JP2017125742A - Mass/rigidity distribution setup method for determining soundness of building and mass/rigidity distribution setup system for determining soundness of building - Google Patents
Mass/rigidity distribution setup method for determining soundness of building and mass/rigidity distribution setup system for determining soundness of building Download PDFInfo
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本発明は、建物の健全性を判定するための建物モデルの初期情報の質量及び剛性の分布を特別な動的解析モデルを必要とせずに容易に求めることを可能にする建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムに関する。 The present invention is for building health judgment that makes it possible to easily obtain the mass and stiffness distribution of the initial information of a building model for judging the health of the building without requiring a special dynamic analysis model. The present invention relates to a mass / rigidity distribution setting method and a mass / rigidity distribution setting system for determining the soundness of a building.
建築・土木構造物にセンサを設置し、このセンサからの情報に基づいて構造物(建物)の損傷の度合いを把握し、構造物の損傷検知や健全性評価を行う構造ヘルスモニタリングが注目されている。特に、オフィスビルやマンション等の多層構造の建物においては、地震が発生した際に、その被災状況を早期に且つ精度よく判定(確認、把握、評価)することが求められる。 Sensors have been installed in buildings and civil engineering structures, and structural health monitoring has been attracting attention, as it determines the degree of damage to structures (buildings) based on information from these sensors, and detects damage and evaluates soundness of structures. Yes. In particular, in a multi-layered building such as an office building or an apartment building, when an earthquake occurs, it is required to determine (confirm, grasp, evaluate) the state of the damage early and accurately.
また、振動センサを用いて対象構造物の振動特性の変化から損傷(劣化による損傷を含む)を検出する手法は、変形や歪み等を計測するセンサを利用して損傷を直接的に検出する手法と比較し、センサ設置位置が損傷個所と同一である必要がない点で優れている。このため、対象の構造物が大きく、事前に損傷が発生する場所を予測・特定することが困難な建築・土木構造物に好適な損傷検出手法と言える。 In addition, a technique for detecting damage (including damage due to deterioration) from a change in vibration characteristics of a target structure using a vibration sensor is a technique for directly detecting damage using a sensor that measures deformation, distortion, and the like. Compared to the above, it is excellent in that the sensor installation position does not have to be the same as the damaged part. For this reason, it can be said that it is a damage detection method suitable for a building / civil engineering structure in which the target structure is large and it is difficult to predict and specify the place where damage occurs in advance.
建物の階層毎に多数のセンサを設置すれば、地震時の建物の各階(層)の応答、さらに建物の全体の応答を精度よく把握することができる(例えば、特許文献1参照)。この場合には、多数のセンサをそれぞれケーブル(配線)で一つのデータ収録処理装置に接続し、各センサの検出情報(データ)を一カ所に集約して詳細な分析を行うようにしている。そして、このように建物の階層毎に設置した多数のセンサで地震時の応答加速度や変位などを検出し、記録された加速度の波形情報などから構造体としての健全性や被害状況(損傷、安全性)などを判断することができる。 If a large number of sensors are installed for each level of the building, it is possible to accurately grasp the response of each floor (layer) of the building and the overall response of the building during an earthquake (see, for example, Patent Document 1). In this case, a large number of sensors are connected to one data recording processing device by cables (wiring), and the detection information (data) of each sensor is collected in one place for detailed analysis. The response acceleration and displacement during an earthquake are detected by a number of sensors installed at each level of the building in this way, and the soundness and damage status (damage, safety, etc.) of the structure is determined from the recorded acceleration waveform information. Sex).
一方、任意に設定した建物の観測層にセンサを設置し、地震時にセンサで取得した観測層の応答情報に基づき、ベイズの定理(学習型応答推定機能/ベイズ更新)を用いて建物のモデルの初期パラメータ(初期情報)を最適な値に修正し、修正したモデルのパラメータを用いて建物の各層の応答を推定する建物の健全性確認方法(地震時建物健全性判定システム(構造ヘルスモニタリングシステム/地震時建物健全性判定装置)がある(例えば、特許文献2参照)。 On the other hand, a sensor is installed in the observation layer of an arbitrarily set building, and based on the response information of the observation layer acquired by the sensor at the time of an earthquake, the model of the building is calculated using Bayes' theorem (learning type response estimation function / Bayes update). The initial parameter (initial information) is corrected to an optimum value, and the response of each layer of the building is estimated using the parameters of the corrected model. (Building health check system for earthquakes (Structural health monitoring system / (For example, see Patent Document 2).
この方法においては、ある地震時に、限られた観測層に設置したセンサで取得した建物の地震時応答情報に基づいて建物の設計モデルの情報(パラメータ)を学習的に修正(更新)し、この修正したモデルの情報を用いて建物の各層(各階)の応答を推定する。これにより、少ないセンサによって、精度よく建物各層の応答を推定することが可能になり、信頼性の高い健全性、耐震性評価を行うことができる。 In this method, in the event of an earthquake, the building design model information (parameters) is corrected (updated) based on the earthquake response information obtained from the sensors installed in a limited observation layer. The response of each layer (each floor) of the building is estimated using the corrected model information. This makes it possible to accurately estimate the response of each layer of the building with a small number of sensors, and perform highly reliable soundness and earthquake resistance evaluation.
ここで、例えば、上記の学習型応答推定機能(ベイズ更新)を持つ構造ヘルスモニタリングシステムにおいては、建物モデルを初期情報として設定する必要があり、この初期情報(パラメータ)を設定する際には、一般に建物を質点系解析モデルとして扱い質量及び剛性の分布を利用する。 Here, for example, in the structural health monitoring system having the learning type response estimation function (Bayes update) described above, it is necessary to set the building model as initial information, and when setting this initial information (parameter), Generally, a building is treated as a mass system analysis model, and mass and stiffness distributions are used.
