JP2012173001A - Estimation method of damaged part - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an estimation method of a damaged part with which the damaged part in a building can be estimated even with a small number of sensors.SOLUTION: A building T relating to an estimation target is modeled as a multilayer structure model A with an (n)-degree-of-freedom system. Then, (1) a primary eigen-circular vibration number λafter earthquake and a primary eigen-vector {Φ} are temporarily determined to calculate rigidity kafter earthquake and a rigidity matrix [K], (2) a "primary eigen-vector {Ψ}" corresponding to a mass matrix [M] and the rigidity matrix [K] are calculated, (3) the rigidity k,is multiplied by inter-layer pseudo displacement udetermined from the primary eigen-vector {Ψ} to calculate an inter-layer pseudo inertia force Q, and (4) the inter-layer pseudo inertia force Qis multiplied by an inverse of an inter-layer pseudo inertia force Qbefore earthquake to calculate a determination reference value q. After repeating the steps (1) to (4) multiple times until the determination reference value qmeets a predetermined condition, a damaged part is estimated by collating the determination reference value q.

Description

  The present invention relates to a method for estimating a damaged part of a building subjected to disturbance or a deteriorated building.

  Patent Document 1 discloses a method for estimating a damaged part of a building. The method of Patent Document 1 is to calculate a reduction rate of the stiffness of a column or a beam by using an output value of a sensor installed on each floor, and to estimate a damaged portion based on the obtained reduction rate.

JP 2004-264235 A

  In Patent Document 1, it is necessary to install a sensor on each floor of a building. However, if a sensor is to be installed on each floor of a building in service, not only wiring work becomes complicated, but also the usage status of office space and room space Depending on the situation, it may not be possible to secure the installation location of the sensor.

  From such a point of view, an object of the present invention is to provide a method for estimating a damaged part, which can estimate a damaged part of a building layer or a member with a small number of sensors.

The invention according to claim 1 for solving the above-mentioned problem is
(1) A post-measurement step of performing vibration measurement on the upper floor of a building after disturbance or deterioration and obtaining a frequency response function G for vibration at a reference point;
(2) An initial setting step for obtaining a peak frequency f _p in a function obtained by multiplying the frequency response function G by the inverse of the initial frequency response function G ₀ acquired before disturbance or deterioration;
(3) A vibration characteristic assumption step for setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for an n-degree-of-freedom multi-layer structure model that models the building;
(4) Substituting the temporary primary natural frequency λ _S , the temporary primary eigenvector {Φ _S } and the mass matrix [M ₀ ] of the multilayer structure model into the non-damped free vibration equation, A stiffness calculation step for calculating the stiffness k _{S, i} for the structural element;
(5) Mode for calculating the primary natural circular frequency ω _S and the primary eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ] created based on the stiffness k _{S, i} Calculation step,
(6) An interlayer pseudo displacement calculating step for determining an interlayer pseudo displacement u _{S, i} of each layer of the multilayer structure model based on a component of the primary eigenvector {Ψ _S } normalized so that the maximum value is a constant a.
(7) a pseudo inertia force calculation step of calculating the interlayer pseudo inertia force Q _{S, i} by multiplying the rigidity k _{S, i} by the interlayer pseudo displacement u _{S, i} ;
(8) The criterion value q is obtained by multiplying the inter-layer pseudo inertia force Q _{S, i} by the reciprocal of the inter-layer pseudo inertia force Q _{0, i} corresponding to the rigidity k _{0, i} before disturbance or deterioration and the inter-layer pseudo displacement u _{0, i. A} criterion value calculation step for calculating _{S and i} ,
(9) A determination step of determining whether or not the determination reference value q _{S, i} is between the lower limit threshold and the upper limit threshold set with 1 therebetween,
The method of estimating the damage location which arose in the building by repeating said (3)-(9) in multiple times,
(A) In the first of the vibration characteristics assumption step, the temporary mode the value obtained by multiplying 2π peak frequency f _p and the temporary first natural circular frequency [lambda _1, and normalized so that the maximum value becomes constant a Let the vector {Φ ₀ } be a temporary primary eigenvector {Φ ₁ },
(B) In the second and subsequent vibration characteristic assumption steps, the primary natural circular frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary natural vibration. Let the number λ _S and the temporary primary eigenvector {Φ _S },
(C) In the second and subsequent determination reference value calculation steps, the determination reference value q _{S−1, i is the same} as the determination reference value q _{S−1, i} for all the determination reference values q _S− 1i calculated in the previous determination reference value calculation step. It determines whether or not accommodated between the lower threshold and the upper threshold if the determination reference value is determined not accommodated q _{S-1, i} is present, the determination reference value q _{S-1 , i} by multiplying the current interlayer pseudo inertia force Q _{S, i} of the layer corresponding to _{i by} the inverse of the interlayer pseudo inertia force Q _{0, i} and 2πf _p / ω _S , calculate q _{S, i} ,
(D) When an affirmative determination is continuously obtained at least twice in the determination step after the S-th time, the determination reference value calculated in the determination reference value calculation step at any time after the S-th time is checked, This is an invention in which a layer having a judgment reference value less than 1 is used as a damaged portion.

The subscripts of the temporary primary eigenfrequency λ _S , the temporary primary eigenvector {Φ _S }, the stiffness matrix [K _S ], the primary eigencircle frequency ω _S , and the primary eigenvector {Ψ _S } are repeated. It corresponds to “number of times”.
The first subscript “S” of the stiffness k _{S, i} , the interlayer pseudo-displacement u _{S, i,} and the interlayer pseudo-inertial force Q _{S, i} corresponds to the number of repetitions, and the second The subscript “i” is a natural number equal to or less than n and corresponds to the number of the mass point.

In short, the invention according to claim 1
A vibration characteristic assumption step for “temporarily determining” a primary eigencircle frequency and a primary eigenvector after the earthquake;
Stiffness calculation step to calculate post-earthquake stiffness k _{S, i} using non-damped free vibration equation,
Temporarily determined by calculating the eigenvalue analysis of the first eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] (which reflects the post-earthquake stiffness k _{S, i} ) and the mass matrix [M ₀ ] A mode calculation step for correcting the primary eigenvector;
An interlayer pseudo displacement calculating step for calculating an interlayer pseudo displacement u _{S, i} based on the primary eigenvector {Ψ _S };
A pseudo inertial force calculation step for calculating an inter-layer pseudo inertial force Q _{S, i} (= u _{S, i} × k _{S, i} ) after the earthquake;
A method of estimating a damaged portion including a determination reference value calculation step for calculating a determination reference value q _{S, i} (= Q _{S, i} / Q _{0, i} ), wherein the determination reference value q _{S, i} is a predetermined condition Each step is repeated a plurality of times until the condition is satisfied, and then the damaged portion is estimated by checking the determination reference value q _{S, i} that satisfies the condition.

Further, the invention according to claim 2 is replaced with the above (6) to (9),
(10) a determination reference value calculation step for calculating a determination reference value r _{S, i} by multiplying the rigidity k _{S, i} by the reciprocal of the rigidity k _{0, i} before disturbance or deterioration;
(11) includes a determination step of determining whether or not the determination reference value r _{S, i} is between the lower limit threshold and the upper limit threshold set with 1 therebetween,
It is a method of estimating a damaged part generated in a building by repeating the above (3) to (5), (10) and (11) a plurality of times,
(A) In the first of the vibration characteristics assumption step, the temporary mode the value obtained by multiplying 2π peak frequency f _p and the temporary first natural circular frequency [lambda _1, and normalized so that the maximum value becomes constant a Let the vector {Φ ₀ } be a temporary primary eigenvector {Φ ₁ },
(B) In the second and subsequent vibration characteristic assumption steps, the primary natural circular frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary natural vibration. Let the number λ _S and the temporary primary eigenvector {Φ _S },
(C ′) In the second and subsequent determination reference value calculation steps, between all the determination reference values r _{S−1, i} calculated in the previous determination reference value calculation step, between the lower limit threshold value and the upper limit threshold value. If there is a determination reference value r _{S-1, i} determined not to be stored, the current layer of the layer corresponding to the determination reference value r _{S-1, i} is determined. stiffness k _S, the _i, said by multiplying the stiffness k _{0, i} reciprocal and 2πf _p / ω _S of calculating the current criterion value r _{S, i} in the layer,
(D ′) When a positive determination is obtained at least twice continuously in the determination step after the S-th time, the determination reference value calculated in the determination reference value calculation step at any time after the S-th time is checked. In this invention, a layer having a criterion value lower than 1 is regarded as a damaged portion.

