JP4992084B2 - Structure damage diagnostic system and method - Google Patents

Description

  The present invention relates to a technique for monitoring and diagnosing the soundness of a structure.

  A technique for monitoring and diagnosing the soundness of a structure is called a structural health monitoring technique, and in recent years, the importance has rapidly increased in each field. In particular, there is an urgent need to develop a health monitoring system that can evaluate in advance the risk of accidents due to deterioration of social infrastructure structures that are approaching their useful lives and the risk of collapse of houses due to earthquakes. Damage occurs locally, and detection as early as possible is desirable, so a location that can be identified and sensitive to the smallest possible level of damage is required.

  In one conventional monitoring method, a change in natural frequency due to a decrease in structure rigidity is monitored. In order to evaluate the natural frequency, it is only necessary to measure an arbitrary dynamic physical quantity from one point to several points, and this method has an advantage that it is extremely simple. However, it cannot be detected unless it is a large damage that changes the characteristics of the entire structure, and it is difficult to identify the damaged part.

  On the other hand, there is a nondestructive inspection technique using ultrasonic waves or the like as a technique for individually detecting a crack or the like in a structural member. It is extremely effective when a thorough inspection can be performed after a temporary stop of service, such as a periodic overhaul inspection, and is used for inspection of aircraft and plants. However, in addition to requiring dedicated inspection equipment, the range that can be inspected at one time is very narrow, on the order of cm. In order to be used for constant monitoring of structures, it is necessary to install them very densely at all times, which is too expensive and impractical.

  In order to construct a realistic system for monitoring the soundness of structures, it is necessary to balance damage sensitivity and spatial resolution with measurement costs. For this reason, a method for evaluating the soundness of each critical part (for example, a bolted joint or a welded joint) of the target structure using a small number of relatively inexpensive sensors has been proposed. For example, in Patent Document 1 (Japanese Patent Laid-Open No. 2001-099760), a piezoelectric impedance method is used. In the piezoelectric impedance method, a change in structural characteristics in the vicinity of the piezoelectric element is detected by a change in impedance of the piezoelectric element attached to the surface of the structure. Patent Document 2 (Japanese Patent Laid-Open No. 2000-131197) proposes a method for measuring the transmission admittance between two piezoelectric elements attached to two points.

In addition, damage sensitivity is inferior to that of the piezoelectric impedance method, but as a method that can detect local damage with a small number of vibration sensors, a method that calculates the flexibility of a structure from a dynamic response has been proposed. Effectiveness is pointed out as a damage evaluation method with sensitivity and measurement cost. The inventors have so far proposed a damage detection method based on the local flexibility of a structure (Non-Patent Document 1). The local flexibility is defined as a relative deformation amount between two points when a pair of unit loads having opposite signs is applied to two points on the structure, and is effective as a localized soundness index. Further, Non-Patent Document 2 proposes an evaluation method for local rotational flexibility based on angular velocity measurement, focusing on the fact that local flexibility against bending deformation of structures such as beams can be evaluated.
JP 2001-099760 A JP 2000-131197 A JP 11-281111 A JP 2000-283800 A Shin Masuda, Shinya Morita, Akira Sone, Damage monitoring of beam-like structures by time-frequency analysis, Proceedings of the 8th Symposium on “Control of Motion and Vibration”, pp.641-644, 2003 A. Masuda, A. Sone and S. Morita, Continuous damage monitoring of civil structures using vibratory gyroscopes, Proceedings of SPIE, Vol. 5391, pp. 40-49, 2004

  Although the methods based on the above-described piezoelectric impedance method (Patent Documents 1 and 2) have damage sensitivity comparable to the nondestructive inspection method, the physical meaning of impedance change is difficult to grasp. Furthermore, in order to perform highly sensitive damage evaluation, the accuracy of the impedance measuring device is important, and there is a problem that it is necessary to compensate for a change in characteristics of the piezoelectric element due to a temperature change or the like.

  The methods based on the evaluation of local flexibility proposed by the inventors (Non-Patent Document 1 and Non-Patent Document 2) have a clear physical meaning of the evaluation index, and have various deformation modes depending on the sensor arrangement and the sensor type. Can be evaluated for flexibility. However, since the normalization constant of the normal mode is necessary for the calculation, it is necessary to know the mode shape and mass matrix of the entire structure. For this reason, even if only the local flexibility in one place of the structure is interested, the point that the information on the whole structure is necessary is an obstacle to practical use.

