Layer stiffness estimation method and layer stiffness estimation device for a given layer

Abstract

To provide a layer rigidity estimation method and a layer rigidity estimation device for a predetermined layer that can greatly reduce the number of points of measurement of acceleration compared to before.SOLUTION: A layer rigidity estimation method for a predetermined layer according to the present invention is a method for estimating the layer rigidity of the predetermined layer in a multi-layered structure by using a multi-material point-based model, and the method includes the steps of: performing Fourier transformation on acceleration at the i-th material point from counted from below a material point corresponding to the rooftop of the structure and acceleration at material points above and below the i-th material point, thereby calculating the Fourier spectrum of respective accelerations; calculating the layer rigidities (ki) of the predetermined layer located between the i-th material point and the i-1-th material point by using the obtained Fourier spectrum of the respective accelerations and the mass of the i-th material point; and extracting, from the layer rigidities (ki) of the predetermined layer, only layer rigidities having a predetermined reference value or more where an estimated value of S / (S+N) ratio is closer to 1.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a method and an apparatus for estimating story stiffness of a predetermined story in a building. [Background technology]

[0002] In recent years, importance has been attached to structural health monitoring technology in order to ensure the safety of buildings. For example, a method has been proposed to identify the story stiffness of each story of a building in order to evaluate damage to the building caused by earthquakes, etc. (Patent Document 1, Non-Patent Documents 1 and 2). When a member of a certain story of a building is damaged by an earthquake, etc., the stiffness of the story decreases, so the degree of damage can be evaluated by comparing the story stiffness before and after the earthquake. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2016-194514 A [Non-patent literature]

[0004] [Non-Patent Document 1] Mitsuru Nakamura, Yuzuru Yasui, "Evaluation of Story Damage of Earthquake-damaged Steel-framed Buildings Based on Microtremor Measurements," Journal of the Architectural Institute of Japan, Structural and Building Engineering Society, No. 517, pp. 61-68, 1999 [Non-Patent Document 2] Yoshimura, Tomotake, Mita, Akira, "Online Identification of Architectural Structural Parameters Based on Multi-Input Multi-Output Model", Journal of the Architectural Institute of Japan, Structural Engineering and Systems Engineering, Vol. 574, pp. 39-44, 2003 Summary of the Invention [Problem to be solved by the invention]

[0005] In general, in the case of high-rise buildings, damage to structural members due to earthquakes is likely to occur in the lower stories. However, in the methods of Patent Document 1 and Non-Patent Documents 1 and 2, in order to calculate the story stiffness of the story to be evaluated, it is necessary to calculate the story stiffness based on the accelerations in at least all stories above the story to be evaluated.

[0006] Therefore, an object of the present invention is to provide a method and device for estimating layer stiffness of a predetermined layer, which can significantly reduce the number of acceleration measurement points compared to the conventional method. [Means for solving the problem]

[0007] The present invention has been made to solve at least some of the above-mentioned problems, and can be realized in the following aspects or application examples.

[0008] [1] One aspect of the method for estimating layer stiffness of a predetermined layer according to the present invention comprises: A method for estimating a story stiffness of a predetermined story in a multi-story building using a multi-mass system model, comprising the steps of: A step of performing a Fourier transform on the acceleration of the i-th mass point counting from below the mass point corresponding to the roof of the building and the accelerations of mass points above and below the i-th mass point to calculate a Fourier spectrum of each acceleration; Using the Fourier spectrum of each acceleration obtained in the above step and the mass of the i-th mass point, the story stiffness (k i ) and The layer stiffness (k i extracting only those layer stiffnesses having an estimated S / (S+N) ratio of equal to or greater than a predetermined reference value close to 1, which is obtained by the following formula (3); The present invention is characterized by comprising:

[0009]

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[0010]

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[0011]

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[0012] [2] One aspect of the layer stiffness estimation device according to the present invention is A layer stiffness estimation device for executing one aspect of the layer stiffness estimation method for a predetermined layer, A calculation unit and a storage unit are provided, The calculation unit is A process of acquiring the acceleration of the i-th mass point and the accelerations of the mass points above and below the i-th mass point; A process of performing a Fourier transform on each of the acquired accelerations to calculate the Fourier spectrum of each acceleration; The story stiffness (k i ) and The calculated layer stiffness (k i ) extracting only those story stiffnesses having an estimated S / (S+N) ratio close to 1 and equal to or greater than a predetermined reference value; The present invention is characterized by carrying out the following steps. Effect of the Invention

