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 prescribed layer, with which a number of measurement points of acceleration can be significantly reduced compared to prior art.SOLUTION: A layer rigidity estimation method for a prescribed layer is a method for estimating the rigidity of a prescribed layer in a multi-layer building by using a multi-mass point system model. The layer rigidity estimation method includes: a process (S20) of calculating a Fourier spectrum of each acceleration by subjecting acceleration at an i-th mass point counted from below a mass point corresponding to the roof floor of a building and acceleration at mass points above and below the i-th mass point, respectively, to Fourier transform; and a process (S30) of calculating a layer rigidity (ki) of a prescribed layer that is located between the i-th mass point and an (i-1)th mass point by using the Fourier spectrum of each acceleration obtained in the process (S20), and using a mass of the i-th mass point.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 placed on structural health monitoring technology to ensure the safety of buildings. For example, methods have been proposed to identify the story stiffness of each story of a building in order to evaluate damage to buildings caused by earthquakes and other events (Patent Document 1, Non-Patent Documents 1 and 2). When a member of a certain story of a building is damaged by an earthquake or other event, the stiffness of that 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] Japanese Patent Application Laid-Open No. 2016-194514 [Non-patent literature]

[0004] [Non-Patent Document 1] Mitsuru Nakamura and Yuzuru Yasui, "Evaluation of Story Damage in Earthquake-Damaged Steel Buildings Based on Microtremor Measurements," Journal of Structural Engineering, Architectural Institute of Japan, No. 517, pp. 61-68, 1999 [Non-patent document 2] Yoshimura, R. and Mita, A., "Online Identification of Building Structural Parameters Based on Multi-Input Multi-Output Models," Journal of Structural Engineering, Architectural Institute of Japan, 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 more 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 story stiffness of a predetermined story that can significantly reduce the number of acceleration measurement points compared to conventional methods. [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 as the following aspects or application examples.

[0008] [1] One aspect of the method for estimating the story stiffness of a predetermined story according to the present invention is to A method for estimating the story stiffness of a predetermined story in a multi-story building using a multi-mass system model, comprising: a step of performing a Fourier transform on the acceleration at 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 the 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 Including fruit, The step of calculating the Fourier spectrum of each acceleration and the step of calculating the story stiffness (k i ) of the predetermined story are performed for an arbitrary q. It is characterized by:

[0009]

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[0010]

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[0011] [2] In one aspect of the method for estimating layer stiffness of a predetermined layer, The layer stiffness (k i The method may further include a step of extracting only those layer stiffnesses having an estimated S / (S+N) ratio obtained by the following formula (3) that is equal to or greater than a predetermined reference value close to 1 from the total stiffnesses.

[0012]

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[0013] [3] 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 A process of acquiring the acceleration of the i-th mass point and the accelerations of the upper and lower mass points; A process of Fourier transforming each of the acquired accelerations to calculate the Fourier spectrum of each acceleration; The story stiffness (k i ) and The present invention is characterized by carrying out the following. [Effects of the Invention]

[0014] According to one aspect of the method for estimating story stiffness of a predetermined story and one aspect of the story stiffness estimation device of the present invention, the number of acceleration measurement points can be significantly reduced compared to the conventional method. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a diagram conceptually showing a schematic diagram of a building used in a story stiffness estimation method according to an embodiment of the present invention and a multi-mass system model thereof. FIG. [Figure 2] 1 is a block diagram showing an example of the configuration of a layer stiffness estimation device for a predetermined layer according to an embodiment of the present invention; [Figure 3] 10 is a flowchart illustrating an example of a method for estimating the layer stiffness of a predetermined layer according to the present embodiment. [Figure 4] 10 is a flowchart showing another example of the method for estimating the layer stiffness of a predetermined layer according to a modified example. [Figure 5] 5 is a flowchart showing an example of processing for each section in FIG. 4. [Figure 6] 5 is a flowchart showing an example of a filtering process in FIG. 4. [Figure 7] 5 is a flowchart showing an example of an S / (S+N) estimation process in FIG. 4. [Figure 8] 10 shows an input (simulated ground motion ug··) in the embodiment. [Figure 9] FIG. 10 is a diagram showing the results of verification calculations of the layer stiffness estimation method of the first embodiment. [Figure 10] FIG. 10 is a diagram showing the results of verification calculations of the layer stiffness estimation method of the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] 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 content of the present invention as defined in the claims. Furthermore, not all of the configurations described below are necessarily essential components of the present invention.