The invention according to claim 3
(1 ′) a post-measurement step of performing vibration measurement on an upper floor of a building after disturbance or deterioration, and obtaining a frequency response function G for vibration at a reference point;
(2 ') disturbance or the function obtained by multiplying the frequency response function G the inverse of the initial frequency response function G ₀ obtained before degradation, initialization step of obtaining a peak frequency f _p,
(3 ′) A vibration characteristic assumption step for setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for an n-degree-of-freedom multi-layer structure model that models the building;
(4 ′) a rigidity calculating step for calculating rigidity k _{S, i} for the structural element of each layer of the multilayer structure model;
(5 ′) Calculate the primary eigenfrequency ω _S and the primary eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ] created based on the stiffness k _{S, i.} Mode calculation step,
(6 ') to calculate the relative error of the first natural circular frequency [omega _S with respect to the value obtained by multiplying 2π peak frequency f _p, determining whether or not the relative error is less than convergence criterion value,
(7 ′) Interlayer pseudo displacement calculation step for obtaining the interlayer pseudo displacement u _{S, i} of each layer of the multilayer structure model based on the component of the primary eigenvector {Ψ _S } normalized so that the maximum value is a constant a ,
(8 ′) a determination reference value calculation step of calculating a determination reference value μ _{S, i} by multiplying the interlayer pseudo displacement u _{S, i} by the reciprocal of the interlayer pseudo displacement u _{0, i} before disturbance or deterioration;
Including the above, and repeating the above (3 ′) to (6 ′) a plurality of times to estimate the damaged part in the building,
(A ′) In the first vibration characteristic assumption step, a value obtained by multiplying the peak frequency f _p by 2π is a temporary primary natural circular frequency λ ₁ and normalized so that the maximum value is a constant a. Let the mode vector {Φ ₀ } be a temporary primary eigenvector {Φ ₁ },
(B ′) In the second and subsequent vibration characteristic assumption steps, the primary eigencircle frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary eigencircle. Let the frequency λ _S and the temporary primary eigenvector {Φ _S },
(C ′) In the first stiffness calculation step, the temporary primary natural circular frequency λ ₁ , the temporary primary eigenvector {Φ ₁ }, and the mass matrix [M ₀ ] of the multilayer structure model are converted into a non-damped free vibration equation. Substituting to calculate stiffness k _{1, i}
(D ′) In the second and subsequent stiffness calculation steps, the stiffness ratio κ _{S, i} obtained by multiplying the stiffness k _{S-1, i} calculated in the previous stiffness calculation step by the reciprocal of the initial stiffness k _{0 , i.} Is smaller than the threshold value d _S, the stiffness k _{S−1, i} calculated in the previous stiffness calculation step is set as the current stiffness k _{S, i} , and the stiffness ratio κ _{S, i} is equal to or greater than the threshold value d _S. In this case, the value obtained by multiplying the stiffness k _{S−1, i} calculated in the previous stiffness calculation step by the adjustment coefficient C _S , which is a value less than _1, is defined as the current stiffness k _{S, i} .
(E ′) When an affirmative determination is obtained in the Sth determination step, an interlayer pseudo displacement calculation step (7 ′) and a determination reference value calculation step (8 ′) are performed, and the determination reference value μ _{S, i} is 1. This is an invention in which a layer exceeding the thickness is regarded as a damaged portion.
The contents of (1 ′) to (3 ′), (5 ′), (7 ′), (A ′) and (B ′) are the contents of (1) to (3) and (5), respectively. , (6), (A) and (B).

Here, the temporary primary natural frequency λ _S , the temporary primary eigenvector {Φ _S }, the stiffness matrix [K _S ], the primary natural circular frequency ω _S , the primary eigenvector {Ψ _S }, the adjustment coefficient C _S , The subscript of the threshold value d _k corresponds to the “number of times” of repetition.
In addition, the first subscript of the stiffness k _{S, i} , the stiffness ratio κ _{S, i} , the interlayer pseudo displacement u _{S, i} , and the criterion value μ _{S, i} corresponds to the “number of times” of repetition, The second subscript corresponds to the mass number (natural number less than n).

The “threshold value d _S ” of (D ′) may be a constant, but when the rigidity ratio κ _{S, i} is greater than 1 in at least one layer, the maximum value of the rigidity ratio κ _{S, i} is When the arithmetic average value with 1 is the threshold value d _S and the rigidity ratio κ _{S, i} is 1 or less in all layers, the maximum value of the rigidity ratio κ _{S, i is} the threshold value d _S. Is desirable. The “maximum value of the stiffness ratio κ _{S, i} ” means “the largest value among the _n stiffness ratios κ _{S, 1} , κ _{S, 2} ,..., Κ _{S, n} ”.

The “adjustment coefficient C _S ” in (D ′) may be a constant, and is obtained by multiplying the peak frequency f _p by 2π and the inverse of the primary natural circular frequency ω _S−1. It is desirable to do. In this way, the number of times until an affirmative determination is obtained can be reduced.

  ADVANTAGE OF THE INVENTION According to this invention, a damage location can be estimated, reducing the score of the vibration measurement implemented with respect to a disturbance (for example, an earthquake, a strong wind, etc.) or a building after deterioration. In other words, in the present invention, vibration measurement may be performed at least on the upper floor of the building (for example, the rooftop) and the reference point (for example, on the first floor surface or the ground around the building). There is no need to install a sensor.

  According to the present invention, it is possible to estimate a damaged portion while reducing the number of vibration measurements performed on a building after disturbance or deterioration.

(A) is a schematic diagram of the building which concerns on an estimation object, (b) is a schematic diagram of the n-degree-of-freedom multilayer model. It is a flowchart for demonstrating the procedure of the estimation method of the damage location which concerns on 1st embodiment of this invention. It is a flowchart for demonstrating the procedure of the estimation execution process in FIG. (A) Pre-earthquake input spectrum, (b) Pre-earthquake response spectrum, (c) Post-earthquake input spectrum, (d) Post-earthquake response spectrum This is a function obtained by dividing the frequency response function by the initial frequency response function. It is a figure which shows the vibration mode corresponding to the primary eigenvector before an earthquake, a temporary mode vector (the 1st temporary primary eigenvector), and the temporary primary eigenvector after the 2nd time. (A)-(f) is a graph which shows the transition of a criterion value. It is a flowchart for demonstrating the procedure of the estimation method of the damage location which concerns on 2nd embodiment of this invention. It is a flowchart for demonstrating the procedure of the estimation execution process in FIG. It is a table | surface for demonstrating the calculation process in an estimation execution process (S = 1-5). It is a table | surface for demonstrating the calculation process in an estimation execution process (S = 5-8).

(First embodiment)
As shown in FIG. 1 (a), the damage location estimation method according to the first embodiment of the present invention is based on the upper floor of the building T (the roof in the present embodiment) and the reference point (the building T in the present embodiment). 1), the building T is modeled as an n-degree-of-freedom multilayered model A and a non-damped free vibration equation is used, as shown in FIG. It is to estimate the damaged part after disturbance or deterioration.

  The general formula of the non-damped free vibration equation of the n-degree-of-freedom system is as shown in Formula 1. Assuming that the displacement solution of Equation 1 is a harmonic vibration with no phase difference (see Equation 2), it can be transformed as Equation 3.

In the present embodiment, it is assumed that a large earthquake (disturbance) of a scale that can damage the building T occurs for a five-story building T. The multilayer structure model A is a five-degree-of-freedom shear model corresponding to a five-story building T, and includes five mass points a1 to a5 and five structural elements (shear springs) b1 to b5. . The initial stiffness k _{0, 1} to k _{0, 5} mass m ₁ ~m ₅ and structural elements b1~b5 mass point a1~a5 can be calculated from the design drawing or the like (which is a known value.).

  In the present embodiment, a “shear type model” is illustrated, but it is not intended to limit the types of structural elements. Depending on the structure type of the building T, it may be a “bending shear type model”.

The mass matrix [M ₀ ] of the multilayer structure model A is as shown in Equation 4. The mass matrix [M ₀ ] is unchanged before and after the earthquake. Further, the stiffness matrix [K ₀ ] of the multilayer structure model A before the earthquake is as shown in Equation 5.

  As shown in FIG. 2, the method for estimating a damaged portion according to the present embodiment includes an initial vibration characteristic acquisition process 1 performed at an appropriate timing before the occurrence of the earthquake, an estimation preparation process 2 performed after the earthquake occurs, and an estimation execution. Process 3 is included.

  The initial vibration characteristic acquisition process 1 is performed for the purpose of acquiring the vibration characteristic (initial vibration characteristic) of the building T that has not undergone an earthquake. The initial vibration characteristic acquisition process 1 includes a sensor installation step 11 and an initial measurement step 12.

  The sensor installation step 11 is a step of installing sensors 101 and 102 that acquire physical quantities correlated with vibration (for example, displacement, velocity, acceleration, voltage output from a laser Doppler vibrometer, etc.) at two locations above and below the building T. It is. The sensor of this embodiment is an acceleration sensor, and is installed on the first floor of the building T and the roof slab. The sensors 101 and 102 are preferably installed in a common part of the building T.

The pre-measurement step 12 is a step of performing vibration measurement at two locations above and below the building T before the earthquake and obtaining an initial frequency response function G ₀ . In the pre-measurement step 12, first, vibrations input to the building T (for example, vibration caused by an exciter, small-scale earthquake, constant tremor) are measured by the sensors 101 and 102. The acquired acceleration time history data is temporarily stored in a storage device (not shown). Next, Fourier transformation is performed on the acceleration time history data read from the storage device, and a Fourier spectrum corresponding to the sensor 101 (hereinafter referred to as “pre-earthquake input spectrum”) and a Fourier spectrum corresponding to the sensor 102 (hereinafter referred to as “pre-earthquake input spectrum”). , Response spectrum before earthquake). ) (See (a) and (b) of FIG. 4), and the “pre-earthquake response spectrum” is divided by the “pre-earthquake input spectrum” to calculate the initial frequency response function G ₀ . The initial frequency response function G ₀ is stored in a storage device. The initial frequency response function G ₀ reflects the vibration characteristics of the building T before the earthquake.

  The estimation preparation process 2 is performed for the purpose of acquiring the vibration characteristics of the building T that has received an earthquake. The estimation preparation process 2 includes a post measurement step 21 and an initial setting step 22.

  The post-measurement step 21 is a step in which vibration measurement is performed at two locations above and below the building T after the earthquake, and a frequency response function G is acquired. In the post-measurement step 21, first, vibrations input to the building T (for example, vibrations from an exciter, aftershocks, constant tremors, etc.) are measured by the sensors 101 and 102. The acquired acceleration time history data is temporarily stored in a storage device (not shown). Next, Fourier transformation is performed on the acceleration time history data read from the storage device, and a Fourier spectrum corresponding to the sensor 101 (hereinafter referred to as “post-earthquake input spectrum”) and a Fourier spectrum corresponding to the sensor 102 (hereinafter referred to as “input spectrum after earthquake”). Response spectrum after earthquake). ) (See (c) and (d) of FIG. 4), the “post-earthquake response spectrum” is divided by the “post-earthquake input spectrum” to calculate the frequency response function G. The frequency response function G is stored in a storage device. The frequency response function G reflects the vibration characteristics of the building T after the earthquake.