[0013] According to one aspect of the layer stiffness estimation method and one aspect of the layer stiffness estimation device of the present invention, the number of acceleration measurement points can be significantly reduced compared to the conventional art. [Brief description of the drawings]

[0014] [Figure 1] FIG. 2 is a schematic diagram of a building used in the story stiffness estimation method according to the present embodiment, and a conceptual diagram of a multi-mass system model thereof. [Diagram 2] 1 is a block diagram showing an example of the configuration of a layer stiffness estimation device for a predetermined layer according to the present embodiment. FIG. [Diagram 3]10 is a flowchart illustrating an example of a method for estimating layer stiffness of a predetermined layer according to the present embodiment. [Figure 4] 4 is a flowchart showing an example of processing for each section in FIG. 3. [Diagram 5] 4 is a flowchart showing an example of an S / (S+N) estimation process in FIG. 3. [Figure 6] 4 shows an input (simulated ground motion ug··) in the embodiment. [Figure 7] FIG. 11 is a diagram showing the results of a verification calculation of the layer stiffness estimation method of the first embodiment. [Figure 8] FIG. 13 is a diagram showing the results of a verification calculation of the layer stiffness estimation method of the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Preferred embodiments of the present invention will be described in detail below with reference to the drawings. Note that the embodiments described below do not unduly limit the contents of the present invention described in the claims. In addition, not all of the configurations described below are necessarily essential components of the present invention.

[0016] 1.Layer stiffness estimation device A story stiffness estimation device 2 according to one embodiment of the present invention will be described with reference to Figures 1 and 2. Figure 1 is a schematic diagram (a) of a building 1 used in a story stiffness estimation method according to this embodiment, and a conceptual diagram (b) of a multi-mass system model 1a thereof, and Figure 2 is a block diagram showing an example of the configuration of the story stiffness estimation device 2 for a predetermined story according to this embodiment.

[0017] The multi-story building 1 shown in (a) of Figure 1 can be replaced with a multi-mass system model 1a shown in (b) of the same figure. The masses of the mass points corresponding to the floors of each floor are m0, m1, m2, ..., m i-1 ,m i ,m i+1 ,…m n-1In the initial system position, n mass points are placed at intervals from the ground (GL) in the vertical direction. Mass m1 is the mass of the first mass point below the roof mass point (corresponding to the 10th floor in a 10-story building), and mass m i indicates the mass of the i-th mass point (corresponding to the 10-(i-1)th floor if the building has 10 floors) counting from the mass point below the rooftop mass point. The stiffness k 1…n and damping (or viscosity) c 1…n The story stiffness k1 is the stiffness of the first story counting from the top floor, and the story stiffness k i is the stiffness of the i-th floor counting from the top floor. In this embodiment, the story stiffness of the i-th floor (k i ) is estimated by estimating the story stiffness (k i ) is estimated.

[0018] In addition, in FIG. 1(b), u i is the time distribution of the horizontal displacement of the i-th mass point, u i (t) and u g is the time distribution of the ground (GL) displacement of building 1, u g (t). Furthermore, the time distribution of the displacement u i The derivative of (t) with respect to time (velocity) is expressed as u i (t), u g (t), and similarly, the second derivative with respect to time (acceleration) is expressed by adding two dots as u i (t), u g This is expressed as ··(t).

[0019] In the building 1, acceleration sensors 14 are attached to at least three floors corresponding to the i-th mass point and the mass points above and below it. The acceleration sensors 14 can measure at least the horizontal acceleration of the floors of each floor, that is, can measure the acceleration at the (i-1)th, i-th, and (i+1)th mass points. The building 1 may be provided with acceleration sensors 14 on floors of all floors. The acceleration sensors 14 may be triaxial accelerometers.

