Method for estimating vibration characteristics of building, program, and system for estimating vibration characteristics of building

Abstract

To estimate the vibration characteristics of a building with high accuracy.SOLUTION: A device for estimating vibration characteristic 100 comprises: a target transfer function calculation unit 150 which calculates a target transfer function at each response position where a vibration sensor is installed from responses of the vibration sensors installed at multiple floors of a building; a target eminent response extraction unit 152 which extracts a target eminent response for a vibration mode where the peak of the target transfer function is eminent at each response position; an estimated transfer function calculation unit 154 which calculates an estimated transfer function of a response point corresponding to the response position from a forward analysis model of the building; an estimated eminent response extraction unit 156 which extracts an estimated eminent response for the same vibration mode as the corresponding response position at each response point from the estimated transfer function; and an inverse analysis unit 158 which estimates a vibration parameter by repeating re-calculation of the estimated transfer function and re-extraction of the estimated eminent response by correcting the vibration parameter of the forward analysis model until an error vector between target eminent response and the estimated eminent response becomes equal to or less than an allowable error or reaches an upper limit frequency.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to a method, a program, and a system for estimating vibration properties of a building. [Background technology]

[0002] A technology relating to a vibration measuring device and a vibration measuring method for measuring vibrations of bridges, buildings, etc. is disclosed. This prior art is equipped with a measuring means having a sensor installed at one or two places on the structure, and an analyzing means for calculating the vibration mode of the structure based on the signal from the measuring means. The analyzing means calculates the primary and secondary vibration modes based on the signal from the measuring means when an impact is applied to the structure.

[0003] Non-Patent Document 1 discloses a technique for estimating the vibration response of an architectural structure using only one acceleration sensor. In this prior art, a single acceleration sensor installed on the top floor of a building is used to estimate the maximum story drift angle of the structure. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2015-183362 A [Non-patent literature]

[0005] [Non-Patent Document 1] Yuji Shinagawa and Akira Mita, "A Method to Estimate Vibration Response of Building Structures Using Only One Acceleration Sensor", Architectural Institute of Japan Technical Report Vol. 19, No. 42, 461-464, June 2013 Summary of the Invention [Problem to be solved by the invention]

[0006] In the technology of Non-Patent Document 1, the vibration response of a building structure is estimated using only one acceleration sensor, and therefore there is a limit to how accurately the vibration response can be estimated.

[0007] In view of the above, an object of the present invention is to estimate the vibration characteristics of a building with higher accuracy than when only one acceleration sensor is used. [Means for solving the problem]

[0008] The first aspect is a method for estimating vibration properties of a building, comprising: a target transfer function calculation step of calculating a target transfer function for each response position at which a vibration sensor is installed on any multiple floors of a building from the response of the vibration sensor; a target dominant response extraction step of extracting a target dominant response of a vibration mode in which a peak of the target transfer function is dominant for each response position; an estimated transfer function calculation step of calculating an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated dominant response extraction step of extracting, from the estimated transfer function, an estimated dominant response of the same vibration mode as the response position corresponding to each response point; and an inverse analysis step of correcting vibration parameters of the forward analysis model and repeating recalculation of the estimated transfer function and reextraction of the estimated dominant response until an error vector between the target dominant response and the estimated dominant response becomes equal to or less than an allowable error or until an upper limit number of times is reached, thereby estimating the vibration parameters.

[0009] In the first aspect of the method for estimating vibration properties of a building, a target predominant response of a vibration mode with a predominant peak is extracted for each response position from a target transfer function obtained for each response position where a vibration sensor is installed from the response of the vibration sensor installed on multiple floors. Also, an estimated transfer function of a response point corresponding to the response position is calculated from a forward analysis model created by simulating the building, and an estimated predominant response of the same vibration mode as the corresponding response position for each response point is extracted from the estimated transfer function. Then, a reverse analysis is performed until the error vector between the target predominant response and the estimated predominant response falls below an allowable error or reaches an upper limit number of times, and vibration parameters are estimated to estimate the vibration properties of the building. Therefore, the vibration properties of the building can be estimated with high accuracy compared to the case where only one acceleration sensor is used.

[0010] A second aspect is the method for estimating vibration properties of a building according to the first aspect, wherein the target dominant response extraction step includes extracting the target dominant response of the vibration mode in which a peak is most prominent.

[0011] In the second aspect of the method for estimating vibration properties of a building, the target predominant response of the vibration mode with the most prominent peak is also extracted, so that the vibration properties of the building can be estimated with high accuracy compared to the case where the target predominant response of the vibration mode with the most prominent peak is not included at all.

[0012] A third aspect is a method for estimating vibration characteristics of a building described in the first or second aspect, wherein, in the target dominant response extraction process, the response position where there is no peak in the target transfer function is extracted as the target dominant response between any two vibration points.

[0013] In the method for estimating vibration properties of a building according to the third aspect, even if there is a response position without a peak, the response position is used, and therefore the vibration properties of the building can be estimated with high accuracy compared to a case where a response position without a peak is not used when such a response position is present.

[0014] A fourth aspect is a program that causes a computer to execute the following steps: a target transfer function calculation step of calculating a target transfer function for each response position at which a vibration sensor is installed from the response of the vibration sensor installed on any multiple floors of a building; a target dominant response extraction step of extracting a target dominant response of a vibration mode in which the peak of the target transfer function is dominant for each response position; an estimated transfer function calculation step of calculating an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated dominant response extraction step of extracting, from the estimated transfer function, an estimated dominant response of the same vibration mode as the response position corresponding to each response point; and an inverse analysis step of modifying vibration parameters of the forward analysis model and repeatedly recalculating the estimated transfer function and reextracting the estimated dominant response until an error vector between the target dominant response and the estimated dominant response becomes equal to or less than an allowable error or until an upper limit number of times is reached, thereby estimating the vibration parameters.

[0015] As with the first aspect, the program of the fourth aspect can estimate the vibration characteristics of a building with high accuracy compared to the case where only one acceleration sensor is used.

[0016] A fifth aspect is a system for estimating vibration properties of a building, comprising: a target transfer function calculation unit that calculates a target transfer function for each response position at which a vibration sensor is installed from the response of the vibration sensor installed on any multiple floors of the building; a target dominant response extraction unit that extracts a target dominant response of a vibration mode at which the peak of the target transfer function is dominant for each response position; an estimated transfer function calculation unit that calculates an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated dominant response extraction unit that extracts, for each response point, an estimated dominant response of the vibration mode that is the same as the response position corresponding to the response point from the estimated transfer function; and an inverse analysis unit that modifies vibration parameters of the forward analysis model and repeatedly recalculates the estimated transfer function and reextracts the estimated dominant response until an error vector between the target dominant response and the estimated dominant response becomes equal to or less than an allowable error or reaches an upper limit number of times, thereby estimating the vibration parameters.

