the selected impulse seismic motion to determine the arrangement, performance, stiffness, damping coefficient, yield load, etc., of seismic isolation members, vibration control members, or dampers.

[0075] In one example of damper design, a total of 28 seismic waves can be set as design ground motions: 13 random phase ground motions, 3 long-period, long-duration ground motions, and 12 pulsed ground motions. These ground motions can be classified into groups A, B, and C, and design targets may be set to ensure that each inter-story drift angle is 1 / 150 or less for group A, 1 / 100 or less for group B, and 1 / 60 or less and the layer plasticity ratio is 2 or less for group C. In this design example, the impulse ground motions corresponding to each ground motion can be evaluated, and damper optimization may be performed using only the impulse ground motions. Linear oil dampers and hysteresis dampers may be used as dampers, with a usage ratio of 1:4. For example, the hysteresis damper may have bilinear restoring force characteristics, a secondary stiffness ratio of 0.1, a yield inter-story drift angle of 1 / 290 on the first floor, and a yield inter-story drift angle of 1 / 400 on the other floors. For the structural model, for example, a 20-story building model may be used. The equivalent first-order periods corresponding to the design targets for seismic motion in Groups A, B, and C may be 2.68 seconds, 3.13 seconds, and 3.70 seconds, respectively.

[0076] Figure 6 shows a comparison of the design objectives, inter-story drift angle distribution for impulse ground motions, inter-story drift angle distribution for ground motions corresponding to the impulse ground motions, and inter-story drift angle distribution for the original ground motions for each of the groups A, B, and C. As shown in Figure 6, designing using the transformed impulse ground motions allows for a damper design that satisfies the design objectives while suppressing underestimation or overestimation of the structural model's response to the original ground motions. Furthermore, impulse ground motions have shorter durations and simpler waveforms compared to the original ground motions. This makes it easier to select a dominant impulse ground motion from among multiple impulse ground motions, suppressing stagnation during the application of mathematical optimization methods. In one example, optimization can be completed in approximately 1 / 90th of the time compared to using the original ground motions directly for damper optimization. Note that the inter-story drift angle distributions, design objectives, number of ground motions, number of layers in the structural model, damper type, damping constant, stiffness, design conditions, and optimization methods shown in Figure 6 are examples and may be appropriately changed depending on the design target and analysis conditions.

[0077] [Differentiation] This disclosure is not limited to the embodiments described above, and various modifications are possible without departing from the gist of this disclosure. For example, in the embodiments described above, the example of using the strain energy of the structural model as a predetermined response index was mainly explained. However, the predetermined response index is not limited to strain energy. The predetermined response index may be, for example, mechanical energy, displacement, top displacement, inter-story drift angle, inter-story velocity, velocity, acceleration, floor acceleration, member stress, member plasticity ratio, damage index, or an evaluation value based on a combination thereof. Furthermore, the predetermined response index may be an index that represents the response of the entire structural model, or an index that represents the response of a specific layer, a specific member, a seismic isolation layer, a vibration control member, or a damper.

[0078] In the embodiment described above, the time at which the strain energy of the structural model reaches its maximum value is defined as the termination time t. EAn example of how to identify a response index has been explained. However, the identification unit 114 is not limited to identifying only the time when the response index reaches its maximum value. The identification unit 114 may identify the time when the response index shows a value close to the maximum value, the time when it shows a local maximum value, or the time when it exceeds a predetermined threshold as the time when the response index reaches its maximum value. In addition, the identification unit 114 may identify candidate times for each of multiple response indices and, depending on the design or evaluation purpose, select one of the candidate times as the termination time t E You may choose this option.

