Seismic motion estimation system for design

Abstract

To accurately estimate design site vibration used for design of a building by appropriately generating a tomographic model corresponding to assumed earthquake motion when a plurality of uncertain hypocenter characteristics are included.SOLUTION: The earthquake motion estimation system for design 1 includes a tomographic model generation unit 3 that generates a plurality of tomographic models in which different values are set from values that can be taken by each of a plurality of uncertainty hypocenter characteristics, an earthquake motion evaluation unit 4 that evaluates earthquake motion for each of the plurality of tomographic models, a response surface construction unit 5 that constructs a response surface in which each of the plurality of uncertainty hypocenter characteristics is an explanatory variable and an evaluation result of earthquake motion is an objective variable, an uncertainty hypocenter characteristic value extraction unit 7 that searches for and extracts a combination in which a difference between a value of the objective variable and a value designated from the outside is within a threshold value by grid search, and an earthquake motion estimation unit for design 8 that estimates earthquake motion for design using the tomographic model for design.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a design earthquake motion estimation system that estimates design earthquake motion used in the design of a building. [Background technology]

[0002] For example, when designing a super-high-rise building with a height of over 60m, the seismic performance can be confirmed by a time history response analysis using the design earthquake motion with a time history used in the design of the building as input. Design earthquake motion can be determined by inputting information such as the magnitude of the earthquake and the distance between the construction site and the fault into the earthquake motion prediction formula, and then assigning a random phase to the response spectrum, or by calculating it using a fault model with semi-empirical, theoretical, or numerical analysis methods. Methods that use earthquake motion prediction formulas cannot take into account the effects of fault rupture. For this reason, it is more desirable to use a method based on a fault model in order to create earthquake motion that is closer to the actual phenomenon.

[0003] Among the source characteristics used in earthquake ground motion evaluations using fault models such as those described above, there are some that have variability in their values ​​and require consideration of uncertainty (hereinafter referred to as "uncertain source characteristics"). When generating a fault model, if a unique value is determined for such uncertain source characteristics, for example, so that it is an average value, then in cases where there are cases where values ​​other than the average value correspond to a mega-earthquake, a fault model corresponding to that case will not be generated, and as a result, earthquake ground motion evaluation for that case may not be performed. Therefore, with regard to uncertain source characteristics, it is desirable to estimate the design earthquake ground motion by setting the design external force taking into account the variability in values.

[0004] For example, one value can be selected and determined from the possible values ​​for each of the uncertainty source characteristics, and a single fault model can be generated by using the sampled values ​​for each of the multiple uncertainty source characteristics. By sampling different values ​​each time, multiple different fault models can be generated, each with different values ​​set for the uncertainty source characteristics. Therefore, when considering the variation in values ​​for the uncertainty source characteristics, evaluating seismic ground motion for each of the multiple different fault models generated in this way allows for a rough relationship between the possible values ​​for each uncertainty source characteristic and the evaluation results of seismic ground motion. Furthermore, by constructing a response surface using each of the uncertain source characteristics as an explanatory variable and the evaluation result of seismic motion as a target variable based on the relationship between the values ​​determined for each of the uncertain source characteristics in each of the multiple fault models obtained in this way and the evaluation result of seismic motion, it may be possible to express a function that outputs the evaluation result of the corresponding seismic motion by inputting the values ​​that each uncertain source characteristic can take as an explanatory variable. Patent Document 1 describes a response surface creation method that is thought to be applicable to such cases.

[0005] However, even if a response surface is constructed as described above such that the evaluation results of the corresponding earthquake motion can be obtained by inputting the possible values ​​of each of the uncertainty source characteristics into the explanatory variables, it is not easy to calculate the evaluation results of this earthquake motion when the reverse direction, that is, when earthquake motion equivalent to a mega-earthquake, is assumed.If it is not possible to calculate the values ​​of each of the uncertainty source characteristics that correspond to the evaluation results of the assumed earthquake motion, it is not possible to set appropriate values ​​for the fault model, and it is not possible to construct a fault model, making it difficult to estimate the design earthquake motion. When the source characteristics set for a seismic source include multiple uncertain source characteristics whose values ​​vary and require consideration of uncertainty, it is desirable to appropriately generate a fault model equivalent to the expected seismic motion and accurately estimate the design seismic motion used in the design of a building. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2023-111806 Summary of the Invention [Problem to be solved by the invention]

[0007] The problem that the present invention aims to solve is to provide a design earthquake motion estimation system that appropriately generates a fault model equivalent to the expected earthquake motion and accurately estimates the design earthquake motion to be used in the design of a building when the earthquake source characteristics set for the earthquake source include multiple uncertain earthquake source characteristics whose values ​​vary and require consideration of uncertainty. [Means for solving the problem]

[0008] The present invention employs the following means to solve the above problems: That is, the present invention is a design earthquake motion estimation system that estimates design earthquake motion to be used in the design of a building when earthquake source characteristics set for a hypocenter include a plurality of uncertainty earthquake source characteristics whose values ​​vary and require consideration of uncertainty, the system comprising: a fault model generation unit that selects one value for each of the uncertainty earthquake source characteristics from the values ​​that each of the plurality of uncertainty earthquake source characteristics can take and sets the selected value in a fault model, thereby generating a plurality of fault models in which different values ​​are set; an earthquake motion evaluation unit that evaluates earthquake motion for each of the plurality of fault models, and that uses each of the plurality of uncertainty earthquake source characteristics as an explanatory variable based on the relationship between the value selected for each of the plurality of uncertainty earthquake source characteristics in each of the plurality of fault models and the evaluation result of the earthquake motion, a response surface construction unit that constructs a response surface using the evaluation results of the above as objective variables; an uncertainty seismic source characteristic value extraction unit that searches for and extracts, by a predetermined search and estimation method, combinations of values ​​obtained by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the plurality of uncertainty seismic source characteristics can take, such that when each of the values ​​included in the combination is substituted for the corresponding explanatory variable of the response surface, the difference between the value of the objective variable and an externally specified value is within a threshold; and a design seismic motion estimation unit that generates a design fault model by setting each of the plurality of uncertainty seismic source characteristics to the value included in the extracted combination, and estimates the design seismic motion using the design fault model. According to the above configuration, when the seismic source characteristics set for a hypocenter include multiple uncertainty seismic source characteristics whose values ​​vary and require consideration of uncertainty, one value is selected for each of the multiple uncertainty seismic source characteristics from the possible values ​​each of the multiple uncertainty seismic source characteristics can take, and this is repeatedly set in the fault model to generate multiple different fault models in which different values ​​for the uncertainty seismic source characteristics are set. Furthermore, seismic motion is evaluated for each of the multiple fault models generated in this way, and a response surface is constructed in which each of the multiple uncertainty seismic source characteristics is used as an explanatory variable and the evaluation result of the seismic motion is used as a response variable based on the relationship between the value selected for each of the multiple uncertainty seismic source characteristics in each of the multiple fault models and the evaluation result of the seismic motion. In this way, the relationship between the possible values ​​of each uncertainty seismic source characteristic and the evaluation result of the seismic motion can be obtained. For the response surface obtained in this way, to obtain a combination of explanatory variables, i.e., values ​​obtained by selecting one for each of the uncertainty source characteristics from among the possible values ​​for each of the multiple uncertainty source characteristics, such that the value of the objective variable corresponds to an evaluation result corresponding to some assumed seismic motion, such as a mega-earthquake, the combination is extracted using a predetermined search and estimation method in the uncertainty source characteristic value extraction unit, where the difference between the value of the objective variable when each value included in the combination is substituted for the corresponding explanatory variable on the response surface and, for example, an externally specified value as the evaluation result corresponding to the assumed seismic motion is within a threshold. The design fault model generated by setting each value included in the combination obtained in this way as each uncertainty source characteristic corresponds to the assumed seismic motion. Therefore, the design seismic motion estimated using the design fault model generated in this way is the design seismic motion corresponding to the assumed seismic motion. In this way, when the source characteristics set for a seismic source include multiple uncertain source characteristics whose values ​​vary and require consideration of uncertainty, it is possible to appropriately generate a fault model equivalent to the expected seismic motion and accurately estimate the design seismic motion used in the design of a building.

[0009] In one aspect of the present invention, the response surface constructor expresses the objective variable using a plurality of the explanatory variables by polynomial approximation based on the relationship, and the response surface is realized as a quadratic equation including quadratic terms corresponding to each of the plurality of explanatory variables and an interaction term obtained by multiplying two different explanatory variables among the plurality of explanatory variables. According to the above configuration, the response surface can be appropriately realized as a relatively simple formula.

[0010] In another aspect of the present invention, the uncertainty seismic source characteristic value extraction unit sets a search range for each of the plurality of uncertainty seismic source characteristics, generates a plurality of candidate values ​​that are different from each other within the search range, and then extracts a combination of candidate values ​​obtained by selecting one candidate value for each of the plurality of uncertainty seismic source characteristics from the plurality of candidate values ​​for each of the plurality of uncertainty seismic source characteristics, where the combination of candidate values ​​is obtained by substituting each of the candidate values ​​included in the combination of candidate values ​​for the corresponding explanatory variable of the response surface, such that the difference between the value of the target variable and the specified value is minimized when the candidate value is substituted for the corresponding explanatory variable of the response surface, resets the search range for each of the plurality of uncertainty seismic source characteristics to a smaller range centered on the candidate value of the uncertainty seismic source characteristic in the extracted combination of candidate values, and regenerates a plurality of candidate values ​​that are different from each other within the search range, repeatedly executing this process until the difference between the value of the target variable calculated for the extracted combination of candidate values ​​and the specified value falls within the threshold. According to the above configuration, the uncertain earthquake source characteristic value extracting unit sets a search range for each of the plurality of uncertain earthquake source characteristics, and generates a plurality of candidate values ​​that are different from each other within the search range. Thereafter, the uncertainty source characteristic value extraction unit repeatedly executes the following process. The uncertainty seismic source characteristic value extraction unit first extracts a combination of candidate values ​​obtained by selecting one candidate value for each of the uncertainty seismic source characteristics from among multiple candidate values ​​for each of the multiple uncertainty seismic source characteristics. The combination of candidate values ​​is then extracted so that, when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable on the response surface, the difference between the value of the objective variable and, for example, an externally specified value as an evaluation result corresponding to the assumed seismic motion is minimized. The combination of candidate values ​​extracted in this manner is considered to be the one that, among all the combinations of candidate values, can produce the design seismic motion closest to the assumed seismic motion when each candidate value included in the combination is set in a fault model to estimate the design seismic motion. If there is a desirable combination of candidate values ​​whose value of the objective variable matches or is very close to the specified value, it is likely to exist on the response surface near the combination of candidate values ​​extracted as described above. Based on this idea, the uncertainty seismic source characteristic value extraction unit then resets the search range for each of the multiple uncertainty seismic source characteristics to a smaller range centered on the candidate value of the uncertainty seismic source characteristic in the combination of candidate values ​​extracted as described above, and regenerates multiple candidate values ​​that are different from each other within the reset search range. In this way, it is possible to reset multiple candidate values ​​with finer granularity near the combination of candidate values ​​extracted as described above, which is thought to contain a desirable combination of candidate values. The above process is repeated until the difference between the value of the objective variable calculated for the extracted combination of candidate values ​​and the specified value falls within a threshold. In this way, for each of the multiple uncertain source characteristics, the search range is narrowed down to a portion of the response surface where a desirable combination of candidate values ​​is considered to exist. If the difference between the value of the objective variable calculated for the extracted combination of candidate values ​​and the specified value finally falls within a threshold, it is considered that the design seismic motion estimated using the fault model in which the candidate values ​​included in the combination of candidate values ​​are set represents, with sufficiently high accuracy, the seismic motion assumed when the values ​​were externally specified. In this way, it is possible to efficiently calculate combinations of values ​​obtained by selecting one value for each of a plurality of uncertain source characteristics from the possible values ​​that each of the uncertain source characteristics can take, and in which, when each of the values ​​included in the combination is substituted for the corresponding explanatory variable on the response surface, the difference between the value of the objective variable and the specified value is within a threshold value.