[0017] As with the first aspect, the vibration properties estimation system of the fifth aspect can estimate the vibration properties of a building with higher accuracy than when only one acceleration sensor is used. Effect of the Invention

[0018] According to the present invention, it is possible to estimate the vibration characteristics of a building with high accuracy, compared to the case where only one acceleration sensor is used. [Brief description of the drawings]

[0019] [Figure 1] FIG. 2 is a schematic diagram showing an example of a building to be estimated; [Diagram 2] FIG. 2 is a model diagram showing an example of a forward analysis model (SR model) of the building in FIG. 1. [Diagram 3] 1 is a block diagram showing an example of a hardware configuration of a vibration characteristic estimation device according to an embodiment; [Figure 4]1 is a block diagram showing an example of a functional configuration of a vibration characteristics estimation device according to an embodiment; [Diagram 5] 5 is a flowchart illustrating an example of a procedure of a vibration characteristic estimation process according to the embodiment. [Figure 6] In the vibration characteristic estimation process of the embodiment, (A) is a diagram showing a state in which the upper structure is shaking to the right due to an assumed vibration wave input from the ground to the foundation in the forward analysis model of Figure 2, (B) is a graph showing the target transfer function of the rooftop response position and the target transfer function of the first floor response position, and (C) is a graph showing a schematic diagram of the target predominant response of the rooftop response position and the target predominant response of the first floor response position being extracted. [Figure 7] In the vibration characteristic estimation process of the embodiment, (A) is a diagram showing a state in which the upper structure is shaking to the right due to an assumed vibration wave input from the ground to the foundation in the forward analysis model of Figure 2, which is the same as Figure 6 (A), (B) is a graph showing the estimated transfer function of the response point corresponding to the response position of the roof and the estimated transfer function of the response point corresponding to the response position of the first floor, and (C) is a graph showing a schematic diagram of the extraction of the estimated dominant response of the response point on the roof and the estimated dominant response of the response point on the first floor. [Figure 8] In the vibration characteristic estimation process of the embodiment, (A) is a graph showing the target dominant response, the estimated dominant response, and the error vector before back analysis, and (B) is a graph showing the target dominant response, the estimated dominant response, and the error vector after back analysis. [Figure 9] In the vibration characteristic estimation process of the comparative example, (A) is a diagram showing the state in which the upper structure is shaking to the right due to an assumed vibration wave input from the ground to the foundation in the forward analysis model of Figure 2, (B) is a graph showing the target transfer function of the rooftop response position and the target transfer function of the first floor response position, and (C) is a schematic graph showing the extraction of the target dominant response of the rooftop response position and the target dominant response of the first floor response position. [Figure 10]In the vibration characteristic estimation process of the comparative example, (A) is a diagram of the state in which the upper structure is shaking to the right due to an assumed vibration wave input from the ground to the foundation in the forward analysis model of Figure 2, which is the same as Figure 6 (A), (B) is a graph showing the estimated transfer function of the response point corresponding to the response position of the roof and the estimated transfer function of the response point corresponding to the response position of the first floor, and (C) is a graph showing a schematic diagram of the extraction of the estimated dominant response of the roof response point and the estimated dominant response of the response point on the first floor. [Figure 11] In the vibration characteristic estimation process of the comparative example, (A) is a graph showing the target predominant response, the estimated predominant response, and the error vector before back analysis, and (B) is a graph showing the target predominant response, the estimated predominant response, and the error vector after back analysis. [Figure 12] FIG. 1 is a model diagram showing a forward analysis model (SR model) in an analysis example. [Figure 13] (A) is a table showing the building specifications set in the direct analysis model, (B) is a table showing the specifications of the dynamic ground spring, and (C) is a table showing the initial values ​​of the vibration parameters. [Figure 14] In the input seismic wave under consideration, (A) is the acceleration response spectrum, (B) is the Fourier spectrum, and (C) is the acceleration time history. [Figure 15]The target transfer function and target predominant response of each response position for the input earthquake wave are shown. (A-1) is the target transfer function and target predominant response of the primary vibration mode of the roof response position in the primary mode analysis, (A-2) is the target transfer function and target predominant response of the primary vibration mode of the first floor response position in the primary mode analysis, (A-3) is the target transfer function and target predominant response of the primary vibration mode of the foundation response position C in the primary mode analysis, and (B-1) is the target transfer function and target predominant response of the primary vibration mode of the roof response position in the higher mode analysis. (B-1) is the target transfer function and target predominant response of the second vibration mode at the roof response location in the higher mode analysis, (B-2) is the target transfer function and target predominant response of the second vibration mode at the roof response location in the higher mode analysis, (B-3) is the target transfer function and target predominant response of the third vibration mode at the first floor response location in the higher mode analysis, (B-4) is the target transfer function and target predominant response of the fourth vibration mode at the first floor response location in the higher mode analysis, and (B-5) is the target transfer function and target predominant response of the fifth vibration mode at the foundation response location C in the higher mode analysis. [Figure 16] The figures show the estimated transfer function and estimated predominant response of the response point before inverse analysis for the input seismic wave. (A-1) is the estimated transfer function and estimated predominant response of the primary vibration mode of the roof response point in the primary mode analysis. (A-2) is the estimated transfer function and estimated predominant response of the primary vibration mode of the response position of the first floor in the primary mode analysis. (A-3) is the estimated transfer function and estimated predominant response of the primary vibration mode of the response point C of the foundation in the primary mode analysis. (B-1) is the estimated transfer function and estimated predominant response of the primary vibration mode of the roof response point in the higher mode analysis. (B-1) is the estimated transfer function and estimated predominant response of the second order vibration mode of the roof response point in the higher mode analysis, (B-2) is the estimated transfer function and estimated predominant response of the second order vibration mode of the roof response point in the higher mode analysis, (B-3) is the estimated transfer function and estimated predominant response of the third order vibration mode of the first floor response point in the higher mode analysis, (B-4) is the estimated transfer function and estimated predominant response of the fourth order vibration mode of the first floor response point in the higher mode analysis, and (B-5) is the estimated transfer function and estimated predominant response of the fifth order vibration mode of the foundation response point C in the higher mode analysis. [Figure 17]The figures show the estimated transfer function and the estimated predominant response after the inverse analysis of the response point for the input seismic wave. (A-1) is the estimated transfer function and the estimated predominant response of the primary vibration mode of the rooftop response point in the primary mode analysis. (A-2) is the estimated transfer function and the estimated predominant response of the primary vibration mode of the response position of the first floor in the primary mode analysis. (A-3) is the estimated transfer function and the estimated predominant response of the primary vibration mode of the response point C of the foundation in the primary mode analysis. (B-1) is the estimated transfer function and the estimated predominant response of the primary vibration mode of the rooftop response point in the higher mode analysis. (B-1) is the estimated transfer function and estimated predominant response of the second order vibration mode of the roof response point in the higher mode analysis, (B-2) is the estimated transfer function and estimated predominant response of the second order vibration mode of the roof response point in the higher mode analysis, (B-3) is the estimated transfer function and estimated predominant response of the third order vibration mode of the first floor response point in the higher mode analysis, (B-4) is the estimated transfer function and estimated predominant response of the fourth order vibration mode of the first floor response point in the higher mode analysis, and (B-5) is the estimated transfer function and estimated predominant response of the fifth order vibration mode of the foundation response point C in the higher mode analysis. [Figure 18] 1 is a table showing a list of target dominant responses of a target transfer function and estimated dominant responses of an estimated transfer function. [Figure 19] Graph (A) shows the convergence of RSS (residual sum of squares) error in first-order vibration mode analysis, and graph (B) shows the convergence of RSS (residual sum of squares) error in higher-order vibration mode analysis. [Figure 20] These are graphs showing the true values ​​(actual measured values), initial values, and optimal values ​​(estimated values) of vibration parameters in primary vibration mode analysis. (A) is a graph of the shear rigidity of the seismic isolation layer to the third floor of the building, (B) is a graph of the damping constant of the seismic isolation layer to the third floor of the building, and (C) is a graph of the rotational ground spring. [Figure 21] These are graphs showing the true values ​​(actual measured values), initial values, and optimal values ​​(estimated values) of vibration parameters in higher-order vibration mode analysis. (A) is a graph of the shear rigidity of the seismic isolation layer to the third floor of the building, (B) is a graph of the damping constant of the seismic isolation layer to the third floor of the building, and (C) is a graph of the rotational ground spring. [Figure 22]13A and 13B are conceptual diagrams of the building response of the forward analysis model in the analysis example. (A) is a conceptual diagram when subjected to earthquake motion, and (B) is a conceptual diagram when subjected to an excitation force on the top of the building due to external wind forces, etc. [Figure 23] (A) is the target transfer function of the horizontal response of the foundation to an input when subjected to external forces such as wind, and (B) is the estimated transfer function of the horizontal response of the foundation when the vibration parameters are at their initial values. [Figure 24] (A) is a graph superimposing the estimated transfer function after back analysis, the estimated transfer function before back analysis, and the target transfer function, (B) is a graph showing the change in the norm of the error vector between the target dominant response and the estimated dominant response, and (C) is a graph showing the estimated stiffness and damping coefficient of the horizontal ground spring. [Diagram 25] 13 is a table showing a comparison of a list of eigenvalue frequencies obtained by real eigenvalue analysis using vibration parameters after inverse analysis, between true values ​​(actual measured values) and eigenvalues ​​similarly obtained using first-order mode analysis and higher-order mode analysis. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] <Embodiment> A vibration characteristics estimating device as an example of a vibration characteristics estimating system will be described with reference to the drawings.