In initialization step 22, the initial frequency response function function inverse obtained by multiplying the frequency response function G of G _0; in (= G / G ₀ see FIG. 5) is a step of obtaining the peak frequency f _p. Peak frequency f _p, the peak frequency of the "post-earthquake response spectrum" is selected in a low frequency region than the (response magnification frequency having the maximum) (in FIG. 5, f _p = 6.77 Hz). In FIG. 5, 6Hz also can be a candidate of the peak frequency f _p, in FIG. 4 (b), the peak in the "6Hz" does not occur in the step (d), the in FIG. 4 (b), ( also selecting "6.77Hz" peak occurs as a peak frequency f _p in d).

  The estimation execution process 3 is performed for the purpose of specifying a damaged part, and is repeated a plurality of times. As shown in FIG. 3, the estimation execution process 3 includes a vibration characteristic assumption step 31, a stiffness calculation step 32, a mode calculation step 33, an interlayer pseudo displacement calculation step 34, a pseudo inertia force calculation step 35, and a determination. A reference value calculation step 36, a determination step 37, a continuous number confirmation step 38, and an estimation step 39 are included.

The vibration characteristic assumption step 31 is a step of setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for the multilayer structure model A. The temporary primary eigenvector {Φ _S } is as shown in Equation 6. The temporary primary eigenvector {Φ _S } is normalized so that the maximum value is a constant a.

Here, the subscripts of the temporary primary eigenfrequency λ _S and the temporary primary eigenvector {Φ _S } correspond to the number of executions of the estimation execution process 3. Subscripts “1” to “5” attached to the components φ _{S, 1 to} φ _{S , 5} of the temporary primary eigenvector {Φ _S } correspond to the mass points a1 to a5.

As described above, the estimation execution process 3 is repeatedly executed a plurality of times. However, in the first vibration characteristic assumption step 31 (S = 1), the peak frequency f _p obtained in the initial setting step 22 is multiplied by 2π. The temporary primary natural circular frequency λ ₁ (= 2πf _p ) and the temporary mode vector {Φ ₀ } normalized so that the maximum value is a constant a is the temporary primary eigenvector {Φ ₁ }.

The temporary mode vector {Φ ₀ } is a temporary vibration mode of the multilayer structure model A after the earthquake (that is, the multilayer structure model A having a damaged portion). For example, the pseudo displacement (vector component) of each mass point is Set to increase in order. In this embodiment, as shown in FIG. 6 and Expression 7, all the components are positive values, and the tentative mode vector {Φ so that the pseudo displacement of each mass point increases by a / n sequentially from the bottom. ₀ } is set. In Expression 7, a = 1 is set, and the tentative mode vector {Φ ₀ } is set so that the pseudo displacement of each mass point increases by 0.2 in order from the bottom.

In the vibration characteristic assumption step 31 for the second and subsequent times, the primary eigenfrequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous (S-1) mode calculation step 33 are temporarily set to 1. A secondary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } are assumed. Details of the mode calculation step 33 will be described later.

The stiffness calculation step 32 substitutes the temporary primary natural frequency λ _S , the temporary primary eigenvector {Φ _S }, and the mass matrix [M ₀ ] into the non-damped free vibration equation (Equation 3), and the structural element after the earthquake This is a step of calculating the rigidity k _{S, i} (i = 1 to 5) for b1 to b5. When the post-earthquake stiffness matrix [K _S ] of the multilayer structure model A is expressed based on the stiffness k _{S, i} , Equation 8 is obtained. In Equation 3, when [M] = [M ₀ ], [K] = [K _S ], {X} = {Φ _S }, and Ω = λ _S , Equation 9 is obtained. When the matrix product is obtained on the right side, the equation shown in Equation 10 can be obtained.

Here, the subscript of the stiffness matrix [K _S ] corresponds to the number of executions of the estimation execution process 3. The first subscript of the stiffness k _{S, i} corresponds to the number of executions of the estimation execution process 3, and the second subscript corresponds to the numbers of the structural elements b1 to b5.

Here, the masses m _{1 to} m ₅ are known values set based on the specifications of the building T, etc., and the component φ _{S of the} temporary primary natural circular frequency λ _S and the temporary primary eigenvector {Φ _S }. _{, 1 to} φ _{S, 5} are known values set in the vibration characteristic assumption step 31, and m ₅ , λ _S , φ _{S, 4,} and φ _{S, 5} are substituted into (10) of Equation 10. Thus, the rigidity k _{S, 5} of the structural element b5 is obtained. If the stiffness k _{S, 5} is obtained, the unknown of (b) in Equation 10 is only the stiffness k _{S, 4} of the structural element b4. Therefore, m ₄ , λ _S , φ _S, By substituting _{3 to} φ _{S, 5} and k _{S, 5} , the rigidity k _{S, 4} is obtained. Similarly, in (c), m ₃ , λ _S , φ _{S, 2 to} φ _{S, 4} and k Substituting _{S, 4} gives the stiffness k _{S, 3} of the structural element b3, and substituting m ₂ , λ _S , φ _{S, 1 to} φ _{S, 3} and the rigidity k _{S, 3} into (d) of the structural element b2 The rigidity k _{S, 2} is obtained, and if m ₁ , λ _S , φ _{S, 1} and k _{S, 2} are substituted into (e), the rigidity k _{S, 1} of the structural element b1 is obtained.

The mode calculation step 33 is a step of calculating the primary eigencircle frequency ω _S and the primary eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ]. The subscripts of the primary natural circular frequency ω _S and the primary eigenvector {Ψ _S } correspond to the number of executions of the estimation execution process 3.

Since the stiffness matrix [K _S ] of Equation 8 is already known by the stiffness calculation step 32, the coefficient determinant of Equation 11 is expanded with respect to the natural circular frequency Ω _S , and the obtained characteristic equation (frequency equation) To solve for the natural circular frequency Ω _S (eigenvalue Ω _S ² ).

Incidentally, n in the multilayer structure model A degree of freedom system, although natural circular frequency [Omega _S satisfying Formula 11 is the n exist, the lowest order the natural circular frequency [Omega _S "first natural circular of which Frequency “ω _S ”. “Primary eigenvector {Ψ _S }” is an eigenvector corresponding to the primary eigenfrequency ω _S. The component ψ _{S, i} (i = 1 to 5) of the primary eigenvector {ψ _S } is normalized so that the maximum value is a constant a.

If primary natural circular frequency [omega _S is calculated, compared to the initial setting step 22 obtained peak frequency f _p to a value obtained by multiplying a 2 [pi (= tentative first natural circular frequency [lambda ₁₎ if there was a 2πf _p ≠ ω _S, divided by 2 [pi] f _p in omega _S, calculates the correction coefficient _{c s (= 2πf p / ω} S).

The inter-layer pseudo displacement calculation step 34 is based on the component ψ _{S, i} of the primary eigenvector {ψ _S } normalized so that the maximum value is a constant a, and the inter-layer pseudo displacement u _{S, This} is a step for obtaining _i (= ψ _{S, i} −ψ _{S, i-1} ). The first subscript of the inter-layer pseudo displacement u _{S, i} corresponds to the number of executions of the estimation execution process 3, and the second subscript corresponds to the layer number (the number of the structural elements b1 to b5). ing. The inter-layer pseudo displacements u _{S, 5 to} u _{S, 1} are calculated by (f) to (co) in Expression 12, respectively.

The pseudo inertia force calculation step 35 is a step of calculating the interlayer pseudo inertia force Q _{S, i} (= k _{S, i} · u _{S, i} ) by multiplying the stiffness k _{S, i} by the interlayer pseudo displacement u _{S, i.} . The inter-layer pseudo inertial forces Q _{S, 5 to} Q _{S, 1} are calculated by (S) to (S) in Equation 13, respectively.

The determination reference value calculation step 36 is performed by multiplying the inter-layer pseudo inertia force Q _{S, i} by the reciprocal of the inter-layer pseudo inertia force Q _{0, i} corresponding to the stiffness k _{0, i} and the inter-layer pseudo displacement u _{0, i} before the earthquake. This is a step of calculating a reference value q _{S, i} (= Q _{S, i} / Q _{0, i} ). The determination reference values q _{S, 5 to} q _{S, 1} are calculated according to (14) to (g) of Expression 14, respectively.

The inter-layer pseudo inertia force Q _{0, i} before the earthquake can be calculated by multiplying the stiffness k _{0, i} before the earthquake by the inter-layer pseudo displacement u _{0, i} in the multilayer structure model A before the earthquake (Equation 15 (See (na) to (no)). The inter-layer pseudo displacement u _{0, i} is calculated based on the component X _{0, i} of the “primary eigenvector {X ₀ } before the earthquake” normalized so that the maximum value is a constant a. primary eigenvector {X _0} "is calculated from the mass matrix [M _0] (equation 4 refer) and before the earthquake stiffness matrix [K _0] (see equation 5). The “primary eigenvector {X ₀ } before the earthquake” is as shown in FIG.