[0011] In another aspect of the present invention, the uncertainty seismic source characteristic value extraction unit extracts the plurality of combinations by the predetermined search and estimation method, then performs kernel density estimation for each of the plurality of uncertainty seismic source characteristics to calculate the maximum value of a probability density function, calculates a weight for each of the plurality of uncertainty seismic source characteristics based on the maximum value, and for each of the plurality of combinations, calculates the sum of the products of the probability density obtained by the kernel density estimation corresponding to the value of the uncertainty seismic source characteristic included in the combination and the weight of the uncertainty seismic source characteristic as a likelihood score, and selects the combination with the maximum likelihood score to further extract one of the combinations, and the design seismic motion estimation unit generates the design fault model for the one combination and estimates the design seismic motion using the design fault model. For example, if a specific search and estimation method is used to extract only one combination from the possible values ​​of multiple uncertain source characteristics, and the values ​​included in that combination are used to generate a design fault model and estimate the design earthquake motion, the generated fault model and the design earthquake motion estimated based on it may not be appropriate. In contrast to this, with the above configuration, a plurality of combinations are extracted using a predetermined search and estimation method. As a result, different values ​​may be set for each of the multiple uncertain source characteristics in each combination. Therefore, the uncertain source characteristic value extraction unit performs kernel density estimation for each of the multiple uncertain source characteristics based on the set of values ​​set for that uncertain source characteristic to calculate a probability density function. In the probability density function calculated in this way, the value of the uncertain source characteristic that gives a probability density value close to the maximum value can be considered to be the most appropriate value for that uncertain source characteristic (the most likely value that the uncertain source characteristic can take). Therefore, by extracting one combination that is considered to be the closest possible combination of values ​​for the multiple uncertain source characteristics to the maximum values, and using this combination to generate a fault model, a fault model that is considered to be appropriate can be generated. Based on this concept, the uncertainty source characteristic value extraction unit calculates the maximum value of the probability density function for each of the plurality of uncertainty source characteristics and calculates a weight for each of the plurality of uncertainty source characteristics based on each of these maximum values. Furthermore, for each of the plurality of combinations, the unit calculates a likelihood score as the sum of the products of the probability density obtained by kernel density estimation corresponding to the value of the uncertainty source characteristic included in the combination and the weight of the uncertainty source characteristic. The uncertainty source characteristic value extraction unit further extracts one combination from the plurality of combinations by selecting the combination with the maximum likelihood score calculated in this way. The design seismic motion estimation unit then generates a design fault model for the one combination. In this way, it is possible to generate an appropriate design fault model, and by using this design fault model, it is possible to estimate appropriate design earthquake motion. [Effects of the Invention]

[0012] According to the present invention, when the source characteristics set for a seismic source include multiple uncertain source characteristics whose values ​​vary and require consideration of uncertainty, it is possible to provide a design earthquake motion estimation system that appropriately generates a fault model equivalent to the expected earthquake motion and accurately estimates the design earthquake motion to be used in the design of a building. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a block diagram of a design earthquake motion estimation system according to an embodiment of the present invention. [Figure 2] FIG. 10 is a diagram showing an example of hypocenter characteristics whose values ​​are definite values ​​without any variation. [Figure 3] FIG. 2 is a diagram illustrating an example of a ground model. [Figure 4] FIG. 1 is a diagram showing an example of source characteristics whose values ​​have variations and require consideration of uncertainty. [Figure 5] FIG. 1 is a schematic diagram of a fault region and an explanatory diagram showing an overview of the source characteristics. [Figure 6] This figure shows the results of a three-dimensional finite element analysis of each of the multiple fault models, which were created by sampling values ​​for each of the uncertain source characteristics using the Monte Carlo method, using the ground model shown in Figure 3 as the target. [Figure 7] FIG. 1 is an explanatory diagram of the Latin Hypercube method. [Figure 8] This figure shows the results of a three-dimensional finite element analysis of the ground model shown in Figure 3 for each of the multiple fault models, which were created by sampling values ​​for each uncertainty source characteristic using the Latin Hypercube method. [Figure 9] FIG. 1 is an explanatory diagram of a response surface. [Figure 10] FIG. 9 shows the response surface generated for the results shown in FIG. 8. [Figure 11] FIG. 10 is a diagram showing an example of a state in which a search range is set for each of a plurality of uncertain source characteristics and the search range is divided into a grid. [Figure 12] FIG. 12 is a diagram showing an example of a state in which the search range is reset and divided into grids again, with the intersection point of the grids shown in FIG. 11 at the center where the response surface value is most appropriate. [Figure 13] FIG. 13 is a diagram showing an example of a state in which the search range is re-set around the intersection of the re-divided grid shown in FIG. 12 where the response surface value is most appropriate, and the search range is divided into grids. [Figure 14] FIG. 13 is a diagram showing an example of a state in which the search range is reset and divided into grids when, among the intersections of the re-divided grid shown in FIG. 12, the intersection where the response surface value is most appropriate is on the periphery of the re-divided grid. [Figure 15] 1 is a flowchart of a design earthquake motion estimation method according to an embodiment of the present invention. [Figure 16] 10 is a flowchart illustrating details of a process for extracting values ​​of uncertainty source characteristics in the design earthquake motion estimation method. [Figure 17] This is an example of a fault model that is considered inappropriate. [Figure 18] This is another example of a fault model that may not be appropriate. [Figure 19] FIG. 10 is an explanatory diagram showing a region where combinations of values ​​of uncertainty source characteristics are searched for in the design earthquake motion estimation system according to the modified example of the embodiment. [Figure 20] FIG. 10 is a diagram showing an example of a state in which a search range is set for each of a plurality of uncertain source characteristics and the search range is divided into grids in the design earthquake motion estimation system according to the above modification. [Figure 21]FIG. 10 is an explanatory diagram showing the relationship between the response surface, the first response surface, and the second response surface when the velocity response spectrum pSv as the evaluation result of the earthquake motion is specified as 100 cm / s in the design earthquake motion estimation system according to the above modified example. [Figure 22] 10 is a table showing the values ​​of each uncertainty source characteristic for each of a plurality of combinations extracted by grid search. [Figure 23] FIG. 1 shows the results of kernel density estimation for a certain uncertain source characteristic (source characteristic A). [Figure 24] 10 is a table showing the weights calculated for each uncertainty source characteristic. [Figure 25] 10 is a table showing probability densities obtained by performing kernel density estimation on each of a plurality of combinations extracted by grid search. [Figure 26] 10 is a flowchart illustrating details of a process for extracting values ​​of uncertainty source characteristics in the design earthquake motion estimation method according to the above-described modified example. [Figure 27] 10 is an example of a fault model that is calculated in the design earthquake motion estimation system of the above modified example and is considered to be appropriate. [Figure 28] 10 is another example of a fault model that is calculated in the design earthquake motion estimation system of the above modified example and is considered to be appropriate. [Figure 29] FIG. 1 is a diagram showing an example of seismic performance grades. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The design earthquake motion estimation system of this embodiment estimates the design earthquake motion to be used in the design of a building when the earthquake source characteristics set for the earthquake source include multiple uncertain earthquake source characteristics whose values ​​vary and require consideration of uncertainty. Figure 1 is a block diagram of the design earthquake motion estimation system. The design earthquake motion estimation system 1 is composed of a computer terminal such as a server, personal computer, or tablet terminal, and performs required functions by executing a pre-set program. Functionally, the design earthquake motion estimation system 1 comprises a source characteristic input reception unit 2, a fault model generation unit 3, a seismic motion evaluation unit 4, a response surface construction unit 5, an expected earthquake motion specification unit 6, an uncertainty source characteristic value extraction unit 7, and a design earthquake motion estimation unit 8.

[0015] The processing contents of each component included in the design earthquake motion estimation system 1 will be explained below based on an example. Fig. 2 is a diagram showing an example of source characteristics whose values ​​are definite without any variation, and Fig. 3 is a diagram showing an example of a ground model. The source characteristics used in earthquake motion evaluation using fault models include source characteristics whose values ​​do not vary and are certain, i.e., definite values ​​(hereinafter referred to as certain source characteristics), and source characteristics whose values ​​vary and require consideration of uncertainty (hereinafter referred to as uncertain source characteristics). The source characteristics include macroscopic characteristics such as the source location, area, and earthquake magnitude, as well as microscopic characteristics such as the slip amount of asperities and the regions within each asperity. In the example of this embodiment, each of the macroscopic source characteristics shown in FIG. 2 is treated as a reliable source characteristic. The fault reference point shown in FIG. 2 is shown as point DO in FIG. 3. FIG. 3 also shows a source region DR, which indicates the entire fault region, as a rectangular region with the fault reference point DO as its base point. The strike angle shown in FIG. 2 is the rotation angle of the source region DR with the fault reference point DO as the base point and north as the reference direction, and the fault sizes L and W are the lengths of each side of the rectangular shape of the source region DR. In addition to each of the source characteristics shown in Fig. 2, the number of asperities is treated as a reliable source characteristic in the example of this embodiment. In particular, the number of asperities is set to two in the example of this embodiment. It goes without saying that the values ​​of the reliable source characteristics are not limited to the values ​​used in the example of this embodiment, and may be other values.

[0016] In the example of this embodiment, the asperity configuration and the rupture starting point are treated as uncertain source characteristics. Fig. 4 is a diagram showing an example of source characteristics whose values ​​vary and require consideration of uncertainty. Fig. 5 is a schematic diagram of a fault region, and is an explanatory diagram showing an overview of source characteristics. In Figure 5, two asperities, the first asperity A1 and the second asperity A2, are shown in the source region DR, which indicates the area of ​​the entire fault. The area of ​​the first asperity A1 is S a1 , the area of ​​the second asperity A2 is S a2 In addition, the area of ​​the source region DR excluding the first asperity A1 and the second asperity A2 (background area) is S b Let's say.

[0017] In the example of this embodiment, the uncertainty of the source characteristics is calculated by the area (S a1 +S a2 +S b ) to find the total area of ​​the asperity (S a1 +S a2 ) divided by the asperity area ratio (S a1 +S a2 ) / (S a1 +S a2 +S b ), the area of ​​the first asperity A1 S a1 The area S of the second asperity A2 is a2 The area ratio between asperities (S a1 / S a2) The uncertain source characteristics include the position startX in the X direction and the position startY in the Y direction of the rupture starting point within the source region DR, the position asp1X in the X direction and the position asp1Y in the Y direction of the first asperity A1 within the source region DR, and the position asp2X in the X direction and the position asp2Y in the Y direction of the second asperity A2 within the source region DR. Thus, in this example of the present embodiment, the uncertain source characteristics include eight types of source characteristics: the asperity area ratio, the area ratio between asperities, the position of the rupture starting point in the X direction, the position of the rupture starting point in the Y direction, the position of the first asperity A1 in the X direction, the position of the first asperity A1 in the Y direction, the position of the second asperity A2 in the X direction, and the position of the second asperity A2 in the Y direction. The values ​​of each uncertainty source characteristic vary according to a distribution such as a normal distribution or a uniform distribution. In Figure 4, the "Distribution" column indicates whether the distribution of each uncertainty source characteristic follows a normal distribution or a uniform distribution. If the uncertainty source characteristic follows a normal distribution, its mean value and standard deviation are shown in the "μ" and "σ" columns, respectively.

[0018] The source characteristic input receiving unit 2 receives input of values ​​of all source characteristics, including both the certainty source characteristics and the uncertainty source characteristics, by an operator via an input device such as a keyboard.

[0019] The fault model generating unit 3 generates a three-dimensional ground model and a fault model. The fault model generation unit 3 first generates a three-dimensional ground model. In the example of this embodiment, a three-dimensional ground model GM as shown in FIG. 3 is used. This three-dimensional ground model GM is created for an area of ​​260 km east to west, 180 km north to south, and 60 km deep, which includes the source region DR. The period to be analyzed is set to 3 seconds or more, and element division is performed so that one wavelength can be expressed by five elements. In the example of this embodiment, the evaluation point EP is located on the hanging wall side of the source in the fault width direction.