[0079] In the above-described embodiment, the start time t S to, end time t E An example was described in which the time is set by the duration of the impulse seismic motion. However, the method of specifying the time interval by the extraction unit 118 is not limited to this. The extraction unit 118 determines the end time t by adding a predetermined margin time to the duration of the impulse seismic motion. E The time calculated by going back from the start time t S This may also be done. Furthermore, the extraction unit 118 determines the start time t based on the time when the cumulative amount of input energy, decayed energy consumption, strain energy, or mechanical energy reaches a predetermined ratio. S The extraction unit 118 may also set the time interval in which the response index is greater than or equal to a predetermined threshold, the time interval in which the response index shows an increasing trend, or the time interval in which the energy input is greater than or equal to a predetermined value as a time interval that contributes to the response of the structural model.

[0080] In the embodiments described above, an example was explained in which a one-degree-of-freedom system model having a natural circular frequency ω and a damping constant h was used as the evaluation model. However, the evaluation model is not limited to a one-degree-of-freedom system model. The evaluation model may be a multi-degree-of-freedom system model that reflects multiple major modes of the structural model, or it may be a low-dimensional model obtained by reducing the structural model. Furthermore, the evaluation model may be the structural model itself. The evaluation model may be set based on the first-order mode, second-order or higher vibration modes, equivalent mass, equivalent stiffness, equivalent period, equivalent damping, or a combination thereof of the structural model.

[0081] In the above-described embodiment, the number of impulses N I An example was explained in which the ratio of the maximum values ​​of the mechanical energy of the evaluation model subjected to seismic motion to the ratio of the maximum values ​​of the mechanical energy of the evaluation model subjected to impulse seismic motion is made close to each other. However, the number of impulses N I The method for determining the impulse number N is not limited to this. The first determination unit 116 determines the impulse number N based on the duration of the seismic motion, the dominant period, the response spectrum, the energy spectrum, the cumulative history of the input energy, the number of peaks of the response index, the number of repetitions of the response index, or a combination thereof. I The first determination unit 116 may also determine the number of candidate impulses or the upper limit number of impulses input via the user terminal 102, and within the acquired range, the number of impulses N I You may decide that.

[0082] In the embodiments described above, examples were explained in which two different damping constants h1 and h2 are used in equations (2) and (3). However, the number of damping constants is not limited to two. The first determination unit 116 calculates the mechanical energy for an evaluation model having three or more damping constants, and determines the number of impulses N based on the maximum value, ratio, difference, or distribution of multiple mechanical energies corresponding to multiple damping constants. I The first determination unit 116 may also use, in place of or in addition to the damping constant, multiple evaluation models with different natural frequencies, stiffness, mass, or hysteresis characteristics.

[0083] In the embodiments described above, an example was explained in which the vibration characteristics of a structural model are determined using natural frequencies and damping constants evaluated by stiffness based on equivalent linearization. However, the method for determining the vibration characteristics of a structural model is not limited to this. The vibration characteristics of a structural model may be determined based on eigenvalue analysis, modal analysis, system identification based on response analysis results, identification based on measured data, or design values ​​set by the designer. Furthermore, the vibration characteristics of a structural model may be determined based on the structural model before design, or based on the structural model after the installation of seismic isolation members, vibration damping members, or dampers.

[0084] In the embodiments described above, an example was explained in which the second determination unit 120 determines the input velocity V of an impulse seismic motion based on the energy response due to seismic motion in a specific section. However, the method for determining the input velocity V is not limited to the relationships shown in equations (8) to (10). The second determination unit 120 may perform a response analysis for impulse seismic motion for a plurality of candidate input velocities and select a candidate input velocity that encompasses the response to the original seismic motion for a predetermined response index. The second determination unit 120 may also multiply the input velocity V by a safety factor or a margin factor. Furthermore, the second determination unit 120 may set the input velocity V to the same value for all impulses, or to a different value for each impulse.

