JP2015001483A - Soundness confirmation method of building - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a soundness confirmation method of a building, allowing high-accuracy and short-time acquisition of maximum likelihood estimation value of parameters for representing building properties from observation data by sensors.SOLUTION: In a soundness confirmation method of a building, observation data in time of an earthquake are obtained from sensors, a posterior distribution of θ is obtained by Bayes' theorem, and p(D|θ) of a likelihood function is obtained. The likelihood function is approximated by a similar figure of a normal distribution near an estimation value. Next, a logarithmic likelihood log p(D|θ) is calculated, and θ=θmaximizing it is selected. About each θ, parameters except it are fixed equally to θ, and a logarithmic likelihood log L(θ) corresponding to θ=-γ, 0, γ is represented by a quadratic, coefficients of the quadratic are obtained, and θ=θ(^ above it) maximizing the quadratic is obtained. About each θ, the above procedure is performed, and a maximum likelihood estimation value θ(^ above it) is obtained.

Description

  The present invention relates to a method for checking the health of a building.

  Attention has been focused on structural health monitoring in which a sensor is installed in a building, the degree of damage and deterioration of the building is grasped based on information from the sensor, and damage detection and soundness evaluation of the building are performed (for example, Patent Document 1). , See Patent Document 2). In particular, it is required to confirm (understand) and determine the damage status at the time of an earthquake at an early stage and with high accuracy for a multi-layered building such as an office building or a condominium.

  Furthermore, it is required to quickly evaluate and judge the degree of damage and deterioration from the change in building characteristics, that is, the soundness of the building, especially after the occurrence of a large earthquake. There is a need to make the calculation time as short as possible.

JP 2011-132680 A JP 2001-99760 A

  However, in the conventional method for confirming building health (structural health monitoring), the parameter expressing the building characteristics is obtained as a maximum likelihood estimated value based on the observation data from the sensor, and the estimation is generally repeated using a nonlinear least square method or the like. It uses an optimization method that performs calculations. Furthermore, the time history response analysis of a building is performed in each repetition step. For this reason, in the conventional method for checking the soundness of a building, the calculation time required for estimation is inevitably long.

  In view of the above circumstances, the present invention provides a building soundness confirmation method that makes it possible to accurately obtain a maximum likelihood estimation value of a parameter for representing a building characteristic from observation data obtained by a sensor in a short time. The purpose is to do.

  In order to achieve the above object, the present invention provides the following means.

In the building health check method according to the present invention, a maximum likelihood estimation value, which is a parameter for representing building characteristics, is obtained from observation data obtained by sensors installed in the observation layer of the building, and the building health check is performed using the maximum likelihood estimation value. The general eigenvalue problem shown in the following equation (1) is solved from the mass matrix M, the damping coefficient matrix C, and the stiffness matrix K of the building design model to solve the j-th order natural angular frequency w. Introducing a function Δk (θ) for correcting the stiffness distribution k using the first step of obtaining _j and the stimulation function φ _j and the model parameter (n _p is the number of parameters) of the random variable shown in the following equation (2) Thus, the second step of correcting the stiffness distribution to k ′ = θ + θ (θ) and the stiffness matrix K to K ′ (θ), and the building response absolute angle y _p (θ) of the observation layer Is expressed by the following equation (3) and the probability model of building response absolute acceleration Is obtained from the sensor in the third step represented by the following formula (4) and the following formula (5) at the time of the earthquake, and the posterior distribution of θ is represented by the following formula (6) by Bayes' theorem. A fourth step to obtain; a fifth step to obtain p (θ) of a prior distribution from the following equation (7); a p (D | θ) of a likelihood function from the following equation (8); and a likelihood function to be estimated In the vicinity of the value θ _L (above ^), a similar approximation of the normal distribution as in the following equation (9) is used, and the following equation (10) is obtained by taking the logarithm of both sides of the equation (9). a step,-gamma in each of theta _j, 0, by substituting γ log likelihood logp | calculates the (D theta), it and a seventh step of selecting the theta = theta _M that maximizes each theta _j for, after equal fixed parameters other than it _{θ M, θ j = -γ,} 0, logarithmic likelihood logL _j corresponding to γ (θ _j) the formula The coefficient α = [α ₀ α ₁ α ₂ ] ^T of the eighth step represented by the quadratic formula of (11) and the quadratic formula of formula (11) is expressed by the following formula (12), formula (13), formula ( 14), the 10th step of obtaining θ _j = θ _j (^) above maximizing the equation (11) by the following equations (15) and (16), and each θ _j The eighth step to the tenth step are carried out, and the eleventh step for obtaining the maximum likelihood estimated value θ _L (^) is obtained by the following equation (17).