[0020] The fault model generation unit 3 then generates a fault model. The fault model generation unit 3 places a plurality of point seismic sources at appropriate intervals within the seismic source region DR. The fault model generation unit 3 individually sets values ​​of seismic source characteristics for each of the plurality of point seismic sources. The fault model generating unit 3 sets a definite value for each of the point seismic sources for each of the plurality of certainty seismic source characteristics. The fault model generation unit 3 also selects one value for each of the multiple uncertain source characteristics according to the distribution set for each, and sets this value for each point hypocenter. If the distribution of the uncertain source characteristics is normal, the fault model generation unit 3 selects one value taking into account the mean value and standard deviation of the uncertain source characteristics. If the distribution of the uncertain source characteristics is uniform, the fault model generation unit 3 selects one value from a range of values ​​separately set for the uncertain source characteristics. For example, in this embodiment, eight types of uncertain source characteristics are used. Therefore, the above operation corresponds to selecting one value from each of the eight types of uncertain source characteristics and determining one combination of eight values. In the following description, selecting one value from each uncertain source characteristic to generate one combination is referred to as "sampling" as appropriate.

[0021] Here, the fault model generation unit 3 repeats the process of selecting one value for each of the plurality of uncertain source characteristics from the possible values ​​for each of the plurality of uncertain source characteristics, i.e., performing sampling, and using the selected values ​​to generate a fault model. Basically, a different combination of values ​​is obtained each time sampling is performed. Therefore, the plurality of fault models generated by the above repetition are different from each other, with different values ​​set for the uncertain source characteristics. In this way, the fault model generating unit 3 generates a wide variety of fault models for a plurality of values ​​of uncertain source properties.

[0022] When generating such various fault models, the Monte Carlo method can be used to sample values ​​of uncertain source properties, which means randomly selecting values. Figure 6 shows the results of a 3D finite element analysis performed on the ground model shown in Figure 3 for each of the multiple fault models, using the Monte Carlo method to sample values ​​for each uncertain source characteristic. Figure 6 shows the velocity response spectrum pSv as the result of the 3D finite element analysis. Figure 6 also shows results for horizontal motion in two directions: north-south (NS) and east-west (EW). For each of these, Figure 6 shows the results for all fault models in light gray. Figure 6 also shows the average of these values ​​(line LAm), the average plus the standard deviation (line LSm+), and the average minus the standard deviation (line LSm-). Figure 6 also shows multiple dark gray lines representing results from similar analyses performed in known literature. These results generally fall within the range between lines LSp and LSm, demonstrating that the Monte Carlo method sampling from each uncertain source characteristic was performed appropriately and without significant bias.

[0023] However, when using the Monte Carlo method, it is necessary to collect a large number of samples by performing sampling many times to reduce the possibility of bias in the values ​​included in the combinations (samples) obtained by sampling. In the case of Figure 6, 1,000 samples were collected and 3D finite element analysis was performed 1,000 times. To limit the number of samples collected, it is more desirable to use various experimental design methods, such as Box-Behnken designs, central composite designs, and Latin hypercubes, to sample values ​​from each uncertain source characteristic.

[0024] Fig. 7 is an explanatory diagram of the Latin Hypercube algorithm. For simplicity, Fig. 7 shows how four combinations of two values ​​are generated by sampling values ​​for each of two uncertain source characteristics, namely, source characteristics A and B. In the Latin Hypercube algorithm, the range of values ​​that seismic source characteristic A and seismic source characteristic B can take are each divided into multiple ranges (four in Figure 7). Then, each sample is acquired so as to ensure orthogonality between the samples. For example, the first sample, shown as point p1 in Figure 7, is selected. In this case, one range of values ​​to be selected is selected from each of seismic source characteristic A and seismic source characteristic B. In the example in Figure 7, the topmost range is selected for seismic source characteristic A, and the leftmost range is selected for seismic source characteristic B. Specific values ​​within each of these ranges are determined by random numbers. Next, the second sample, shown as point p2 in Figure 7, is selected. In this case, a range different from the previously selected range is selected for each of seismic source characteristic A and seismic source characteristic B, and the second sample is selected by randomly determining a value from this range. Similarly, when acquiring the third and fourth samples, shown as points p3 and p4 in Figure 7, values ​​are selected from ranges different from the previously selected ranges.

[0025] Unlike Box-Behnken designs and central composite designs, Latin hypercube designs do not depend on a specified sampling level, so there are few cases where combinations of uncertain source property values ​​that are inappropriate for a fault model, such as when the first asperity A1 and the second asperity A2 overlap, are sampled. Furthermore, as explained using Figure 7, the Latin Hypercube method basically performs sampling so that the samples are not orthogonal to each other in the range into which each uncertainty source characteristic is divided, so there is less bias in the samples compared to the Monte Carlo method. As a result, the total number of samples obtained can be reduced.

[0026] Figure 8 shows the results of a 3D finite element analysis of the ground model shown in Figure 3 for each of the fault models, which were created by sampling values ​​for each uncertainty source characteristic using the Latin Hypercube method. Figure 8 shows the velocity response spectrum (pSv) as a result of the 3D finite element analysis. Figure 8 also shows results for horizontal motion in two directions, north-south (NS) and east-west (EW). For each of these, Figure 8 shows the results for all fault models in light gray (line LHS). Figure 8 also shows the average of these results (line LAl), and the average plus the standard deviation (line LSL+). Figure 8 also shows the line LAm, which corresponds to the average of all cases in the case of the Monte Carlo method shown in Figure 6, the line LSm+, which corresponds to the average plus the standard deviation, and the line LSm-, which corresponds to the average minus the standard deviation. The lines LAl and LAm, and the lines LSL+ and LSm+ generally correspond to each other and are close to each other. In the case of Figure 8, 92 samples were collected and 3D finite element analysis was performed 92 times. In this way, when sampling is performed using the Latin Hypercube method, statistical results with roughly the same mean and standard deviation as those obtained using the Monte Carlo method can be obtained using about one-tenth the number of samples compared to the Monte Carlo method.

[0027] As described above, the fault model generation unit 3 generates a fault model by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the uncertainty seismic source characteristics can take. The fault model generation unit 3 repeats this process to generate a plurality of different fault models in which different values ​​are set. The earthquake motion evaluation unit 4 evaluates earthquake motion for each of the multiple fault models generated by the fault model generation unit 3. The earthquake motion evaluation unit 4 applies each of the multiple fault models generated by the fault model generation unit 3 to a three-dimensional ground model GM as shown in FIG. 3 and performs three-dimensional finite element method analysis on the model to evaluate earthquake motion. In this embodiment, the evaluation of earthquake motion is performed by calculating a velocity response spectrum pSv. When the fault model generation unit 3 uses the Latin Hypercube method to sample values ​​of uncertain source characteristics, for example, 92 velocity response spectra pSv are obtained, as shown by line LHS in FIG. 8.

[0028] As described above, for each of the plurality of fault models, the relationship between the value selected (by sampling) for each of the plurality of uncertain source characteristics in the fault model and the evaluation result of the seismic motion (velocity response spectrum pSv in this embodiment) is obtained. In the example of this embodiment, as shown in Fig. 8, the relationship between the value selected for each of the 92 plurality of uncertain source characteristics and the velocity response spectrum pSv is obtained. Based on the multiple relationships between the values ​​selected for each of the multiple uncertain source characteristics and the evaluation results of seismic motion obtained in this way, the response surface construction unit 5 constructs a response surface in which each of the multiple uncertain source characteristics is used as an explanatory variable and the evaluation results of seismic motion are used as a target variable.

[0029] In this embodiment, the evaluation result of the earthquake motion is the velocity response spectrum pSv. Since the velocity response spectrum pSv is a function of the period, first, one value to be used as the objective variable of the response surface is extracted from each of the multiple (92) velocity response spectra pSv. For example, when the design earthquake motion estimated by the design earthquake motion estimation system 1 of this embodiment is used to evaluate a building that is currently being designed or that already exists, the first natural period of the building can be calculated from design documents, etc. Therefore, this first natural period can be used as the target period, and the value of the velocity response spectrum pSv corresponding to this target period can be extracted. In this example of this embodiment, the target period is, for example, 5 seconds. That is, in this example of this embodiment, the earthquake motion evaluation unit 4 constructs a response surface using each of the multiple uncertain source characteristics as an explanatory variable and the value of the velocity response spectrum pSv when the target period is 5 seconds as the objective variable.

[0030] Fig. 9 is an explanatory diagram of a response surface. For ease of explanation, Fig. 9 shows a response surface 100 for two cases of uncertain source characteristics: source characteristic A and source characteristic B. In the example of this embodiment, eight types of uncertain source characteristics are provided, and therefore the response surface 100 is expressed as a curved surface in an eight-dimensional space. The response surface constructor 5 expresses the response surface 100 as a function. For this, approximation methods such as polynomial approximation and Gaussian process approximation can be used. In the example of this embodiment, a second-order polynomial approximation is used, which can stably obtain a surface, and the objective variable is expressed as a quadratic expression of multiple explanatory variables, specifically as shown in the following equation (1).

number

[0031] For example, in the example of this embodiment, eight types of uncertain source characteristics are used, and therefore, the above formula (1) is configured as shown in the following formula (2), which includes eight second-order terms, 8C2=28 interaction terms, and eight first-order terms.

number

[0032] In this way, the response surface constructing unit 5 constructs a response surface 100 for each of a plurality of fault models based on the relationship between the values ​​selected for each of a plurality of uncertain source characteristics in the fault model and the evaluation results of seismic motion. The values ​​selected for each of a plurality of uncertain source characteristics, i.e., samples, that construct this relationship are simply discrete points located in a space whose order is the type of uncertain source characteristic. In the example of this embodiment, 92 points are located in an eight-dimensional space. By constructing the response surface 100 based on these discrete points and connecting them, the relationship between the discrete points is interpolated, and it is possible to obtain interpolated values ​​as the evaluation results of seismic motion (values ​​of the velocity response spectrum pSv) even for combinations of values ​​of uncertain source characteristics that are not actually obtained as samples.

[0033] FIG. 10 shows a response surface generated for the results shown in FIG. 8. FIG. 10 shows a response surface 100 constructed for the velocity response spectrum pSv in the north-south (NS) direction with a period of 5 seconds, as shown on the left side of FIG. 8. In FIG. 10, each value of the uncertain source characteristics is normalized to be between -1 and 1. To visualize the response surface 100 realized in eight-dimensional space, FIG. 10 depicts the response surface 100 when, for each combination of two of the eight types of uncertain source characteristics in Equation (2) above, the values ​​of the explanatory variables corresponding to the uncertain source characteristics other than the two types of uncertain source characteristics included in the combination are set to 0 (more specifically, the average value of the distribution of each uncertain source characteristic). In FIG. 10, the steeper the slope of the response surface 100, the greater the influence that the uncertainty in the source characteristics has on the velocity response spectrum pSv.

[0034] Next, the expected earthquake motion designation unit 6 will be described. For example, when a building is about to be designed or when an existing building is actually evaluated, some kind of earthquake motion can be assumed as the design earthquake motion to be applied to the building during analysis, such as the earthquake motion equivalent to the average of all cases as shown by line LAl in Figure 8, or the earthquake motion equivalent to the average plus the standard deviation as shown by line LSL+. After the response surface 100 as described above has been constructed, the assumed earthquake motion designation unit 6 accepts the designation of the value of the evaluation result of the earthquake motion equivalent to the assumed earthquake motion. The expected earthquake motion designation unit 6 accepts values ​​input from an operator from the outside via an input device such as a keyboard. When the evaluation result of earthquake motion is expressed as a velocity response spectrum pSv, as in the example of this embodiment, the value of the evaluation result of earthquake motion can be the value of the velocity response spectrum pSv at a specific period (e.g., 5 seconds), such as the first natural period of the building.

[0035] Next, the design earthquake motion estimation system 1 of this embodiment specifies specific values ​​for each of the plurality of uncertain source characteristics such that the evaluation result of the earthquake motion becomes the value specified as above by the expected earthquake motion specifying unit 6. Once the values ​​of the plurality of uncertain source characteristics have been specified, these values ​​can be set in a fault model and then a three-dimensional finite element method analysis can be performed to estimate the design earthquake motion. Identifying the values ​​of the multiple uncertain source characteristics described above corresponds to identifying a combination of values ​​of each explanatory variable that will result in a specified value for the objective variable when the response surface 100 is viewed as a function of equation (1). However, it is not easy to identify this combination using some mathematical method for equation (1). Therefore, in this embodiment, the uncertainty source characteristic value extraction unit 7 searches for and extracts combinations of values ​​obtained by selecting one value for each uncertainty source characteristic from among the values ​​that each uncertainty source characteristic can take, using a predetermined search and estimation method, such that when each of the values ​​included in the combination is substituted as an explanatory variable for the response surface 100, the difference between the value of the objective variable and an externally specified value is within a threshold. In this embodiment, the predetermined search and estimation method is a grid search.