[0085] In the embodiments described above, an example of representing impulse ground motion using a delta function was explained. However, impulse ground motion is not limited to the delta function itself. Impulse ground motion may be represented by pulses with finite width, rectangular pulses, triangular pulses, trapezoidal pulses, Gaussian pulses, or approximate waveforms treated as impulses in numerical analysis, within a range that can represent the impulse intensity or energy input corresponding to the input velocity V. In this case, each pulse with finite width may be set to give an input velocity, input energy, or response effect equivalent to or corresponding to the impulse input represented by the delta function. Furthermore, the time interval of multiple impulses or the intensity of each impulse is not limited to the example shown in equation (1). The time interval of multiple impulses or the intensity of each impulse may be set based on the vibration characteristics, response phase, or energy input timing of the structural model or evaluation model, within a range where the input velocity V is determined to envelop the response of the structural model.

[0086] In the embodiments described above, an example was given in which the impulse time interval t0 is set based on the primary natural period of the structural model or the period of the evaluation model. However, the impulse time interval t0 is not limited to this. The impulse time interval t0 may be determined based on the response phase of the structural model, the time when the sum of inertial forces satisfies a predetermined condition, the time when the input energy becomes large, the peak interval of the response index, or a time interval set by the user. Furthermore, the impulse time interval t0 may be constant among all impulses, or it may differ from impulse to impulse.

[0087] In the above-described embodiment, the conversion device 110 performs time history response analysis, time identification, and impulse number N. I An example was described of determining the input velocity V, extracting seismic motion in a specific section, determining the input velocity V, and converting it to impulse seismic motion. However, these processes are not limited to being performed by a single device. For example, time history response analysis may be performed by an external analysis device or cloud server, and the conversion device 110 may acquire the time history response analysis results from the external analysis device. Furthermore, each functional part of the conversion device 110 may be implemented in a distributed manner across multiple computers, multiple servers, or a cloud environment.

[0088] In the embodiments described above, examples were given of using the converted impulse ground motion for seismic performance evaluation, design of seismic isolation or damping members, and damper design. However, the uses of the converted impulse ground motion are not limited to these. The converted impulse ground motion may be used for structural safety evaluation, post-earthquake soundness diagnosis, reinforcement design, performance design, maintenance planning, risk assessment, or comparative evaluation of multiple design options. Furthermore, the converted impulse ground motion may be presented to the designer or input into other analysis programs or design support programs.

[0089] In the embodiments described above, an example was given in which a building model was used as the structural model. However, the structural model is not limited to a building model. The structural model may represent a high-rise building, a base-isolated structure, a vibration-damping structure, a bridge, a tower-like structure, plant equipment, piping equipment, mechanical equipment, or a part thereof. Furthermore, the structural model may be a multi-degree-of-freedom system model, a single-degree-of-freedom system model, a finite element model, a frame model, a shear type model, a bending-shear type model, or a model that combines these.

[0090] In the embodiment described above, an example was explained in which the evaluation unit 124 evaluates the response of the structural model to the converted impulse ground motion. However, the evaluation process by the evaluation unit 124 is not mandatory. The conversion device 110 performs the processing up to generating and outputting the impulse ground motion, and the evaluation of the response to the converted impulse ground motion may be performed by an external analysis device, design device, or designer. Furthermore, the evaluation unit 124 may not only compare the response to the original ground motion with the response to the impulse ground motion, but may also evaluate the satisfaction with the design objective, the dominant impulse ground motion, or the superiority or inferiority of multiple design proposals.

[0091] In the embodiment described above, an example was described in which the conversion device 110 is connected to the user terminal 102 via a network N. However, the user terminal 102 and the conversion device 110 may be configured as a single integrated device. Furthermore, the conversion device 110 is not limited to receiving data from the user terminal 102, but may also acquire seismic motion data, structural model data, analysis conditions, design goals, evaluation model setting conditions, etc., from an external database, analysis server, design support device, or storage medium. [Explanation of symbols]

[0092] 100 Conversion Systems 102 User terminals 110 Conversion device 112 Analysis Department 114 Specific section 116 First Decision Section 118 Extraction part 120 Second Decision Section 122 Conversion section 124 Evaluation Department 130 Data Storage Unit