In the Sth (second and subsequent) determination reference value calculation step 36, the determination reference values q _{S-1,5 to} q _S−1 calculated in the previous (S-1) determination reference value calculation step 36 are used _. For each of ₁ , it is determined whether or not it falls between a lower limit threshold α and an upper limit threshold β, which will be described later, and when there is a determination reference value q _{S-1, i} determined not to be In this time (S-th) interlayer pseudo inertia force Q _{S, i} of the layer corresponding to the judgment reference value q _{S-1, i} , “reciprocal of interlayer pseudo inertia force Q _{0, i} before earthquake” and “correction coefficient” c _s (= 2πf _p / ω _S ) ”is calculated to calculate the current (S-th) determination reference value q _{S, i} in the layer. The calculation formula of the determination reference value q _{S, i} when multiplying by the correction coefficient c _s is as shown in Formula 16. As is clear from Equation 16, multiplying the inter-layer pseudo inertia force Q _{S, i} by the correction coefficient c _s results in a calculated value (primary natural circular frequency ω _S ) and an actual measurement value (peak frequency f _p ). Based on this, it is synonymous with correcting the rigidity k _{S, i} .

The determination step 37 is a step of determining whether or not the determination reference value q _{S, i} is between the lower limit threshold α and the upper limit threshold β set with 1 therebetween.

In the estimation method of the rigidity-decreasing location according to the present embodiment, it is assumed that the reference vibration mode (primary eigenvector) after the earthquake has a distribution shown in “provisional mode vector” in FIG. Since k _{S, i} and the first order eigenvector {Ψ _S } are calculated, the stiffness k _{S, i} and the first order eigenvector {Ψ _S } may be extreme values that are not possible in practice. is there. The lower limit threshold value α and the upper limit threshold value β are reference values provided to exclude “extreme values”. In this embodiment, β = 2 and α = 0.2.

Note that when the rigidity of the building T is evaluated based on vibrations with small amplitude (such as microtremors and small-scale earthquakes), the rigidity may be evaluated higher than the actual rigidity due to the influence of non-structural members. In the present embodiment, since vibration with a small amplitude is measured, a stiffness higher than the actual stiffness may be calculated (that is, the determination reference value q _{S, i} may be less than 1). If the lower limit threshold value α is close to 1, the above-described influence can be eliminated. However, if the lower limit threshold value α is too close to 1, there is a possibility that a “positive determination” cannot be obtained. It is desirable to set appropriately within the range of 0.1 to 0.8, taking into account the magnitude of the input seismic motion.

The upper threshold value β may be set in consideration of the rigidity at the end time or yield. If the upper limit threshold β is too far from 1, the “positive determination” may be obtained even if the value of the stiffness k _{S, i} is not appropriate. It is desirable to set appropriately in the range of 2.5.

In determination step 37, when at least one of all determination reference values q _{S, 5 to} q _{S, 1} is below the lower threshold α (q _{S, i} <α), or exceeds the upper threshold β If (β <q _{S, i} ), the result is “No (No)”. If a negative determination is made, the process returns to the vibration characteristic assumption step 31 and the estimation execution process is continued until all the determination reference values q _{S, 5 to} q _{S, 1} fall within the lower threshold α and the upper threshold β. Repeat step 3.

  In the determination step 37, when “affirmation determination (Yes)” is obtained, the process proceeds to the continuous number confirmation step 38. In the continuous number confirmation step 38, it is determined whether or not the determination result of the determination step 37 is “positive determination” twice in succession. If “No” is determined in the continuous number confirmation step 38, the process returns to the vibration characteristic assumption step 31 to perform the estimation execution process 3 in order to confirm the convergence of the solution. In the present embodiment, the number of consecutive “affirmative determinations” is “2”, but it may be set to 3 or more.

  If “Yes” is determined in the continuous number confirmation step 38, the process proceeds to the estimation step 39. That is, for example, in the determination step 37 of the S-th time and the (S + 1) -th time, when “positive determination (Yes)” is obtained (“positive determination” is continuously obtained twice in the determination step 37 after the S-th time). ), The process proceeds to the estimation step 39.

In the estimation step 39, the determination reference value q _{S, i} calculated in the determination reference value calculation step 36 is checked, and a layer in which the determination reference value q _{S, i} is less than 1 is estimated as a “damage location”. If a positive determination is obtained twice in the determination step 37 after the S-th time, the estimation step 39 checks the determination reference value q _{S, i} calculated in the S-th determination reference value calculation step 36. Needless to say _, the determination reference value q _{S + 1, i} calculated in the (S + 1) th determination reference value calculation step 36 may be checked.

An example of the flow of the estimation execution process 3 will be described with reference to (a) to (f) of FIG. FIG. 7A is a graph showing the distribution of the determination reference values q _{1,5 to} q _1,1 obtained in the first estimation execution process 3 (S = 1), and FIG. These are graphs showing the distribution of the judgment reference values q _{2,5 to} q _2,1 obtained in the second (S = 2) estimation execution step 3. Similarly, (c) to (f) in FIG. 7 show distributions of the determination reference values q _{S, 5 to} q _{S, 1} (S = 3 to 6) obtained in the third to sixth estimation execution steps 3. It is a graph to show.

In the first estimation execution process 3, as shown in FIG. 7A, all the determination reference values q _{1,5 to} q _1,1 are set to the lower threshold α (= 0.2) and the upper threshold β ( = 2.0), the determination result in the determination step 37 is “affirmation determination”, but in the subsequent continuous number confirmation step 38, it is determined “No”, so 2 A second estimation execution process is performed. Note that, in the determination reference value calculation step 36 in the second estimation execution process, all of the determination reference values q _{1,5 to} q _1,1 calculated in the previous (first) determination reference value calculation step 36 are the lower threshold values. Since it is within the range between α and the upper threshold β, the (second) judgment reference values q _{2,5 to} q _2,1 are calculated using (14) to (g) It is not necessary to use and multiply by the correction coefficient c ₂ (= 2πf _p / ω ₂ ). As shown in FIG. 7B, in the second estimation execution process 3, the determination reference value q _2,5 of the fifth layer exceeds the upper threshold β, so the determination result in the determination step 37 is “No” It becomes "determination". In this case, the third estimation execution process 3 is executed.

Since the judgment reference value q _2,5 of the fifth layer calculated in the second (previous) judgment reference value calculation step 36 is not within the lower threshold α and the upper threshold β, the third (present) estimation is performed. In the determination reference value calculation step 36 of the execution process, when calculating the current determination reference value q _3,5 in the fifth layer (layer corresponding to the determination reference value q _2,5 ), Multiplying the pseudo inertial force Q _3,5 by “reciprocal of inter-layer pseudo inertia force Q _0,5 before earthquake” and “correction coefficient c ₃ (= 2πf _p / ω ₃ )” The determination reference values q ₃ , ₅ are calculated (see Equation 16). That is, when calculating the determination reference values q _{3,1 to} q _3,4 of the first to fourth layers, Expressions 14 (h) to (g) are used to determine the determination reference value q 3,5 of the fifth layer _{. When} calculating ₅ , Equation 16 is used instead of Equation 14 (T). Thus, in the third estimation execution process 3, as shown in FIG. 7C, all the judgment reference values q _{3,5 to} q _3,1 are between the lower threshold α and the upper threshold β. Therefore, the determination result in the determination step 37 is “affirmation determination”. However, in the subsequent continuous number confirmation step 38, it is determined “No”, so the fourth estimation execution process is performed. It will be. In calculating the _fourth criterion value q _{4, i} , it is not necessary to multiply by the correction coefficient c ₄ (= 2πf _p / ω ₄ ) (that is, the criterion values q _{4,5 to} q _4,1). Is calculated by equation 14). As shown in (d) of FIG. 7, in the fourth estimation execution process 3, the determination reference value q _{4, 4} of the fourth layer exceeds the upper limit threshold β, so the determination result in the determination step 37 is “No” The judgment execution process 3 is executed for the fifth time. In addition, this time (fifth) judgment reference value q _5,4 in the fourth layer is the reciprocal number of the inter-layer pseudo inertia force Q _0,4 before the earthquake in the inter-layer pseudo inertia force Q _5,4 of the fourth layer. It is calculated by multiplying by “correction coefficient c ₅ (= 2πf _p / ω ₅ )” (see Expression 16).

In the fifth estimation execution process 3, as shown in FIG. 7E, all the determination reference values q _{5,5 to} q _5,1 are _placed between the lower threshold α and the upper threshold β. Therefore, the determination result in the determination step 37 is “affirmative determination”. Furthermore, as shown in FIG. 7F, all the determination reference values q _{6,5 to} q are also obtained in the sixth estimation execution process 3. _{Since 6 and 1} are within the lower threshold α and the upper threshold β, the determination result in the determination step 37 is “positive determination”. In this case, the determination result of the continuous number confirmation step 38 is “Yes”. Incidentally, the primary eigenvector {Ψ ₅ } calculated in the fifth mode calculation step 33 becomes a vibration mode as shown in FIG. In addition, although illustration is abbreviate | omitted, also in the estimation execution process 3 after the 7th time, the determination result in the determination step 37 became "affirmation determination."

If “Yes” is determined in the continuous number confirmation step 38, the process proceeds to the estimation step 39. In the case of FIG. 7, “affirmation determination” is obtained in the fifth and sixth estimation execution processes 3. Therefore, the judgment reference value q _{5,5 to} q _5,1 or q _{6,5 to} q _6,1 calculated in the fifth or sixth judgment reference value calculation step 36 is checked.

Thus, when the fifth criterion value q _{5,5 to} q _5,1 is checked, in the first layer (structural element b1), the criterion value q _{S, i} is less than 1, and the second to fifth layers In (structural elements b2 to b5), since the determination reference value q _{S, i} exceeds 1, it is possible to estimate that a damaged portion (rigidity decreased portion) due to the earthquake is the structural element b1. That is, in the case of FIG. 7, the rigidity of the structural element b1 is reduced and damaged. If the damaged portion can be estimated, the subsequent inspection work can be performed efficiently. Incidentally, even if the sixth criterion value q _{6,5 to} q _6,1 is checked, the result is the same.