[0036] FIG. 11 is a diagram showing an example of a state in which a search range is set for each of a plurality of uncertain source characteristics and the search range is divided into grids. The source characteristic uncertainty value extraction unit 7 first sets a search range for each of the multiple source characteristic uncertainty values ​​to search for the value of the source characteristic uncertainty. Because the example of this embodiment uses eight types of source characteristic uncertainty as described above, the subsequent processing is essentially performed in eight-dimensional space. However, for simplicity, the source characteristic uncertainty value extraction unit 7 assumes that there are two types of source characteristic uncertainty, source characteristic A and source characteristic B, and describes the processing in two-dimensional space. For example, for source characteristic A, the source characteristic uncertainty value extraction unit 7 sets a search range RA1 so that all values ​​of source characteristic A acquired by the fault model generation unit 3 are included. In FIG. 11, the search range RA1 is shown as a range from value a1 to value a7. For example, the uncertainty source characteristic value extraction unit 7 may normalize the value of the source characteristic A acquired by the fault model generation unit 3 to a value between -1 and 1, and set the search range RA1 to a range between -1 (corresponding to value a1) and 1 (corresponding to value a7). The uncertainty source characteristic value extraction unit 7 similarly sets a search range RB1 for the source characteristic B. In Fig. 11, the search range RB1 is shown as a range from value b1 to value b7.

[0037] Next, the uncertainty source characteristic value extraction unit 7 divides the search ranges RA1 and RB1, for example, at equal distances, for each of the plurality of uncertainty source characteristics. In Fig. 11, each of the source characteristics A and B is divided into six regions. In this way, the uncertain source characteristic value extracting unit 7 divides the search ranges RA1 and RB1 of each of the plurality of uncertain source characteristics into grids. Then, the uncertainty source characteristic value extraction unit 7 sets, for each of the plurality of uncertainty source characteristics, a value corresponding to the boundary of the region generated by dividing the region into a grid as a candidate value. For example, with regard to the source characteristic A, the search range RA1 is divided into six adjacent regions, resulting in seven boundary values ​​a1 to a7 of the region generated by division. The uncertainty source characteristic value extraction unit 7 sets the values ​​a1 to a7 of the source characteristic A corresponding to each of these boundaries as a plurality of candidate values ​​a1 to a7. Similarly, the uncertainty source characteristic value extraction unit 7 generates a plurality of candidate values ​​b1 to b7 for the source characteristic B. It goes without saying that the number of candidate values ​​generated by creating a grid is not limited to seven and may be any other number. In this way, the uncertainty earthquake source characteristic value extraction unit 7 sets search ranges RA1 and RB1 for each of the plurality of uncertainty earthquake source characteristics, and generates a plurality of candidate values ​​a1 to a7 and b1 to b7 that are different from each other within the search ranges RA1 and RB1.

[0038] Then, the uncertainty seismic source characteristic value extraction unit 7 selects one candidate value for each of the uncertainty seismic source characteristics from among the multiple candidate values ​​a1 to a7, b1 to b7 for each of the multiple uncertainty seismic source characteristics, and for all combinations of candidate values, calculates the value of the objective variable when each of the candidate values ​​included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface. In the example of FIG. 11, seven candidate values ​​a1 to a7 and b1 to b7 are calculated for each of the uncertainty seismic source characteristics A and B. Therefore, there are, for example, 49 combinations of candidate values ​​obtained by selecting one candidate value for each of the uncertainty seismic source characteristics from among the multiple candidate values ​​for each of the multiple uncertainty seismic source characteristics. For all of these 49 combinations of candidate values, the uncertainty seismic source characteristic value extraction unit 7 substitutes each of the candidate values ​​included in the combination of candidate values ​​into the explanatory variable of Equation (1) to calculate the value of the objective variable in that case. For example, for the candidate value a3 of the source characteristic A and the candidate value b4 of the source characteristic B, the uncertainty source characteristic value extraction unit 7 extracts the values ​​a3 and b4 from the corresponding explanatory variables X i to calculate the objective variable, i.e., the velocity response spectrum pSv. The uncertainty source characteristic value extraction unit 7 calculates the difference between the calculated value of the objective variable and the value externally specified as the evaluation result corresponding to the assumed seismic motion for all combinations of candidate values.The uncertainty source characteristic value extraction unit 7 then extracts the combination of candidate values ​​that minimizes the difference from all combinations of candidate values. In this way, the uncertainty source characteristic value extracting unit 7 searches for the optimum solution among the combinations of candidate values ​​at this time based on the grid created at this time.

[0039] However, the grid created as described above is very rough after the above process has been performed once. Therefore, it is highly unlikely that the candidate value combinations generated by performing the above process once will contain a candidate value combination in which the difference between the response variable value and the specified value is sufficiently small and the response variable value is sufficiently close to the specified value. However, due to the continuity of the response surface 100, it is highly likely that a candidate value combination in which the difference between the response variable value and the specified value is sufficiently small will exist on the response surface 100 near the candidate value combination extracted by the above process that has the smallest difference between the response variable value and the specified value. Therefore, when the uncertainty epicenter characteristic value extraction unit 7 continues to search for the optimal solution, it resets the search range so that the combination of candidate values ​​with the smallest difference between the value of the objective variable and the specified value is at the center and so that the search range is divided into finer grids, thereby performing a more detailed search around the combination of candidate values ​​with the smallest difference between the value of the objective variable and the specified value.

[0040] Here, we will explain, using as an example, the case where the difference between the value of the objective variable and the specified value is smallest at the grid intersection OP1 corresponding to the combination of candidate value a5 of source characteristic A and candidate value b4 of source characteristic B in Figure 11. FIG. 12 shows an example of a state in which the search range is reset around the intersection of the grids shown in FIG. 11 that has the most appropriate response surface value, and the search range is then divided into grids again. The uncertainty source characteristic value extraction unit 7 resets the search range for each of the plurality of uncertainty source characteristics to a smaller range. For example, as shown in Fig. 12, the uncertainty source characteristic value extraction unit 7 resets the search range RA2 for the source characteristic A to be smaller, for example, half the range of the search range RA1 used in the previous search. Similarly, for the source characteristic B, the uncertainty source characteristic value extraction unit 7 resets the search range RB2 to be smaller, for example, half the range of the search range RB1 used in the previous search. Next, the uncertainty extracting unit 7 resets the search range for each of the uncertainty seismic source characteristics so that it is centered on the candidate value of the uncertainty seismic source characteristic in the combination of candidate values ​​extracted in the previous search. For example, as shown in Fig. 12, the uncertainty extracting unit 7 resets the search range RA2 for the seismic source characteristic A so that it is centered on the candidate value a5 of the seismic source characteristic A in the combination of candidate values ​​extracted in the previous search. Similarly, for the seismic source characteristic B, the uncertainty extracting unit 7 resets the search range RB2 so that it is centered on the candidate value b4 of the seismic source characteristic B in the combination of candidate values ​​extracted in the previous search. As a result, in Fig. 12, search range RA2 is shown as a range from value a11 to value a17 centered around value a5, and search range RB2 is shown as a range from value b11 to value b17 centered around value b4.

[0041] The uncertainty source characteristic value extraction unit 7 divides the search ranges RA2 and RB2 of each of the plurality of uncertainty source characteristics reset as described above into grids, thereby dividing each of the search ranges RA2 and RB2 into equal distances, for example. In Fig. 12, each of the source characteristics A and B is divided into six regions. The uncertainty earthquake source characteristic value extraction unit 7 then regenerates candidate values ​​for each of the plurality of uncertainty earthquake source characteristics by setting values ​​corresponding to the boundaries of the regions generated by dividing the region into grids as candidate values. For example, with regard to earthquake source characteristic A, the search range RA2 is divided into six adjacent regions, resulting in seven boundaries of the divided regions, values ​​a11 to a17. The uncertainty earthquake source characteristic value extraction unit 7 regenerates the values ​​a11 to a17 of earthquake source characteristic A corresponding to each of these boundaries as a plurality of candidate values ​​a11 to a17. Similarly, the uncertainty earthquake source characteristic value extraction unit 7 regenerates a plurality of candidate values ​​b11 to b17 for earthquake source characteristic B. In this way, the uncertainty earthquake source characteristic value extraction unit 7 resets the search ranges RA2 and RB2 for each of the plurality of uncertainty earthquake source characteristics, and regenerates a plurality of candidate values ​​a11 to a17, b11 to b17 that are different from each other within the search ranges RA2 and RB2.

[0042] Then, the uncertainty seismic source characteristic value extraction unit 7 selects one candidate value for each of the uncertainty seismic source characteristics from among the multiple regenerated candidate values ​​a11-a17 and b11-b17 for each of the multiple uncertainty seismic source characteristics, and calculates the value of the objective variable for all combinations of candidate values ​​obtained by substituting each of the candidate values ​​included in the combination of candidate values ​​for the corresponding explanatory variable of the response surface. In the example of FIG. 12, seven candidate values ​​a11-a17 and b11-b17 are calculated for each of the uncertainty seismic source characteristics A and B. Therefore, there are, for example, 49 combinations of candidate values ​​obtained by selecting one candidate value for each of the uncertainty seismic source characteristics from among the multiple candidate values ​​for each of the multiple uncertainty seismic source characteristics. For all 49 combinations of candidate values, the uncertainty seismic source characteristic value extraction unit 7 substitutes each of the candidate values ​​included in the combination of candidate values ​​into the explanatory variables of Equation (1) to calculate the value of the objective variable for that case. The uncertainty source characteristic value extraction unit 7 calculates the difference between the calculated value of the objective variable and the value externally specified as the evaluation result corresponding to the assumed seismic motion for all combinations of candidate values.The uncertainty source characteristic value extraction unit 7 then extracts the combination of candidate values ​​that minimizes the difference from all combinations of candidate values. In this way, the uncertainty source characteristic value extracting unit 7 searches for the optimum solution among the combinations of candidate values ​​at this time based on the grid created at this time.

[0043] The uncertainty source characteristic value extraction unit 7 repeats the above-described processes of resetting the search range, regenerating multiple candidate values ​​by dividing the search range into grids, and extracting the combination of the regenerated candidate values ​​that has the smallest difference between the value of the objective variable and the specified value. FIG. 13 shows an example of a state in which the search range is re-set around the intersection of the re-divided grids shown in FIG. 12 where the response surface value is most appropriate, and the search range is divided into grids. For example, in FIG. 12, if the difference between the value of the objective variable and the specified value is smallest at grid intersection OP2 corresponding to the combination of candidate value a15 of earthquake source characteristic A and candidate value b15 of earthquake source characteristic B, then, as shown in FIG. 13, search ranges RA3 and RB3 are reset so that they are centered around intersection OP2 and have a smaller range, and similar processing is then performed thereafter. The uncertainty source characteristic value extraction unit 7 repeats the above process for the combination of extracted candidate values ​​until the difference between the value of the objective variable calculated by equation (1) and the externally specified value falls within the threshold value. In this embodiment, the threshold value is set to a small value such that if the difference between the value of the objective variable calculated by formula (1) and the externally specified value is within the threshold value, it can be determined that the value of the objective variable and the externally specified value are sufficiently close to each other and therefore nearly identical. After this processing, if a combination of candidate values ​​for uncertainty source characteristics for which the difference between the value of the objective variable and the specified value is within the threshold is set in a fault model and a 3D finite element method analysis is performed, the result will be an evaluation result of seismic motion that is close to the externally specified value.

[0044] When performing the processing in the uncertainty source characteristic value extraction unit 7 as described above, it is conceivable that, among multiple combinations of candidate values, the combination that produces the smallest difference between the value of the objective variable and the specified value is located on the periphery of the search range. For example, consider the case in Fig. 12 where the difference between the value of the objective variable and the specified value is smallest at grid intersection OP3 corresponding to the combination of candidate value a13 of source characteristic A and candidate value b17 of source characteristic B, which have been reset for search ranges RA2 and RB2. For source characteristic B, candidate value b17 is located at the edge of search range RB2, i.e., on the outer periphery. Even in such a case, the uncertainty source characteristic value extraction unit 7 resets the search range for each of the plurality of uncertainty source characteristics so that the search range is centered on the candidate value of the uncertainty source characteristic in the combination of candidate values ​​extracted in the previous search.