[0020] The multi-mass system model 1a is a model in which the masses m0...m of each mass point are calculated based on the design specifications of the building 1, for example. n-1 can be obtained in advance, and the absolute accelerations (hereinafter simply referred to as accelerations) u at the (i-1)th, i-th, and (i+1)th mass points can be calculated from the output of the acceleration sensor 14. i (t)+u g (t), u i-1 (t)+u g (t), u i+1 (t)+u g ··(t) can be obtained.

[0021] In this case, the equation of motion (force balance equation) of the multi-mass system model 1a is given by the following equation (4).

[0022]

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[0023] Based on this equation, the following formula (1) and formula (2) can be derived as described below.

[0024]

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[0025]

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[0026] The layer stiffness estimation device 2 according to this embodiment shown in FIG. 2 is a device for executing an embodiment of a layer stiffness estimation method for a predetermined layer, which will be described later. The layer stiffness estimation device 2 calculates the layer stiffness (k i ) can be estimated.

[0027] The layer stiffness estimation device 2 includes a calculation unit 21 and a storage unit 22. The layer stiffness estimation device 2 is, for example, a personal computer or a server, and includes a CPU (Central Processing Unit) (not shown), memories such as ROM and RAM, a storage device such as a hard disk drive, a communication interface for communicating with external devices, and the like. The calculation unit 21 can be composed of a CPU, RAM, and the like, and executes a program stored in the storage unit 22. The storage unit 22 can be composed of a storage device such as a hard disk drive, and stores the mass of each mass point of the multi-mass point model 1a, the above formula (1) and the above formula (2), and the like. The storage unit 22 may store measurement data acquired from the acceleration sensor 14.

[0028] The story stiffness estimation device 2 can connect to a plurality of acceleration sensors 14 installed in the building 1 via a communication network and receive measurement data. As long as it is possible to obtain the measurement data of the acceleration sensors 14, it is acceptable to use a method other than a communication network, such as importing the measurement data using a USB memory. In addition, the story stiffness estimation device 2 can be operated by The estimation device may be provided with known input devices such as a keyboard and a mouse for inputting the estimation results, and known output devices such as a display and a printer for outputting the estimation results.

[0029] The calculation unit 21 calculates the acceleration u i (t)+u g (t) and the acceleration of the upper and lower mass points u i-1 (t)+u g (t), u i+1 (t)+u g The process of obtaining (t) and Fourier transforming each of the obtained accelerations to obtain the Fourier spectrum u i ··(ω)+u g (ω), ui-1 ··(ω)+u g (ω), u i+1 ··(ω)+u g (ω), and the Fourier spectrum of each of the calculated accelerations and the mass m of the i-th mass point stored in the memory unit 22. i and the layer stiffness (k i Each step will be described later in the section on the method for estimating story stiffness.

[0030] The story stiffness (k i ) is the story stiffness (k i ), it is an estimate of the story stiffness of a given story in the actual building 1.

[0031] A story stiffness estimation device 2 estimates the story stiffness (k i ), the degree of damage and deterioration of the building 1 can be grasped. Moreover, the story stiffness estimation device 2 does not require acceleration data for many stories as in the past, and only requires acceleration data for at least three mass points (floors on three floors), so in the case of a super-high rise building, the number of acceleration measurement points can be significantly reduced. If the story stiffness can be estimated, for example, if there is a story whose story stiffness has decreased before and after an earthquake, it is possible to know that the story has been damaged. Even if there is no record before the earthquake, if the story stiffness of each story is compared and there is a story whose story stiffness is unnaturally small, it is possible to know that the story has been damaged. Furthermore, if the story stiffness is estimated by periodically measuring vibrations not only during earthquakes but also during earthquakes, the degree of deterioration of the building 1 over time can be grasped.

[0032] Next, it will be explained that the above formula (1) and formula (2) can be derived from the above formula (4). Hereinafter, where necessary, the mass matrix (matrix in which mi is arranged) in the above formula (4) may be written as M, the damping matrix (matrix in which ci is arranged) as C, and the stiffness matrix (matrix in which ki is arranged) as K.

[0033] First, the time distribution of the displacement, velocity, and acceleration of a mass point is Fourier transformed to obtain the frequency distribution of the displacement, velocity, and acceleration. i (ω), u i ·(ω), u i (ω), u g It can be written as u(ω), where t is replaced by the angular frequency ω. i (ω), u i ·(ω), u i (ω), u g The above formula (4) also holds true for (ω), but due to the nature of the Fourier transform, i (ω), u i ·(ω), u i (ω), u g Between ··(ω), the following equations (5) and (6) hold.