  According to the method for estimating a damaged portion according to the present embodiment, the damaged portion can be estimated even when the number of vibration measurement points is smaller than the number of degrees of freedom of the multilayer structure model A. That is, according to the method for estimating a damaged portion according to the present embodiment, it is only necessary to perform vibration measurement on the first floor and the roof, and it is not necessary to install sensors on each floor, so that wiring work is not complicated. There is no problem with the location of the sensor.

In the estimation execution process 3 of the present embodiment, the determination reference value q _{S, i} is calculated based on the inter-layer pseudo inertia force Q _{S, i} and the damaged portion is estimated using the determination reference value q _{S, i.} Although the case has been exemplified, the determination reference value r _{S, i} may be calculated based on the rigidity k _{S, i} and the damaged portion may be estimated using the determination reference value r _{S, i} .

When the determination reference value r _{S, i} is used, the interlayer pseudo displacement calculation step 34 and the pseudo inertia force calculation step 35 are not required. In the judgment reference value calculation step 36, the judgment reference value r _{S, i} (= k _{S, i} / k _{0, i} ) is obtained by multiplying the rigidity k _{S, i} by the reciprocal of the rigidity k _{0, i} before the earthquake. In the determination step 37, it is only necessary to determine whether or not the determination reference value r _{S, i} is between the lower limit threshold and the upper limit threshold set with 1 therebetween. It is desirable that the lower limit threshold is appropriately set in the range of 0.1 to 0.8, and the upper limit threshold is appropriately set in the range of 1.5 to 2.5.

In the Sth (second and subsequent) determination reference value calculation step 36, the lower limit is set for all the determination reference values r _{S−1, i} calculated in the previous (S−1) determination reference value calculation step 36. determines whether or not accommodated between the threshold and the upper threshold, when the determination reference value is determined not accommodated r _{S-1, i} is present, the determination reference value r _{S-1, i} Is multiplied by the reciprocal of the stiffness k _{0, i} and 2πf _p / ω _S for the current (S-th) stiffness k _{S, i} of the layer corresponding to _{S, i} is calculated.

Even in the case where the determination reference value r _{S, i} is used, the determination reference value calculation step for the Sth time or the (S + 1) th time is obtained when an affirmative determination is obtained at least twice in the determination step 37 after the Sth time. The judgment reference value r _{S, i} or r _{S + 1, i} calculated in 36 is checked, and the layer where the judgment reference value r _{S, i} or r _{S + 1, i} is less than 1 is determined as the damaged portion. .

In the above-described embodiment, the case where the vibration measurement is performed on the first floor and the roof slab is illustrated, but the vibration measurement may be performed at three or more locations. In this way, since a plurality of frequency response functions G can be obtained in the post-measurement step, the peak frequency f _p can be determined more accurately, and as a result, the estimation accuracy of the damaged portion is improved. .

  Also, for example, if the building has an elongated planar shape, if the sensors are installed at two locations on the roof slab, one end side and the other end side in the longitudinal direction of the building, the vibration of the building is referred to as “translational vibration” and “ Since it can be decomposed into “torsional vibration”, the damage location estimation method according to the present invention may be carried out for each of translational vibration and torsional vibration. If it does in this way, it will become possible to estimate separately the damage location by translation vibration, and the damage location by torsional vibration.

(Second embodiment)
The damage location estimation method according to the second embodiment of the present invention performs vibration measurement on the upper floor (the rooftop) and the reference point (the first floor) of the building T, as in the first embodiment. T is modeled as an n-degree-of-freedom multi-layered structure model A, and a non-damped free vibration equation is used to estimate a damaged or deteriorated damaged portion.

In the present embodiment, it is assumed that a large-scale earthquake (disturbance) of a scale that can damage the building T occurs for a five-story building T. The mass matrix [M ₀ ] and the stiffness matrix [K ₀ ] of the multilayer structure model A are as shown in equations 4 and 5, respectively.

  As shown in FIG. 8, the method for estimating a damaged portion according to the present embodiment includes an initial vibration characteristic acquisition process 1 performed at an appropriate timing before the occurrence of an earthquake, an estimation preparation process 2 performed after the occurrence of the earthquake, and an estimation execution. Process 4 is included. Since the initial vibration characteristic acquisition process 1 and the estimation preparation process 2 are the same as those in the first embodiment, detailed description thereof is omitted.

  The estimation execution process 4 is performed for the purpose of specifying a damaged part, and is repeated a plurality of times. As shown in FIG. 9, the estimation execution process 4 includes a vibration characteristic assumption step 41, a rigidity calculation step 42, a mode calculation step 43, an interlayer pseudo displacement calculation step 44, a determination reference value calculation step 45, a determination Step 46 and estimation step 47 are included.

The vibration characteristic assumption step 41 is a step of setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for the multilayer structure model A. The temporary primary eigenvector {Φ _S } is the same as Expression 6 shown in the first embodiment.

The estimation execution process 4 is repeatedly executed a plurality of times. However, in the first (S = 1) vibration characteristic assumption step 41, as in the vibration characteristic assumption step 31 of the first embodiment, the initial setting step 22 is performed. A value ω ₀ (= 2πf _p ; hereinafter referred to as “peak circular frequency ω ₀ ”) obtained by multiplying the obtained peak frequency f _p by 2π is a temporary primary natural circular frequency λ ₁ , and the maximum value is a constant a ( In the present embodiment, the provisional mode vector {Φ ₀ } normalized so that a = 1) is assumed to be a provisional primary eigenvector {Φ ₁ }. The temporary mode vector {Φ ₀ } is as shown in FIG.

In the second and subsequent vibration characteristic assumption step 41, as in the vibration characteristic process step 31 of the first embodiment, the primary natural circular frequency ω _S− calculated in the previous (S-1) mode calculation step 43 is obtained. _{The 1st} and 1st order eigenvectors {ψ _S-1 } are assumed to be a temporary 1st order natural circular frequency λ _S and a temporary 1st order eigenvector {Φ _S }.

The stiffness calculation step 42 is a step of calculating the stiffness k _{S, i} (i = 1 to 5) for the structural elements b1 to b5 after the earthquake.

In the first stiffness calculation step 42, the temporary primary natural circular frequency λ ₁ , the temporary primary eigenvector {Φ ₁ }, and the mass matrix [M ₀ ] of the multilayer structure model are converted into an undamped free vibration equation (Equation 3). The stiffness k _{1, i} is calculated by substituting.

The masses m _{1 to} m ₅ are known values set based on the specifications of the building T, etc., and the components φ _{1, 1} of the temporary primary natural circular frequency λ ₁ and the temporary primary eigenvector {Φ ₁ } _{. Since 1 to} φ _1,5 are known values set in the vibration characteristic assumption step 41, the structural elements b1 to b1 after the earthquake are obtained by sequentially substituting them into (a) to (e) of Equation 10. it is possible to obtain the rigidity k _1,1 ~k _1,5 on b5.

Since it is difficult to think that the rigidity of the building T that has undergone an earthquake is greater than before the earthquake, if the rigidity k _{S-1, i} calculated in the previous rigidity calculation step 42 is greater than the initial rigidity k _{0, i} The previous stiffness k _{S-1, i} is not directly used as the present stiffness k _{S, i} , but is obtained by multiplying the previous stiffness k _{S-1, i} by a value less than 1 (adjustment coefficient C _S ). It is preferable that the value is the current rigidity k _{S, i} .

That is, in the second and subsequent stiffness calculation step 42, the stiffness obtained by multiplying the stiffness k _{S-1, i} calculated in the previous stiffness calculation step 42 by the reciprocal of the initial (ie, before the earthquake) stiffness k _{0, i.} When the ratio κ _{S, i} (= k _{S−1, i} / k _{0, i} ) is calculated and the rigidity ratio κ _{S, i} is smaller than the threshold value d _S , the rigidity calculated in the previous rigidity calculation step 42 is calculated. If k _{S−1, i} is the current stiffness k _{S, i} and the stiffness ratio κ _{S, i} is greater than or equal to the threshold value d _S , the stiffness k _{S−1, i} calculated in the previous stiffness calculation step 42 will be used. A value obtained by multiplying the adjustment coefficient C _S (<1) is defined as the current stiffness k _{S, i} .

In the present embodiment, the threshold value d _S is not set to a constant value but is set every time. Specifically, when the stiffness ratio κ _{S, i} is greater than 1 in at least one layer (that is, when at least one of the stiffness ratios κ _{S, 1 to} κ _{S, 5} exceeds 1), As shown in (a) of Expression 17, the arithmetic average value of the maximum value of the stiffness ratio κ _{S, i} and 1 is set as a threshold value d _S, and the stiffness ratio κ _{S, i} is 1 or less in all layers. In this case (that is, when the stiffness ratios κ _{S, 1 to} κ _{S, 5} are all equal to or less than 1), the maximum value of the stiffness ratio κ _{S, i} is set to the threshold value d as shown in (b) of Expression 17. _S. The threshold value d _S calculated by the formula. 17 (a) becomes a value larger than 1, the threshold d _S calculated by the formula. 17 (b), a value of 1 or less.

In the present embodiment, as the adjustment coefficient C _S , a value obtained by multiplying the peak frequency f _p by 2π and the reciprocal of the primary natural circular frequency ω _S-1 (= 2πf as shown in Expression 18). _p / ω _S-1 = ω ₀ / ω _S-1 ).