  In addition, although angular velocity measurement is used in the embodiment of the present invention, the following documents have been found by conducting a prior art search from this viewpoint. In patent document 3 (Unexamined-Japanese-Patent No. 11-281131), the dynamic strain is measured using an angular velocity sensor. Specifically, two angular velocity sensors are attached to the surface of the structure in which the steel frame is embedded in the concrete so as to receive a force in the bending direction. Then, the measured value of the detected angular velocity signal is integrated to calculate the relative angle between the two points, and this is used as an approximate value of the curvature to obtain the bending distortion of the beam. Also in the embodiment of the present invention, angular velocity sensors arranged at two points are used, but the difference is that the rigidity deterioration regarding rotational deformation between the two points is approximately calculated from the measured values. Moreover, in patent document 4 (Unexamined-Japanese-Patent No. 2000-283800), the geological displacement of one point of the ground is detected using the angular velocity sensor. In this method, an angular velocity sensor is fixed in a cylinder embedded in the ground, and the displacement of the ground is detected from a signal from each velocity sensor. Here, an integration operation is required to obtain the angular displacement from the angular velocity, and a separate inclinometer is required to correct the influence of the sensor drift, resulting in a complicated system. On the other hand, since the embodiment of the present invention does not require an integration operation, it is not affected by the drift of the angular velocity sensor, and the rigidity deterioration related to the rotational deformation between two points on the structure can be evaluated.

  An object of the present invention is to make it easier to monitor displacement, distortion, and the like inside a structure.

で定義されるｄ_ｎを算出し、
下記の式

（ここで添え字presentは現在の評価値を、添え字baselineは評価の基準となる健全状態における評価値を表す）で定義される損傷指標ＤＩを評価することを含むデータ処理の少なくとも一部を実行する。 The structure damage diagnosis system according to the present invention includes a plurality of vibration response detection sensors installed at two points x _i and x _j sandwiching a portion to be monitored of the structure and a reference point x different from the positions x _i and x _j. a reference response detection sensor installed at _k , and a data processing device. The data processing device acquires vibration measurement data from the vibration response detection sensor and the reference response detection sensor, and from the input vibration measurement data, in each of the vibration modes of the number N of natural vibrations, an n-order mode (1 ≦ n ≦ N) relative mode shape Ψ _n (x _i , x _j ) which is a relative displacement amount in the direction of the axis of interest between two points x _i and x _j extracted from the mode shape of N), and the mode of the n-th mode at the reference point x _k Obtain a reference mode shape φ _n ^r (x _k ) that is a reference axial component of the shape and a natural frequency ω _n of the _n-th mode,
The following formula

In calculating the d _n to be defined,
The following formula

(Here, the subscript present represents the current evaluation value, and the subscript baseline represents the evaluation value in the healthy state that is the basis of the evaluation.) At least part of the data processing including evaluation of the damage index DI defined in Execute.

In the diagnostic system, for example, the reference point x _k is the same position as one of the positions x _i and x _j , and one of the plurality of vibration response detection sensors is also used as the reference response detection sensor. In the diagnostic system, for example, the vibration response detection sensor is a sensor that detects an angle, an angular velocity, or an angular acceleration. Alternatively, in the diagnostic system, for example, the vibration response detection sensor is a sensor that detects displacement, speed, or acceleration. In the diagnostic system, for example, the reference response detection sensor is a sensor that detects displacement, speed, or acceleration. Alternatively, the reference response detection sensor is a sensor that detects an angle, an angular velocity, an angular acceleration, or a distortion.

  The diagnostic system preferably further includes a host computer that receives a data processing result from the data processing device provided for each of a plurality of monitoring target locations. For example, the data processing device executes a part of the data processing, and the host device executes the remaining part of the data processing based on the data processing result received from the data processing device. Preferably, data relating to vibration measurement (the vibration measurement data, a data processing intermediate result or a data processing result) is transmitted between the data processing device and the host computer wirelessly.

Wherein the diagnostic system, the data processing device, for example, two points x _i, obtains the d _n the cross spectrum and the ratio of the power spectrum of the reference response data and the relative amount of vibrational response data (difference) in the x _j, wherein d _n reference vector _{d n (x i, x j} ) changed in the non-damaged | evaluated at norm of variation from _baseline.