[0034]

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[0035]

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[0036] Then, by substituting the above formulas (5) and (6) into the above formula (4), the following formulas (7) and (8) hold.

[0037]

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[0038]

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[0039] In addition, the j-th natural angular frequency in the multi-mass system model 1a in Fig. 1 is λ j Let the j-th eigenvector be {φ0,φ 1j ,…,φ n-1 , jIn this case, due to the nature of the eigenfrequency and the eigenvalue vector, the eigenvector {φ0,φ 1j ,…,φ n-1 , j} is the angular frequency λ j The ground displacement is zero (u g (ω=λ j )=0), the equation of motion in eigenspace is given by the following equation (9) from the above equation (8).

[0040]

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[0041] Here, the masses of all mass points are known from, for example, design specifications, and the accelerations at mass points of three floors including a given floor (actually, since this is a building 1, the floors of three consecutive floors) can be obtained from the acceleration sensor 14. i The recording of (t) is performed at regular intervals. Let this time interval be dt, and let t p = dt(p-1) (p = 1, 2, 3, ...), the time distribution of the actual acceleration record is a continuous u i Not (t) but discrete u i (tp), and its Fourier transform also becomes a discrete value (u i (ω q ) (written as q=1,2,3,…).

[0042] If we collect the known terms in the equations of motion of the above formulas (4), (7), and (9) on the right-hand side, we obtain the following formulas (10) to (12).

[0043]

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[0044]

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[0045]

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[0046] In addition, for the sake of simplicity, symbols can be defined as in the following formulas (2) and (13).

[0047]

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[0048]

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[0049] At this time, the relationships of the following formulas (14) and (15) hold.

[0050]

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[0052] The right-hand sides of the above formula (14) and formula (15) can be written as the following formula (16) and formula (17).

[0053]

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[0054]

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[0055] In the conventional technique, Non-Patent Document 1, the above formula (10) is used, in Non-Patent Document 2, the above formula (12) is used, and in Patent Document 1, the above formula (11) is used.

[0056] In the present invention, the above formula (11) is modified as follows based on the integration rule of the Fourier transform (the above formula (5)).

[0057]

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[0058] If we extract only the (i+1)th row from the above equation (18), we get the following equation (19).

[0059]

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[0060] By rearranging the above formula (19), the following formula (20) is obtained.

[0061]

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[0062] s i In the definition formula (above formula (2)), ω q Since it contains k, there is frequency dependence. i ,c i The fact that does not change with time or frequency is a property of the multi-mass system model 1a in FIG. 1, and is not necessarily the case in the actual building 1. q-b From ω q+b In the range of s i and s i+1 If the change in is sufficiently small, the above From equation (20), the following equation (21) holds.

[0063]

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[0064] Furthermore, the matrix of the displacement differences on the left side of the above equation (21) is D i (ω q), then, from the above formula (21), s i ,s i+1 is determined by the following formula (1).

[0065]

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[0066] As explained above, it can be seen that the above formula (1) and the above formula (2) hold true from the above formula (4). And, from the above formula (1) or the above formula (21), s i ,s i+1 is determined, so as in Non-Patent Documents 1 and 2 and Patent Document 1, s i From the definition of (above formula (2)), the layer stiffness of a given layer (k i ) and k i+1 ,c i ,c i+1 In this case, if the frequency width b used in the calculation is at least 1, a solution can be obtained. However, If b is too small, the solution will not be stable, and if it is too large, s i ,s i+1 If b is set to a value between 10 and 100, an average result will be obtained that ignores frequency changes, and the calculation accuracy will be adversely affected for reasons described later.

[0067] Next, the calculation unit 21 executes a process of extracting only the layer stiffnesses (ki) of the predetermined layer that have an estimated S / (S+N) ratio equal to or greater than a predetermined reference value close to 1 from the calculated layer stiffnesses (ki). Details of this process will be described in "2. Layer stiffness estimation method."