The mode calculation step 43 is a step of calculating the first-order natural circular frequency ω _S and the first-order eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ]. Since the stiffness matrix [K _S ] of Equation 8 is already known by the stiffness calculation step 42, the coefficient determinant of Equation 11 is expanded with respect to the natural circular frequency Ω _S , and the obtained characteristic equation (frequency equation) To solve for the natural circular frequency Ω _S (eigenvalue Ω _S ² ). In n-degree-of-freedom system having a multilayer structure model A, although natural circular frequency [Omega _S satisfying Formula 11 is the n exist, "primary natural circular frequency of the lowest order natural circular frequency [Omega _S of which ω _S ”. “Primary eigenvector {Ψ _S }” is an eigenvector corresponding to the primary eigenfrequency ω _S. The component ψ _{S, i} (i = 1 to 5) of the primary eigenvector {ψ _S } is normalized so that the maximum value is a constant a.

The interlayer pseudo displacement calculation step 44 performs interlayer pseudo displacement u _S, of each layer of the multilayer model A based on the component ψ _{S, i} of the primary eigenvector {Ψ _S } normalized so that the maximum value is a constant a _{. This} is a step for obtaining _i (= ψ _{S, i} −ψ _{S, i-1} ). The inter-layer pseudo displacements u _{S, 5 to} u _{S, 1} are calculated by (f) to (co) in Expression 12, respectively.

In the judgment reference value calculation step 45, the judgment reference value μ _{S, i} (= u _{S, i} / u _{0, i} ) is obtained by multiplying the interlayer pseudo displacement u _{S, i} by the reciprocal of the interlayer pseudo displacement u _{0, i} before the earthquake. Is a step of calculating. The determination reference values μ _{S, 5 to} μ _{S, 1} are calculated by Equations 19 (a) to (e), respectively.

In the determination step 46, a relative error δ _s of the primary natural circular frequency ω _S with respect to the peak circular frequency ω ₀ (= 2πf _p ) is calculated, and whether or not the relative error δ _s is equal to or less than the convergence determination value ε. It is a step which determines. Relative error [delta] _s, as shown in Equation 20, by dividing the absolute value of the difference between the first natural circular frequency [omega _S and peak circle angular frequency omega ₀ (error) in the first natural circular frequency [omega _S Calculated by The convergence determination value ε may be set as appropriate, but in the present embodiment, ε = 0.100 (= 10.0%).

In the determination step 46, when the relative error δ _s exceeds the convergence determination value ε (ε <δ _s ), a “negative determination (No)” is made. If a negative determination is made, the process returns to the vibration characteristic assumption step 41, and the estimation execution process 4 is repeatedly executed until the relative error δ _s becomes equal to or less than the convergence determination value ε.

  In this embodiment, the interlayer pseudo displacement calculation step 44 and the determination reference value calculation step 45 are executed in each time from the first time to the Sth time, but “Yes” is obtained in the determination step 46. It may be executed only when it is issued.

  In the determination step 46, when “affirmation determination (Yes)” is obtained, the process proceeds to the estimation step 47.

In the estimation step 47, the determination reference value μ _{S, i} calculated in the determination reference value calculation step 45 is checked, and a layer having the determination reference value μ _{S, i} exceeding 1 is estimated as a “damage point”.

An example of the flow of the estimation execution process 4 will be described with reference to FIGS. 10 and 11.
As described above, the peak frequency f _p is “6.77 Hz”, and the components of the normalized provisional mode vector {Φ ₀ } are “φ _0,5 = 1.0, φ _0,4 = 0.8, φ _0,3 = 0.6, φ _0,2 = 0.4, φ _0,1 = 0.2 ”(see equation (7)). The masses m _{1 to} m ₅ of the mass points a1 to a5 of the multilayer structure model A are all “0.236 t / m ² ”, and the initial stiffness k _{0,1 to} k _0,5 of the structural elements b1 to b5 is , Both were designated as “1866.67 kN / m ² ”. The convergence determination value ε used in the determination step 46 is “0.100”.

In the first (S = 1) vibration characteristic assumption step 41, as shown in FIG. 10, the peak circular frequency ω ₀ (= 2πf _p = 42.54 rad / s) is set as the temporary primary natural circular frequency λ ₁ , Let the normalized provisional mode vector {Φ ₀ } be the provisional primary eigenvector {Φ ₁ }.

In the first rigidity calculation step 42, rigidity k _1,1 to k _1,5 is calculated based on the temporary primary natural frequency λ _{1, the} temporary primary eigenvector {Φ ₁ }, and the masses m _{1 to} m _5. . That is, in Equation (a), if λ ₁ = 42.54 (rad / s), φ _1,4 = 0.8, φ _1,5 = 1.0, m ₅ = 0.236 (t / m ² ), then k _{1, 5} = 2136.38 (kN / m ² ), and when substituting sequentially into (a) to (e) in Equation 10, k _1,4 = 3845.48 (kN / m ² ), k _1,3 = 5127.31 (kN / m ² ), k _1,2 = 5981.86 (kN / m ² ), k _1,1 = 6409.13 (kN / m ² ).

When the first stiffness k _{1,5 to} k _1,1 is obtained, the stiffness matrix [K ₁ ] is created and the mass matrix [M ₀ ] having the masses m _{5 to} m ₁ as diagonal components is created. The first mode calculation step 43 is performed to calculate the primary eigencircle frequency ω ₁ and the primary eigenvector {Ψ ₁ }. In the present embodiment, the component of the primary eigenvector {Ψ ₁ } normalized so that the primary natural circular frequency ω ₁ is “85.03 (rad / s)” and the maximum value is 1, is “ψ _{1 , 5} = 1.000, ψ _1,4 = 0.800, ψ _1,3 = 0.601, ψ _1,2 = 0.401, ψ _1,1 = 0.200 ".

When the first primary eigenvector {Ψ ₁ } is obtained, the interlayer pseudo displacement calculation step 44 and the judgment reference value calculation step 45 are performed, and the interlayer pseudo displacement u _{1,5 to} u _1,1 (see Expression 12) and judgment are performed. Reference values μ _{1,5 to} μ _1,1 (see Equation 19) are calculated.

When the first primary natural circular frequency ω ₁ is obtained, the process proceeds to the determination step 46, and first, the relative error δ ₁ is calculated by the equation 18. In the present embodiment, the relative error δ ₁ = 0.500, and the relative error δ ₁ > convergence determination value ε (= 0.100). Therefore, the determination result in the determination step 46 is “negative determination”, and the second estimation execution process 4 Is executed.

In the second (S = 2) vibration characteristic calculation step 41, the primary natural circular frequency ω ₁ (= 85.03 rad / s) obtained in the first mode calculation step 43 is used as the temporary primary natural circular frequency λ. ₂ and let the normalized primary eigenvector {Ψ ₁ } be the temporary primary eigenvector {Φ ₂ }.

In the second rigidity calculation step 42, first, the rigidity ratio κ _{2, i} (= k _{1, i} / k _{0, i} ) and the adjustment coefficient C _S are calculated. The rigidity k _{1,5 to} k _1,1 is calculated in the first rigidity calculation step 42 (k _1,5 = 2136.38, k _1,4 = 3845.48, k _1,3 = 5127.31, k _{1 , 2} = 5981.86, k _1,1 = 6409.13), and the initial stiffness k _{0,5 to} k _0,1 is “1866.67”, the stiffness ratio κ _{2, i} is expressed as “κ _2,5 = 1.14, κ _2,4 = 2.06, κ _2,3 = 2.75, κ _2,2 = 3.20, κ _2,1 = 3.43 ".
Since all of the rigidity ratios κ _{2,5 to} κ _2,1 are larger than 1, the threshold value d ₂ is calculated from Equation 17 (a). The maximum value of rigidity ratio κ _2,5 ~κ _2,1, since a "kappa _2,1 = 3.43", the threshold value d ₂ is "2.22". In addition, the peak frequency f _p is "6.77Hz", since the first of the primary natural circle vibration number ω ₁ is "85.03rad / s", the adjustment coefficient _{C 2 (= 2πf p / ω} 1) is , “0.500”.

Here, the rigidity ratio κ _2,5 (= 1.14) corresponding to the structural element b5 and the rigidity ratio κ _2,4 (= 2.06) corresponding to the structural element b4 are both smaller than the threshold value d ₂ (= 2.22). The stiffness k _1,5 , k _1,4 calculated in the first stiffness calculation step 42 is set as the current stiffness k _2,5 , k _2,4 (see the black arrows in FIG. 10). Also, since the stiffness ratios κ _{2,4 to} κ _2,1 corresponding to the structural elements b3 to b1 are all equal to or greater than the threshold value d ₂ , the stiffness k _1,3 to ₃ calculated in the first stiffness calculation step 42 is used. The value obtained by multiplying k _1,1 by the adjustment coefficient C ₂ (= 0.500) is the current stiffness k _{2,3 to} k _2,1 (see the white arrow in FIG. 10). Thus, k _2,5 to k _2,1 obtained in the second stiffness calculation step 42 are k _2,5 = 2136.38, k _2,4 = 3845.48, k _2,3 = 2563.66, k _2,2 = 2990.93, k _2,1 = 3204.57.

When the second stiffness k _{2,5 to} k _2,1 is obtained, the stiffness matrix [K ₂ ] and the mass matrix [M ₀ ] are created and the second mode calculation step 43 is performed to perform first-order natural circular vibration The number ω ₂ and the primary eigenvector {Ψ ₂ } are calculated. In the present embodiment, the component of the primary eigenvector {Ψ ₂ } normalized so that the primary eigenfrequency ω ₂ is “64.05 (rad / s)” and the maximum value is 1, is “ψ _{2 , 5} = 1.000, ψ _2,4 = 0.887, ψ _2,3 = 0.766, ψ _2,2 = 0.516, ψ _2,1 = 0.260 ".

When the second primary eigenvector {Ψ ₂ } is obtained, an interlayer pseudo displacement calculation step 44 and a determination reference value calculation step 45 are performed, and the interlayer pseudo displacement u _{2,5 to} u _2,1 and the determination reference value μ _{2, are performed.} Calculate _{5 to} μ _2,1 .