[0017] 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 (a) is a schematic diagram of a building 1 used in a story stiffness estimation method according to this embodiment, and Figure 1 (b) is a conceptual diagram 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.

[0018] 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 masses corresponding to the floors of each floor are m0, m1, m2, ..., m i-1 ,mi ,m i+1 ,…m n-1 In the initial system position, n mass points are placed at vertical intervals from the ground (GL). Mass m1 is the mass of the first mass point counting from the mass point on the roof (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 in a 10-story building) counting from the mass point below the roof mass point. Between adjacent mass points above and below, 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. In other words, the story stiffness (k i ) is estimated.

[0019] Also, in Figure 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 displacement (GL) 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 as u i (t), u g This is expressed as ··(t).

[0020] 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 all floors. The acceleration sensors 14 may be triaxial accelerometers.

[0021] The multi-mass system model 1a is a system in which the masses m0...m of each mass are calculated from 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.

[0022] In this case, the equation of motion (force balance equation) of the multi-mass system model 1a is as shown in the following equation (4).

[0023]

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[0024] Based on this equation, the following formulas (1) and (2) can be derived as described below.

[0025]

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[0026]

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[0027] The layer stiffness estimation device 2 according to this embodiment shown in FIG. 2 is a device that executes an embodiment of the 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.

[0028] 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), 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 (not shown). The calculation unit 21 can be configured from a CPU, RAM, etc., and executes a program stored in the storage unit 22. The storage unit 22 can be configured from a storage device such as a hard disk drive, and stores the mass of each mass point of the multi-mass system model 1a, the above formula (1) and formula (2), etc. The storage unit 22 may also store measurement data acquired from the acceleration sensor 14.

[0029] 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 the measurement data of the acceleration sensors 14 can be acquired, it can be acquired by a method other than a communication network, for example, by importing the measurement data using a USB memory. In addition, the story stiffness estimation device 2 can be operated by The apparatus 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.

[0030] The calculation unit 21 calculates the acceleration u at at least the i-th mass point. 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 the obtained accelerations to obtain the Fourier spectrum u of each acceleration. 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 of a given layer (k i Each step will be described later in the section on the story stiffness estimation method.

[0031] The story stiffness (k i ) is the story stiffness (k i ), it is an estimated value of the story stiffness of a specific story in the actual building 1.

[0032] The story stiffness estimation device 2 estimates the story stiffness (k i ) can be estimated, 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 from many stories as in the past; it is sufficient to acquire acceleration data from at least three mass points (floors on three floors). This makes it possible to significantly reduce the number of acceleration measurement points in a super-high-rise building. If story stiffness can be estimated, for example, if there is a story whose story stiffness has decreased before and after an earthquake, it can be determined that that story has been damaged. Furthermore, even if there are no pre-earthquake records, if there is a story whose story stiffness is unnaturally low when comparing the story stiffness of each story, it can be determined that that story has been damaged. Furthermore, by estimating story stiffness by periodically measuring vibrations, not just after an earthquake, it is possible to grasp the degree of deterioration of the building 1 over time.

[0033] Next, it will be explained that the above formulas (1) and (2) can be derived from the above formula (4). Hereinafter, where necessary, the mass matrix (matrix where mi is arranged) in the above formula (4) will be written as M, the damping matrix (matrix where ci is arranged) as C, and the stiffness matrix (matrix where ki is arranged) as K.

[0034] First, by Fourier transforming the time distribution of the displacement, velocity, and acceleration of a mass point, we obtain the frequency distribution of the displacement, velocity, and acceleration. i (ω), u i ·(ω), u i ··(ω), u g It can be written in a symbol such as (ω) where time t is replaced by angular frequency ω. i (ω), u i ·(ω), u i ··(ω), u g The above equation (4) also holds true for (ω), but due to the nature of the Fourier transform, u i (ω), u i ·(ω), u i ··(ω), u g Between (ω), the following equations (5) and (6) hold.

[0035]

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[0036]

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[0037] Then, by substituting the above formulas (5) and (6) into the above formula (4), the following formulas (7) and (8) are established.