そして、従来、構造設計者が建物構造設計で行う動的解析モデルの設計情報からこの質量及び剛性の分布を設定するようにしており、専門家による高度な設計により設定値の判断が必要になっている。これにより、動的解析情報が得られていない建物ではこのシステム自体を適用できず、また、多くの建物にこのシステムを適用することが難しくなっている。 In the past, structural designers set the distribution of mass and stiffness from the design information of the dynamic analysis model that is used in building structure design, and it is necessary to judge the set values by advanced design by experts. ing. As a result, this system itself cannot be applied to buildings where dynamic analysis information is not obtained, and it is difficult to apply this system to many buildings.
本発明は、上記事情に鑑み、建物の健全性を判定するための建物モデルの初期情報の質量及び剛性の分布を、特別な動的解析モデルを必要とせずに容易に求めることを可能にする建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムを提供することを目的とする。 In view of the above circumstances, the present invention makes it possible to easily obtain the mass and stiffness distribution of the initial information of the building model for determining the soundness of the building without requiring a special dynamic analysis model. It is an object of the present invention to provide a mass / rigidity distribution setting method for building health judgment and a mass / rigidity distribution setting system for building health judgment.
上記の目的を達するために、この発明は以下の手段を提供している。 In order to achieve the above object, the present invention provides the following means.
本発明の建物の健全性判定用の質量/剛性分布設定方法は、建物の構造形式、建物の階層数及び建物の最下層においける剛性分布係数Nを入力する建物構造入力工程と、建物階層数及び標準階高から建物の軒高を求め、該軒高、及び予め求められた実験式の回帰式によって建物の第1固有周期を求める第1固有周期算出工程と、建物の各階層の質量を一定の質量に設定し、前記第1固有周期における第1剛性k1をk1=m×(2π/T1)2で求める第1剛性算出工程と、建物の最上層を1、最下層を最上層の剛性分布係数N倍とし、全体に前記第1剛性を乗じた台形形状の第1剛性分布を作成する第1剛性分布作成工程と、建物の一定の質量分布及び前記第1剛性分布から固有値解析によって第2固有周期を求める第2固有周期算出工程と、前記第2固有周期/前記第1固有周期を計算して補正係数を求める補正係数算出工程と、前記補正係数を2乗した値を前記第1剛性分布に乗じて第2剛性分布を求める第2剛性分布算出工程と、前記建物の一定の質量分布及び前記第2剛性分布から固有値解析によって第3固有周期及び刺激関数を求める第3固有周期/刺激関数算出工程と、前記第3固有周期と前記第1固有周期を比較し、前記第3固有周期が前記第1固有周期と一致している場合に、前記建物の一定の質量分布及び前記第2剛性分布を建物の健全性判定用の質量分布及び剛性分布として決定する健全性判定用質量/剛性分布決定工程とを備えることを特徴とする。 The mass / rigidity distribution setting method for determining the soundness of a building according to the present invention includes a building structure input process for inputting the structure type of the building, the number of building levels, and the stiffness distribution coefficient N at the lowest layer of the building, The first eigenperiod calculation step of obtaining the eave height of the building from the number and the standard floor height, and obtaining the first eigenperiod of the building by the regression equation of the eave height and the empirical formula obtained in advance, and the mass of each level of the building Is set to a constant mass, and the first stiffness calculation step of obtaining the first stiffness k 1 in the first natural period by k 1 = m × (2π / T 1 ) 2 , the top layer of the building is 1, the bottom layer A first rigidity distribution creating step of creating a trapezoidal first rigidity distribution obtained by multiplying the rigidity distribution coefficient of the uppermost layer by N times, and multiplying the first rigidity by the whole, a constant mass distribution of the building, and the first rigidity distribution 2nd natural period calculation process to obtain the 2nd natural period from eigenvalue analysis A correction coefficient calculating step of calculating the second natural period / the first natural period to obtain a correction coefficient; and multiplying the first rigidity distribution by a value obtained by squaring the correction coefficient to obtain the second rigidity distribution. A second stiffness distribution calculation step to be obtained; a third natural cycle / stimulus function calculation step to obtain a third natural cycle and a stimulus function by eigenvalue analysis from the constant mass distribution of the building and the second stiffness distribution; and When the period is compared with the first natural period, and the third natural period is coincident with the first natural period, the constant mass distribution and the second rigidity distribution of the building are used to determine the soundness of the building. A mass determination / stiffness distribution determining step for determining soundness, which is determined as a mass distribution and a stiffness distribution.