[0021] [building] First, the configuration of a building that is the subject of estimation for which the vibration properties estimation device estimates vibration properties will be described. In this specification, the horizontal direction will be illustrated and described as being along the X direction, but in actual vibration property estimation, the orthogonal X and Y directions are estimated.

[0022] The "vibration characteristics of a building" refers to vibration parameters such as rigidity, damping constant, and damping coefficient in an analytical model used when estimating the state of damage caused by an earthquake to a building, including its foundation, as well as natural mode characteristics that can be calculated based on these vibration parameters.

[0023] 1 is a schematic diagram of a building 10 in this embodiment. The building 10 is a reinforced concrete building with a base isolation structure, which includes a foundation 12, a seismic isolation layer 20 provided on the foundation 12, and an upper structure 14 provided on the seismic isolation layer 20. The upper structure 14 has multiple floors, three above ground in this embodiment: a first floor 21, a second floor 22, and a third floor 23, and the upper part of the third floor 23 is the rooftop 24. The seismic isolation layer 20 is provided with seismic isolation bearings 18 such as laminated rubber bearings and damping devices such as dampers (not shown).

[0024] The building to be estimated in the present invention is not limited to a reinforced concrete structure and a base isolation structure, but may be of other structures such as an intermediate isolation structure, a vibration control structure, and an earthquake-resistant structure. In other words, the building to be estimated in the present invention may be of any structure.

[0025] Vibration sensors 50A, 50B are installed on the first floor 21 and rooftop 24 of the upper structure 14. Since vibration sensor 50A and vibration sensor 50B are the same, when it is possible to explain them without distinguishing between them, the A and B after the reference number 50 may be omitted and they may be referred to as vibration sensor 50.

[0026] The vibration sensor 50 of this embodiment is composed of an acceleration sensor that can detect responses with three degrees of freedom in the horizontal direction (X direction and Y direction) and the vertical direction (Z direction) and six degrees of freedom in the rotational direction calculated from each response, and detects building vibration data, which is time-series data of the vibration response at the position where it is installed.

[0027] In this embodiment, the vibration sensors 50A, 50B are installed at least one of the center of rigidity and center of gravity on the first floor 21 and rooftop 24 of the superstructure 14 of the building 10. In this embodiment, the superstructure 14 is an orthogonal building, and the center of rigidity and center of gravity coincide with each other, so the vibration sensors 50 are installed approximately in the center when viewed from above.

[0028] The positions where the vibration sensors 50A, 50B are installed on the first floor 21 and rooftop 24 of the building 10 are response positions 51A, 51B, which will be described later. Note that when there is no need to distinguish between the response positions 51A and 51B, the "A" and "B" after the reference numeral 51 may be omitted and the response position may be referred to as 51.

[0029] The vibration sensors 50 must be installed on two or more different floors. However, the floors on which they are installed may be appropriately selected depending on the structure of the building 10 to be estimated and the range of vibration mode orders to be considered. When considering the entire building 10, it is desirable to install the sensors on the rooftop 24, which is the top floor, and the first floor 21, which is the bottom floor.

[0030] Fig. 2 shows a forward analysis model 11 (described later) that simulates a building 10 in this embodiment. In the figure, the symbol k is the shear stiffness k of the building 10, and the symbol h is the damping constant h of the building 10. The symbol KR is the stiffness KR of the rocking ground spring, and the symbol CR is the damping coefficient CR of the rocking ground spring. The shear stiffness k of the building 10, the damping constant h of the building 10, the stiffness KR of the rocking ground spring, and the damping coefficient CR of the rocking ground spring are the vibration parameters of this embodiment.

[0031] This forward analysis model 11 is an SR model, which is an example of an earthquake response analysis model created using structural software and finite element codes used in earthquake resistance analysis, etc. In the forward analysis model 11, vibration parameters and their initial values ​​are set in advance.

[0032] Note that positions corresponding to response positions 51A, 51B (see FIG. 1) where vibration sensors 50A, 50B are installed in the forward analysis model 11 are referred to as response points 52A, 52B. As with the response positions 51A, 51B, when there is no need to distinguish between them, the "A" and "B" after the reference numeral 52 may be omitted and the response point may be referred to as 52.

[0033] [Vibration property estimation device] Next, a description will be given of a configuration of a vibration property estimating device 100 as an example of a vibration property estimating system. The vibration property estimating device 100 is, for example, an information processing device such as a personal computer or a server computer.

[0034] As shown in FIG. 3, the vibration characteristics estimation device 100 includes a CPU (Central Processing Unit) 102, a memory 104 as a temporary storage area, a non-volatile storage unit 106, an input unit 108 such as a keyboard and a mouse, a display unit 110 such as a liquid crystal display, a medium read / write device (R / W) 112, and a communication interface (I / F) unit 114.

[0035] The CPU 102, memory 104, storage unit 106, input unit 108, display unit 110, medium reading / writing device 112, and communication I / F unit 114 are connected to one another via a bus 101. The medium reading / writing device 112 reads information written in a recording medium 116 and writes information to the recording medium 116.

[0036] The storage unit 106 is realized by a hard disk drive (HDD), a solid state drive (SSD), a flash memory, etc. A vibration characteristic estimation program 106A is stored in the storage unit 106 as a storage medium.

[0037] The vibration characteristics estimation program 106A is stored in the memory unit 106 by setting the recording medium 116 on which the vibration characteristics estimation program 106A is written in the medium reading and writing device 112 and causing the medium reading and writing device 112 to read the vibration characteristics estimation program 106A from the recording medium 116.

[0038] The CPU 102 reads out the vibration characteristic estimation program 106A from the storage unit 106, loads it into the memory 104, and sequentially executes the processes of the vibration characteristic estimation program 106A. Note that the vibration characteristic estimation program 106A may be composed of a plurality of programs.

[0039] Next, the functional configuration of the vibration characteristics estimating device 100 according to this embodiment will be described with reference to FIG.

[0040] 4, the vibration characteristics estimation device 100 is configured to have, as its functional components, a target transfer function calculation section 150, a target dominant response extraction section 152, an estimated transfer function calculation section 154, an estimated dominant response extraction section 156, and an inverse analysis section 158. Each functional component is realized by the CPU 102 reading and executing the vibration characteristics estimation program 106A.

[0041] In the following description of the building 10 and the direct analysis model 11, please refer to Figures 1 and 2 as appropriate.

[0042] The target transfer function calculation unit 150 calculates a target transfer function for each response position 51 where the vibration sensor 50 is installed from the response of the vibration sensor 50 installed on any of a plurality of floors (the first floor 21 and the rooftop 24 in this example) of the building 10. The target transfer function calculation unit 150 calculates a target transfer function for each response position 51 using building vibration data of various vibrations during normal times (for example, vibrations caused by vibrations caused by vehicle vibrations, wind external forces, etc.) and building vibration data during an earthquake that does not damage the building 10, which are obtained by the vibration sensors 50 installed on the building 10. The building vibration data is collected and stored in advance. In this embodiment, the building vibration data stored via a recording medium 116 such as a USB memory is input to the vibration property estimation device 100, but is not limited to this.