[0068] 2. Layer stiffness estimation method A story stiffness estimation method for a predetermined story according to one embodiment of the present invention will be described with reference to Figs. 1 to 5. Fig. 3 is a flowchart showing an example of the story stiffness estimation method for a predetermined story according to this embodiment, Fig. 4 is a flowchart showing an example of processing for each section in Fig. 3, and Fig. 5 is a flowchart showing an example of S / (S+N) estimation processing in Fig. 3. In the following description, the story stiffness of a predetermined story of a building 1 in Fig. 1(a) is estimated by a story stiffness estimation device 2 in Fig. 2 using a multi-mass system model 1a shown in Fig. 1(b). Portions that overlap with the description of the story stiffness estimation device 2 will be omitted.

[0069] The method for estimating the story stiffness of a given story (i-th story) shown in FIG. 3 is to estimate the story stiffness (k i ) using a multi-mass system model 1a, the method includes a step (S21) of calculating at least the Fourier spectrum of acceleration, and a step (S22) of estimating the story stiffness (k i ) and extracting only the layer stiffnesses equal to or greater than a predetermined reference value (S41). In the example of FIG. 3, the processes of S10, S11, S12, S21, S23, S27, S29, S31, S32, and S41 are executed.

[0070] S10: In the step of acquiring acceleration data (S10), the story stiffness estimation device 2 acquires acceleration measurement data (hereinafter, "acceleration data") from the acceleration sensors 14 of a predetermined story and the two stories adjacent thereto above and below. The acceleration data may be acquired directly from data output from the acceleration sensors 14 due to a currently occurring earthquake or vibration, or may be acquired by saving past acceleration data in the memory unit 22. The acceleration data is the acceleration u at the i-th mass point counting from below the mass point corresponding to the roof of the building 1. i (t)+u g (t) and the acceleration u of the mass points above and below the i-th mass point i-1 (t)+u g (t), u i+1 (t)+u g t.

[0071] Next, before explaining each process, in order to extract a reliable value from the value of the story stiffness calculated from the acceleration data, the reliability evaluation index H i (ω q First, the above formula (1) can be transformed to obtain the following formula (22).

[0072]

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[0073] Multiplying each row on both sides of the above equation (22) by the complex conjugate of the acceleration Fourier spectrum gives the following equation (23).

[0074]

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[0075] The matrix on the left side of the above equation (23) is H i (ω q ) is defined as follows:

[0076]

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[0077] In this embodiment, H i (ω q ) is used to extract a layer stiffness value that is less affected by measurement errors. The SN (signal / noise) ratio (in this embodiment, the S / (S+N) ratio is used) is a value generally defined for a scalar quantity, and represents the ratio of the signal component S (true value) and the noise component N (measurement error, deviation between the measurement and the true value) contained in the squared value of the absolute value of the scalar quantity to be evaluated. In this embodiment, H i (ω q ) signal-to-noise ratio is higher than H i (ω qIt may be desirable to consider the S / N ratio of each element constituting the matrix H, but this would result in a band in which the S / N ratio is excessively high (relative to the low accuracy of the estimation of the story stiffness), making it difficult to extract only estimated values ​​close to the true value. In this embodiment, the S / N ratio of each element of the matrix is ​​not only considered individually, but also the relationship between the elements. For this reason, in this embodiment, the matrix H i (ω q ) is the square of the absolute value of det(H i * (ω q )H i (ω q )) (where detA represents the determinant of matrix A) is taken as "matrix H i (ω q ) power (hereafter referred to as powH i (ω q ) and powH i (ω q By estimating the ratio of the signal component S to the noise component N in the model, a reliable estimate of the story stiffness can be extracted.

[0078] S11: Setting value of section length (S11) provides data of a preset setting value of the section length to the step of S12. The section length is set, for example, between 10 and 100 times the first natural period of the building 1 to be examined.

[0079] S12: Data division into sections (S12) is performed by dividing the acceleration data acquired by the calculation unit 21 in S10 by the set value of the section length called up in S11. For example, if there is 100 seconds of acceleration data, it is divided into five sections with a section length of 20 seconds.

[0080] S21: The process for each section (S21) includes a step of calculating the Fourier spectrum of the acceleration. In the process for each section (S21), the calculation unit 21 calculates the Fourier spectrum of each acceleration obtained in the step of S12, and calculates the SN (signal / noise) ratio of the data by subtracting H i (ω q The detailed process will be described later with reference to FIG.