[0038]

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[0039]

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[0040] In addition, the jth 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 , j}. In this case, due to the properties of the natural angular frequency and the eigenvalue vector, the eigenvector {φ0,φ 1j ,…,φ n-1 , j} is the angular frequency λ j When the ground displacement is zero (u g (ω=λ j )=0), the equation of motion in the eigenspace is given by the following equation (9) from the above equation (8).

[0041]

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[0042] Here, the masses of all mass points are assumed to be known from, for example, the design specifications, and the accelerations at mass points on three floors including the predetermined floor (actually, in the case of 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 time intervals. Let this time interval be dt. p = dt(p-1) (p=1,2,3,...), the time distribution of the actual acceleration record is a continuous u i (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,…).

[0043] If the known terms in the equations of motion of the above formulas (4), (7), and (9) are collected on the right-hand side, the following formulas (10) to (12) are obtained.

[0044]

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[0045]

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[0046]

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[0047] Furthermore, for the sake of simplicity, symbols can be defined as in the following formulas (2) and (13).

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[0050] In this case, the relationships of the following formulas (14) and (15) hold.

[0051]

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[0053] The right-hand sides of the above formulas (14) and (15) can be written as the following formulas (16) and (17).

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[0055]

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[0056] In Non-Patent Document 1, which is a conventional technique, 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.

[0057] In the present invention, the above formula (11) is transformed as follows based on the integration rule of the Fourier transform (the above formula (5)):

[0058]

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[0059] If we extract only the (i+1)th row from the above equation (18), we get the following equation (19).

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[0061] By rearranging the above equation (19), the following equation (20) is obtained.

[0062]

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[0063] s i In the definition formula (above formula (2)), ω q Since there is a frequency dependency, i ,c i The fact that does not change with time or frequency is a property of the multi-mass system model 1a in Figure 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, From equation (20), the following equation (21) holds.

[0064]

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[0065] 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 equation (21), s i ,s i+1 is determined as shown in the following formula (1).

[0066]

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[0067] As explained above, it can be seen that the above formulas (1) and (2) hold true from the above formula (4). 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 story stiffness of a given story (k i ) as well as k i+1 ,c i ,c i+1 At this time, the value used in the calculation is discrete If the frequency width b is at least 1 or more, a solution can be found. However, discrete If the frequency band 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 too low, an average result will be obtained that ignores frequency changes, and for reasons described later, this may have a negative effect on the calculation accuracy. Therefore, it is preferable to set b appropriately, for example, between 10 and 100.

[0068] 2. Layer stiffness estimation method A method for estimating story stiffness of a predetermined story according to one embodiment of the present invention will be described with reference to Figures 1 to 3. Figure 3 is a flowchart showing an example of the method for estimating story stiffness of a predetermined story according to this embodiment. In the following explanation, the story stiffness of a predetermined story of a building 1 shown in Figure 1(a) is estimated by a story stiffness estimation device 2 shown in Figure 2 using a multi-mass system model 1a shown in Figure 1(b). Portions that overlap with the explanation of the story stiffness estimation device 2 will be omitted.

[0069] The method for estimating the story stiffness of a predetermined 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 (S20) of calculating at least the Fourier spectrum of acceleration, and a step (S21) of estimating the story stiffness (k i ) (S30). In this embodiment, the method may further include the step of acquiring acceleration data (S10).

[0070] S10: In the step of acquiring acceleration data (S10), the story stiffness estimation device 2 acquires acceleration measurement data (hereinafter referred to as "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 the bottom of 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] S20: In the step (S20) of calculating the Fourier spectrum of acceleration, the calculation unit 21 performs a Fourier transform on each of the accelerations acquired in S10 to obtain the Fourier spectrum u of each acceleration. i ··(ω)+u g ··(ω), u i-1 ··(ω)+u g ··(ω), u i+1 ··(ω)+u g Calculate (ω).

[0072] S30: Story stiffness of a given story (k i The step (S30) of calculating the Fourier spectrum u of each acceleration obtained in the step S20 by the calculation unit 21 is i ··(ω)+u g ··(ω), u i-1 ··(ω)+u g ··(ω), u i+1 ··(ω)+u g(ω) and the mass m of the i-th particle i and the story stiffness (k i ) is calculated.