本発明の建物の健全性判定用の質量/剛性分布設定システムは、建物階数と標準階高から軒高を求める建物軒高算出手段と、前記軒高と予め求められている軒高と建物の固有周期の関係を示す実験式の回帰式とから建物の第1固有周期を求める第1固有周期算出手段と、第1固有周期における第1剛性を計算する第1剛性算出手段と、建物の質量分布及び前記第1剛性の分布から固有値解析によって建物の第2固有周期を求める第2固有周期算出手段と、前記第2固有周期/前記第1固有周期を計算して補正係数を求める補正係数算出手段と、前記補正係数を2乗した値を第1剛性分布に乗じて第2剛性分布を求める第2剛性分布算出手段と、建物の質量分布及び前記第2剛性の分布から固有値解析によって第3固有周期及び刺激関数を求める第3固有周期/刺激関数算出手段と、前記第3固有周期と前記第1固有周期を比較する第3固有周期/第1固有周期比較手段と、前記第3固有周期が前記第1固有周期と一致している場合に、前記第1固有周期となる建物の質量分布及び前記第2剛性分布を、建物の健全性判定用の質量分布及び剛性分布として決定する健全性判定用質量分布/剛性分布決定手段とを備えることを特徴とする。 The mass / rigidity distribution setting system for determining the soundness of a building according to the present invention includes a building eave height calculation means for obtaining an eave height from the number of building floors and a standard floor height, and A first natural period calculating means for obtaining a first natural period of a building from an empirical regression equation indicating a relation between natural periods; a first rigidity calculating means for calculating a first rigidity in the first natural period; and a mass of the building A second natural period calculating means for obtaining a second natural period of the building by eigenvalue analysis from the distribution and the distribution of the first stiffness, and a correction coefficient calculating for calculating a correction coefficient by calculating the second natural period / the first natural period A second stiffness distribution calculating means for obtaining a second stiffness distribution by multiplying the first stiffness distribution by a value obtained by squaring the correction coefficient, and a third value by eigenvalue analysis from the mass distribution of the building and the second stiffness distribution. Find natural period and stimulus function A third natural period / stimulus function calculating means; a third natural period / first natural period comparing means for comparing the third natural period and the first natural period; and the third natural period is the first natural period. Soundness determination mass distribution / stiffness distribution for determining the building's mass distribution and the second rigidity distribution as the building's soundness determination mass distribution and rigidity distribution when they coincide with each other And a determining means.
本発明の建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムにおいては、特別な動的解析モデルを必要とせず、建物階数と構造種別の情報から建物の初期モデル情報としての建物の質量及び剛性の分布を自動で作成することができる。 In the mass / rigidity distribution setting method for building soundness judgment and the mass / rigidity distribution setting system for building soundness judgment according to the present invention, no special dynamic analysis model is required, and From the information, the building mass and stiffness distribution as the initial model information of the building can be automatically created.
以下、図1から図13を参照し、本発明の一実施形態に係る建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムについて説明する。 Hereinafter, a mass / rigidity distribution setting method for building soundness determination and a mass / rigidity distribution setting system for building soundness determination according to an embodiment of the present invention will be described with reference to FIGS. 1 to 13.
ここで、本実施形態では、学習型応答推定機能(ベイズ更新)を有する構造ヘルスモニタリングシステムを用いてオフィスビルやマンション等の多層構造の建物の健全性を確認、把握、評価(判定)する際に必要な建物モデルの初期情報としての建物の質量及び剛性の分布を、本発明の建物の健全性判定用の質量/剛性分布設定方法で設定するものである。
なお、本発明の建物の健全性判定用の質量/剛性分布設定方法は、他の構造ヘルスモニタリングシステムを適用する際にも用いることが可能である。
Here, in this embodiment, when confirming, grasping, and evaluating (determining) the soundness of multi-layered buildings such as office buildings and apartments using a structural health monitoring system having a learning type response estimation function (Bayes update) The building mass and stiffness distribution as initial information of the building model necessary for the building is set by the mass / rigidity distribution setting method for building soundness judgment according to the present invention.
The mass / rigidity distribution setting method for building soundness determination according to the present invention can also be used when other structural health monitoring systems are applied.
はじめに、本実施形態の建物の健全性確認方法(学習型応答推定機能を有する構造ヘルスモニタリングシステム)においては、図1、図2に示すように、ある地震時に、限られた観測層に設置したセンサで取得した建物の地震時応答情報に基づいて建物の設計モデルの情報(パラメータ)を学習的に修正(更新)し、この修正したモデルの情報を用いて建物の各層(各階)の応答を推定する。 First, in the building health check method (structural health monitoring system having a learning type response estimation function) according to the present embodiment, as shown in FIGS. 1 and 2, it is installed in a limited observation layer during a certain earthquake. Based on the earthquake response information of the building acquired by the sensor, the building design model information (parameters) is corrected (updated) by learning, and the response of each layer (each floor) of the building using the corrected model information. presume.
具体的に、本実施形態の建物の健全性確認方法においては、まず、設計モデルの質量行列M、減衰係数行列C、剛性行列Kが与えられ、式(1)に示す一般固有値問題を解いてj次の固有角振動数wjと刺激関数φjが得られる。 Specifically, in the building soundness confirmation method of the present embodiment, first, a mass matrix M, an attenuation coefficient matrix C, and a stiffness matrix K of a design model are given, and the general eigenvalue problem shown in Equation (1) is solved. A j-th order natural angular frequency w j and a stimulation function φ j are obtained.
ここで、「従来の学習型応答推定機能を有する構造ヘルスモニタリングシステム(建物の健全性確認方法)」では、剛性分布kを修正する関数△k(θ)を導入する。これにより、剛性分布がk’=k+△k(θ)に修正され、これに対応して剛性行列KがK’(θ)に修正される。このとき、モデルパラメータは、式(2)に示すように確率変数である(npはパラメータ数)。 Here, in the “structural health monitoring system having a conventional learning type response estimation function (building soundness confirmation method)”, a function Δk (θ) for correcting the stiffness distribution k is introduced. Thereby, the stiffness distribution is corrected to k ′ = k + Δk (θ), and the stiffness matrix K is corrected to K ′ (θ) correspondingly. At this time, the model parameter is a random variable as shown in Expression (2) (n p is the number of parameters).
一方、センサ設置階(観測層)の建物応答絶対加速度yp(θ)は式(3)で表され、この建物応答絶対加速度の確率モデルは式(4)で表せる。 On the other hand, the building response absolute acceleration y p (θ) of the sensor installation floor (observation layer) is expressed by Equation (3), and the probability model of this building response absolute acceleration can be expressed by Equation (4).
ns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)、yp(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σy 2で独立に正規分布していることを示している。 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.