When the second primary natural circular frequency ω ₂ is obtained, the process proceeds to the second determination step 46, and first, the relative error δ ₂ is calculated by Equation 20. In the present embodiment, since the relative error δ ₂ = 0.336 and the relative error δ ₂ > the convergence determination value ε (= 0.100), the determination result in the determination step 46 is “negative determination”, and the third estimation execution process 4 Is executed.

In the third (S = 3) vibration characteristic calculation step 41, the primary natural circular frequency ω ₂ (= 64.05 rad / s) obtained in the second mode calculation step 43 is used as the temporary primary natural circular frequency λ. ₃ and the normalized primary eigenvector {Ψ ₂ } is defined as a temporary primary eigenvector {Φ ₃ }.

In the third rigidity calculation step 42, the rigidity ratio κ _{3, i} (= k _{2, i} / k _{0, i} ) is “κ _3,5 = 1.14, κ _3,4 = 2.06, κ _3,3 = 1.37, κ _3,2 = 1.60, κ _3,1 = 1.72 ”, both of which are larger than 1. Therefore, when the threshold value d ₃ is calculated according to (a) of Equation 17, the threshold value d ₃ is“ 1.53 ”. Further, when the adjustment coefficient C ₃ is calculated by Equation 18, the adjustment coefficient C ₃ is “0.664”. Since the stiffness ratios κ _3,5 and κ _3,3 corresponding to the structural elements b5 and b3 are both smaller than the threshold value d ₃ (= 1.53), the stiffness k _2,5 , Let k _2,3 be the current stiffness k _3,5 , k _3,3 (see the black arrows in FIG. 10), and the stiffness ratios κ _3,4 , κ _3,2 , corresponding to the structural elements b4, b2, b1, Since κ _3,1 is not less than the threshold value d ₃ , the adjustment coefficients C ₃ (=) are respectively _added to the stiffnesses k _2,4 , k _2,2 , k _2,1 calculated in the second stiffness calculation step 42. The values obtained by multiplying 0.664) are the current stiffnesses k _3,4 , k _3,2 , and k _3,1 (see the white arrows in FIG. 10). Thus, k _3,5 to k _3,1 obtained in the third stiffness calculation step 42 are k _3,5 = 2136.38, k _3,4 = 2553.40, k _3,3 = 2563.66, k _3,2 = 1985.98, k _3,1 = 2127.83.

When the third stiffness k _{3,5 to} k _3,1 is obtained, the third mode calculation step 43 is performed to calculate the first natural circular frequency ω ₂ and the first eigenvector {Ψ ₂ }. When the first natural circular frequency ω ₃ is obtained, the process proceeds to the third determination step 46, where the relative error δ ₃ is calculated by Equation 20. In the present embodiment, the relative error δ ₃ = 0.225 and the relative error δ ₃ > convergence determination value ε (= 0.100), so the determination result in the determination step 46 is “No” and the fourth estimation execution process 4 Is executed.

Thereafter, the estimation execution process 4 is repeated in the same manner. As shown in FIG. 11, in the seventh stiffness calculation step 42, the stiffness ratio κ _{7, i} (= k _{6, i} / k _{0, i} ) Becomes κ _7,5 = 0.921, κ _7,4 = 0.89, κ _7,3 = 0.89, κ _7,2 = 0.89, κ _7,1 = 0.918, and the stiffness ratio κ _{7, i} in all layers Therefore, the maximum value (κ _7,5 = 0.921) of the stiffness ratio κ _{7, i} is set as the threshold value d ₇ based on (b) of Expression 17. The adjustment coefficient C ₇ is “0.885”. Rigidity ratio κ _7,4 ~κ corresponding to the structural elements B4～b1 _{7, 1} are both the threshold value d ₇ (= 0.921) is less than the rigidity k _{6, 4} ~ calculated by the sixth stiffness calculation step 42 k _6,1 and the current rigidity k _7,4 ~k _7,1 (see black arrows in FIG. 11), the rigidity ratio kappa _{7, 5} corresponding to the structural element b5 is equal to the threshold value d ₇ course (Ie, the rigidity ratio κ _7,5 ≧ threshold value d ₇ is established), the value obtained by multiplying the stiffness k _6,5 calculated in the sixth stiffness calculation step 42 by the adjustment coefficient C ₇ (= 0.85). This rigidity is k _7,5 (see the white arrow in FIG. 11). And _Thus, k _7,5 ~k _7,1 obtained in the seventh rigidity calculation step _{42, k 7,5 = 1522.01, k 7,4} = 1662.26, k 7,3 = 1668.94, k 7,2 = 1668.22, a k _7,1 = 1712.90.

After 7 th stiffness k _{7, 5} to k _{7, 1} is obtained, performs a mode calculating step 43 of 7th calculates the first natural circular frequency [omega ₇ 1 eigenvector {[psi _7}, 7th When the first natural circular frequency ω ₇ is obtained, the process proceeds to the seventh determination step 46, where the relative error δ ₇ is calculated by Equation 20. In this embodiment, since the relative error δ ₇ = 0.113 and the relative error δ ₇ > the convergence determination value ε (= 0.100), the determination result in the determination step 46 is “negative determination”, and the eighth estimation execution process 4 Is executed.

In the eighth (S = 8) vibration characteristic calculation step 41, the primary natural circular frequency ω ₇ (= 47.96 rad / s) obtained in the seventh mode calculation step 43 is used as the temporary primary natural circular frequency λ. ₈ and the normalized primary eigenvector {Ψ ₇ } is set as a temporary primary eigenvector {Φ ₈ }.

Rigidity ratio _{κ 8, i (= k 7} , i / k 0, i) is _{"κ 8,5 = 0.82, κ 8,4 =} 0.89, κ 8,3 = 0.89, κ 8,2 = 0.89, κ 8 _{, 1} = 0.918 ”, and the stiffness ratio κ _{8, i} is 1 or less in all layers, and therefore the maximum value of the stiffness ratio κ _{8, i} (κ _8,1 = 0.918) based on equation (b). ) As a threshold value d ₈ . The adjustment coefficient C ₈ is “0.887”. Rigidity ratio corresponding to the structural elements b5~b2 κ _8,5 ~κ _8,2 are both threshold d ₈ (= 0.918) is less than the rigidity k _{7, 5} ~ calculated at 7 th stiffness calculation step 42 the k _{7, 2} and this stiffness k _8,5 ~k _8,2 (see black arrows in FIG. 11), the rigidity ratio kappa _{8, 1} which correspond to the structural elements b1, since the threshold value d ₈ or more, seventh rigidity calculation step 42 adjustment factor C ₈ stiffness k _{7, 1} calculated in (= 0.887) a value obtained by multiplying the a current stiffness k _{8, 1} (refer to the outlined arrow in FIG. 11) . And Thus, the k _8,5 to k _{8, 1} obtained in the eighth rigidity calculation step _{42, k 8,5 = 1522.01, k} 8,4 = 1662.26, k 8,3 = 1668.94, k 8,2 = 1668.22, k _8,1 = 1524.48.

When the eighth stiffness k _{8,5 to} k _8,1 is obtained, the eighth mode calculation step 43 is performed to calculate the first natural circular frequency ω ₈ and the first eigenvector {Ψ ₈ }. When the first natural circular frequency ω ₈ is obtained, the process proceeds to the determination step 46 for the eighth time, and the relative error δ ₈ is calculated by Expression 20. In the present embodiment, since the relative error δ ₈ = 0.093 and the relative error δ ₇ <the convergence determination value ε (= 0.100), the determination result in the determination step 46 is “positive determination”.

Since “positive determination” is obtained, the process proceeds to the estimation step 47. In the estimation step 47, when the determination reference values μ _{8,5 to} μ _8,1 calculated in the eighth determination reference value calculation step 45 are checked, the determination reference values corresponding to the first layer (lowermost layer) and the second layer Since μ _8,2 and μ _8,1 exceed 1, it is estimated that the first layer (lowermost layer) and the second layer are “damaged portions (stiffness decreased portions)”. In addition, the criterion value μ _8,2 of the second layer is a value close to 1 (= 1.200), whereas the criterion value μ _8,1 of the first layer is a value that greatly exceeds 1 (= 4.343). Therefore, it can be estimated that the first layer is more damaged than the second layer.

  As described above, the damaged portion can be estimated also in the damaged portion estimating method according to the second embodiment. Moreover, according to the damage location estimation method according to the second embodiment, it is only necessary to perform vibration measurement on the first floor and the roof, and it is not necessary to install a sensor on each floor, so that the wiring work becomes complicated. There is no problem with the location of the sensor.

The rigidity calculation step 42, the mode calculation step 43, the interlayer pseudo displacement calculation step 44, the determination reference value calculation step 45, the determination step 46, and the estimation step 47 can be executed by a computer (not shown). That is, the estimation execution process 4 includes a stiffness calculation step 42, a mode calculation step 43, an interlayer pseudo displacement calculation step 44, a determination reference value calculation step 45, a determination step 46 and an estimation step 47 that can execute arithmetic processing means, initial conditions ( Peak frequency f _p , provisional mode vector {Φ ₀ }, masses m _{1 to} m ₅ of mass points a1 to a5, initial stiffness k _{0,1 to} k _0,5 of structural elements b1 to b5, convergence judgment value ε, etc. ), A storage means for storing the value calculated in each step and an initial condition input via the input means, and a display means for displaying the calculation result.