[0073]

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[0075] The above equation (1) is based on the known condition of mass m i and the Fourier spectrum u of each acceleration calculated in S20 i ··(ω)+u g The calculation can be performed by the calculation unit 21 using the above formula (1). i Then, s in the above formula (2) is obtained. i From the real part of k i From the above formula (2), s i-1 is calculated as a side effect. i The imaginary part of ω q By dividing by c i is obtained. Here, k i and c i are the story stiffness and viscosity of a predetermined story of the multi-mass system model 1a, and therefore are estimated values ​​for the actual building 1.

[0076] According to one aspect of the method for estimating story stiffness of a predetermined story and one aspect of the story stiffness estimation device of the present invention, the number of acceleration measurement points can be significantly reduced compared to the conventional method.

[0077] 3. Variations A method for estimating story stiffness of a predetermined story according to a modified example will be described with reference to Figs. 4 to 7. Fig. 4 is a flowchart showing another example of a method for estimating story stiffness of a predetermined story according to a modified example, Fig. 5 is a flowchart showing an example of processing for each section in Fig. 4, Fig. 6 is a flowchart showing an example of filtering processing in Fig. 4, and Fig. 7 is a flowchart showing an example of S / (S+N) estimation processing in Fig. 4. In the following description, the method for estimating story stiffness of a predetermined story according to a modified example will be described with reference to Figs. 4 to 7. The story stiffness of a predetermined story is estimated using the story stiffness estimation device 2 shown in FIG.

[0078] The layer stiffness estimation method for a predetermined layer according to the modified example can further include step S41 in addition to the layer stiffness estimation method described using Fig. 3. In this modified example, step S31 is performed using equation (25) described below, which is a modification of equation (1) above, instead of step S30.

[0079] The method for estimating story stiffness according to the modification shown in FIG. 4 executes, for example, the processes of S10, S11, S12, S21, S23, S25, S27, S31, S32, and S41. The method described in "2. Story stiffness estimation method" also estimates the story stiffness (k i However, the data acquired from the acceleration sensor 14 may contain measurement errors, and it is desirable to extract a value of the layer stiffness that is less affected by the measurement errors. In this modification, the more reliable layer stiffness (k i ) is extracted. The step of acquiring acceleration data (S10) is the same as that described in the above embodiment, and therefore a description thereof will be omitted.

[0080] First, before explaining each process, in order to extract a highly reliable value from the value of the story stiffness calculated from the acceleration data, we use the above formula (1) to calculate H, which is an evaluation index of reliability. i (ω q ) is defined. First, the above formula (1) can be transformed to obtain the following formula (22).

[0081]

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[0082] For each row, it is possible to divide "the displacement difference vector on the left side by the acceleration value on the right side", and the following equation (23) holds.

[0083]

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[0084] The matrix on the left side of the above equation (23) is H i (ω q ) is defined as follows:

[0085]

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[0086] In this modification, H i (ω q The S / (S+N) ratio of the scalar quantity is used to extract a value of the layer stiffness that is less affected by measurement errors. The SN (signal / noise) ratio (in this modification, 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 modification, H i (ω q ) than the S / N ratio of H i (ω q ), it may be desirable to consider the SN ratio of each element that makes up the matrix H. However, this would result in a band where the SN ratio is excessively high (relative to the low accuracy of the estimated story stiffness), making it difficult to extract only estimated values ​​that are close to the true value. In this modified example, we will not only consider the SN ratio of each element of the matrix individually, but also the relationship between the elements. Therefore, in this modified example, the matrix H i (ω q ) is the quantity equivalent to 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 expressed as "matrix H i (ω q ) power (hereinafter referred to as powH i (ω q ) and define it as powH i (ω q By estimating the ratio of the signal component S to the noise component N in the eigenvalue, a reliable estimate of the story stiffness can be extracted.

[0087] S11: Setting value of section length (S11) provides data of a preset setting value of section length to step S12. The section length is set, for example, between 10 and 100 times the primary natural period of the building 1 to be examined.

[0088] 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 acceleration data of 100 seconds, it is divided into five sections of 20 seconds each.