ｎ_ｓは、建物に設置されたセンサの数（地動計測用のものを除く）、ｙ_ｐ（上に^（ハット））（θ）は、Ｍ、Ｃ、Ｋ’（θ）で規定される修正設計モデルに観測された地動ｕを入力したときの各時刻におけるセンサ設置階の応答絶対加速度であり、その値を期待値として等しい分散σ_ｙ ^２で独立に正規分布していることを示す。

n _s (except those for ground motion measurement) The number of sensors installed in a building, y p _(^ (hat) on) (theta) is defined M, C, in K '(theta) This is the absolute response acceleration of the sensor installation floor at each time when the observed ground motion u is input to the modified design model, and indicates that the value is an expected value and independently distributed normally with the same variance σ _y ² .

ｃ、ｃ’はスケーリング係数、Ｃ_Ｌは推定値近傍でのθの誤差共分散行列である。

c and c ′ are scaling coefficients, and _CL is an error covariance matrix of θ near the estimated value.

  In the building soundness confirmation method of the present invention, the maximum likelihood estimated value can be estimated in a very short calculation time while maintaining the same level of accuracy as in the conventional optimization method. Therefore, it is possible to quickly estimate changes in building characteristics immediately after an earthquake.Especially after a large earthquake, it is possible to quickly evaluate and judge the degree of damage and deterioration from the changes in building characteristics, that is, the soundness of buildings. It becomes possible to use.

It is a figure which shows the target building in the soundness confirmation method of the building which concerns on one Embodiment of this invention. It is a figure shown in the soundness confirmation method of the building which concerns on one Embodiment of this invention. It is a figure which shows a simulation result. It is the figure which compared the maximum likelihood estimated value calculated | required with the soundness confirmation method of the building which concerns on one Embodiment of this invention by the conventional method. It is the figure which compared the time which calculates the maximum likelihood estimated value by the soundness confirmation method of the building which concerns on one Embodiment of this invention, and the conventional method.

  Hereinafter, a soundness confirmation method for a building according to an embodiment of the present invention will be described with reference to FIGS. 1 to 4.

  Here, the soundness confirmation method for a building according to the present embodiment relates to a method for confirming and grasping the soundness of a multi-layered building such as an office building or an apartment using a structural health monitoring system.

  And the building 1 which concerns on this embodiment is provided in the floor (observation layer) from which several vibration sensors 2, 3, 4, ... n differ as shown in FIG. The accompanying vibration is detected. In addition, detection data (observation data) 2 to n of each sensor is transmitted to the health monitoring system via the interface unit 5, and this detection data is converted into a log data form as a response of the building at the time of the earthquake. Is memorized.

  The health monitoring system that constitutes the structural health monitoring apparatus together with the sensors 2 to n and the interface unit 5 includes, for example, a system bus 6, a CPU (Central Processing Unit) 7, a RAM (Random Access Memory) as shown in FIG. 8, ROM (Read Only Memory) 9, communication control unit 10 for performing transmission / reception with an external information device, input control unit 11 such as a keyboard controller, output control unit 12 such as a display controller, external storage device control unit 13, An input unit 14 including input devices such as a keyboard, a pointing device, and a mouse, an output unit 15 including a display device such as an LCD display and a printing device, and an external storage device 1 such as an HDD (Hard Disk Drive) It is configured to include a.

  The CPU 7 communicates with an external device in accordance with a program ROM stored in the ROM 8 or a program stored in the large-capacity external storage device 16 to search and acquire data, and to display graphics, images, characters, and tables. The arithmetic processing is performed, such as processing of output data in which etc. are mixed, or management of a database stored in advance in the external storage device 16. Further, the CPU 7 comprehensively controls each device connected to the system bus 10.

  Furthermore, in the health monitoring system of the present embodiment, when evaluating the soundness of a building, a maximum likelihood estimated value that is a parameter for expressing the building characteristics is obtained from observation data obtained by the sensors 2 to n installed in the observation layer of the building. An estimation algorithm is mounted on the CPU 7.

  Incidentally, the program ROM in the ROM 9 or the external storage device 16 stores an operating system program (hereinafter referred to as OS) which is a basic program for controlling the CPU 7. The ROM 9 or the external storage device 16 stores various data used when performing output data processing or the like. The RAM 8 functions as a main memory and work area for the CPU 7.