そして、地震時に、式(5)で表す観測データDが得られると、ベイズの定理によってθの事後分布が式(6)で求められる。 Then, when observation data D represented by Equation (5) is obtained during an earthquake, the posterior distribution of θ is obtained by Equation (6) according to Bayes' theorem.
ここで、p(θ)は、事前分布で、式(7)のような互いに独立で平均が0の一様分布である。また、p(D|θ)は、尤度関数で、式(8)で求められる。 Here, p (θ) is a prior distribution, and is a uniform distribution that is independent from each other and has an average of 0 as in Expression (7). Further, p (D | θ) is a likelihood function, and is obtained by Expression (8).
このようにして得られる事後分布p(θ|D)を最大化するθをθMAP(上に^(ハット))とすると、θMAP(^)によって修正された剛性行列K’( θMAP(^))から、式(1)と同様の固有値問題を解いて、対応する刺激関数φj’が得られる。 Thus posteriori obtained distribution p | When the theta maximizing (θ D) θ MAP (^ ( hat) above), theta MAP (^) is modified by a stiffness matrix K '(θ MAP ( From ^)), the same eigenvalue problem as in equation (1) is solved to obtain the corresponding stimulus function φ j ′.
これは、事前情報である設計モデルを実際の観測データに基づいて、より現実に近づけるように更新したことを意味する。なお、この更新した事後分布p(θ|D)を次回の地震に対する事前分布として用いることにより継続的な学習を行うようにしてもよい。 This means that the design model, which is prior information, has been updated to be closer to reality based on actual observation data. The updated posterior distribution p (θ | D) may be used as a prior distribution for the next earthquake so that continuous learning may be performed.
そして、建物の応答に支配的な影響を与えるモードを1〜nm次とすると、センサ設置階の応答絶対加速度は、式(9)で近似できる。 And if the mode which has a dominant influence on the response of a building is 1 to nm , the response absolute acceleration on the sensor installation floor can be approximated by equation (9).
Dは、D=[1・・・1]T∈Rnsであり、Фpは、Ф=[φ1’・・・φnm’]からセンサ設置階に対応した行を抜き出した行列であり、qは、q=[q1(t)・・・qnm(t)]Tで表される1〜nm次のモード応答相対加速度ベクトルである。すると、観測応答加速度波形yp(上に〜(チルダ))からモード応答相対加速度の推定値q(^)が式(10)で得られる。 D is D = [1... 1] T ∈ R ns , and Ф p is a matrix obtained by extracting the row corresponding to the sensor installation floor from Ф = [φ 1 '... Φ nm ']. , q is q = [q 1 (t) ··· q nm (t)] 1~n m order mode response relative acceleration vector represented by T. Then, the observed response acceleration waveform y p estimate of modal response relative acceleration from (~ (tilde) above) q (^) is obtained by Equation (10).
Фp +はФpの一般化逆行列である。これにより、全層の応答y∈Rnf(nfは建物層数)が式(11)で推定できる。 Ф p + is a generalized inverse matrix of p p . Thereby, the response y∈R nf (n f is the number of building layers) of all layers can be estimated by the equation (11).
なお、D’=[1・・・1]T∈Rnfである。また、式(10)で一般化逆行列を用いていることにより、推定に使用する主要モードの数を任意に設定することが可能になっている。 Note that D ′ = [1... 1] T ∈ R nf . Further, by using the generalized inverse matrix in Expression (10), the number of main modes used for estimation can be arbitrarily set.
一方、本実施形態では、上記の建物の健全性確認方法(学習型応答推定機能(ベイズ更新)を有する構造ヘルスモニタリングシステム)によってオフィスビルやマンション等の多層構造の建物の健全性を確認、把握、評価(判定)する際に必要な建物モデルの初期情報としての建物の質量分布m及び剛性分布kを、以下に示す本実施形態の建物の健全性判定用の質量/剛性分布設定方法によって設定するようにした。 On the other hand, in the present embodiment, the soundness of multi-layered buildings such as office buildings and apartments is confirmed and grasped by the above-described soundness confirmation method (structural health monitoring system having a learning type response estimation function (Bayes update)). The mass distribution m and stiffness distribution k of the building as initial information of the building model required for evaluation (determination) are set by the mass / rigidity distribution setting method for building soundness judgment of the present embodiment shown below. I tried to do it.
具体的に、本実施形態の建物の健全性判定用の質量/剛性分布設定方法は、専門家による構造設計の動的解析モデルの情報を必要としないで建物固有周期に合わせた剛性分布を自動で作成する方法である。 Specifically, the mass / rigidity distribution setting method for building soundness determination according to the present embodiment does not require information on the dynamic analysis model of structural design by an expert, and automatically calculates the rigidity distribution according to the natural period of the building. It is a method to create with.
そして、この建物の健全性判定用の質量/剛性分布設定方法では、建物設計用の1次周期T1の実験式(回帰式)を予め求めておく。 In this mass / rigidity distribution setting method for determining the soundness of a building, an empirical formula (regression formula) for the primary period T1 for building design is obtained in advance.
この実験式としては、図3に示すように、構造種別(S造、RC/SRC造)により分けられ、実建物での軒高とその建物での振動計測から得られた1次固有周期の関係を示す回帰式を用いる。また、この実験式の回帰式としては、例えば、図3に示すように、1次回帰式、2次回帰式、両対数回帰式を選択的に用いる。 As shown in FIG. 3, the empirical formula is divided according to the structural type (S structure, RC / SRC structure), and the eigen height of the eave height in the actual building and the primary natural period obtained from the vibration measurement in the building. A regression equation showing the relationship is used. Moreover, as a regression formula of this empirical formula, for example, as shown in FIG. 3, a primary regression formula, a quadratic regression formula, and a logarithmic regression formula are selectively used.