[0045] FIG. 14 shows an example of a state in which the search range is reset and divided into grids when, among the intersections of the re-divided grid shown in FIG. 12 , the intersection with the most appropriate response surface value is on the periphery of the re-divided grid. For example, as shown in Fig. 14, the uncertainty source characteristic value extraction unit 7 resets the search range RA4 for the source characteristic A so that it is centered on the candidate value a13 of the source characteristic A in the combination of candidate values ​​extracted in the previous search. Similarly, for the source characteristic B, the uncertainty source characteristic value extraction unit 7 resets the search range RB4 so that it is centered on the candidate value b17 of the source characteristic B in the combination of candidate values ​​extracted in the previous search. When candidate value b17 is located on the outer periphery of search range RB2 as described above, a combination of candidate values ​​that results in a sufficiently small difference between the value of the response variable and the specified value is likely to be located outside search range RB2, for example, in the upper part in FIG. 12. Even in such a case, the above-described processing is used to reset a new search range RB4 so as to include an area outside search range RB2. Therefore, search range RB4 can be reset so that a combination of candidate values ​​that results in a sufficiently small difference between the value of the response variable and the specified value is more likely to be included in the new search range RB4.

[0046] However, in such a case where candidate value b17 is located at the edge of search range RB2, i.e., on the outer periphery, it is unclear how far outside search range RB2 the combination of candidate values ​​to be ultimately searched for, which will sufficiently minimize the difference between the value of the objective variable and the specified value, is located. Therefore, in such a case, when resetting search range RB4 as described above, the process of narrowing the search range, as described with reference to search ranges RA3 and RB3 in FIG. 13, is not performed. In other words, when resetting search ranges RA4 and RB4, in a case where candidate value b17 is located on the outer periphery of search range RB2, the search ranges RA4 and RB4 maintain the size of the previously set search ranges RA2 and RB2. By doing so, when a combination of candidate values, which will sufficiently minimize the difference between the value of the objective variable and the specified value, is likely to be located on the outer periphery of search range RB2, the likelihood that the combination of candidate values ​​will be included in the new search range RB4 can be increased.

[0047] In this way, the uncertainty source characteristic value extraction unit 7 searches for and extracts a combination of candidate values ​​such that the difference between the value of the objective variable calculated by equation (1) and the specified value is within the threshold value. The design seismic motion estimation unit 8 generates a fault model by setting each value of the plurality of uncertainty source characteristics to a value included in the combination of candidate values ​​searched and extracted, and uses this as the design fault model. The design earthquake motion estimation unit 8 uses the design fault model generated in this way to perform a three-dimensional finite element method analysis on the ground model, thereby estimating the design earthquake motion. In this way, the design earthquake motion estimation unit 8 generates a design fault model by setting each of the multiple uncertainty source characteristics to a value included in the extracted combination, and estimates the design earthquake motion using the design fault model.

[0048] Next, a design earthquake motion estimation method using the above-described design earthquake motion estimation system 1 will be described with reference to Figures 1 to 14, 15 and 16. Figure 15 is a flowchart of the design earthquake motion estimation method. The source characteristic input receiving unit 2 receives input of values ​​of all source characteristics, including both certainty source characteristics and uncertainty source characteristics, via an input device such as a keyboard by an operator (step S1). The fault model generation unit 3 generates a three-dimensional ground model and a fault model (step S2). The fault model generation unit 3 places multiple point seismic sources at appropriate intervals within the seismic source region DR. The fault model generation unit 3 individually sets values ​​of seismic source characteristics for each of these multiple point seismic sources. The fault model generation unit 3 repeats the process of selecting one value for each uncertainty seismic source characteristic from the values ​​that each of the multiple uncertainty seismic source characteristics can take, i.e., performing sampling, and using this to generate a fault model. In this way, the fault model generation unit 3 generates multiple different fault models. The earthquake motion evaluation unit 4 evaluates earthquake motion for each of the plurality of fault models generated by the fault model generation unit 3 (step S3).

[0049] In this manner, for each of the plurality of fault models, the relationship between the value selected for each of the plurality of uncertain source characteristics in the fault model and the evaluation result of seismic motion is obtained. Based on the plurality of relationships thus obtained between the value selected for each of the plurality of uncertain source characteristics and the evaluation result of seismic motion, the response surface construction unit 5 constructs a response surface in which each of the plurality of uncertain source characteristics is used as an explanatory variable and the evaluation result of seismic motion is used as a target variable (step S4). The expected earthquake motion designation unit 6 accepts the designation of a value of the evaluation result of earthquake motion that corresponds to the expected earthquake motion. The expected earthquake motion designation unit 6 accepts an input of the value from an external source by an operator via an input device such as a keyboard (step S5).

[0050] The uncertainty source characteristic value extraction unit 7 searches for and extracts combinations of values ​​obtained by selecting one value for each uncertainty source characteristic from among the values ​​that each uncertainty source characteristic can take, using a grid search, such that when each of the values ​​included in the combination is substituted as an explanatory variable for the response surface 100, the difference between the value of the objective variable and an externally specified value is within a threshold value (step S6). FIG. 16 is a flowchart illustrating the details of the process of extracting values ​​of uncertainty source characteristics in the design earthquake motion estimation method. As shown in FIG. 16, the uncertainty source characteristic value extracting unit 7 first sets a search range for searching for the value of each of a plurality of uncertainty source characteristics (step S11). The uncertainty source characteristic value extracting unit 7 divides the search ranges RA1 and RB1 of each of the plurality of uncertainty source characteristics into grids (step S12). The uncertainty source characteristic value extracting unit 7 sets values ​​corresponding to the boundaries of the regions generated by dividing into grids as candidate values ​​for each of the plurality of uncertainty source characteristics. The source characteristic uncertainty extraction unit 7 then selects one candidate value for each of the source characteristic uncertainty from among the multiple candidate values ​​for each of the multiple source characteristic uncertainty. For all combinations of candidate values, the unit calculates the value of the response variable when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface. The source characteristic uncertainty extraction unit 7 then calculates the difference between the value of the response variable calculated for all combinations of candidate values ​​as described above and a value externally specified as an evaluation result corresponding to the assumed seismic motion. The source characteristic uncertainty extraction unit 7 then extracts the combination of candidate values ​​that minimizes the difference from among all combinations of candidate values. In this way, the source characteristic uncertainty extraction unit 7 searches for an optimal solution among the current combinations of candidate values ​​based on the grid created at this time (step S13).

[0051] The uncertain source characteristic value extracting unit 7 resets the search range for each of the plurality of uncertain source characteristics to a smaller range (step S14). The uncertainty source characteristic value extraction unit 7 resets the search range for each of the plurality of uncertainty source characteristics so that the search range is centered on the candidate value of the uncertainty source characteristic in the combination of candidate values ​​extracted in the previous search (step S15). The uncertainty hypocenter characteristic value extracting unit 7 divides the search ranges RA2, RB2 of each of the plurality of uncertainty hypocenter characteristics reset as described above into grids, thereby dividing each of the search ranges RA2, RB2, for example, at equal distances. The uncertainty hypocenter characteristic value extracting unit 7 regenerates candidate values ​​for each of the plurality of uncertainty hypocenter characteristics by setting values ​​corresponding to the boundaries of the regions generated by dividing into grids as candidate values ​​(step S16). The source characteristic uncertainty extraction unit 7 then selects one candidate value for each of the source characteristic uncertainty from among the multiple regenerated candidate values ​​for each of the source characteristic uncertainty. For all combinations of candidate values, the unit calculates the value of the response variable when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface. The source characteristic uncertainty extraction unit 7 calculates the difference between the calculated value of the response variable for all combinations of candidate values ​​and a value externally specified as an evaluation result corresponding to the assumed seismic motion. The source characteristic uncertainty extraction unit 7 then extracts the combination of candidate values ​​that minimizes the difference from among all combinations of candidate values. In this way, the source characteristic uncertainty extraction unit 7 searches for an optimal solution among the current combinations of candidate values ​​based on the grid created at this time (step S17).

[0052] The uncertainty source characteristic value extracting unit 7 determines whether the combination of candidate values ​​extracted as described above is located on the outer periphery of the search range (step S18). If it is determined that the extracted combination of candidate values ​​is located on the periphery of the search range (Yes in step S18), the process proceeds to step S15, where a process of resetting the center of the search range is executed, after which a grid is created (step S16), and the optimal solution is searched for again (step S17).In this way, in this case, the size of the search range is not reduced, and only the center is reset while maintaining the size of the search range used when the optimal solution was last searched, and the optimal solution is searched for.

[0053] If it is determined that the extracted combination of candidate values ​​is not located on the periphery of the search range (No in step S18), the uncertainty source characteristic value extraction unit 7 determines whether the difference between the value of the objective variable calculated by equation (1) for the extracted combination of candidate values ​​and the value specified externally is less than or equal to a threshold value (step S19). If it is equal to or less than the threshold value (Yes in step S19), the process ends. If it is not equal to or less than the threshold (No in step S19), the process proceeds to step S14, where the size and center of the search range are reset, a grid is created (step S16), and the optimal solution is searched for again (step S17). In this way, the size and center of the search range are reset, and the optimal solution is searched for again.

[0054] In this way, the uncertainty source characteristic value extraction unit 7 searches for and extracts a combination of candidate values ​​such that the difference between the value of the objective variable calculated by equation (1) and the specified value is within the threshold value. The design earthquake motion estimation unit 8 generates a design fault model by setting each of the multiple uncertainty source characteristics to a value included in the extracted combination, and estimates the design earthquake motion using the design fault model (step S7).

[0055] The design earthquake motion estimation system 1 as described above is a system for estimating design earthquake motions to be used in the design of a building when the earthquake source characteristics set for the earthquake source include a plurality of uncertain earthquake source characteristics whose values ​​vary and require consideration of uncertainty, and includes a fault model generation unit 3 which selects one value for each of the plurality of uncertain earthquake source characteristics from the values ​​that each of the plurality of uncertain earthquake source characteristics can take and sets the selected value in the fault model, repeatedly generating a plurality of fault models in which different values ​​are set; an earthquake motion evaluation unit 4 which evaluates earthquake motions for each of the plurality of fault models; and an earthquake motion evaluation unit 5 which evaluates the earthquake motions for each of the plurality of uncertain earthquake source characteristics based on the relationship between the value selected for each of the plurality of uncertain earthquake source characteristics in each of the plurality of fault models and the evaluation result of the earthquake motion. The system is equipped with: a response surface construction unit 5 that constructs a response surface 100 with each of the uncertainty seismic source characteristics as an explanatory variable and the evaluation result of seismic motion as a response variable; an uncertainty seismic source characteristic value extraction unit 7 that searches for and extracts combinations of values ​​obtained by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the multiple uncertainty seismic source characteristics can take, using a predetermined search and estimation method (grid search), such that when each of the values ​​included in the combinations is substituted for the corresponding explanatory variable of the response surface 100, the difference between the value of the response variable and an externally specified value is within a threshold; and a design seismic motion estimation unit 8 that sets each of the multiple uncertainty seismic source characteristics to a value included in the extracted combination, generates a design fault model, and estimates design seismic motion using the design fault model. According to the above configuration, when the seismic source characteristics set for a hypocenter include multiple uncertainty seismic source characteristics whose values ​​vary and require consideration of uncertainty, one value is selected for each of the multiple uncertainty seismic source characteristics from the possible values ​​each of the multiple uncertainty seismic source characteristics can take, and this is repeatedly set in the fault model to generate multiple different fault models in which different values ​​are set for the uncertainty seismic source characteristics. Furthermore, seismic motion is evaluated for each of the multiple fault models generated in this way, and a response surface 100 is constructed in which each of the multiple uncertainty seismic source characteristics is used as an explanatory variable and the evaluation result of the seismic motion is used as a response variable based on the relationship between the value selected for each of the multiple uncertainty seismic source characteristics in each of the multiple fault models and the evaluation result of the seismic motion. In this way, the relationship between the possible values ​​of each uncertainty seismic source characteristic and the evaluation result of the seismic motion can be obtained. For the response surface 100 obtained in this way, when a combination of explanatory variables, i.e., values ​​obtained by selecting one value for each of a plurality of uncertain source characteristics from among the possible values ​​of each of the explanatory variables, is to be obtained, such that the value of the objective variable is an evaluation result corresponding to some assumed seismic motion, such as a mega-earthquake, the combination is extracted by using a predetermined search and estimation method in the uncertainty source characteristic value extraction unit 7, such that when each value included in the combination is substituted for the corresponding explanatory variable in the response surface 100, the difference between the value of the objective variable and, for example, an externally specified value as an evaluation result corresponding to the assumed seismic motion is within a threshold. The design fault model generated by setting each of the values ​​included in the combinations obtained in this way as each uncertain source characteristic corresponds to the assumed seismic motion. Therefore, the design seismic motion estimated using the design fault model generated in this way is the design seismic motion corresponding to the assumed seismic motion. In this way, when the source characteristics set for a seismic source include multiple uncertain source characteristics whose values ​​vary and require consideration of uncertainty, it is possible to appropriately generate a fault model equivalent to the expected seismic motion and accurately estimate the design seismic motion used in the design of a building.