  The input control unit 11 controls the input unit 14 from a keyboard or a pointing device (not shown). The output control unit 12 performs output control of the output unit 15 of a display device such as an LCD display or a printing device such as a printer.

  The external storage device control unit 13 controls access to the external storage device 16 such as an HDD (Hard Disk Drive) that stores a boot program, various applications, font data, user files, edit files, printer drivers, and the like. .

  In addition, the communication control unit 10 controls communication with an external device via a network, whereby data necessary for the system can be appropriately acquired from a database held by an external device on the Internet or an intranet. Information can be transmitted to an external device.

In the building soundness confirmation method of the present embodiment, first, the mass matrix M, the attenuation coefficient matrix C, and the stiffness matrix K of the design model of the building 1 are given, and the general eigenvalue problem shown in Equation (18) is solved. The j-th order natural angular frequency w _j and the stimulation function φ _j are obtained by solving (first step).

Here, a function Δk (θ) for correcting the stiffness distribution k is introduced. As a result, the stiffness distribution is corrected to k ′ = k + Δk (θ), and the stiffness matrix K is corrected to K ′ (θ) correspondingly (second step). At this time, the model parameter is a random variable as shown in Expression (19) (n _p is the number of parameters).

On the other hand, the building response absolute angle y _p (θ) of the sensor installation floor (observation layer) is expressed by equation (20), and the probability model of this building response absolute acceleration can be expressed by equation (21) (third step).

n _s (except those for ground motion measurement) The number of sensors installed in a building, y p _(^ (hat) on) (theta) is defined M, C, in K '(theta) This is the absolute response acceleration of the sensor installation floor at each time when the observed ground motion u is input to the modified design model, and shows that it is normally distributed independently with the same variance σ _y ² as the expected value. Yes.

  Then, when the observation data D represented by the equation (22) is obtained at the time of the earthquake, the posterior distribution of θ is obtained by the equation (23) by Bayes' theorem (fourth step).

  Here, heretofore, p (θ) is a prior distribution, and is a normal distribution that is independent of each other and has an average of 0 as shown in Equation (24). Further, p (D | θ) is a likelihood function, and is obtained by Expression (25) (fifth step).

On the other hand, in the building health check method according to the present embodiment, the likelihood function is approximated by the estimation algorithm of the CPU 7 in the vicinity of the estimated value θ _L (upward ^) and the normal distribution is similar to the following equation (26). Approximate. Here, c and c ′ are scaling coefficients, and _CL is an error covariance matrix of θ near the estimated value. Note that the normal distribution similar to equation (26) is not a probability distribution.

Then, the logarithm of both sides of the formula (26) is taken to obtain the formula (27) (sixth step). In the building soundness confirmation method of this embodiment, this formula (27) is a quadratic of each θ _j . Paying attention to the equation, the maximum likelihood estimated value θ _L (upper ^) is estimated without repeated calculation in the following procedure 1) to procedure 6) (step 7 to step 11). .

Procedure 1): Substituting -γ, 0, γ for each θ _j to calculate the log likelihood logp (D | θ), and selects θ = θ _M that maximizes it (seventh step).

Procedure 2): For each θ _j , other parameters are fixed equal to θ _M, and log likelihood logL _j (θ _j ) corresponding to θ _j = −γ, 0, γ is expressed by the following equation (28): ) (Second step).

Procedure 3): The coefficient α = [α ₀ α ₁ α ₂ ] ^T of the quadratic formula of the above formula (28) is obtained by the following formula (29), formula (30), formula (31) (9th step) ).

Procedure 4): θ _j = θ _j (^) is maximized by the equation (33) taking the following equation (32) into consideration (10th step).

Procedure 5): For each θ _j , the above procedure 2) to procedure 4) (eighth process to tenth process) are performed.

Procedure 6): Then, the maximum likelihood estimated value θ _L (^) is obtained by the following equation (34) (11th step).

As described above, in the building soundness confirmation method according to the present embodiment, the maximum likelihood estimation value θ _L (θ _L ) with a very small calculation amount without using repetitive calculation according to the above procedure 1) to procedure 4). We can estimate ^) above.

  Here, FIG. 3 and FIG. 4 actually estimate the maximum likelihood estimation value of θ using the method of the present embodiment, and how much accuracy is maintained compared to the normal optimization method. The result of confirming how much the time required for calculation is shortened is shown.