T Building A Multi-layer structure model a1 to a5 Mass points b1 to b5 Structural elements

Claims (5)

A post-measurement step of performing vibration measurement on the upper floor of the building after disturbance or deterioration and obtaining a frequency response function G for vibration at a reference point;
An initial setting step for obtaining a peak frequency f _p in a function obtained by multiplying the frequency response function G by the reciprocal of the initial frequency response function G ₀ obtained before disturbance or deterioration;
A vibration characteristic assumption step for setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for an n-degree-of-freedom multi-layer structure model modeling the building;
Substituting the temporary first-order natural circular frequency λ _S , the temporary first-order eigenvector {Φ _S }, and the mass matrix [M ₀ ] of the multilayer structure model into the non-damped free vibration equation, the structural elements of each layer of the multilayer structure model A stiffness calculation step for calculating the stiffness k _{S, i} ;
A mode calculation step for calculating a first-order natural circular frequency ω _S and a first-order eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ] created based on the stiffness k _{S, i} ; ,
An interlayer pseudo displacement calculating step for obtaining an interlayer pseudo displacement u _{S, i} of each layer of the multilayer structure model based on a component of the primary eigenvector {Ψ _S } normalized so that the maximum value is a constant a;
A pseudo inertial force calculation step of calculating the interlayer pseudo inertia force Q _{S, i} by multiplying the rigidity k _{S, i} by the interlayer pseudo displacement u _{S, i} ;
The criterion value q _{S, i} is obtained by multiplying the inter-layer pseudo inertia force Q _{S, i} by the reciprocal of the inter-layer pseudo inertia force Q _{0, i} corresponding to the rigidity k _{0, i} before the disturbance or deterioration and the inter-layer pseudo displacement u _{0 , i.} A criterion value calculation step for calculating
A determination step for determining whether or not the determination reference value q _{S, i} is between the lower limit threshold and the upper limit threshold set with 1 therebetween,
The vibration characteristic assumption step, the stiffness calculation step, the mode calculation step, the interlayer pseudo displacement calculation step, the pseudo inertia force calculation step, the determination reference value calculation step, and the determination step are repeated in the building a plurality of times. A method for estimating damaged parts,
In the first of the vibration characteristics assuming step, a value obtained by multiplying 2π peak frequency f _p and the temporary first natural circular frequency [lambda _1, the temporary mode vector maximum value is normalized to a constant a {[Phi ₀ } is a temporary primary eigenvector {Φ ₁ },
In the second and subsequent vibration characteristic assumption steps, the primary natural circular frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary natural circular frequency λ _S. And a temporary primary eigenvector {Φ _S },
In the second and subsequent determination reference value calculation steps, all the determination reference values q _{S−1, i} calculated in the previous determination reference value calculation step are within the lower limit threshold and the upper limit threshold. determines whether, if the determination reference value is determined not accommodated q _{S-1, i} is present, this interlayer pseudo inertial force of the layer corresponding to the determination reference value q _{S-1, i} By multiplying Q _{S, i} by the reciprocal of the inter-layer pseudo inertia force Q _{0, i} and 2πf _p / ω _S , the current criterion value q _{S, i} in the layer is calculated,
When a positive determination is obtained at least twice in the determination step after the S-th time, the determination reference value calculated in the determination reference value calculation step at any time after the S-th time is checked, and the determination reference value A method for estimating a damaged portion, characterized in that a layer having a value of less than 1 is a damaged portion. A post-measurement step of performing vibration measurement on the upper floor of the building after disturbance or deterioration and obtaining a frequency response function G for vibration at a reference point;
An initial setting step for obtaining a peak frequency f _p in a function obtained by multiplying the frequency response function G by the reciprocal of the initial frequency response function G ₀ obtained before disturbance or deterioration;
A vibration characteristic assumption step for setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for an n-degree-of-freedom multi-layer structure model modeling the building;
Substituting the temporary first-order natural circular frequency λ _S , the temporary first-order eigenvector {Φ _S }, and the mass matrix [M ₀ ] of the multilayer structure model into the non-damped free vibration equation, the structural elements of each layer of the multilayer structure model A stiffness calculation step for calculating the stiffness k _{S, i} ;
A mode calculation step for calculating a first-order natural circular frequency ω _S and a first-order eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ] created based on the stiffness k _{S, i} ; ,
A determination reference value calculation step for calculating a determination reference value r _{S, i} by multiplying the rigidity k _{S, i} by the reciprocal of the rigidity k _{0, i} before disturbance or deterioration;
A determination step of determining whether or not the determination reference value r _{S, i} is between the lower limit threshold and the upper limit threshold set with 1 therebetween,
It is a method for estimating a damage location generated in a building by repeating the vibration characteristic assumption step, the rigidity calculation step, the mode calculation step, the determination reference value calculation step and the determination step a plurality of times,
In the first of the vibration characteristics assuming step, a value obtained by multiplying 2π peak frequency f _p and the temporary first natural circular frequency [lambda _1, the temporary mode vector maximum value is normalized to a constant a {[Phi ₀ } is a temporary primary eigenvector {Φ _S },
In the second and subsequent vibration characteristic assumption steps, the primary natural circular frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary natural circular frequency λ _S. And a temporary primary eigenvector {Φ _S },
In the second and subsequent determination reference value calculation steps, all the determination reference values r _{S−1, i} calculated in the previous determination reference value calculation step are within the lower limit threshold and the upper limit threshold. whether judges, when accommodated the determined criterion value and non r _{S-1, i} is present, the determination reference value r _S-1, the stiffness of _i corresponding to layer k _S, the _i , By multiplying the reciprocal of the stiffness k _{0, i} by 2πf _p / ω _S , the current criterion value r _{S, i} for the layer is calculated,
When a positive determination is obtained at least twice in the determination step after the S-th time, the determination reference value calculated in the determination reference value calculation step at any time after the S-th time is checked, and the determination reference value A method for estimating a damaged portion, characterized in that a layer having a value of less than 1 is a damaged portion. A post-measurement step of performing vibration measurement on the upper floor of the building after disturbance or deterioration and obtaining a frequency response function G for vibration at a reference point;
An initial setting step for obtaining a peak frequency f _p in a function obtained by multiplying the frequency response function G by the reciprocal of the initial frequency response function G ₀ obtained before disturbance or deterioration;
A vibration characteristic assumption step for setting a temporary primary natural circular frequency λ _S and a temporary primary eigenvector {Φ _S } for an n-degree-of-freedom multi-layer structure model modeling the building;
A stiffness calculating step for calculating the stiffness k _{S, i} for the structural element of each layer of the multilayer structure model;
A mode calculation step for calculating a first-order natural circular frequency ω _S and a first-order eigenvector {Ψ _S } corresponding to the stiffness matrix [K _S ] and the mass matrix [M ₀ ] created based on the stiffness k _{S, i} ; ,
Calculating the relative error of the first natural circular frequency [omega _S with respect to the value obtained by multiplying 2π peak frequency f _p, and the determination step of determining whether the relative error is less than convergence criterion value,
An interlayer pseudo displacement calculating step for obtaining an interlayer pseudo displacement u _{S, i} of each layer of the multilayer structure model based on a component of the primary eigenvector {Ψ _S } normalized so that the maximum value is a constant a;
A determination reference value calculation step for calculating a determination reference value μ _{S, i} by multiplying the interlayer pseudo displacement u _{S, i} by the reciprocal of the interlayer pseudo displacement u _{0, i} before disturbance or deterioration,
It is a method for estimating a damage location generated in a building by repeating the vibration characteristic assumption step, the rigidity calculation step, the mode calculation step, and the determination step a plurality of times,
In the first of the vibration characteristics assuming step, a value obtained by multiplying 2π peak frequency f _p and the temporary first natural circular frequency [lambda _1, the temporary mode vector maximum value is normalized to a constant a {[Phi ₀ } is a temporary primary eigenvector {Φ ₁ },
In the second and subsequent vibration characteristic assumption steps, the primary natural circular frequency ω _S-1 and the primary eigenvector {Ψ _S-1 } calculated in the previous mode calculation step are used as the temporary primary natural circular frequency λ _S. And a temporary primary eigenvector {Φ _S },
In the first stiffness calculation step, by substituting the temporary primary natural circular frequency λ ₁ , the temporary primary eigenvector {Φ ₁ }, and the mass matrix [M ₀ ] of the multilayer structure model into the non-damped free vibration equation. Calculate stiffness k _{1, i}
In the second and subsequent stiffness calculation steps, the stiffness ratio κ _{S, i} obtained by multiplying the stiffness k _{S-1, i} calculated in the previous stiffness calculation step by the reciprocal of the initial stiffness k _{0 , i} is the threshold d _S. If smaller, the stiffness k _{S−1, i} calculated in the previous stiffness calculation step is taken as the current stiffness k _{S, i} , and if the stiffness ratio κ _{S, i} is greater than or equal to the threshold d _S , The value obtained by multiplying the stiffness k _{S-1, i} calculated in the previous stiffness calculation step by the adjustment coefficient C _S-1 , which is a value less than _1, is defined as the current stiffness k _{S, i} .
When an affirmative determination is obtained in the Sth determination step, the interlayer pseudo displacement calculation step and the determination reference value calculation step are performed, and a layer in which the determination reference value μ _{S, i} exceeds 1 is determined as a damaged portion. A method for estimating a damaged portion, characterized by that. When the rigidity ratio κ _{S, i} is greater than 1 in at least one layer, the arithmetic average value of the maximum value of the rigidity ratio κ _{S, i} and 1 is set as the threshold value d _S ,
If said rigidity ratio kappa _{S, i} in all of the layers is 1 or less, damage to the described maximum value of the rigidity ratio kappa _{S, i} to claim 3, characterized in that said threshold value d _S How to estimate the location. 5. The adjustment coefficient C _S is a value obtained by multiplying the peak frequency f _p by 2π and the reciprocal of the primary natural circular frequency ω _S−1 , as the adjustment coefficient C _S. How to estimate the damage location.

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