なお、両対数回帰式は低層から超高層建物まで相関(適合性)が高い。1次回帰式は中層、高層で相関が高く、低層で相関が低く、2次回帰式は高層で相関が高く、低層で相関が低い傾向がある。 The log-log regression equation has a high correlation (fitness) from low-rise to high-rise buildings. The primary regression equation has a high correlation at the middle and high layers, the correlation is low at the low layer, and the secondary regression equation tends to have a high correlation at the high layer and a low correlation at the low layer.
そして、低層から超高層建物まで適合性がよい両対数回帰式を用いるとすると、この回帰式は、S造で式(12)、RC/SRC造で式(13)となる。T1は1次固有周期(s)、Hは軒高(m)を示す。 If a log-logarithmic regression equation having good compatibility from a low-rise building to a super-high-rise building is used, this regression equation becomes an equation (12) for the S structure and an equation (13) for the RC / SRC structure. T 1 represents the primary natural period (s), and H represents the eave height (m).
次に、本実施形態の建物の健全性判定用の質量/剛性分布設定方法では、情報として建物の階数のみを与え、標準階高さから軒高を決定する。また、標準的な階高さを、S造で4.0m、RC/SRC造で3.3mとする。 Next, in the mass / rigidity distribution setting method for building soundness determination according to the present embodiment, only the number of floors of the building is given as information, and the eave height is determined from the standard floor height. In addition, the standard floor height is 4.0 m for S and 3.3 m for RC / SRC.
階数から建物の固有周期となるように、質点系モデルにおいて各層の質量mは一定の1.0tとし、各層の剛性は最上層が1、最下層を剛性分布係数N倍(例えば4倍)となる台形分布として与える。 In the mass system model, the mass m of each layer is a constant 1.0 t so that the natural period of the building is based on the number of stories, and the rigidity of each layer is 1 for the top layer and N times (for example, 4 times) the stiffness distribution coefficient for the bottom layer. Given as a trapezoidal distribution.
なお、建物モデルの剛性分布は、任意の台形分布で作成することが可能であり、4k(N=4)以外で台形分布を設定してもよい。このとき、例えば2倍〜5倍(N=2〜5)の範囲で台形分布を設定することが好ましい。 Note that the rigidity distribution of the building model can be created with an arbitrary trapezoidal distribution, and a trapezoidal distribution other than 4k (N = 4) may be set. At this time, it is preferable to set the trapezoidal distribution in a range of 2 to 5 times (N = 2 to 5), for example.
また、この剛性(1次自由度系の剛性)kとしては、1自由度系の固有周期である下記の式(14)を変換した式(15)から求めたものを利用し、階数倍したものとする。 Further, the rigidity (stiffness of the first degree of freedom system) k is multiplied by the rank by using a value obtained from the expression (15) obtained by converting the following expression (14) which is the natural period of the one degree of freedom system. Shall.
上記の計算によって得られる本システムでの初期情報のモデルイメージを示すと、図4のようになる。 A model image of the initial information in the present system obtained by the above calculation is shown in FIG.
また、図5(a)はこの計算によって得られるモデルの1層から100層(1階建てから100階建て)のS造建物での固有振動数(固有周期の逆数)の変化を示している。 FIG. 5 (a) shows the change in the natural frequency (reciprocal of the natural period) in an S-structure building of 1 to 100 layers (1 floor to 100 floors) of the model obtained by this calculation. .
ここで、図5(a)において、横軸が設定したい固有振動数、縦軸が質点系モデルでの固有振動数を示しており、〇線が変化を表している。
また、×線は、実際の計算では固有振動数でのずれがあるため、その補正に必要な固有振動数の係数値(補正倍率)を示している。
Here, in FIG. 5A, the abscissa represents the natural frequency to be set, the ordinate represents the natural frequency in the mass system model, and a circle represents a change.
Further, the x-rays indicate the coefficient value (correction magnification) of the natural frequency necessary for the correction because there is a deviation in the natural frequency in the actual calculation.
そして、本実施形態では、この固有振動数毎の係数値によって補正を行い、解析モデルの剛性を修正する。図5(b)は最終的に修正された質点系モデルでの固有振動数の関係を示しており、この図5(b)に示すように、固有振動数の関係がほぼ1となり、各層の質量を1.0tとした場合の剛性分布を決定できる。 And in this embodiment, it correct | amends with the coefficient value for every natural frequency, and corrects the rigidity of an analysis model. FIG. 5B shows the relationship of the natural frequency in the finally corrected mass system model. As shown in FIG. 5B, the relationship of the natural frequency is almost 1, and each layer has The stiffness distribution when the mass is 1.0 t can be determined.
また、図6(a)、図6(b)はRC/SRC造の建物の補正前と補正後の固有振動数分布を示しており、上記のS造の建物と同様にして各層の質量を1.0tとした場合の剛性分布を決定できることを示している。 6 (a) and 6 (b) show the natural frequency distribution before and after the correction of the RC / SRC building, and the mass of each layer is the same as that of the S building. This shows that the rigidity distribution can be determined when 1.0 t is set.
次に、階層数を20、40に指定して自動作成される建物モデルの例を図7(20階)及び図8(40階)に示す。どちらの例も、同じ台形分布の剛性を作成していることから刺激関数の形状は相似となる。 Next, FIG. 7 (20th floor) and FIG. 8 (40th floor) show examples of building models that are automatically created by designating the number of levels as 20 and 40. In both examples, the shape of the stimulus function is similar because the rigidity of the same trapezoidal distribution is created.