In this simulation, the number of model parameters is n _p = 2, the number of building floors is 24th, the number of sensors is 3, and the time history waveform length is 4000 steps. The specifications of the computer are OS: Windows (registered trademark) XP Professional SP3, CPU: Intel Prnium D 3.20 GHz.

  Actually, the maximum likelihood estimation value of θ is estimated using the method of the present embodiment, and the relative value of the logarithmic likelihood is also displayed in contour lines in FIG. 3 compared with the normal optimization method. From this result, it can be seen that the estimated value by the method of the present embodiment closely approximates the estimated value by the conventional optimization method.

  Next, from FIG. 4 showing the comparison results of the calculation time, it takes 20 seconds or more to obtain the estimated value in the conventional method, but only about 0.4 seconds using the method of this embodiment is required. I understand.

  Therefore, in the building health check method of the present embodiment, it is possible to estimate the maximum likelihood estimated value in a very short calculation time while maintaining the same level of accuracy as in the conventional optimization method. Therefore, it is possible to quickly estimate changes in building characteristics immediately after an earthquake.Especially after a large earthquake, it is possible to quickly evaluate and judge the degree of damage and deterioration from the changes in building characteristics, that is, the soundness of buildings. It becomes possible to use.

  As mentioned above, although one Embodiment of the soundness confirmation method of the building which concerns on this invention was described, this invention is not limited to said embodiment, In the range which does not deviate from the meaning, it can change suitably.

1 Building 2 Sensor (vibration sensor)
3 Sensor (vibration sensor)
4 sensor (vibration sensor)
n Sensor (vibration sensor)
5 Interface section 6 System bus 7 CPU
8 RAM
9 ROM
DESCRIPTION OF SYMBOLS 10 Communication control part 11 Input control part 12 Output control part 13 External storage device control part 14 Input part 15 Output part 16 External storage device

Claims (1)

A method for obtaining a maximum likelihood estimate that is a parameter for representing building characteristics from observation data obtained by sensors installed in an observation layer of the building, and confirming the soundness of the building using the maximum likelihood estimate,
From the mass matrix M, the damping coefficient matrix C, and the stiffness matrix K of the building design model, the general eigenvalue problem shown in the following equation (1) is solved to obtain the j-th order natural angular frequency w _j and the stimulation function φ _j . 1 process,
By using a model parameter (n _p is the number of parameters) of a random variable shown in the following equation (2) and introducing a function Δk (θ) for correcting the stiffness distribution k, the stiffness distribution is expressed as k ′ = k + Δk. A second step of correcting to (θ) and correcting the stiffness matrix K to K ′ (θ);
A third step of expressing the building response absolute angle y _p (θ) of the observation layer by the following equation (3) and a probability model of the building response absolute acceleration by the following equation (4):
The fourth step of obtaining observation data D represented by the following equation (5) from the sensor at the time of the earthquake and obtaining the posterior distribution of θ by the following equation (6) by Bayes' theorem:
A fifth step of obtaining p (θ) of the prior distribution from the following equation (7) and p (D | θ) of the likelihood function from the following equation (8);
The likelihood function is approximated in the vicinity of the estimated value θ _L (upward ^) with a normal distribution similar to the following equation (9), and the logarithm of both sides of equation (9) is taken to obtain the following equation (10 ) For the sixth step,
A seventh step of calculating logarithmic likelihood logp (D | θ) by substituting −γ, 0, γ for each θ _j and selecting θ = θ _M to maximize it;
For each θ _j , the other parameters are fixed to be equal to θ _M , and then the log likelihood logL _j (θ _j ) corresponding to θ _j = −γ, 0, γ is the second order of the following equation (11). An eighth step represented by the formula;
A ninth step of obtaining a coefficient α = [α ₀ α ₁ α ₂ ] ^T of the quadratic equation of Equation (11) by the following Equation (12), Equation (13), and Equation (14);
A tenth step of obtaining θ _j = θ _j (^) on the equation (11) by the following equation (15) and equation (16);
For each θ _j , the building is provided with an eleventh step that performs the eighth step to the tenth step and obtains a maximum likelihood estimated value θ _L (upward ^) by the following equation (17): How to check the soundness of

n _s (except those for ground motion measurement) The number of sensors installed in a building, y p _(^ (hat) on) (theta) is defined M, C, in K '(theta) This is the absolute response acceleration of the sensor installation floor at each time when the observed ground motion u is input to the modified design model, and indicates that the value is an expected value and independently distributed normally with the same variance σ _y ² .

c and c ′ are scaling coefficients, and _CL is an error covariance matrix of θ near the estimated value.

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