[0081] S23: Processing to check whether all sections have been processed (S23) proceeds to S25 if S21 indicates that all sections have been processed (Yes), and returns to S21 if S21 indicates that all sections have not been processed (No).

[0082] S27:H i (ω q The S / (S+N) ratio estimation process (S27) is carried out by the calculation unit 21 by estimating the S / (S+N) ratio of m sections filtered in S25. i (ω q ) using powH i (ω q ) the S / (S+N) ratio, which is the estimated value R m The hat is calculated. Note that the detailed process will be described later with reference to FIG.

[0083] S29:H i (ω q The ensemble averaging process (S29) of the filtered H i (ω q ) to calculate the ensemble average of H i (ω q ) the effect of measurement error (noise component) can be reduced by calculating the ensemble average.

[0084] S31: Layer stiffness (k i The estimation process (S31) of the story stiffness (k i The estimation process (S31) of H i (ω q ) and the mass m of the i-th mass point i and the story stiffness (k i The following formula (25) is a basic equation obtained by modifying the above formula (1), and is obtained by executing the above-mentioned step (S29). Then, s i Calculate s using the following formula (2) iThe story stiffness of a given story (k i ) and the attenuation c i can be calculated.

[0085]

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[0086]

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[0087] S32: The reference value of S / (S+N) (S32) provides data of a preset reference value to the step S41. By setting the preset reference value to a value close to 1, for example 0.97, a value close to the true value of the estimated layer stiffness can be extracted in the step S41.

[0088] S41: The process of extracting the story stiffness at the frequency where S / (S+N) is equal to or greater than the reference value (S41) is The calculation unit 21 calculates the layer stiffness (k i ), only those layer stiffnesses whose estimated S / (S+N) ratio obtained by the following formula (3) is equal to or greater than a predetermined reference value close to 1 set in step S32 are extracted. Step S41 makes it possible to extract layer stiffness values ​​that are less affected by measurement errors.

[0089]

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[0090] According to one aspect of the layer stiffness estimation method and one aspect of the layer stiffness estimation device of the present invention, the number of acceleration measurement points can be significantly reduced compared to the conventional art.

[0091] 2.1. Processing by Section The process for each section (S21) will be described with reference to Fig. 4. The process for each section (S21) shown in Fig. 4 executes the processes of S210, S212, S214, S216, S218, and S220.

[0092] S210: Baseline correction process (S210) is a process in which the calculation unit 21 performs baseline correction on the acceleration data of each section divided in S12 of FIG.

[0093] S212: In the process of applying a window function (S212), the calculation unit 21 applies a window function to the acceleration data of each section that has been baseline-corrected in S210.

[0094] S214: The Fourier transform process (S214) is performed by the calculation unit 21 converting the acceleration data (u i (t)+u g Perform a Fourier transform on (t) (u i ··(ω)+u g ··(ω)) to do so.

[0095] S216: The process of calculating the inter-story displacement (S216) is carried out by the calculation unit 21 by calculating the acceleration (u i ··(ω)+u g (ω)) for all ω in the test band q For H i (ω q )

[0096] 2.2.H i (ω q ) S / (S+N) ratio estimation process Using Figure 5, i (ω q The estimation process (S27) of the S / (S+N) ratio of H shown in FIG. i (ω q The S / (S+N) ratio estimation process (S27) is performed using the H reconstructed at the frequency filtered in S266. i (ω q ) the calculation unit 21 executes the processes of S290, S292, S294, S296, S298 and S300.

[0097] In step S290, the calculation unit 21 calculates H i (ω q) from the storage unit 22. In step S292, the calculation unit 21 reads m H i * (ω q )H i (ω q In step S294, the calculation unit 21 calculates the ensemble average of m H i * (ω q ) and the ensemble average of m H i (ω q ) and multiplying it by the ensemble average. In step S296, N is calculated using the following formula (26), in step S298, S is calculated using the following formula (27), and in step S300, R is calculated using the following formula (28). m Calculate the hat, where R m Hat is the H of m intervals i (ω q ) using powH i (ω q ) is an estimate of the S / (S+N) ratio.