ここで、上記の建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムをまとめると図9のようになる。 Here, the mass / rigidity distribution setting method for determining the soundness of the building and the mass / rigidity distribution setting system for determining the soundness of the building are summarized as shown in FIG.
すなわち、建物の構造形式(S造、RC/SRC造)、建物階数、及び最下層における剛性分布係数Nを入力すると(Step1:建物構造入力工程)、建物の健全性判定用の質量/剛性分布設定システムの建物軒高算出手段によって建物階数と標準階高から軒高が求められ、第1固有周期算出手段によって、この軒高と、予め求められている実験式の回帰式によって、建物の第1固有周期が計算される(Step2:第1固有周期算出工程)。 That is, when the building structure type (S structure, RC / SRC structure), the number of building floors, and the stiffness distribution coefficient N in the lowest layer are input (Step 1: building structure input process), the mass / rigidity distribution for building soundness judgment The eave height is obtained from the building floor height and the standard floor height by the building eave height calculating means of the setting system, and the first natural period calculating means calculates the eave height from the eave height and the regression equation of the empirical formula obtained in advance. One natural period is calculated (Step 2: first natural period calculating step).
そして、建物の各階層の質量を予め設定した一定の質量(1ton)とし、第1剛性算出手段により、第1固有周期における第1剛性を式(15)を用いて計算する(Step3:第1剛性算出工程)。また、最上層1、最下層を剛性分布係数N倍とし、第1剛性分布算出手段によって、全体に第1剛性を乗じた台形形状の第1剛性分布を作成する(Step4:第1剛性分布作成工程/図4参照)。
Then, the mass of each level of the building is set to a predetermined constant mass (1 ton), and the first stiffness calculation means calculates the first stiffness in the first natural period using the formula (15) (Step 3: First) Rigidity calculation step). Also, the
次に、第2固有周期算出手段により、質量分布(全層1ton)及び第1剛性分布から固有値解析によって第2固有周期を求める(Step5:第2固有周期算出工程)。さらに、補正係数算出手段により、第2固有周期/第1固有周期を計算し、補正係数とする(Step6:補正係数算出工程/図5(a)、図6(a)参照)。
Next, the second natural period calculation means obtains the second natural period from the mass distribution (all
次に、第2剛性分布算出手段により、式(15)に基づいて補正係数を2乗した値を第1剛性分布に乗じて第2剛性分布を求める(Step7:第2剛性分布算出工程)。さらに、第3固有周期/刺激関数算出手段により、質量分布(1ton)及び第2剛性分布から固有値解析によって第3固有周期及び刺激関数を求める(Step8:第3固有周期/刺激関数算出工程)。 Next, the second stiffness distribution calculating means obtains the second stiffness distribution by multiplying the first stiffness distribution by the value obtained by squaring the correction coefficient based on the equation (15) (Step 7: second stiffness distribution calculating step). Further, the third natural period / stimulus function calculating means obtains a third natural period and a stimulus function from the mass distribution (1 ton) and the second stiffness distribution by eigenvalue analysis (Step 8: third natural period / stimulus function calculating step).
次に、第3固有周期/第1固有周期比較手段により、第3固有周期が第1固有周期と一致していることを確認する(Step9/図5(b)、図6(b)参照)。そして、健全性判定用質量分布/剛性分布決定手段により、第3固有周期が第1固有周期と一致していることが確認されれば、第1固有周期となる質量分布及び第2剛性分布を、建物の健全性判定用の質量分布及び剛性分布として決定することができる(Step10:健全性判定用質量/剛性分布決定工程/図4参照)。 Next, it is confirmed by the third natural period / first natural period comparison means that the third natural period coincides with the first natural period (see Step 9 / FIG. 5 (b) and FIG. 6 (b)). . When the soundness determination mass distribution / rigidity distribution determining means confirms that the third natural period coincides with the first natural period, the mass distribution and the second rigidity distribution that become the first natural period are obtained. It can be determined as the mass distribution and rigidity distribution for building soundness determination (Step 10: soundness determination mass / rigidity distribution determining step / see FIG. 4).
上記のようにして本実施形態の建物の健全性判定用の質量/剛性分布設定方法で求めた質量分布及び剛性分布を建物モデルの初期情報として用い、24階建てのS造の建物モデルに適用し、本実施形態の建物の健全性確認方法(学習型応答推定機能(ベイズ更新)を有する構造ヘルスモニタリングシステム)で応答推定を行ったシミュレーション結果について説明する。 The mass distribution and stiffness distribution obtained by the mass / rigidity distribution setting method for building soundness judgment according to the present embodiment as described above are used as initial information of the building model, and are applied to a 24-story S building model. And the simulation result which performed the response estimation by the soundness confirmation method (structural health monitoring system which has a learning type response estimation function (Bayes update)) of this embodiment is demonstrated.
このシミュレーションでは、多層構造の建物の1階と9階と17階と24階に加速度センサを設置し、これら4点の加速度波形によって全階の応答を推定した。 In this simulation, acceleration sensors were installed on the 1st, 9th, 17th and 24th floors of a multi-layered building, and the responses of all floors were estimated from these four acceleration waveforms.
そして、建物モデルに地動を入力し、応答解析を行なって各層の絶対加速度応答などを計算した結果を真値とした。また、センサによって取得したセンサ設置階のみの波形を用い、本発明の建物の健全性判定用の質量/剛性分布設定方法、本実施形態の建物の健全性確認方法によって全層の絶対加速度波形を推定し、真値と全層の推定値とを比較した。 Then, the ground motion was input to the building model, the response analysis was performed, and the absolute acceleration response of each layer was calculated as the true value. Moreover, using the waveform of only the sensor installation floor acquired by the sensor, the absolute acceleration waveform of all layers is obtained by the mass / rigidity distribution setting method for building soundness judgment of the present invention and the building soundness confirmation method of this embodiment. We estimated and compared the true value with the estimated value of all layers.