[0056] Furthermore, based on the relationships obtained as described above, the response surface constructor 5 expresses the objective variable using a plurality of explanatory variables by polynomial approximation, and the response surface 100 is realized as a quadratic equation (1) including quadratic terms corresponding to each of the plurality of explanatory variables and an interaction term obtained by multiplying two different explanatory variables among the plurality of explanatory variables. According to the above configuration, the response surface 100 can be appropriately realized as a relatively simple formula (1).

[0057] The uncertainty seismic source characteristic value extraction unit 7 also sets a search range for each of the multiple uncertainty seismic source characteristics, generates multiple candidate values ​​that are different from each other within the search range, and then extracts a combination of candidate values ​​obtained by selecting one candidate value for each of the multiple uncertainty seismic source characteristics from the multiple candidate values ​​for each of the multiple uncertainty seismic source characteristics, where the combination of candidate values ​​minimizes the difference between the value of the objective variable and a specified value when each of the candidate values ​​included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface 100.The unit 7 then resets the search range for each of the multiple uncertainty seismic source characteristics to a smaller range centered on the candidate value of the uncertainty seismic source characteristic in the extracted combination of candidate values, and regenerates multiple candidate values ​​that are different from each other within the search range, repeatedly executing this process until the difference between the value of the objective variable calculated for the extracted combination of candidate values ​​and the specified value falls within a threshold. According to the above configuration, the uncertain earthquake source characteristic value extracting unit 7 sets a search range for each of a plurality of uncertain earthquake source characteristics, and generates a plurality of candidate values ​​that are different from each other within the search range. Thereafter, the uncertainty source characteristic value extracting unit 7 repeatedly executes the following process. The uncertainty seismic source characteristic value extraction unit 7 first extracts a combination of candidate values ​​obtained by selecting one candidate value for each of the uncertainty seismic source characteristics from among multiple candidate values ​​for each of the multiple uncertainty seismic source characteristics. The combination of candidate values ​​is then extracted so that, when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable on the response surface 100, the difference between the value of the objective variable and, for example, an externally specified value as an evaluation result corresponding to the assumed seismic motion is minimized. The combination of candidate values ​​extracted in this manner is considered to be the one that, among all the combinations of candidate values, can produce a design seismic motion closest to the assumed seismic motion when each candidate value included in the combination is set in a fault model and the design seismic motion is estimated. If there is a desirable combination of candidate values ​​whose value of the objective variable matches or is very close to the specified value, it is likely to exist on the response surface 100 near the combination of candidate values ​​extracted as described above. Based on this idea, the uncertainty source characteristic value extraction unit 7 then resets the search range for each of the multiple uncertainty source characteristics to a smaller range centered on the candidate value of the uncertainty source characteristic in the combination of candidate values ​​extracted as described above, and regenerates multiple candidate values ​​that differ from each other within the reset search range. In this way, it is possible to reset multiple candidate values ​​with finer granularity near the combination of candidate values ​​extracted as described above, which is thought to contain a desirable combination of candidate values. The above process is repeated until the difference between the value of the objective variable calculated for the extracted combination of candidate values ​​and the specified value falls within a threshold. In this way, for each of the multiple uncertain source characteristics, the search range is narrowed down to a portion of the response surface 100 where a desirable combination of candidate values ​​is considered to exist. If the difference between the value of the objective variable calculated for the extracted combination of candidate values ​​and the specified value finally falls within the threshold, it is considered that the design seismic motion estimated using the fault model in which the candidate values ​​included in the combination of candidate values ​​are set represents, with sufficiently high accuracy, the seismic motion assumed when the values ​​were externally specified. In this way, it is possible to efficiently calculate combinations of values ​​obtained by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the multiple uncertainty seismic source characteristics can take, and such combinations are such that when each of the values ​​included in the combination is substituted for the corresponding explanatory variable of the response surface 100, the difference between the value of the objective variable and the specified value is within a threshold value.

[0058] (Modification of the embodiment) In the above embodiment, a combination of values ​​is extracted by selecting one value for each of the uncertainty seismic source characteristics from among the possible values ​​of each of the multiple uncertainty seismic source characteristics, and essentially only one combination is extracted by a predetermined search and estimation method (grid search) such that when each of the values ​​included in the combination is substituted for the corresponding explanatory variable of the response surface, the difference between the value of the objective variable and the externally specified value is within a threshold (set as a very small value).In such a case, if a fault model is actually generated using the values ​​included in the combination, there is a possibility that the fault model will be inappropriate. Figure 17 is an example of a fault model that is considered inappropriate. Figure 18 is another example of a fault model that is considered inappropriate. In the fault model shown in Figure 17, two asperities are located at the center of the fault model. In the fault model shown in Figure 18, two asperities are located at the edge of the fault model.

[0059] When using the design earthquake motion estimation system 1 according to the above embodiment, it is possible to generate a design fault model assuming a worst-case scenario in which as much damage as possible occurs over as wide an area as possible, and then estimate the design earthquake motion using the design fault model. Using the design earthquake motion estimated in this way, disaster prevention measures against earthquakes can be considered assuming the worst-case scenario. From the viewpoint of disaster prevention, fault models in which asperities are biased, such as those shown in Figures 17 and 18, are unlikely to be appropriate because there are areas located far from the asperities where the impact of the earthquake is thought to be less severe than in the worst-case scenario. In the design seismic motion estimation system 1A (see Figure 1) of this modified example, multiple combinations of values ​​are extracted by repeatedly performing a grid search, where the combinations are obtained by selecting one value for each of the uncertainty source characteristics, and when each of the values ​​included in the combinations is substituted for the corresponding explanatory variables of the response surface, the difference between the value of the objective variable and an externally specified value is within a threshold. Then, from these multiple combinations, one combination is extracted that is considered to have the most appropriate value for the uncertainty source characteristics. A design fault model that is considered to be appropriate is generated by setting the values ​​included in the combination extracted in this way.

[0060] The design earthquake motion estimation system 1A of this modification differs from the above embodiment in the operation of the response surface construction unit 5A and the uncertainty source characteristic value extraction unit 7A. The following mainly describes these differences. FIG. 19 is an explanatory diagram showing a region where combinations of values ​​of uncertainty source characteristics are searched for in the design earthquake motion estimation system of this modified example. In the following, for simplicity of explanation, each process will be explained as a process in a two-dimensional space, as in the above embodiment.

[0061] The response surface constructor 5A constructs the response surface 100 in the same manner as in the above embodiment. In this modification, similar to the above embodiment, polynomial approximation is used to construct the response surface 100. In this case, the response surface constructor 5A uses the approximation residual ε t More specifically, for each combination of values ​​selected (by sampling using the Latin Hypercube method or the like) for each of the plurality of uncertain source characteristics used when constructing the response surface 100, the response surface construction unit 5A calculates the difference between the value (true value) of the evaluation result of the seismic motion (e.g., velocity response spectrum pSv) itself corresponding to the combination and the value of the objective variable when each value of the uncertain source characteristics included in the combination is substituted as an explanatory variable of the response surface 100, as the approximation residual ε t Calculate as follows. When constructing the response surface 100 using Gaussian process regression, it is possible to use the uncertainty of the estimated value instead of the residual of the approximation described above. In this case, the same explanation can be obtained by replacing the word "residual" below with the word "uncertainty of the estimated value."

[0062] Next, the response surface construction unit 5A calculates the standard deviation σ of the residuals, assuming that the residuals follow a normal distribution. c Calculate. Then, the response surface construction unit 5A constructs a first response surface 100A, which is a response surface that takes values ​​that are a fixed value smaller than the response surface 100, and a second response surface 100B, which is a response surface that takes values ​​that are a fixed value larger than the response surface 100. In this modification, the constant value is the standard deviation σ of the residuals. c The constant value is the standard deviation of the residuals σ c Not only the standard deviation of the residuals, but also σ c A value based on the residual standard deviation σ c It may be a value obtained by multiplying by some coefficient or other value.

[0063] As in the above embodiment, the expected earthquake motion designation unit 6 receives designation of the value of the evaluation result of earthquake motion that corresponds to the expected earthquake motion.

[0064] Fig. 20 shows an example of a state in which a search range is set for each of a plurality of uncertain source characteristics and the search range is divided into grids. Fig. 20 shows a case in which the velocity response spectrum pSv as the evaluation result of the seismic motion is specified as 100 cm / s in the expected seismic motion specification unit 6. Fig. 20 also shows the portions (curves in the case of two dimensions) of the response surface 100, first response surface 100A, and second response surface 100B where the velocity response spectrum pSv is 100 cm / s, respectively, and is assigned the symbols 100L, 100AL, and 100BL. In this modified example, the uncertainty source characteristic value extraction unit 7A uses a grid search to search for a combination of values ​​that are included in a range RL between a portion 100AL of the first response surface 100A where the evaluation result of the seismic motion is an externally specified value and a portion 100BL of the second response surface 100B where the evaluation result of the seismic motion is an externally specified value. In the above embodiment, the threshold value used to extract the above combinations was set to a small value such that, if the difference between the value of the objective variable calculated by equation (1) and the externally specified value is within the threshold value, it can be determined that the value of the objective variable and the externally specified value are sufficiently close and substantially identical. Instead, in this modification, the threshold value is set to a larger value than in the above embodiment in order to realize a search in the range RL between the portion 100AL and the portion 100BL. In this modification, the threshold value is set to the above-mentioned constant value, and a grid search is performed. That is, in this embodiment, the threshold value is set to, for example, the standard deviation σ of the residuals. c is.

[0065] Figure 21 is an explanatory diagram showing the relationship between the response surface, the first response surface, and the second response surface when the velocity response spectrum pSv, which is the evaluation result of the earthquake motion, is specified as 100 cm / s. Figure 21 can be said to be a diagram of Figure 20 viewed from the side of the paper on which it is drawn. For example, at point P5 in FIG. 21, when each of the values ​​included in the combination of values ​​of the uncertainty source characteristics corresponding to point P5 is substituted as an explanatory variable of the response surface 100, the difference LP5 between the value VP5 of the objective variable and the value (pSv=100) input from outside in the assumed earthquake motion designation unit 6 is a constant value (standard deviation of the residual σ c ) in Fig. 20. Such a point is included in a range RL between a portion 100AL of the first response surface 100A where the evaluation result of the earthquake motion is an externally specified value and a portion 100BL of the second response surface 100B where the evaluation result of the earthquake motion is an externally specified value. Furthermore, for example, at point P6 in FIG. 21, when each of the values ​​included in the combination of values ​​of the uncertainty source characteristics corresponding to point P6 is substituted as an explanatory variable of the response surface 100, the difference LP6 between the value VP6 of the objective variable and the value (pSv=100) input from outside in the assumed earthquake motion designation unit 6 is a constant value (standard deviation of the residual σ c ) in Fig. 20. Such points are not included in the range RL between the portion 100AL of the first response surface 100A where the evaluation result of the earthquake motion is an externally specified value and the portion 100BL of the second response surface 100B where the evaluation result of the earthquake motion is an externally specified value.