[0043] The "target transfer function" is a transfer function calculated based on the response of the vibration sensor 50, and the "transfer function" is a function that represents the relationship between the input and output of the system. Also, the "target" refers to a target that approaches the "estimated transfer function, which is a transfer function obtained by calculation of a forward analysis model" described later.

[0044] The transfer function calculated based on the response of the vibration sensor 50, i.e., the target transfer function, can be calculated using existing calculation methods. For example, when earthquake motion is input from the ground G to the building 10 and the response of the vibration sensor 50B on the first floor 21 and the vibration sensor 50A on the rooftop 24 is output, the responses of the vibration sensors 50A and 50B are Fourier transformed to obtain a Fourier spectrum ratio. The transfer function was calculated from this Fourier spectrum ratio. The vibration data of the earthquake motion (input) may be collected by using a vibration sensor on the ground G or the foundation 12 near the building 10 at the same time as the building vibration data, or the building vibration data on the first floor 21 may be used. A specific calculation example will be described later in the analysis example.

[0045] The target dominant response extraction unit 152 extracts a target dominant response of a vibration mode in which the peak of the target transfer function is dominant for each response position 51. The "target dominant response" is a dominant response of a vibration mode in which the peak of each response position 51 is dominant, and more specifically, is the peak frequency and peak amplitude of the vibration mode to be extracted.

[0046] Any method may be used to extract the target dominant response. In this embodiment, the target dominant response is extracted using a bandpass filter (hereinafter referred to as "BPF") that passes only the required frequency band and does not pass (attenuates) other frequencies.

[0047] A response position 51 where there is no clear peak in the target transfer function is extracted as a target predominant response between two arbitrary vibration points. An example of extracting a response position 51 where there is no peak in the target transfer function will be described in an analysis example.

[0048] The method for selecting the vibration mode for extracting the target dominant response at each response point will be described in detail later.

[0049] The estimated transfer function calculation unit 154 calculates estimated transfer functions of the response points 52A and 52B corresponding to the response positions 51A and 51B from the forward analysis model 11 created by simulating the building 10.

[0050] The forward analysis model 11 is created separately by the user. When creating the forward analysis model 11, vibration parameters and initial values ​​such as the shear stiffness k of the building 10, the damping constant h of the building 10, the stiffness KR of the rocking ground spring, and the damping coefficient CR of the rocking ground spring are set. The initial values ​​are arbitrary and may be set appropriately based on the user's knowledge, but if design values ​​and test results are available, they may be set with reference to them. For example, if vibration dampers are installed, the initial values ​​are set with reference to their specifications, etc.

[0051] The estimated predominant response extracting unit 156 extracts, from the estimated transfer function, an estimated predominant response of the same vibration mode as the response point 52 corresponding to each response position 51. The method of extracting the estimated predominant response is the same as the method of extracting the target predominant response.

[0052] The inverse analysis unit 158 ​​estimates the vibration parameters by modifying the vibration parameters of the forward analysis model, repeating recalculation of the estimated transfer function and reextraction of the estimated predominant response until the error vector between the target predominant response and the estimated predominant response becomes equal to or less than the allowable error or until the upper limit number of times is reached.

[0053] Specifically, if the value of the target predominant response is A and the value of the estimated predominant response is B, the "error vector" is |(AB) / A| and A is the normalized value.

[0054] Since there are a plurality of target outstanding responses and estimated outstanding responses, an error vector is calculated for each and recalculated until the residual sum of squares (RSS) of each error vector falls below the allowable error or reaches the upper limit number of times. Note that the setting of the allowable error is not limited to this. For example, the allowable error may be set for the average value of the residual sum of squares.

[0055] Moreover, the allowable error and the upper limit number of times may be appropriately set based on the user's knowledge, etc. The correction of the vibration parameters is appropriately set depending on the method used for the inverse analysis.

[0056] It should be noted that "inverse analysis" refers to an analysis in which unknown analytical conditions, in this example vibration parameters, are estimated from known results, in this example building vibration data detected by the vibration sensor 50 of the building 10.

[0057] The inverse analysis method includes an inverse formulation method, an output error method, and a minimum variance estimation method. The inverse analysis program is incorporated in the vibration property estimation program 106A.

[0058] [Vibration characteristics estimation processing] Next, the vibration property estimation process executed by the vibration property estimation program 106A of the vibration property estimation device 100 will be described with reference to the flowchart of FIG.

[0059] First, in step S100, the CPU 102 (see FIG. 3) acquires responses from the vibration sensors 50A and 50B installed on any of a plurality of floors of the building 10, that is, the first floor 21 and the rooftop 24 in this embodiment.

[0060] The response of the vibration sensor 50 is building vibration data, which is time-series data of the vibration response detected by the vibration sensor at the response position 51 where the vibration sensor 50 is provided. In step S100, the CPU 102 (see FIG. 3) acquires the accumulated building vibration data.

[0061] In step S102, the CPU 102 calculates a target transfer function from the acquired response of the vibration sensor. In step S104, the CPU 102 extracts, for each response position 51, a target dominant response of a vibration mode in which a peak of the target transfer function is dominant.

[0062] In step S106, the CPU 102 calculates an estimated transfer function of a response point 52 corresponding to the response position 51 from the forward analysis model 11 created by simulating the building 10. In step S108, the CPU 102 extracts an estimated predominant response of the estimated transfer function for each response point 52. In step S110, the CPU 102 calculates an error vector between the target predominant response and the estimated predominant response.

[0063] In step S112, the CPU 102 determines whether the error vector is equal to or smaller than the allowable error. If the error vector is equal to or smaller than the allowable error (Yes), the process ends. If the error vector is larger than the allowable error (No), the process proceeds to step S114.

[0064] In step S114, CPU 102 determines whether the number of calculations of the error vector is equal to or greater than the upper limit. If the number of calculations is equal to or greater than the upper limit (Yes), the process ends, and if the number of calculations is less than the upper limit (No), the process proceeds to step S116.

[0065] In step S116, the CPU 102 corrects the vibration parameters of the direct analysis model, and the process returns to step S106.

[0066] [Calculation of target transfer function] Next, the extraction of the target transfer function will be described in detail using a concrete example.

[0067] Fig. 6(A) shows the forward analysis model 11 of the building 10 in Fig. 2. In this example, the building 10 is shown in a state in which the upper structure 14 is shaking to the right due to a vibration wave S assumed to have been input from the ground G to the foundation 12. Fig. 6(B) shows the target transfer function MA of the response position 51A on the rooftop 24 where the vibration sensor 50A (see Fig. 2) is installed, and the target transfer function MB of the response position 51B on the first floor 21 where the vibration sensor 50B (see Fig. 2) is installed.

[0068] As described above, the Fourier spectral ratio (output / input) was calculated by Fourier transforming the response at response position 51B of vibration sensor 50B on the first floor 21 and the response at response position 51A of vibration sensor 50A on the rooftop 24, which is the top floor, and the target transfer functions MA and MB were calculated from this Fourier spectral ratio. The vertical axis in the graph represents the absolute value of the Fourier spectral ratio, and the horizontal axis represents the frequency.

[0069] [Extraction of target dominant responses] Next, the extraction of the target dominant response will be described in detail using a concrete example.

[0070] Fig. 6(C) is a schematic diagram showing the target dominant responses MP1, MP2, and MP3 of the vibration modes in which the peaks of the target transfer functions MA and MB at the response positions 51A and 51B are dominant. As in Fig. 6(B), the vertical axis in the graph is the absolute value of the Fourier spectrum ratio, and the horizontal axis is the frequency.