で定義されるｄ_ｎを算出し、（ｄ）下記の式

（ここで添え字presentは現在の評価値を、添え字baselineは評価の基準となる健全状態における評価値を表す）で定義される損傷指標ＤＩを評価する。
In the structural damage diagnosis system according to the present invention, (a) a plurality of vibration response detection sensors and positions x _i , x _j installed at two points x _i , x _j sandwiching a site to be monitored of the structure are different. enter the vibration measurement data from the reference response detection sensor disposed at the reference point x _k, then, (b) to input vibration measurement data, in each of the vibrational modes of the number n of the natural oscillation, n order mode (1 n order in ≦ n ≦ n 2 points _x i extracted from the mode shapes), the relative mode shapes [psi _n is the relative displacement of the target axial direction between the _{x j (x i, x} j), the reference point _{x k} The reference mode shape φ _n ^r (x _k ) and the natural frequency ω _n of the nth order mode, which are the components of the mode shape of the mode in the reference axis direction, are obtained. (C)

In calculating the d _n to be defined, (d) the following formula

(Here, the subscript present represents the current evaluation value, and the subscript baseline represents the evaluation value in a healthy state as a reference for evaluation).

In the diagnostic method, preferably, the d _n 2 points x _i, determined by the cross-spectrum and the ratio of the power spectrum of the reference response data and the relative amount of vibrational response data (difference) in the x _j, a change in the d _n Reference vector d _n (x _i , x _j ) | at the time of non-damage is evaluated by the norm of the fluctuation from _baseline .

  In the present invention, the local flexibility is evaluated approximately without normalizing the vibration mode. Therefore, the local flexibility (for example, rotational rigidity) of the structure is reduced by a small number of sensors arranged in the vicinity of the target portion. Deterioration can be detected. Since the measurement device and the data processing device can be configured independently for each target region of interest, a system can be flexibly constructed according to the scale of the structure and the number of critical regions.

  Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

  There are many structural parts where strength against bending load is a problem, such as long and narrow structures such as pipes and bridges, and joint parts of frame structures. When damage such as cracks or bolt loosening occurs in such a part, the bending rigidity at the damaged part is lowered, and the deformation amount, that is, the flexibility with respect to the unit load is increased. Flexibility is the inverse of the stiffness matrix and is a static characteristic of the structure, but can be expressed using normal mode shapes and natural frequencies, so it can be obtained from the dynamic response through mode identification. . Therefore, the effectiveness of flexibility has been pointed out as an index of soundness in global structural soundness monitoring.

  Inventors have proposed the damage detection method based on the local flexibility of a structure in the past research (nonpatent literature 1). The local flexibility is defined as a relative deformation amount between two points when a pair of unit loads having opposite signs is applied to two points on the structure, and is effective as a localized soundness index. In Non-Patent Document 2, attention was paid to the fact that local flexibility against bending deformation of a structure such as a beam can be evaluated by angular velocity measurement, and the use of a gyro sensor was proposed. However, this damage detection technique requires normal mode normalization constants.

  The present invention provides a practical method for evaluating local flexibility approximately without performing mode normalization, instead of directly evaluating the local flexibility index LFI. ADVANTAGE OF THE INVENTION According to this invention, the damage diagnostic system which can detect deterioration of the local rigidity of a structure with sufficient sensitivity by the small number of sensor arrange | positioned in the vicinity of an object site | part is provided. Since the measurement device and the data processing device can be configured independently for each target region of interest, a system can be flexibly constructed according to the scale of the structure and the number of critical regions. Further, by making data transmission wireless, a more flexible damage diagnosis system can be provided.

  Here, the evaluation of local flexibility will be described. In the present invention, a decrease in local stiffness caused by structural damage is evaluated by a change in the local flexibility index LFI. The local flexibility index is expressed by equation (1), and causes local deformation in a specific manner at a point of interest on a structure (for example, a bolt joint or a welded joint that is structurally important). Is defined as the amount of deformation with respect to a specific static load pattern loaded with intention. That is, the local flexibility index is a quantity representing the local softness of the structure with respect to a specific deformation mode, and an increase in this quantity means a decrease in local rigidity, that is, the occurrence of damage at the location.