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[0101] 2.3.powH i (ω q ) S / (S+N) ratio estimation formula The process by which the above formula (28) was derived will be explained below.

[0102] (1) Definitions of symbols In what follows, we distinguish between measured values ​​(values ​​containing noise) and true values, and will suffix the measured values ​​with "~". First, we will assume that the S / (S+N) ratio of absolute acceleration is sufficiently high, and that the measured value and the true value are approximately equal.

[0103]

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[0104] On the other hand, for the relative displacement, the ground motion component (u g (ω q Since the power of the signal (true value) decreases when the power of the noise is eliminated, the influence of noise cannot be ignored and the relationship between signal and noise is set as follows:

[0105]

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[0106] For the sake of simplicity, H i (ω q ) are written as follows:

[0107]

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[0108] Furthermore, h k1 ~(k=1,2,…,n),l=1,2) is the signal component h kl and the noise component ε kl It can be divided into the following and written as follows:

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[0110] From the definition of noise, the following properties can be assumed:

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[0114] Also, <H i (ω q )> m Each element of <h kl ~> m +<ε kl ~> m If we write it as such, then due to the properties of random variables with zero expectation, the following relationship holds:

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[0116] Furthermore, n is assumed to be sufficiently large, and H i (ω q ) any variable x l Assume that the following approximation holds for

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[0118] Here, from the above formula (31), H i * (ω q )H i (ω q ) becomes:

[0119]

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[0120] Combining the properties of the above formulas (32) to (37) <H i * (ω q )H i (ω q )> m and <H i * (ω q )> m <H i (ω q )> m is expressed as follows:

[0121]

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[0123] (2) <H i (ω q )> Estimation formula for S / (S+N) ratio First, by taking the difference between the above equation (39) and equation (40), the following equation can be derived.

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[0125] Using the above equation (41), the following approximation holds for the matrix of the noise component N in the above equation (26):

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[0127] Therefore, the following approximation holds for the matrix of the signal component S in the above equation (27):

[0128]

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[0129] From the above formula (40) and the above formula (43), S is <H i * (ω q )>m <H i (ω q )>m, the noise components have been removed, so according to the following equation (28), <H i (ω q It can be derived that the S / (S+N) ratio can be estimated for m.

[0130]

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[0131] (Verification target and input data) In this example, the estimated value of story stiffness calculated using the story stiffness estimation method according to the present invention was verified. The multi-mass system model to be verified had five masses (m0=m1=...=m4=1t), the story stiffness (kN / m) of each story was as shown in Table 1, and the damping was h1=h2=...=h4=0.05. The lower subscript number indicates the upper part of the system. The primary natural frequency was set to 3.3 Hz.

[0132] [Table 1]

[0133] The input was white noise as shown in Figure 6. The sampling rate was 100Hz and the duration was 163.84 seconds.

[0134] (Example 1) The frequency response of the multi-mass system model for the input in FIG. 6 was calculated using a frequency response calculation, and the result was converted back to the time domain to obtain the true value of the mass system response waveform. The true value was used as it is as the simulated earthquake observation record to obtain the acceleration data in Example 1. The simulated earthquake observation record was then Fourier transformed to obtain s using the following formula (1) with a frequency width of 0.5 Hz (±0.25 Hz relative to the center frequency). i Calculate s using the following formula (2) i The real part of the story stiffness ki The estimate of (k i hat) and the attenuation c i The estimated value of (c i hat) was calculated. Furthermore, the attenuation c i About From the relationship between the viscosity coefficient and the damping constant, s i The imaginary part of the hat is k i The value divided by twice the hat is the estimated damping constant (h i The estimated value of the calculated story stiffness (k i hat) and the estimated damping constant (h i hat) are shown in Figure 7.

[0135]

number

[0136]

number

[0137] In Fig. 7, the true value is shown by a dashed line, the estimated value of the story stiffness estimated using the lower point as the reference is shown by a wide line in a light color, and the estimated value of the story stiffness estimated using the upper point as the reference is shown by a narrow line in a dark color. In Fig. 7, the lower point reference and the upper point reference indicate whether the estimation was performed using the mass point located at the top of the estimation target story as the reference point (mass point i in the above formulas (1) and (2)) or whether the lower mass point was used as the reference. The story stiffness of the nth story is s when i=n-1. i+1 and s when i=n _i Here, the story stiffness determined at i=n-1 is taken as the upper point reference, and the story stiffness determined at i=n is taken as the lower point reference. As shown in Figure 7, the true value and the estimated result are in exact agreement, confirming the validity of the theory.