[0071] In this example, the target transfer function MA of response location 51A on the rooftop 24 extracts the target predominant response MP1 of the primary vibration mode P1 and the target predominant response MP2 of the secondary vibration mode P2, and the target transfer function MB of response location 51B on the first floor 21 extracts the target predominant response MP3 of the tertiary vibration mode P3.

[0072] As mentioned above, in this example, the BPF was used to extract the target dominant responses MP1, MP2, and MP3. By passing the signals through the BPF in this way, a single peak is generated for each vibration mode, and the frequency and Fourier spectrum ratio of that single peak is the target dominant response.

[0073] The target dominant response MP1 has a frequency Mf1 and a Fourier spectral ratio Ma1. The target dominant response MP2 has a frequency Mf2 and a Fourier spectral ratio Ma2. The target dominant response MP3 has a frequency Mf3 and a Fourier spectral ratio Ma3.

[0074] The vibration mode for extracting the target dominant response at each response position 51 is selected according to the following rules.

[0075] (Rule A) A different vibration mode is selected for each response point. From another perspective, the same vibration mode is not selected repeatedly at each response point.

[0076] (Rule B) The vibration mode with the most prominent peak of the target transfer function is also selected. From another perspective, the target predominant response of the vibration mode of the response point with the most prominent peak of the target transfer function is also extracted. In this example, the primary vibration mode P1 and the secondary vibration mode P2 have the most prominent peak value (in this example, the absolute value of the Fourier spectrum ratio) at the response position 51A, and the tertiary vibration mode P3 has the most prominent peak value (in this example, the absolute value of the Fourier spectrum ratio) at the response position 51B. Therefore, the response position 51A extracts the target predominant response MP1 of the primary vibration mode P1 and the target predominant response MP2 of the secondary vibration mode M1, and the response position 51B extracts the target predominant response MP3 of the tertiary vibration mode P3.

[0077] (Rule C) The sum of the response contribution rates of the stimulus functions of each vibration mode is set to a predetermined percentage or more, in this example, 99% or more. In this example, the sum of the response contribution rates of the stimulus functions from the first vibration mode P1 to the third vibration mode P3 of the target transfer function of the response position 51A and the response position 51B is 99% or more for each position. If it is less than 99%, the target predominant response of the fourth or higher vibration mode is extracted. In addition, the "response contribution rate of the stimulus function" is the ratio of the stimulus function at each position of the extracted vibration mode to the sum of the stimulus functions at each response position, which is set to 1.

[0078] From another perspective, since the contribution rate of each mode in the stimulus function differs at each response position, regardless of whether or not extraction is performed using the transfer function, the contribution rate is set to a certain percentage or more at each response position for the maximum mode order, in this example, 99% or more.

[0079] For example, the following contribution rates are assumed: On rooftop 24, the contribution rate is 90% for the primary vibration mode, 99% for the primary and secondary vibration modes, and 100% for the primary, secondary, and tertiary vibration modes. On the first floor 21, the contribution rate is 80% for the primary vibration mode, 90% for the primary and secondary vibration modes, and 99% for the primary, secondary and tertiary vibration modes.

[0080] At this time, by taking the primary and secondary vibration modes on the rooftop 24, which has a large predominant response, the primary and secondary vibration modes of the first floor 21 are enveloped and extracted, and conversely, by taking the tertiary vibration mode of the first floor 21, the tertiary vibration mode of the rooftop 24 is enveloped and extracted. Therefore, different vibration modes are extracted at each response position.

[0081] (Rule D) This includes the primary vibration mode and higher order vibration modes from the secondary vibration mode onwards.

[0082] (Rule E) As one moves from the top to the bottom of the building 10, higher vibration modes are selected.

[0083] In this example, the vibration mode is selected so as to satisfy all of the above rules (rule A) to (rule E), but the present invention is not limited to this.

[0084] In addition, in this example, the vibration mode to be extracted at each response position 51 is selected by the user while looking at the target transfer functions MA and MB, and input using the input unit 108 of the vibration characteristics estimation device 100, but this is not limited to this. Also, the setting of the BPF range is determined by the user while looking at the target transfer functions MA and MB, and input using the input unit 108 of the vibration characteristics estimation device 100, but this is not limited to this. The CPU 102 may analyze the target transfer functions MA and MB and perform the same operations.

[0085] Here, if there is a response position 51 where the target transfer function does not have a peak, the frequency between any two or more points of the target transfer function of this response position 51 is extracted as the target dominant response. The target transfer function does not have a peak when an excitation force is applied to the upper part of the building 10 due to external wind force or the like. In this case, the target dominant response can be determined by the user specifying two appropriate frequencies without using the BPF. However, it is desirable to select the two frequencies according to a rule that includes the maximum and the frequencies around the middle so that they are not too close to each other. As described above, an example of extracting a response position 51 where the target transfer function does not have a peak will be described in an analysis example.

[0086] [Extraction of estimated dominant responses] Next, the extraction of the estimated predominant response will be described in detail using a concrete example.

[0087] Fig. 7(A) is a diagram of the same forward analysis model 11 as Fig. 6(A). Fig. 7(B) shows an estimated transfer function SA of a response point 52A corresponding to a response position 51A on the rooftop 24 and an estimated transfer function SB of a response point 52B corresponding to a response position 51B on the first floor 21.

[0088] 7(C) is a schematic diagram showing the extraction of estimated predominant responses SP1, SP2, SP3 of vibration modes in which the peaks of the estimated transfer functions SA, SB at the response positions 51A, 52B are predominant. For each response point 52, the estimated predominant responses SP1, SP2, SP3 of the same vibration mode as the corresponding response position 51 are extracted from the estimated transfer functions SA, SB. That is, the response point 52A corresponding to the response position 51A on the rooftop 24 extracts the estimated predominant responses SP1, SP2 of the primary vibration mode P1 and the secondary vibration mode P2, and the response point 52B corresponding to the response position 51B on the first floor 21 extracts the estimated predominant response SP3 of the tertiary vibration mode P3. The input and BPF range of the vibration mode to be extracted at each response point 52 are the same as those used to extract the target predominant response.

[0089] Incidentally, specific examples of the equation of motion and the estimated transfer function of the forward analysis model 11 will be described later.

[0090] [Back analysis] Next, the reverse analysis method will be explained in detail using a concrete example.

[0091] The error vector between the corresponding target dominant response and the estimated dominant response is calculated. As described above, if the target dominant response value is A and the estimated dominant response value is B, the error vector is expressed as follows: |(AB) / A| and A is the normalized value.

[0092] In this example, Error vector G1 = |target dominant response MP1 - estimated dominant response SP1| / target dominant response MP1 Error vector G2 = |target dominant response MP2 - estimated dominant response SP2| / target dominant response MP2 Error vector G3 = |target dominant response MP3-estimated dominant response SP3| / target dominant response MP3 and Set the tolerance for the residual sum of squares of error vectors G1, G2, and G3.

[0093] [Effect] Next, the operation of this embodiment will be described.

[0094] In the vibration properties estimation device 100 of this embodiment, target predominant responses MP1, MP2, MP3 of the vibration mode having the predominant peak for each response position 51A, 51B are extracted from the target transfer functions MA, MB from the response position 51A of the vibration sensor 50A installed on the rooftop 24 on multiple floors, in this embodiment, and the response position 51B of the vibration sensor 50B installed on the first floor 21.

[0095] In addition, estimated transfer functions SA and SB of response points 52A and 52B corresponding to response positions 51A and 51B are calculated from a forward analysis model created by simulating building 10, and estimated dominant responses SP1, SP2, and SP3 of the same vibration mode as the corresponding response positions 51A and 51B are extracted for each response point 52A, 52B.