[0066] In this way, searching for a combination included in the range RL between the portion 100AL of the first response surface 100A where the evaluation result of the seismic motion is an externally specified value and the portion 100BL of the second response surface 100B where the evaluation result of the seismic motion is an externally specified value is a combination of values ​​obtained by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the uncertainty seismic source characteristics can take, and when each of the values ​​included in the combination is substituted as an explanatory variable of the response surface 100, the difference between the value of the objective variable and the externally specified value is equal to or greater than a threshold (a constant value, i.e., the standard deviation σ of the residuals). c ) is equivalent to searching for a combination that satisfies the above condition.

[0067] The uncertainty source characteristic value extraction unit 7A performs grid search to extract the uncertainty source characteristic value until at least one intersection point generated by dividing the range RL between the portion 100AL corresponding to the first response surface 100A and the portion 100BL corresponding to the second response surface 100B into grids is found, in which the evaluation result of the seismic motion is set to an externally specified value, that is, until the difference between the value of the objective variable calculated by Equation (1) and the externally specified value reaches a threshold (a fixed value, i.e., the standard deviation σ of the residual c As in the above embodiment, the search range is reset to a smaller size, and the reset search range is divided into grids to perform the search repeatedly until at least one combination of values ​​of the uncertainty source characteristics such that: As already explained, in this modification, the threshold value is set to a larger value than in the above embodiment. Therefore, multiple combinations of values ​​may be simultaneously extracted, in which the difference between the value of the objective variable calculated by Equation (1) and the externally specified value is equal to or smaller than the threshold value. For example, in Figure 20, seven combinations are extracted. In such a case, the uncertainty source characteristic value extracting unit 7A registers all the extracted combinations of values ​​of uncertainty source characteristics in a database (not shown) or the like.

[0068] The uncertainty source characteristic value extraction unit 7A repeats a series of grid search processes multiple times, in which the search ranges RA1 and RB1 are set to cover the entire range in which each value of the uncertainty source characteristic can be taken when the grid search is started, and the size of the search range is reset to a smaller size as described above to perform searches, thereby extracting and registering combinations of values ​​of the uncertainty source characteristic.The uncertainty source characteristic value extraction unit 7A repeats a series of grid search processes multiple times until the total number of registered combinations reaches a predetermined number (e.g., 100) or more. Here, if the total number of registered combinations is not a predetermined number (for example, 100) or more after a series of grid search processes is completed for the search ranges RA1 and RB1 set when the grid search is started, the uncertainty source characteristic value extraction unit 7A changes the width by which the search ranges RA1 and RB1 set when the grid search is started, i.e., the interval at which the ranges are divided into grids, when executing the next series of grid search processes. As a result, a different combination of values ​​is extracted and registered each time the series of grid search processes is repeated. The intervals can be determined by any suitable method, such as by using random numbers.

[0069] In this way, by repeating a series of grid searches many times, with different grid spacings for the search ranges RA1 and RB1 that are initially set to cover the entire range in which each value of the uncertainty source characteristic can be taken, a predetermined number (e.g., 100) or more combinations are registered. Figure 22 is a table showing the values ​​of each uncertainty of the source characteristic for each of the multiple combinations extracted by the grid search. Figure 22 shows 100 combinations extracted and registered. Each combination includes the values ​​of eight uncertainty of the source characteristic, labeled source characteristic A to source characteristic H. Hereinafter, the values ​​of the uncertainty of the source characteristic are assumed to be normalized to be between -1 and 1.

[0070] When a predetermined number or more of combinations have been registered, the uncertainty source characteristic value extraction unit 7A then further extracts one combination that is considered to be the most appropriate from the registered combinations that are the predetermined number or more. For this purpose, the uncertain source characteristic value extracting unit 7A first performs kernel density estimation for each of the plurality of uncertain source characteristics. FIG. 23 is a diagram showing the results of kernel density estimation performed on a certain uncertain source characteristic (source characteristic A shown in FIG. 22). The uncertainty source characteristic value extraction unit 7A first collects values ​​corresponding to each uncertainty source characteristic for multiple combinations (i = 1 to m, m = 100 in the example of Figure 23) for each uncertainty source characteristic, and generates a histogram based on these values. Next, the uncertainty source characteristic value extracting unit 7A performs kernel density estimation for each of the uncertainty source characteristics based on the histogram, and derives a probability density function PF.

[0071] The uncertain source characteristic value extracting unit 7A calculates the maximum value of the probability density function PF for each uncertain source characteristic. Figure 24 is a table showing the weights calculated for each uncertainty source characteristic. Next, the uncertainty source characteristic value extraction unit 7A calculates a weight w for each uncertainty source characteristic (j=1 to n, n=8 in the example of FIG. 23) based on the maximum value. j The uncertainty source characteristic value extraction unit 7A calculates the weight w of the uncertainty source characteristic by, for example, dividing the maximum value of the probability density function PF of each of the uncertainty source characteristics by the sum of the maximum values ​​of all the uncertainty source characteristics. j Calculate.

[0072] FIG. 25 is a table showing the probability density obtained by performing kernel density estimation on each of the multiple combinations extracted by the grid search. The uncertainty source characteristic value extraction unit 7A further applies the value of the uncertainty source characteristic in each combination (i=1 to m) to the probability density function PF of the uncertainty source characteristic, thereby obtaining a probability density p i、j Calculate.

[0073] Then, the uncertainty source characteristic value extraction unit 7A extracts, for each of a plurality of combinations (i=1 to m), a probability density p i、j and the weight of the uncertain source characteristics w j The sum of the products of and is the likelihood score, i Calculate as follows.

number

[0074] The likelihood score calculated as above is the probability density p i、j The likelihood score is calculated by performing a weighted sum of the uncertainty scores. A large likelihood score for a certain combination indicates that the probability density of each of the multiple uncertainty source characteristics is more likely to occur probabilistically than other combinations, i.e., it is more "likely." Therefore, by selecting a combination with a large likelihood score from multiple combinations and generating a fault model based on this, a more appropriate fault model can be obtained. Based on the above-mentioned concept, the uncertainty source characteristic value extracting unit 7A selects the combination with the maximum likelihood score from the multiple combinations registered. In this way, the uncertainty source characteristic value extracting unit 7A further extracts one combination from the multiple combinations registered in the database (not shown) by grid search.

[0075] The design earthquake motion estimation unit 8 generates a design fault model for one of the extracted combinations, and estimates the design earthquake motion using the design fault model. In the above description, the uncertainty source characteristic value extraction unit 7A extracts one combination with the highest likelihood score from among the multiple combinations, but this is not limiting. The uncertainty source characteristic value extraction unit 7A may select multiple combinations with the highest likelihood scores from among the multiple combinations in descending order of likelihood scores, and the design seismic motion estimation unit 8 may generate design fault models for these combinations.

[0076] Next, a description will be given of a design earthquake motion estimation method using the design earthquake motion estimation system 1 A. Steps S1 to S3 and S5 shown in Fig. 15 are the same as those in the above embodiment, and therefore description thereof will be omitted. After step S3, multiple relationships between the values ​​selected for each of the multiple uncertain seismic source characteristics and the evaluation results of seismic motion are obtained. Based on the multiple relationships between the values ​​selected for each of the multiple uncertain seismic source characteristics and the evaluation results of seismic motion obtained in this way, the response surface construction unit 5A constructs a response surface 100 in which each of the multiple uncertain seismic source characteristics is used as an explanatory variable and the evaluation results of seismic motion are used as a response variable (step S4). At this time, for each combination of values ​​selected (by sampling using the Latin Hypercube method or the like) for each of the multiple uncertain seismic source characteristics used in constructing the response surface 100, the response surface construction unit 5A calculates the difference between the value (true value) of the evaluation result of seismic motion (e.g., velocity response spectrum pSv) corresponding to the combination and the value of the response variable when each value of the uncertain seismic source characteristic included in the combination is substituted as an explanatory variable of the response surface 100, as an approximation residual ε t Calculate as follows. Next, the response surface construction unit 5A calculates the standard deviation σ of the residuals, assuming that the residuals follow a normal distribution. c Calculate.

[0077] FIG. 26 is a flowchart illustrating in detail the process of extracting values ​​of uncertainty source characteristics in the design earthquake motion estimation method according to this modification. After the expected earthquake motion designation unit 6 receives an input of the value of the evaluation result of earthquake motion corresponding to the expected earthquake motion from the outside by an operator via an input device such as a keyboard (step S5), the uncertainty earthquake motion characteristic value extraction unit 7A selects a combination of values ​​obtained by selecting one value for each uncertainty earthquake motion characteristic from among the values ​​that each uncertainty earthquake motion characteristic can take, and determines whether the difference between the value of the objective variable and the externally specified value when each of the values ​​included in the combination is substituted as an explanatory variable of the response surface 100 is equal to or greater than a threshold value (in this modified example, the standard deviation σ of the residuals c ) are searched for and extracted by grid search (step S6).

[0078] More specifically, the uncertain source characteristic value extracting unit 7A first sets search ranges RA1 and RB1 for searching for the value of each of the uncertain source characteristics (step S11). The uncertainty source characteristic value extracting unit 7A divides the search ranges RA1 and RB1 of each of the plurality of uncertainty source characteristics into grids (step S12). The uncertainty source characteristic value extracting unit 7A sets values ​​corresponding to the boundaries of the regions generated by dividing into grids as candidate values ​​for each of the plurality of uncertainty source characteristics. The source characteristic uncertainty extraction unit 7A then selects one candidate value for each of the source characteristic uncertainty from among the multiple candidate values ​​for each of the multiple source characteristic uncertainty. For all combinations of candidate values, the unit calculates the value of the response variable when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface. The source characteristic uncertainty extraction unit 7A calculates the difference between the value of the response variable calculated for all combinations of candidate values ​​in the above manner and a value externally specified as an evaluation result corresponding to the assumed seismic motion. The source characteristic uncertainty extraction unit 7A then extracts one combination of candidate values ​​that minimizes the difference from among all combinations of candidate values. In this way, the source characteristic uncertainty extraction unit 7A searches for an optimal solution among the current combinations of candidate values ​​based on the grid created at this time (step S13).

[0079] The uncertain source characteristic value extracting unit 7A resets the search range for each of the plurality of uncertain source characteristics to a smaller range (step S14). The uncertainty source characteristic value extraction unit 7A resets the search range for each of the plurality of uncertainty source characteristics so that the search range is centered on the candidate value of the uncertainty source characteristic in the combination of candidate values ​​extracted in the previous search (step S15). The uncertainty source characteristic value extraction unit 7A divides the search ranges RA2 and RB2 (see FIG. 13) of each of the plurality of uncertainty source characteristics reset as described above into grids, thereby dividing each of the search ranges RA2 and RB2, for example, at equal distances. The uncertainty source characteristic value extraction unit 7A regenerates candidate values ​​for each of the plurality of uncertainty source characteristics by setting values ​​corresponding to the boundaries of the areas generated by dividing into grids as candidate values ​​(step S16). The source characteristic uncertainty extraction unit 7A then selects one candidate value for each of the source characteristic uncertainty from among the multiple regenerated candidate values ​​for each of the source characteristic uncertainty. For all combinations of candidate values, the unit calculates the value of the response variable when each candidate value included in the combination of candidate values ​​is substituted for the corresponding explanatory variable of the response surface. The source characteristic uncertainty extraction unit 7A calculates the difference between the calculated value of the response variable for all combinations of candidate values ​​and a value externally specified as an evaluation result corresponding to the assumed seismic motion. The source characteristic uncertainty extraction unit 7A then extracts one combination of candidate values ​​that minimizes the difference from among all combinations of candidate values. In this way, the source characteristic uncertainty extraction unit 7A searches for an optimal solution among the current combinations of candidate values ​​based on the grid created at this time (step S17).

[0080] The uncertainty source characteristic value extracting unit 7A determines whether or not one combination of candidate values ​​extracted as described above is located on the outer periphery of the search range (step S18). If it is determined that the extracted combination of candidate values ​​is located on the periphery of the search range (Yes in step S18), the process proceeds to step S15, where a process of resetting the center of the search range is executed, after which a grid is created (step S16), and the optimal solution is searched for again (step S17).In this way, in this case, the size of the search range is not reduced, and only the center is reset while maintaining the size of the search range used when the optimal solution was last searched, and the optimal solution is searched for.