[0138] (Example 2) Next, the true value of the mass system response waveform in Example 1 was compared with the RMS value of the ground motion (approximately 0.79 m / s 2) was added to the ground motion and the responses at each point and used as a simulated earthquake observation record to obtain acceleration data for Example 2 (S10). Then, processing for each section (S21) was performed for all sections (S22) according to the flowchart described with reference to Figs. 3 to 5. S23) was done. H i (ω q After calculating the ensemble average of (S29), s is calculated using the following formula (25) with a frequency width of 0.5 Hz (±0.25 Hz from the center frequency). i Calculate s from the above formula (2). i The real part of the story stiffness k i (ω q ) estimate (k i hat) was calculated (S31). In addition, H i (ω q ) S / (S+N) ratio estimate (R m The standard value of S / (S+N) was set to 0.97 (S32), and the story stiffness k i The estimated S / (S+N) ratio (R m Only the story stiffnesses with a value of 0.97 or more were extracted (S41). i (ω q The right side of Figure 8 shows the estimated S / (S+N) ratios of the 1000-kDa model. The points with estimated values ​​of 0.97 or more are shown as the estimated story stiffness (k i This is shown on the left side of Figure 8 as a hat.

[0139]

number

[0140]

number

[0141] In Fig. 8, the true value is shown by a dashed line, the estimated value of the story stiffness estimated based on the lower point is shown by a light-colored wide line (or dot), and the estimated value of the story stiffness estimated based on the upper point is shown by a dark-colored narrow line (or dot). The estimated story stiffness (k i hat) are distributed near the true value (dashed line), and Hi (ω q ) S / (S+N) ratio estimate (R m hat) to obtain a reliable estimate of the story stiffness (k i hat) could be extracted.

[0142] The present invention is not limited to the above-described embodiment, and various modifications are possible. For example, the present invention includes configurations that are substantially the same as those described in the embodiment (for example, configurations with the same functions, methods, and results, or configurations with the same purpose and effect). The present invention also includes configurations in which non-essential parts of the configurations described in the embodiment are replaced. The present invention includes configurations that have the same effects as the configurations described in the embodiments or that can achieve the same purpose as the configurations described in the embodiments. The present invention also includes configurations in which publicly known technology is added to the configurations described in the embodiments. [Explanation of symbols]

[0143] 1...building, 1a...multiple mass point system model, 11...story, 14...acceleration sensor, 2...story stiffness estimation device, 21...computing unit, 22...storage unit

Claims

1. A method for estimating a story stiffness of a predetermined story in a multi-story building using a multi-mass system model, comprising the steps of: A step of performing a Fourier transform on the acceleration of the i-th mass point counting from below the mass point corresponding to the roof of the building and the accelerations of mass points above and below the i-th mass point to calculate a Fourier spectrum of each acceleration; Using the Fourier spectrum of each acceleration obtained in the above step and the mass of the i-th mass point, the layer stiffness (k ｉ ) and The layer stiffness (k ｉ extracting only layer stiffnesses having an estimated S / (S+N) ratio of equal to or greater than a predetermined reference value close to 1, the estimated S / (S+N) ratio being calculated using the following formula (3); A method for estimating story stiffness of a predetermined story, comprising: [0010] [0025] [0030]

2. A layer stiffness estimation device for executing the layer stiffness estimation method for a predetermined layer according to claim 1, A calculation unit and a storage unit are provided, The calculation unit is A process of acquiring an acceleration at the i-th mass point and an acceleration of mass points above and below the i-th mass point; A process of performing a Fourier transform on each of the acquired accelerations to calculate a Fourier spectrum of each acceleration; The story stiffness (k ｉ ) and The calculated layer stiffness (k ｉ ) extracting only those layer stiffnesses having an estimated S / (S+N) ratio close to 1 or greater than a predetermined reference value; A layer stiffness estimation device, comprising:

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