[0096] Then, vibration parameters are estimated by performing inverse analysis until the error vectors G1, G2, G3 between the target predominant responses MP1, MP2, MP3 and the estimated predominant responses SP1, SP2, SP3 become equal to or less than the allowable error or reach the upper limit number of times, thereby estimating the vibration characteristics of the building 10. Therefore, compared to the case where only one acceleration sensor is used, the vibration characteristics of the building 10 can be estimated with high accuracy.

[0097] Furthermore, in this embodiment, not only the primary vibration mode but also higher vibration modes, in this example, the secondary vibration mode and the tertiary vibration mode, are estimated, thereby making it possible to estimate the vibration properties of the building 10 with high accuracy.

[0098] Moreover, the vibration properties estimation device 100 of this embodiment extracts the target predominant response of the vibration mode with the most prominent peak as well. Therefore, the vibration properties of the building 10 can be estimated with high accuracy, compared to a case where the target predominant response of the vibration mode with the most prominent peak is not included at all.

[0099] In addition, the sum of the response contribution rates of the stimulus functions of the vibration modes is set to a predetermined percentage or more, in this example, 99% or more. Therefore, the vibration characteristics of the building 10 can be estimated with high accuracy compared to the case where the sum of the response contribution rates of the stimulus functions of the vibration modes is less than 99%.

[0100] Also, higher vibration modes are selected from the top to the bottom of the building 10. Usually, the influence of higher vibration modes increases from the top to the bottom of the building 10. Therefore, the vibration characteristics of the building 10 can be estimated with higher accuracy compared to the case where higher vibration modes are selected from the bottom to the top of the building 10. Depending on the degree of fixation of the ends of each structural member of the building, such as columns and beams, the influence of higher vibration modes may not increase from the top to the bottom. In that case, it is sufficient to select a floor where the influence of higher vibration modes is greater.

[0101] Next, it will be explained how the vibration properties of the building 10 can be estimated with high accuracy by estimating vibration parameters using the vibration properties estimation device 100 of this embodiment.

[0102] Figure 8(A) shows the target predominant responses MP1, MP2, MP3, the estimated predominant responses SP1, SP2, SP3, and the error vectors G1, G2, G3 before the inverse analysis. Figure 8(B) shows the target predominant responses MP1, MP2, MP3, the estimated predominant responses SP1, SP2, SP3, and the error vectors G1, G2, G3 after the inverse analysis.

[0103] In this way, the error vectors G1, G2, and G3 become smaller, and the estimated predominant responses SP1, SP2, and SP3 match or nearly match the target predominant responses MP1, MP2, and MP3. As a result, the estimated transfer functions SA and SB approach the target transfer functions MA and MB, and match or nearly match them.

[0104] Therefore, the vibration parameters of the forward analysis model 11 are close to those of the actual building 10, and the vibration characteristics of the building 10 are estimated with high accuracy, that is, the forward analysis model 11 is a model that estimates with high accuracy the vibration characteristics of the actual building 10. Then, by using the forward analysis model 11 of the vibration parameters after the inverse analysis, it is possible to predict and verify damage to the building 10 when it is hit by a major earthquake with high accuracy.

[0105] [Comparative Example] Next, it will be described how the vibration characteristics of the building 10 can be estimated with high accuracy by estimating not only the primary vibration mode but also higher vibration modes, in this example, the secondary and tertiary vibration modes.

[0106] 9 to 11 are comparative examples in which only the primary vibration mode is extracted from the target dominant response and the estimated dominant response, which are the same as the above example except that only the primary vibration mode is extracted from the target dominant response and the estimated dominant response.

[0107] Fig. 9(A) is a model diagram of the forward analysis model 11 of the building 10. Fig. 9(B) shows the target transfer function MA of the response position 51A and the target transfer function MB of the response position 51B. Fig. 9(C) is a schematic diagram showing the extraction of the target dominant responses HMP1A and HMP1B of the primary vibration mode P1 of the response positions 51A and 52B.

[0108] Fig. 10(A) is a model diagram of the forward analysis model 11 of the building 10. Fig. 10(B) shows an estimated transfer function SA of the response point 52A and an estimated transfer function SB of the response point 52B. Fig. 10(C) is a schematic diagram showing the extraction of estimated dominant responses HSP1A and HSP1B of the primary vibration mode of the response points 52A and 52B.

[0109] Fig. 11(A) shows the target predominant responses HMP1A and HMP1B, the estimated predominant responses HSP1A and HSP1B, and the error vectors HG1A and HG1B before the inverse analysis. Fig. 11(B) shows the target predominant responses HMP1A and HMP1B, the estimated predominant responses HSP1A and HSP1B, and the error vectors HG1A and HG1B after the inverse analysis.

[0110] In this way, the error vectors HG1A and HG1B become smaller and the estimated predominant responses HSP1A and HSP1B match or approximately match the target predominant responses HMP1A and HMP1B. However, it is not possible to estimate higher-order vibration modes other than the primary vibration mode.

[0111] In contrast, as described above, in this example, it is possible to estimate higher vibration modes other than the primary vibration mode as shown in Fig. 8(B). Therefore, it is understood that the vibration characteristics of the building 10 can be estimated with higher accuracy in this example (see Fig. 8(B)), which extracts higher vibration modes as well, than in the comparative example (see Fig. 11(B)), which extracts only the primary vibration mode.

[0112] <Analysis example> Next, a specific analysis example that confirmed the effectiveness of the present invention will be described.

[0113] [Analysis overview] First, an overview of this analysis example will be given.

[0114] Figure 12 of this analysis example shows the same forward analysis model 11 as Figure 2, but a vibration sensor 50C is also installed in the foundation 12 of the building 10 (see Figure 1). The response point where this vibration sensor 50C is installed is the response position 51C. Vibration data of the earthquake motion (input) may be collected using a vibration sensor installed in the ground G near the building 10, or building vibration data of the foundation 12 may be used.

[0115] For the estimated transfer function based on the building response of the forward analysis model 11 in Figure 12, the shear stiffness k and damping constant h of the building 10 and the stiffness KR and damping coefficient CR of the rocking ground spring are vibration parameters, and these vibration parameters are estimated in this analysis example.

[0116] In this analysis example, the forward analysis model 11 of the building 10 in Fig. 12 was created using the frequency response analysis program FDAS developed by the applicant, Takenaka Corporation. Then, an earthquake response analysis is performed using the forward analysis model 11 of the building 10 with arbitrary initial values ​​given to the vibration parameters, and vibration data corresponding to the responses of the vibration sensors 50A, 50B, and 50C is created. Optimal vibration parameters are estimated for the obtained vibration data according to the method shown in the embodiment.

[0117] The inverse analysis used modal error iterative method (MIEC), a general-purpose inverse analysis method for input / output systems, to estimate the vibration parameters through repeated calculations.

[0118] Two cases will be described: a comparative example in which only the primary vibration mode is extracted, and an embodiment in which even higher vibration modes are extracted. The comparative example in which only the primary vibration mode is extracted is referred to as a "primary mode analysis example," and the case in which even higher vibration modes are extracted is referred to as a "higher mode analysis example."

[0119] In the higher mode analysis example, the first and second vibration modes were extracted for the rooftop 24, the third and fourth vibration modes were extracted for the first floor 21, and the fifth vibration mode was extracted for the foundation 12. In this analysis, these vibration modes are the vibration modes in which the peaks of the target transfer function are most prominent.

[0120] [Outline of response results and extraction of dominant responses based on forward analysis model] Next, an overview of the response results based on the forward analysis model and the extraction of the dominant response will be described.