Claims

1. A conversion method for converting seismic motion into impulse seismic motion using a computer, for use in seismic response analysis or seismic design of structures, The aforementioned computer, The process involves performing a time history response analysis of a structural model using the aforementioned seismic motion as input, Based on the results of the time history response analysis, the process involves identifying the time at which a predetermined response index of the structural model reaches its maximum value. A step of determining the number of impulses corresponding to the repeating characteristics of the aforementioned seismic motion, Based on the identified time and the number of impulses, the process involves identifying the time intervals of the seismic motion that contribute to the response of the structural model, and extracting the seismic motion corresponding to those time intervals as seismic motion in a specific interval. A step of determining the input velocity of the impulse seismic motion based on the energy response of the structural model due to seismic motion in the specified section, The process includes converting the seismic motion into impulse seismic motion based on the number of impulses and the input velocity, A conversion method in which the input speed is determined such that the response of the structural model to the impulse seismic motion encompasses the response of the structural model to the seismic motion.

2. The predetermined response index is the strain energy of the structural model, The conversion method according to claim 1, wherein the time interval is defined as an interval in which the time at which the strain energy of the structural model reaches its maximum value is the end time, and the start time is the time obtained by the duration of the impulse seismic motion determined according to the number of impulses, which is set back from the end time.

3. The number of impulses is, The first index is the ratio of the maximum values ​​of the mechanical energy of evaluation models having different damping constants when the aforementioned seismic motion is applied, The second index, which is the ratio of the maximum values ​​of the mechanical energy of the evaluation models having different damping constants when the impulse seismic motion acts, is determined to be close to the second index. The conversion method according to claim 1, wherein the evaluation model is set based on the vibration characteristics of the structural model.

4. The conversion method according to claim 3, wherein the vibration characteristics of the structural model are determined using natural frequencies and damping constants evaluated by stiffness based on equivalent linearization.

5. A conversion device that converts seismic motion into impulse seismic motion for use in seismic response analysis or seismic design of structures, An analysis unit that performs time history response analysis of a structural model using the aforementioned seismic motion as input, Based on the results of the time history response analysis, the identification unit identifies the time at which a predetermined response index of the structural model reaches its maximum value, A first determination unit that determines the number of impulses corresponding to the repeating characteristics of the seismic motion, An extraction unit that identifies a time interval from the seismic motion that contributes to the response of the structural model based on the identified time and the number of impulses, and extracts the seismic motion corresponding to that time interval as the seismic motion in a specific interval, A second determination unit determines the input velocity of the impulse seismic motion based on the energy response of the structural model due to seismic motion in the specified section, Includes a conversion unit that converts the seismic motion into impulse seismic motion based on the number of impulses and the input speed, The input speed is determined in a converter such that the response of the structural model to the impulse seismic motion encompasses the response of the structural model to the seismic motion.

6. A conversion program that causes a computer to perform a process of converting seismic motion into impulse seismic motion for use in seismic response analysis or seismic design of structures, To the aforementioned computer, The process involves performing a time history response analysis of a structural model using the aforementioned seismic motion as input, Based on the results of the time history response analysis, the process involves identifying the time at which a predetermined response index of the structural model reaches its maximum value. A step of determining the number of impulses corresponding to the repeating characteristics of the aforementioned seismic motion, Based on the identified time and the number of impulses, the process involves identifying the time intervals of the seismic motion that contribute to the response of the structural model, and extracting the seismic motion corresponding to those time intervals as seismic motion in a specific interval. A step of determining the input velocity of the impulse seismic motion based on the energy response of the structural model due to seismic motion in the specified section, The process includes converting the seismic motion into impulse seismic motion based on the number of impulses and the input velocity, The input velocity is determined such that the response of the structural model to the impulse seismic motion encompasses the response of the structural model to the seismic motion. A conversion program that performs processing in this manner.

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