まず、図10は、解析と本発明によって求めた質量分布、剛性分布を示している。
図11は、強非線形応答における解析と本発明による最大加速度分布、最大速度分布、最大変位分布、最大層間変位分布を比較した結果である。
図12は、線形応答における解析と本発明による最大加速度分布、最大速度分布、最大変位分布、最大層間変位分布を比較した結果である。
First, FIG. 10 shows the mass distribution and rigidity distribution obtained by the analysis and the present invention.
FIG. 11 shows a result of comparing the analysis in the strong nonlinear response with the maximum acceleration distribution, the maximum velocity distribution, the maximum displacement distribution, and the maximum interlayer displacement distribution according to the present invention.
FIG. 12 shows the result of comparing the analysis in the linear response with the maximum acceleration distribution, the maximum velocity distribution, the maximum displacement distribution, and the maximum interlayer displacement distribution according to the present invention.
これらの結果から、本発明の建物の健全性判定用の質量/剛性分布設定方法を用いた場合であっても、加速度、速度、変位の応答推定結果が解析とほぼ一致することが確認された。また、層間変位(隣接階の変位差:相対変位)は、本発明を用いた場合、解析に対して層間変位の最大点で10%程度の誤差が認められたが、おおむね良好に最大応答を推定できることが確認された。 From these results, it was confirmed that even when the mass / rigidity distribution setting method for determining the soundness of a building according to the present invention was used, the response estimation results of acceleration, velocity, and displacement almost coincided with the analysis. . In addition, when the present invention is used for the inter-layer displacement (displacement difference between adjacent floors: relative displacement), an error of about 10% is recognized at the maximum point of inter-layer displacement for the analysis, but the maximum response is generally good. It was confirmed that it can be estimated.
したがって、本実施形態の建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムによれば、建物モデルの設定において、専門家による構造設計の動的解析モデルの情報を必要としないで建物固有周期に合わせた剛性分布の作成が可能になる。 Therefore, according to the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present embodiment, the structural design movement by an expert in the building model setting. It is possible to create a stiffness distribution that matches the natural period of the building without the need for information on the dynamic analysis model.
また、応答推定に用いる建物モデルの設定に際し、階数と構造種別(S造、RC/SRC造)によって簡便に設定情報を作ることができる。 Moreover, when setting the building model used for response estimation, setting information can be easily created by the number of floors and the structure type (S structure, RC / SRC structure).
さらに、本実施形態の建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムによって得られる建物モデルでの質量及び剛性の分布は、通常の振動解析モデル(線形モデル)のパラメータとして利用することも可能である。 Further, the mass and stiffness distribution in the building model obtained by the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present embodiment is a normal vibration. It can also be used as a parameter of an analysis model (linear model).
ここで、1次の回帰式における計算例を示しておく。図3から、1次の回帰式は、次の式(16):S造、式(17):RC/SRC造となる。T1は1次固有周期(s)、Hは軒高(m)を示す。 Here, an example of calculation in the linear regression equation is shown. From FIG. 3, the first-order regression equations are the following equation (16): S structure, and equation (17): RC / SRC structure. T1 represents the primary natural period (s), and H represents the eave height (m).
この回帰式(S造:式(16))よって得られるモデルの1層から100層(1階建てから100階建て)での固有振動数(固有周期の逆数)の変化を図13(a)に示す。なお、横軸が設定したい固有振動数、縦軸が質点系モデルでの固有振動数を示しており、○線で変化を表す。
実際の計算では固有振動数でのずれがあり、その補正に必要な固有振動数の係数値(補正倍率)として×線で示す。
FIG. 13 (a) shows changes in the natural frequency (reciprocal of the natural period) from the first layer to the 100th layer (from the first floor to the 100th floor) of the model obtained by this regression equation (S structure: Expression (16)). Shown in The horizontal axis indicates the natural frequency to be set, the vertical axis indicates the natural frequency in the mass system model, and the change is indicated by a circle.
In the actual calculation, there is a deviation in the natural frequency, and the coefficient value (correction magnification) of the natural frequency necessary for the correction is indicated by x-rays.
この固有振動数毎の係数値によって補正して解析モデルの剛性を修正する。
図13(b)に最終的に修正された質点系モデルでの固有振動数の関係を示す。
The stiffness of the analysis model is corrected by correcting with the coefficient value for each natural frequency.
FIG. 13B shows the relationship of the natural frequency in the finally corrected mass system model.
これらの結果から、本実施形態に対して回帰式が違っても対応可能であり、最適な1次固有振動数の設定を行い、建物モデルの初期情報の設定を行うことが可能であることが分かる。 From these results, it is possible to cope with this embodiment even if the regression equation is different, and it is possible to set the optimal primary natural frequency and set the initial information of the building model. I understand.
但し、この例で示す回帰式としては、建物階数が低層におい実際のものとはずれが大きくなる傾向を示したものであり(回帰式が高層以上の建物で相関が高いため)、利用する際には最適な回帰式の選択が重要となる。 However, the regression equation shown in this example shows a tendency for the number of building floors to be lower than the actual one in the lower floors (because the regression equation is highly correlated in buildings with higher floors), It is important to select the optimal regression equation.
以上、本発明に係る建物の健全性判定用の質量/剛性分布設定方法及び建物の健全性判定用の質量/剛性分布設定システムの一実施形態について説明したが、本発明は上記の実施形態に限定されるものではなく、その趣旨を逸脱しない範囲で適宜変更可能である。 Although one embodiment of the mass / rigidity distribution setting method for building soundness determination and the mass / rigidity distribution setting system for building soundness determination according to the present invention has been described above, the present invention is based on the above embodiment. It is not limited and can be changed as appropriate without departing from the spirit of the invention.