[0121] As mentioned above, Figure 12 shows the direct analysis model 11 used to create the vibration data. Response position 51A of the rooftop 24, response position 51B of the first floor 21, and response position 51C of the foundation 12 are observed, and responses in the horizontal and rotational directions are obtained, respectively. The table in Figure 13(A) shows the specifications of the building 10 (see Figure 1) set in the direct analysis model 11, and Figure 13(B) shows the specifications of the dynamic ground spring. Additionally, the table in Figure 13(C) shows the initial values ​​of the vibration parameters. Note that "dynamic ground spring" is a general term that combines the horizontal ground spring and the previously mentioned "rocking ground spring."

[0122] [Setting the forward analysis model and estimating the optimized variable parameters using convergence calculation] Next, the setting of the direct analysis model and the estimation results of the optimized variable parameters by convergence calculation will be explained.

[0123] Figure 14 shows the input seismic wave S for the study. Figure 14(A) shows the acceleration response spectrum for the input seismic wave S, Figure 14(B) shows the Fourier spectrum, and Figure 14(C) shows the acceleration time history.

[0124] FIG. 15 shows target transfer functions and target dominant responses of response positions 51A, 51B, and 51C of vibration sensors 50A, 50B, and 50C to an input seismic wave S.

[0125] Specifically, it is calculated by determining the Fourier spectrum ratio (response / input) at response positions 51 A, 51 B, and 51 C. The responses at response positions 51 A and 51 B are horizontal responses, and the response position 51 C is a rotational response.

[0126] As specific examples, (A-1) to (A-3) are examples of first-order mode analysis of a comparative example that extracts only the first-order vibration mode, and (B-1) to (B-5) are examples of higher-order mode analysis that extracts up to higher-order modes. This also applies to the estimated transfer function and estimated dominant response described later.

[0127] Then, (A-1) is the target transfer function and target predominant response of the primary vibration mode of response position 51A, (A-2) is the target transfer function and target predominant response of the primary vibration mode of response position 51B, and (A-3) is the target transfer function and target predominant response of the primary vibration mode of response position 51C.

[0128] Also, (B-1) is the target transfer function and the target predominant response of the first vibration mode of the response position 51A, (B-2) is the target transfer function and the target predominant response of the second vibration mode of the response position 51A, (B-3) is the target transfer function and the target predominant response of the third vibration mode of the response position 51B, (B-4) is the target transfer function and the target predominant response of the fourth vibration mode of the response position 51B, and (B-5) is the target transfer function and the target predominant response of the fifth vibration mode of the response position 51C.

[0129] The same applies to the estimated transfer function and estimated predominant response described below.

[0130] Fig. 16 shows the estimated transfer function and estimated response of response points 52A, 52B, and 52C corresponding to response positions 51A, 51B, and 51C of vibration sensors 50A, 50B, and 50C to an input seismic wave S in the forward analysis model 11 of the building 10 in Fig. 12. Fig. 16 shows the estimated transfer function obtained by inputting initial values ​​for the vibration parameters in the table of Fig. 13(C) for the forward analysis model 11, that is, the estimated transfer function before back analysis.

[0131] Fig. 17 is a graph in which an estimated transfer function is inserted with vibration parameters of optimal values ​​in which the error vector between the target dominant response and the estimated dominant response is within the allowable error by the inverse analysis, that is, the estimated transfer function after the inverse analysis, an estimated transfer function in which the vibration parameters are inserted with initial values ​​(the estimated transfer function before the inverse analysis), and a target transfer function are superimposed. Also, the table in Fig. 18 is a list of the target dominant responses of the target transfer function and the estimated dominant responses of the estimated transfer function.

[0132] From these, in the first vibration mode analysis example, the estimated transfer function and the estimated predominant response of the first vibration mode match with good accuracy. However, the accuracy of the estimated transfer function and the estimated predominant response of the higher vibration modes is not good. In contrast, in the higher vibration mode analysis example, it can be seen that the estimated transfer functions and the estimated predominant responses from the first to the higher vibration modes match with good accuracy.

[0133] Fig. 19(A) is a graph showing the convergence of the RSS (residual sum of squares) error in first-order vibration mode analysis. Fig. 19(B) is a graph showing the convergence of the RSS (residual sum of squares) error in higher-order vibration mode analysis. Note that the RSS (residual sum of squares) error is the sum of the squares of the differences between the target value and the estimated value, and is the sum of the squares of the error vector in this analysis example. As shown above, it can be seen that the higher-order vibration mode analysis takes more runs to converge and has lower analysis efficiency, but it is easier to uniquely determine the solution to be searched for.

[0134] Fig. 20 is a graph showing true values ​​(actual measured values), initial values, and optimal values ​​(estimated values) of vibration parameters in a first-order vibration mode analysis. Fig. 21 is a graph showing true values ​​(actual measured values), initial values, and optimal values ​​(estimated values) of vibration parameters in a higher-order vibration mode analysis. Figs. 20(A) and 21(A) are graphs of the shear rigidity of the base isolation layer to the third floor of a building, Figs. 20(B) and 21(B) are graphs of the damping constants of the base isolation layer to the third floor of a building, and Figs. 20(C) and 21(C) are graphs of the rotational ground spring.

[0135] From these, it can be seen that the higher vibration mode analysis example provides a more accurate match than the first vibration mode analysis example, particularly above the second floor (1.34 m) of the building 10 (see FIG. 1).

[0136] As described above, in the analysis examples, it is found that the higher-order mode analysis example, which extracts higher-order vibration modes, can estimate vibration parameters with higher accuracy than the first-order mode analysis example, which extracts only the first-order vibration mode.

[0137] [Details of the equation of motion and estimated transfer function] Next, the equation of motion and the estimated transfer function will be described in detail.

[0138] Fig. 22 is a conceptual diagram of the building response of the forward analysis model 11 set in this analysis example. Fig. 22(A) is a conceptual diagram of the building response of the forward analysis model 11 when subjected to earthquake motion, and Fig. 22(B) is a conceptual diagram of the building response of the forward analysis model 11 when subjected to an excitation force on the upper part of the building 10 due to external wind force or the like.

[0139] In the figure, ki and ci are the shear stiffness and damping coefficient of building 10, KH, CH, KR, and CR are the stiffness and damping coefficient of the ground spring, mi is the mass of each mass point, J0 is the rotational inertia mass concentrated in the foundation, and Hi is the story height.

[0140] The equation of motion of the direct analysis model 11 in FIG. 22(A) when subjected to an external earthquake force is given by the following [Equation 1], and the estimated transfer function is given by the following [Equation 2].

[0141]

number

[0142]

number

[0143] In addition, [M], [C], and [K] in the above [Formula 1] and [Formula 2] are the following [Formula 3], [Formula 4], and [Formula 5]. Note that there are lines above the letters [M], [C], and [K].

[0144] In addition, {X}={X i X i-1 X1θ0} T is a relative displacement vector corresponding to the shear deformation excluding the rotational displacement from the response position 52C of the base portion 12,

[0145] X0=x0+y is the absolute displacement of the response position 52C of the base portion 12; {H}={ΣH i ΣH i-1 H1} T is the height vector.

[0146]

number

[0147]

number

[0148]

number

[0149] The equation of motion of the forward analysis model 11 when an excitation force is applied to the upper part of the building 10 due to external wind force or the like in FIG. 22(B) is given by the following [Equation 6], and the estimated transfer function is given by the following [Equation 7].

[0150]

number

[0151]

number

[0152] [Example of analysis when no dominant response occurs] Next, an example of analysis in which no predominant response occurs will be described.

[0153] An example of analysis is described below in which the stiffness KH and damping coefficient CH of the horizontal ground spring are estimated for an estimated transfer function based on the building response of the forward analysis model 11 when an excitation force is applied to the top of the building 10 due to external wind force or the like as shown in Fig. 22(B). Note that the "horizontal ground spring" is a spring related to the horizontal response, and the aforementioned "rocking ground spring" is a spring related to the rotational response.