[0089] S21: The process for each section (S21) includes a process corresponding to the process for obtaining the Fourier spectrum of the acceleration (S20) described above. In the process for each section (S21), the calculation unit 21 calculates the Fourier spectrum of each acceleration obtained in the process of S21, and calculates the SN (signal / noise) ratio of the data by using H i (ω q The detailed process will be described later with reference to FIG.

[0090] S23: In the process of checking whether all sections have been processed (S23), if S21 indicates that all sections have been processed (Yes), the process proceeds to S25, and if S21 indicates that all sections have not been processed (No), the process returns to S21.

[0091] S25:H i (ω qThe filtering process (S25) of H is a process in which the calculation unit 21 removes frequencies that cause numerical instability. Only frequencies whose values ​​in all sections satisfy the filter conditions are used to generate the H generated in S21. i (ω q The detailed process will be described later with reference to FIG.

[0092] 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 estimated value R m The hat is calculated. The detailed process will be described later with reference to FIG.

[0093] 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 ) can reduce the influence of measurement errors (noise components).

[0094] S31: Layer stiffness (k i The estimation process (S31) of H ) corresponds to the step (S30) of calculating the story stiffness of the predetermined story. 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 steps (S25 and S29). Then, s is calculated by the following formula (25). i Calculate s using the following formula (2)i The real part of the story stiffness of a given story (k i ) and calculate the attenuation c from the imaginary part. i can be calculated.

[0095]

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[0096]

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[0097] S32: The reference value (S32) of S / (S+N) provides data of a predetermined reference value set in advance to step S41. By setting the predetermined 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 step S41.

[0098] S41: The process of extracting the story stiffness of the frequency where S / (S+N) is equal to or greater than the reference value (S41) is carried out by the calculation unit 21 by extracting the story 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.

[0099]

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[0100] 3.1. Processing by Section The process for each section (S21) will be described with reference to Fig. 5. The process for each section (S21) shown in Fig. 5 executes the processes of S210, S212, S214, S216, S218, and S220.

[0101] S210: Baseline Correction Processing (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.

[0102] 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.

[0103] S214: The Fourier transform process (S214) is performed by the calculation unit 21 to convert the acceleration data (u i (t)+u g ,(t)) and perform a Fourier transform (u i ··(ω)+u g ··(ω))

[0104] S216: The process of calculating the inter-story displacement (S216) is performed by the calculation unit 21 using the acceleration (u i ··(ω)+u g (ω)) to calculate all ω in the target band. q For H i (ω q ) is created. H created in S216 i (ω q ) is expressed as the following equation (26).

[0105]

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[0106] 3.2.H i (ω q ) filtering process Using Figure 6, the above H i (ω q ) filtering process (S25) will be explained. i (ω q ) filtering process (S25) is performed by filtering the H i (ω q ) is filtered by S250, S252, S254, S256, S258, S260, S262 and S254, and only the frequencies that satisfy the filter conditions are used to perform the processing of S266. In general, in numerical calculations, division by a value close to zero causes numerical instability. Hi (ω q ), frequencies that cause numerical instability can be excluded. i ··(ω)+u g When (ω) is approximately 0, it is preferable to use the following equation (27) instead of the above equation (26): ω=ω n By eliminating the element, the arrangement of angular frequencies in the row direction in the following equation (27) becomes discontinuous, but this does not cause any particular problem.

[0107]

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[0108] In Figure 6, m is the total number of sections, p a il is the u in the pth interval i ··(ω q )+u g ··(ω q ) and ε is the absolute value of p a il represents the threshold value for whether or not ε is considered to be close to zero. ε can be set appropriately by the person conducting the analysis. ε can be expressed as, for example, p a il It may be set to a value ranging from a few tenths to a few tens of thousands of the average value in the frequency band under consideration.

[0109] 3.3.H i (ω q ) S / (S+N) ratio estimation process Using Figure 7, the above H 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 calculates S29 Execute the processes of 0, S292, S294, S296, S298, and S300.

[0110] 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 m H i (ω q ) and multiplying it by the ensemble average. In step S296, N is calculated using the following formula (28), in step S298, S is calculated using the following formula (29), and in step S300, R is calculated using the following formula (30). m Calculate the hat, where R m hat is the H i (ω q ) using powH i (ω q ) is an estimate of the S / (S+N) ratio.

[0111]

number

[0112]

number

[0113]

number

[0114] 3.4.powH i (ω q ) S / (S+N) ratio estimation formula The process by which the above formula (30) was derived will be explained below.