Claims (2)
建物階層数及び標準階高から建物の軒高を求め、該軒高、及び予め求められた実験式の回帰式によって建物の第1固有周期を求める第1固有周期算出工程と、
建物の各階層の質量を一定の質量に設定し、前記第1固有周期における第1剛性k1をk1=m×(2π/T1)2で求める第1剛性算出工程と、
建物の最上層を1、最下層を最上層の剛性分布係数N倍とし、全体に前記第1剛性を乗じた台形形状の第1剛性分布を作成する第1剛性分布作成工程と、
建物の一定の質量分布及び前記第1剛性分布から固有値解析によって第2固有周期を求める第2固有周期算出工程と、
前記第2固有周期/前記第1固有周期を計算して補正係数を求める補正係数算出工程と、
前記補正係数を2乗した値を前記第1剛性分布に乗じて第2剛性分布を求める第2剛性分布算出工程と、
前記建物の一定の質量分布及び前記第2剛性分布から固有値解析によって第3固有周期及び刺激関数を求める第3固有周期/刺激関数算出工程と、
前記第3固有周期と前記第1固有周期を比較し、前記第3固有周期が前記第1固有周期と一致している場合に、前記建物の一定の質量分布及び前記第2剛性分布を建物の健全性判定用の質量分布及び剛性分布として決定する健全性判定用質量/剛性分布決定工程とを備えることを特徴とする建物の健全性判定用の質量/剛性分布設定方法。 A building structure input process for inputting the structure type of the building, the number of floors of the building, and the stiffness distribution coefficient N in the lowest layer of the building;
A first eigenperiod calculation step of obtaining the eave height of the building from the number of building hierarchies and the standard floor height, and obtaining the first eigenperiod of the building by a regression equation of the eave height and a predetermined experimental formula;
A first stiffness calculation step of setting a mass of each level of the building to a constant mass, and obtaining a first stiffness k 1 in the first natural period by k 1 = m × (2π / T 1 ) 2 ;
A first stiffness distribution creating step of creating a trapezoidal first stiffness distribution in which the top layer of the building is 1 and the bottom layer is N times the stiffness distribution coefficient of the top layer and is multiplied by the first stiffness;
A second natural period calculation step of obtaining a second natural period from the constant mass distribution of the building and the first rigidity distribution by eigenvalue analysis;
A correction coefficient calculation step of calculating a correction coefficient by calculating the second natural period / the first natural period;
A second stiffness distribution calculating step of obtaining a second stiffness distribution by multiplying the first stiffness distribution by a value obtained by squaring the correction coefficient;
A third natural period / stimulus function calculating step of obtaining a third natural period and a stimulus function by eigenvalue analysis from the constant mass distribution of the building and the second stiffness distribution;
The third natural period and the first natural period are compared, and when the third natural period matches the first natural period, the constant mass distribution and the second rigidity distribution of the building are A mass / rigidity distribution setting method for building soundness determination, comprising: a soundness determination mass / rigidity distribution determining step for determining soundness determination mass distribution and rigidity distribution.
前記軒高と予め求められている軒高と建物の固有周期の関係を示す実験式の回帰式とから建物の第1固有周期を求める第1固有周期算出手段と、
第1固有周期における第1剛性を計算する第1剛性算出手段と、
建物の質量分布及び前記第1剛性の分布から固有値解析によって建物の第2固有周期を求める第2固有周期算出手段と、
前記第2固有周期/前記第1固有周期を計算して補正係数を求める補正係数算出手段と、
前記補正係数を2乗した値を第1剛性分布に乗じて第2剛性分布を求める第2剛性分布算出手段と、
建物の質量分布及び前記第2剛性の分布から固有値解析によって第3固有周期及び刺激関数を求める第3固有周期/刺激関数算出手段と、
前記第3固有周期と前記第1固有周期を比較する第3固有周期/第1固有周期比較手段と、
前記第3固有周期が前記第1固有周期と一致している場合に、前記第1固有周期となる建物の質量分布及び前記第2剛性分布を、建物の健全性判定用の質量分布及び剛性分布として決定する健全性判定用質量分布/剛性分布決定手段とを備えることを特徴とする建物の健全性判定用の質量/剛性分布設定システム。 Building eaves height calculation means for obtaining eave height from the number of building floors and standard floor height,
A first natural period calculating means for obtaining a first natural period of the building from the regression equation of an empirical formula indicating a relationship between the eave height and the eave height obtained in advance and the natural period of the building;
First stiffness calculating means for calculating the first stiffness in the first natural period;
Second natural period calculating means for obtaining a second natural period of the building by eigenvalue analysis from the mass distribution of the building and the distribution of the first rigidity;
Correction coefficient calculation means for calculating the second natural period / the first natural period to obtain a correction coefficient;
Second stiffness distribution calculating means for obtaining a second stiffness distribution by multiplying a value obtained by squaring the correction coefficient by the first stiffness distribution;
A third natural period / stimulus function calculating means for obtaining a third natural period and a stimulus function by eigenvalue analysis from the mass distribution of the building and the distribution of the second stiffness;
A third natural period / first natural period comparing means for comparing the third natural period and the first natural period;
When the third natural period coincides with the first natural period, the mass distribution and the second stiffness distribution of the building that become the first natural period are represented by the mass distribution and the stiffness distribution for building soundness determination. A mass / rigidity distribution setting system for determining the soundness of a building, comprising: a mass distribution / rigidity distribution determining means for determining soundness determined as:
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