[0154] In this analysis, the earthquake wave shown in FIG. 14 is input as an external acceleration force to the response point 52B of the first floor 21 of the forward analysis model 11 shown in FIG.

[0155] FIG. 23(A) shows a target transfer function of the horizontal response of the foundation part 12 (see FIG. 1) to an input when an external force such as wind (see FIG. 22(B)) is applied. Any two points (10 Hz point and 50 Hz point) shown on the target transfer function in the figure are arbitrary points for extracting a target dominant response in the target transfer function when no clear dominant response is recognized as in this study example. FIG. 24(B) shows an estimated transfer function of the horizontal response of the foundation part 12 (see FIG. 1) when the vibration parameters are at their initial values. Also, an estimated dominant response when the vibration parameters corresponding to the two points (10 Hz point and 50 Hz point) set in FIG. 23(B) are at their initial values ​​is shown.

[0156] FIG. 24(A) is a graph superimposing an estimated transfer function in which optimal vibration parameters are inserted when the error vector between the target predominant response and the estimated predominant response at any two arbitrary points (10 Hz and 50 Hz) is below the allowable error by inverse analysis, that is, the estimated transfer function after inverse analysis, an estimated transfer function in which initial values ​​are inserted into the vibration parameters (the estimated transfer function before inverse analysis), and the target transfer function.

[0157] FIG. 24B shows the transition of the norm of the error vector between the target dominant response and the estimated dominant response.

[0158] FIG. 24(C) is a graph showing the results of estimating the stiffness KH and damping coefficient CH of the horizontal ground spring.

[0159] Figure 25 shows a comparison of a list of eigenvalue frequencies obtained by real eigenvalue analysis using vibration parameters after inverse analysis with true values ​​(actual measurements), eigenvalues ​​obtained in the same way using first-order mode analysis and higher-order mode analysis. This shows that there are fewer vibration modes in which the error between the true value and the estimated value is 5% or more in the higher-order mode analysis than in the first-order mode analysis, resulting in better estimation results.

[0160] In this way, it can be seen that this analysis can be effectively applied even in cases including a target transfer function that does not have a clear peak, such as a monotonically increasing one.

[0161] <Other> The present invention is not limited to the above embodiment.

[0162] As described above, the vibration mode to be extracted at each response position 51 is selected to satisfy all of (rule A), (rule B), (rule C), (rule D) and (rule E), but is not limited to this.

[0163] For example, the target predominant response may be extracted by selecting the same vibration mode at multiple response positions 51. For example, the primary vibration mode may be selected at all response positions 51. Specifically, response position 51A selects the primary vibration mode and the secondary vibration mode to extract the target predominant response, and response position 51B selects the primary vibration mode and the tertiary vibration mode to extract the target predominant response, and so on.

[0164] Also, for example, the same vibration mode may be selected for all response positions 51. Specifically, response position 51A selects the primary vibration mode, the secondary vibration mode, and the tertiary vibration mode to extract a target predominant response, and response position 51B also selects the primary vibration mode, the secondary vibration mode, and the tertiary vibration mode to extract a target predominant response, etc.

[0165] Also, for example, depending on the shape and structure of the building 10, the vibration mode of the upper response position 51 may be made higher than that of the lower response position 51.

[0166] However, it is desirable to include (Rule B) and (Rule D).

[0167] Also, for example, vibration sensors 50 may be installed on all floors of the building 10 including the rooftop 24. In this case, the same multiple vibration modes may be selected for the vibration sensors 50 on all floors to extract the target predominant responses. For example, the primary vibration mode, secondary vibration mode, and tertiary vibration mode may be selected for all floors to extract the target predominant responses. In this way, the vibration characteristics can be estimated with high accuracy, but the calculation takes longer.

[0168] Also, for example, the vibration characteristics estimation system may be configured with a plurality of computers and servers. For example, only the inverse analysis process may be performed by a separate computer or server.

[0169] Furthermore, the present invention can be embodied in various forms without departing from the spirit and scope of the present invention. A plurality of embodiments and modifications can be implemented in appropriate combination. [Explanation of symbols]

[0170] 10. Building 11 Forward Analysis Model 12 Foundation 14 Superstructure 18 Seismic isolation bearing 20 Seismic isolation layer 21 First Floor 22 Second Floor 23 Third floor 24 Rooftop 50A Vibration Sensor 50B Vibration Sensor 50C Vibration Sensor 51A Response position 51B Response position 51C Response position 52A Response Point 52B Response point 52C Response point 100 Vibration characteristics estimation device (an example of a vibration characteristics estimation system) 150 Target transfer function calculation unit 152 Target Superior Response Extraction Unit 154 Estimated transfer function calculation unit 156 Estimated Superior Response Extraction Unit 158 Inverse analysis section G. Ground MA target transfer function MB target transfer function MP1 Target Superior Response MP2 Target Superior Response MP3 Target Outstanding Response SA estimated transfer function SB Estimated Transfer Function SP1 Estimated Superior Response SP2 Estimated Superior Response SP3 Estimated Superior Response

Claims

1. a target transfer function calculation step of calculating a target transfer function for each response position where a vibration sensor is installed from responses of the vibration sensors installed on any multiple floors of a building; a target dominant response extraction step of extracting a target dominant response of a vibration mode in which a peak of the target transfer function is dominant for each of the response positions; an estimated transfer function calculation step of calculating an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated predominant response extraction step of extracting, from the estimated transfer function, an estimated predominant response of the vibration mode that is the same as the response position corresponding to each of the response points; an inverse analysis process for estimating the vibration parameters by modifying vibration parameters of the forward analysis model and repeating recalculation of the estimated transfer function and reextraction of the estimated predominant response until an error vector between the target predominant response and the estimated predominant response falls within an allowable error or reaches an upper limit number of times; A method for estimating the vibration characteristics of a building equipped with the above.

2. In the target dominant response extraction step, the target dominant response of the vibration mode having the most prominent peak is extracted. The method for estimating vibration properties of a building according to claim 1.

3. In the target dominant response extraction step, the response position where there is no peak in the target transfer function is extracted as the target dominant response between any two vibration points. The method for estimating vibration properties of a building according to claim 1 or 2.

4. a target transfer function calculation step of calculating a target transfer function for each response position where a vibration sensor is installed from responses of the vibration sensors installed on any multiple floors of a building; a target dominant response extraction step of extracting a target dominant response of a vibration mode in which a peak of the target transfer function is dominant for each of the response positions; an estimated transfer function calculation step of calculating an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated predominant response extraction step of extracting, from the estimated transfer function, an estimated predominant response of the vibration mode that is the same as the response position corresponding to each of the response points; an inverse analysis process for estimating the vibration parameters by modifying vibration parameters of the forward analysis model and repeating recalculation of the estimated transfer function and reextraction of the estimated predominant response until an error vector between the target predominant response and the estimated predominant response falls within an allowable error or reaches an upper limit number of times; A program that causes a computer to execute the following.

5. a target transfer function calculation unit that calculates a target transfer function for each response position where a vibration sensor is installed from responses of the vibration sensors installed on any multiple floors of a building; a target dominant response extracting unit that extracts a target dominant response of a vibration mode in which a peak of the target transfer function is dominant for each of the response positions; an estimated transfer function calculation unit that calculates an estimated transfer function of a response point corresponding to the response position from a forward analysis model created by simulating the building; an estimated predominant response extraction unit that extracts, for each of the response points, an estimated predominant response of the vibration mode that is the same as the response position corresponding to the response point from the estimated transfer function; an inverse analysis unit that estimates the vibration parameters by correcting vibration parameters of the forward analysis model and repeating recalculation of the estimated transfer function and reextraction of the estimated predominant response until an error vector between the target predominant response and the estimated predominant response falls within an allowable error or reaches an upper limit number of times; A building vibration characteristic estimation system equipped with this technology.

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