[0081] If it is determined that the extracted combination of candidate values ​​is not located on the periphery of the search range (No in step S18), the uncertainty source characteristic value extraction unit 7A determines whether the difference between the value of the objective variable calculated by Equation (1) and the externally specified value is greater than or equal to a threshold value (in this modified example, the standard deviation σ of the residuals) for one extracted combination of candidate values. c ) or less (step S21). If it is not equal to or less than the threshold (No in step S21), the process proceeds to step S14, where the size and center of the search range are reset, a grid is created (step S16), and the optimal solution is searched for again (step S17). In this way, the size and center of the search range are reset, and the optimal solution is searched for again.

[0082] If the difference is equal to or less than the threshold (Yes in step S21), the uncertainty source characteristic value extraction unit 7A registers the extracted combination of candidate values ​​in a database (not shown) or the like as a combination of values ​​of uncertainty source characteristics extracted by grid search (step S22). Furthermore, if there are any combinations of candidate values ​​in which the difference between the value of the objective variable and an externally specified value is smaller than the threshold, other than the one combination of candidate values ​​extracted as described above, the uncertainty source characteristic value extraction unit 7A also registers all such combinations as combinations of values ​​of uncertainty source characteristics extracted by grid search. In this way, in this modified example, the difference between the value of the objective variable and the externally specified value is set to a threshold value (a constant value, i.e., the standard deviation of the residual σ c ) The uncertainty source characteristic value extracting unit 7A registers all the extracted combinations in a database (not shown) or the like.

[0083] Thereafter, the uncertainty source characteristic value extracting unit 7A determines whether or not a required number of combinations have been registered (step S23). Specifically, the uncertainty source characteristic value extracting unit 7A determines whether or not the total number of registered combinations is equal to or greater than a predetermined number (for example, 100). If the total number of registered combinations is less than the predetermined number (No in step S23), the intervals at which the search ranges RA1 and RB1 are divided into grids, which are initially set when the grid search is started, are changed to a value different from any previous value (step S24). Then, the process returns to step S12, and the subsequent processes are repeated. In this way, a combination of values ​​different from the previous ones can be searched for in the next series of grid searches (steps S12 to S21).

[0084] When the total number of registered combinations is equal to or greater than a predetermined number (Yes in step S23), the uncertainty source characteristic value extracting unit 7A terminates the processing related to the grid search. The uncertainty source characteristic value extracting unit 7A calculates a likelihood score Score for each of the multiple combinations (i=1 to m) registered in the database (not shown). i is calculated (step S25). The uncertain source characteristic value extracting unit 7A selects the combination with the maximum likelihood score from the registered combinations. In this way, the uncertain source characteristic value extracting unit 7A further extracts one combination from the registered combinations by grid search (step S26).

[0085] Thereafter, as explained as step S7 in the above embodiment, the design earthquake motion estimation unit 8 generates a design fault model by setting each of the plurality of uncertainty source characteristics to a value included in one of the extracted combinations, and estimates the design earthquake motion using the design fault model.

[0086] Figure 27 shows an example of a fault model that is considered to be appropriate, calculated by the design earthquake motion estimation system of this modified example. Figure 28 shows another example of a fault model that is considered to be appropriate, calculated by the design earthquake motion estimation system of this modified example. As shown in Figures 27 and 28, in the fault model generated using the design earthquake motion estimation system 1A of this modified example, two asperities are distributed so as to cover as much of the fault as possible, resulting in a more appropriate fault model than those in Figures 17 and 18.

[0087] In the design earthquake motion estimation system 1A as described above, the uncertainty source characteristic value extraction unit 7A extracts a plurality of combinations by grid search (a predetermined search and estimation method), then performs kernel density estimation for each of the plurality of uncertainty source characteristics, calculates the maximum value of the probability density function, calculates the weight of each of the plurality of uncertainty source characteristics based on the maximum value, and for each of the plurality of combinations, calculates the sum of the products of the probability density obtained by kernel density estimation corresponding to the value of the uncertainty source characteristic included in the combination and the weight of the uncertainty source characteristic as a likelihood score, and selects the combination with the maximum likelihood score to further extract one combination from the plurality of combinations.The design earthquake motion estimation unit generates a design fault model for the one combination and estimates the design earthquake motion using the design fault model. For example, if a grid search is used to extract only one combination from among the possible values ​​of multiple uncertain source characteristics, and the values ​​included in that combination are used to generate a design fault model and estimate the design earthquake motion, the generated fault model and the design earthquake motion estimated based on it may not be appropriate. In contrast to this, with the above configuration, a plurality of combinations are extracted by grid search. As a result, different values ​​may be set for each of the multiple uncertain source characteristics in each combination. Therefore, the uncertainty source characteristic value extraction unit 7A performs kernel density estimation for each of the multiple uncertain source characteristics based on the set of values ​​set for that uncertain source characteristic to calculate a probability density function. In the probability density function calculated in this way, the value of the uncertain source characteristic that gives a probability density value close to the maximum value can be considered to be the most appropriate value for the uncertain source characteristic (the most likely value that the uncertain source characteristic can take). Therefore, by further extracting one combination that is considered to be a combination of values ​​as close as possible to the maximum values ​​of the multiple uncertain source characteristics from the multiple combinations extracted by the grid search and using this combination to generate a fault model, it is possible to generate an appropriate fault model. Based on this concept, the uncertainty source characteristic value extraction unit 7A calculates the maximum value of the probability density function for each of the plurality of uncertainty source characteristics and calculates a weight for each of the plurality of uncertainty source characteristics based on this maximum value. Furthermore, for each of the plurality of combinations, it calculates a likelihood score by summing up the product of the probability density obtained by kernel density estimation corresponding to the value of the uncertainty source characteristic included in the combination and the weight of the uncertainty source characteristic. The uncertainty source characteristic value extraction unit 7A further extracts one combination from the plurality of combinations by selecting the combination with the maximum likelihood score calculated in this way. The design seismic motion estimation unit then generates a design fault model for the one combination. In this way, it is possible to generate an appropriate design fault model, and by using this design fault model, it is possible to estimate appropriate design earthquake motion.

[0088] The design earthquake motion estimation system of the present invention is not limited to the above-described embodiment and modifications explained with reference to the drawings, and various other modifications are conceivable within the technical scope thereof. For example, in the above embodiment, each component has been described in detail based on the examples shown in Figures 2 to 5, etc., but it goes without saying that the application of the design earthquake motion estimation system 1 is not limited to the above examples.

[0089] In the above embodiment, it has been explained that the expected earthquake motion designation unit 6 receives a designation of a value of the evaluation result of earthquake motion that corresponds to some expected earthquake motion. This expected earthquake motion can be set, for example, as follows. FIG. 29 is a diagram showing an example of earthquake resistance performance grades. The magnitude of an earthquake and the state of a building when an earthquake occurs can be determined by a matrix of earthquake resistance grades, as shown in Figure 29. Figure 29 shows three levels of earthquake resistance grades: "Standard Class," which limits damage to a minor extent in an earthquake of less than 5 on the Japanese seismic intensity scale, but may cause major damage in a major earthquake of more than 6 on the Japanese seismic intensity scale, "Advanced Class," and "Special Class," which can limit damage to minor damage or less even in a major earthquake of more than 6 on the Japanese seismic intensity scale. For example, if a building is to be constructed with a "special" seismic resistance grade, it is conceivable to target earthquake motions of all magnitudes, from earthquake motions of magnitude obtained by subtracting the standard deviation from the average value, which encompasses, for example, about 85% of earthquake motions taking uncertainty into account, to earthquake motions of magnitude obtained by adding the standard deviation to the average value, and apply these to the design earthquake motion estimation system 1 of the above embodiment. In this way, when performing earthquake resistance evaluation of a building, it is possible to design it according to the required earthquake resistance grade.

[0090] In the above embodiment, a response surface is constructed using each uncertain source characteristic as an explanatory variable and the seismic motion evaluation result as a target variable. Then, a grid search is used as a search and estimation method for the response surface to extract values ​​for multiple uncertain source characteristics corresponding to the assumed seismic motion. The search and estimation method is not limited to grid search; random search or Bayesian optimization may also be used. When random search is used, the search is based on random sampling within the hyperparameter space, thereby reducing the calculation time even for a diverse search range. When Bayesian optimization is used, the hyperparameters to be next investigated are estimated based on past evaluation results, making it possible to approach the optimal result with fewer trials. In addition to this, it is possible to select and discard the configurations given in the above embodiment and modified examples, or to change them to other configurations as appropriate. [Explanation of symbols]

[0091] 1 Design earthquake motion estimation system 6 Expected earthquake motion designation section 2. Source characteristic input reception unit 7. Uncertainty source characteristic value extraction unit 3 Fault model generation section 8 Design earthquake motion estimation section 4 Earthquake motion evaluation part 100 Response surface 5. Response surface construction section

Claims

1. A design earthquake motion estimation system that estimates design earthquake motions to be used in the design of a building when the earthquake source characteristics set for the earthquake source include multiple uncertain earthquake source characteristics that have variations in values ​​and require consideration of uncertainty, comprising: a fault model generation unit that selects one value for each of the uncertainty seismic source characteristics from the values ​​that each of the plurality of uncertainty seismic source characteristics can take, and repeatedly sets the value in a fault model to generate a plurality of the fault models in which different values ​​are set; a seismic motion evaluation unit that evaluates seismic motion for each of the plurality of fault models; a response surface constructing unit that constructs a response surface in which each of the plurality of uncertain source characteristics is an explanatory variable and the evaluation result of the seismic motion is an objective variable, based on the relationship between the value selected for each of the plurality of uncertain source characteristics in each of the plurality of fault models and the evaluation result of the seismic motion; an uncertainty seismic source characteristic value extraction unit that searches for and extracts, by a predetermined search and estimation method, combinations of values ​​obtained by selecting one value for each of the uncertainty seismic source characteristics from the values ​​that each of the plurality of uncertainty seismic source characteristics can take, such that when each of the values ​​included in the combination is substituted for the corresponding explanatory variable of the response surface, the difference between the value of the objective variable and an externally specified value is within a threshold; a design earthquake motion estimation unit that generates a design fault model by setting each of the uncertainty earthquake source characteristics to the value included in the extracted combination, and estimates the design earthquake motion using the design fault model; and A design earthquake motion estimation system comprising:

2. the response surface constructing unit expresses the objective variable using a plurality of the explanatory variables by polynomial approximation based on the relationship; The response surface is realized as a quadratic equation including quadratic terms corresponding to each of the plurality of explanatory variables and an interaction term obtained by multiplying two different explanatory variables among the plurality of explanatory variables.

2. The design earthquake motion estimation system according to claim 1.

3. The uncertainty source characteristic value extraction unit sets a search range for each of the plurality of uncertainty source characteristics, generates a plurality of candidate values ​​that are different from each other within the search range, and then: extracting a combination of candidate values ​​obtained by selecting one candidate value for each of the plurality of uncertain seismic source characteristics from among the plurality of candidate values ​​for each of the plurality of uncertain seismic source characteristics, the combination of candidate values ​​being such that, when each of the candidate values ​​included in the combination of candidate values ​​is substituted for the corresponding explanatory variable on the response surface, the difference between the value of the objective variable and the specified value is minimized; For each of the plurality of uncertain seismic source characteristics, the search range is reset to a smaller range centered on the candidate value of the uncertain seismic source characteristic in the extracted combination of candidate values, and a plurality of candidate values ​​different from each other are regenerated within the search range. This is repeatedly performed until the difference between the value of the response variable calculated for the combination of the extracted candidate values ​​and the specified value falls within the threshold value.

3. The design earthquake motion estimation system according to claim 1 or 2.

4. The uncertainty source characteristic value extraction unit A plurality of the combinations are extracted by the predetermined search and estimation method, and then: performing kernel density estimation for each of the plurality of uncertain seismic source characteristics, calculating the maximum value of a probability density function, and calculating a weight for each of the plurality of uncertain seismic source characteristics based on the maximum value; For each of the plurality of combinations, calculate a likelihood score by calculating the sum of the products of the probability densities obtained by the kernel density estimation corresponding to the values ​​of the uncertain seismic source characteristics included in the combination and the weights of the uncertain seismic source characteristics; further extracting one of the combinations by selecting the combination with the maximum likelihood score; The design earthquake motion estimation unit generates the design fault model for the one combination and estimates the design earthquake motion using the design fault model.

3. The design earthquake motion estimation system according to claim 1 or 2.

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