[0115] (1) Definition of symbols Hereafter, we will distinguish between measured values ​​(values ​​containing noise) and true values ​​by adding "~" to the measured values. First, we will assume that the absolute acceleration has a sufficiently high S / (S+N) ratio, and that the measured value and true value are approximately equal.

[0116]

number

[0117] 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 noise is eliminated, the influence of noise cannot be ignored, and the relationship between signal and noise is set as follows:

[0118]

number

[0119] For simplicity, H i (ω q ) are written as follows:

[0120]

number

[0121] Additionally, the filtered H i (ω q ) element in the kth row (h k1 ~, h k2 The angular frequency corresponding to ω qk From the above equations (31) and (32), h q1 ~, h q2 ~ can be written as follows:

[0122]

number

[0123]

number

[0124] Here, the elements of the above formula (34) and formula (35) are represented by the following symbols.

[0125]

number

[0126]

number

[0127]

number

[0128]

number

[0129]

number

[0130] Then, when the above formulas (34) and (35) are substituted with the above formulas (36) to (39), the following formulas (41) and (42) are obtained.

[0131]

number

[0132]

number

[0133] (2)h k1 ~, h k2 Probabilistic properties of First, h kl ~(l=1,2) signal part hkl is determined deterministically by the physical characteristics of the mass system, and is therefore considered to have no probabilistic variation, and therefore the following equation holds:

[0134]

number

[0135] From the definition of noise, the following properties can be assumed:

[0136]

number

[0137]

number

[0138]

number

[0139] Furthermore, when considering the expected value of the ensemble average of noise, the following relationship holds due to the properties of random variables with an expected value of zero.

[0140]

number

[0141] Furthermore, H i (ω q ), the following two assumptions hold: First, n is sufficiently large so that the following approximation holds:

[0142]

number

[0143] Second, xk is time-stationary, and E[xq ] also have the same value. Therefore, the following equation holds:

[0144]

number

[0145] (3) H i * (ω q )H i (ω q ) Approximation formula From the above formula (31), H i * (ω q )H i (ω q ) becomes:

[0146]

number

[0147] Combining the above equation (50) and the above equation (48), the following approximation holds:

[0148]

number

[0149] Here, the following relationship holds from the above formula (41), formula (42), and formulas (44) to (46).

[0150]

number

[0151]

number

[0152] Similarly, the following relationship also holds:

[0153]

number

[0154]

number

[0155] Then, by substituting the above formulas (52) to (55) into the above formula (51), the following relationship can be derived.

[0156]

number

[0157] Therefore, based on the assumption of stationarity in the above equation (50), the following equation holds:

[0158]

number

[0159] Furthermore, by combining the above equation (56), the above equation (43), and the above equation (47), the following equation is established.

[0160]

number

[0161] (4) <H i (ω q )> Estimation formula for S / (S+N) ratio First, by taking the difference between the above equation (57) and the above equation (58), the following equation can be derived.

[0162]

number

[0163] Using the above equation (59), the following approximation holds for the matrix of the noise component N in the above equation (28).

[0164]

number

[0165] Therefore, the following approximation holds for the matrix of the signal component S in the above equation (29):

[0166]

number

[0167] From the above equations (58) and (61), S is <H i * (ω q )>m <H i (ω q )>m, the noise component has been removed, so by the following equation (30), <H i (ω q It can be deduced that the S / (S+N) ratio can be estimated for )>m.

[0168]

number

[0169] (Verification target and input data) In this example, the estimated story stiffness values ​​calculated using the story stiffness estimation method according to the present invention were verified. The multi-mass system model used for verification had five masses (m0=m1=...=m4=1t), and the story stiffness (kN / m) of each story was as shown in Table 1, with damping set to 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.

[0170] [Table 1]

[0171] The input was white noise as shown in Figure 8. The sampling rate was 100 Hz and the duration was 163.84 seconds.

[0172] (Example 1) The frequency response of the multi-mass system model for the input in Figure 8 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 is as the simulated earthquake observation record to obtain the acceleration data in Example 1 (S10). Then, according to the flowchart explained using Figure 3, the simulated earthquake observation record was Fourier transformed (S20), and s was calculated using the following formula (1) in a frequency width of 0.5 Hz (±0.25 Hz from the center frequency). i Calculate s using the following formula (2) i From the real part of the story stiffness k i The estimated value of (k i hat) and calculate the attenuation c from the imaginary part i The estimated value of (c i hat) was calculated (S30). i Regarding , 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 value of the damping constant (h i The estimated value of the calculated story stiffness (k i hat) and the estimated damping constant (h i hat) is shown in Figure 9.

[0173]

number

[0174]

number

[0175] In Figure 9, the true value is shown by a dashed line, the estimated value of the story stiffness estimated with the bottom point as the reference is shown by a light-colored wide line, and the estimated value of the story stiffness estimated with the top point as the reference is shown by a dark-colored narrow line. In Figure 9, the bottom point reference and the top point reference indicate whether the estimation was performed using the mass point located at the top of the story to be estimated as the reference point (mass point i in the above equations (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 Therefore, 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 9, the true value and the estimated result matched accurately, confirming the validity of the theory.

[0176] (Example 2) Next, the true value of the mass system response waveform in Example 1 was added to the RMS value of the ground motion (approximately 0.79 m / s 2 Gaussian noise with a standard deviation of 1% of the ground motion and the responses at each point was added to the simulated earthquake observation record to obtain the acceleration data for Example 2 (S10). Then, the processing for each section (S21) was performed for all sections (S23) according to the flowchart explained with reference to FIGS. 4 to 7. i (ω q ) filtering process (S25) is performed to obtain the ensemble average (S29), and then s is calculated using the following equation (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 From 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 base value of S / (S+N) was set to 0.97 (S32), and the layer stiffness k i The estimated S / (S+N) ratio (R m Only those stories with a stiffness of 0.97 or more were extracted (S41). i (ω qThe estimated values ​​of the S / (S+N) ratio of the RC are shown on the right side of Figure 10, and the points where the estimated value is 0.97 or more are the estimated value of the story stiffness (k i hat) on the left side of Figure 10.

[0177]

number

[0178]

number

[0179] In Figure 10, 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). i hat) are distributed near the true value (dashed line), and H i (ω q ) S / (S+N) ratio estimate (R m hat) to obtain a reliable estimate of the story stiffness (k i Only the "hat" could be extracted.

[0180] The present invention is not limited to the above-described embodiments, and various modifications are possible. For example, the present invention includes configurations that are substantially the same as those described in the embodiments (for example, configurations with the same function, method, and result, 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 embodiments are replaced. The present invention also includes configurations that achieve the same effects or purposes 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]

[0181] 1...building, 1a...multi-mass system model, 11...story, 14...acceleration sensor, 2...story stiffness estimation device, 21...computing unit, 22...storage unit

Claims

1. A method for estimating the story stiffness of a predetermined story in a multi-story building using a multi-mass system model, comprising: a step of performing a Fourier transform on the acceleration at 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 the Fourier spectrum of each acceleration; a step of calculating the story stiffness (ki) of the predetermined story between the i-th mass point and the (i-1)-th mass point by the following formulas (1) and (2) using the Fourier spectrum of each acceleration obtained in the step and the mass of the i-th mass point; Including, The method for estimating the story stiffness of a predetermined story, wherein the step of calculating the Fourier spectrum of each acceleration and the step of calculating the story stiffness (ki) of the predetermined story are performed for an arbitrary q. [Equation 1] [Equation 2]

2. In claim 1, A method for estimating layer stiffness of a specified layer, characterized by further comprising a step of extracting only layer stiffnesses (ki) of the specified layer whose estimated value of the S / (S+N) ratio obtained by the following equation (3) is equal to or greater than a specified reference value close to 1. [Equation 3]

3. 3. A layer stiffness estimation device for executing the layer stiffness estimation method for a predetermined layer according to claim 1, comprising: A calculation unit and a storage unit are provided, The calculation unit A process of acquiring the acceleration of the i-th mass point and the accelerations of the upper and lower mass points; A process of performing a Fourier transform on each of the acquired accelerations to calculate the Fourier spectrum of each acceleration; a process of calculating a story stiffness (ki) of the predetermined story using the calculated Fourier spectrum of each acceleration and the mass of the i-th mass point stored in the storage unit; A layer stiffness estimation device, characterized by executing the following.

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