Here, the specific static load pattern is a pair of static unit concentrated loads applied to the two points x _i and x _j sandwiching the point of interest, and the deformation amount is an axis parallel to the load axis. The relative deformation amount between two points evaluated in the direction. By appropriately selecting how to give unit concentrated load pairs, local flexibility for various deformation modes can be evaluated. For example, in order to evaluate local flexibility with respect to tensile deformation between two points, a pair of unit concentration forces parallel to a line segment connecting two points and having opposite directions may be adopted. Similarly, in order to evaluate the local flexibility with respect to the shear deformation between two points, a pair of unit concentration forces perpendicular to the line segment connecting the two points and opposite to each other may be adopted.

  Moreover, local flexibility regarding rotational deformation between two points can be evaluated by considering a moment as a load. That is, by adopting a pair of unit concentration moments whose directions are opposite to each other around an axis parallel to the line connecting the two points, the local flexibility against torsional deformation between the two points can be evaluated, and the line connecting the two points By adopting a pair of unit concentration moments whose directions are opposite to each other around a vertical axis, it is possible to evaluate local flexibility with respect to bending deformation between two points. In particular, the local flexibility regarding bending deformation is useful when performing damage assessment of rigidly connected joints or beam-like or plate-like structures.

ここで、Ｎは固有振動の数であり、固有振動の数Ｎの振動モードの各々において、ｃ_ｎはｎ次モード（１≦ｎ≦Ｎ）のモードシェイプを質量正規化するための、すなわちモード質量を１に正規化するための正規化定数であり、ω_ｎは固有振動数である。また、Ψ_ｎ(ｘ_ｉ、ｘ_ｊ）はｎ次モードのモードシェイプから抽出した２点ｘ_ｉ，ｘ_ｊの間の相対変形量であり、ここでは相対モードシェイプと呼んで次式（２）で定義する。

ここでφ_ｎ ^ｄ(ｘ)はｎ次モードシェイプφ_ｎ(ｘ)から抽出した注目する軸方向の変形成分であり、引張変形やせん断変形などの並進変形に関する局所フレキシビリティ指標を評価する場合には、注目する力の方向と平行な軸方向成分をとり、ねじり変形や曲げ変形などの回転変形に関する局所フレキシビリティ指標を評価する場合には、注目するモーメント軸と平行な軸まわりの回転角をとる。 The above-mentioned local flexibility index LFI is defined by the following formula (1) using a modal parameter of the structure (see Non-Patent Documents 1 and 2).

Here, N is the number of the natural vibration in each vibration mode of the number N of the natural vibration, c _n is for mass normalized mode shapes of order n mode (1 ≦ n ≦ N), i.e. mode This is a normalization constant for normalizing the mass to 1, and ω _n is the natural frequency. Ψ _n (x _i , x _j ) is a relative deformation amount between the two points x _i and x _j extracted from the mode shape of the nth-order mode. Here, it is called a relative mode shape and the following equation (2) Define in.

Here, φ _n ^d (x) is an axial deformation component of interest extracted from the _n- th order mode shape φ _n (x), and is used when evaluating a local flexibility index related to translational deformation such as tensile deformation and shear deformation. Takes an axial component parallel to the direction of the force of interest, and evaluates the local flexibility index related to rotational deformation such as torsional deformation and bending deformation, the rotation angle around the axis parallel to the moment axis of interest. Take.

ここで、右辺のａ_ｎとｄ_ｎはそれぞれ次式（４）で定義される。

ここで、φ_ｎ ^ｒ(ｘ_ｋ)は参照点ｘ_ｋにおけるモードシェイプの適切な参照軸方向成分であり、ここでは参照モードシェイプと呼ぶ。参照点ｘ_ｋは一般には２点ｘ_ｉ、ｘ_ｊと異なる第３の点であるが、２点ｘ_ｉ、ｘ_ｊのいずれか一方と兼用できる場合もある。 Here, the formula (1) defining the local flexibility index LFI is rewritten as the following formula (3).

Here, a _n and d _n on the right side are defined by the following equation (4), respectively.

Here, φ _n ^r (x _k ) is an appropriate reference axial component of the mode shape at the reference point x _k and is referred to herein as a reference mode shape. Reference point _{x k} is generally two points _x i, although a third different from the _{x j,} 2 points _x i, can sometimes be combined with one of _{x j.}

Of the right side of the equation (2), d _n is the amount consisting of the relative mode shapes and natural frequencies normalized by the reference mode shapes, point x _i, vibration measurement data and the reference point of the target axis at x _j from the reference axis of the vibration measurement data in the x _k, can be determined using methods of various modes identified.

On the other hand, a _n is the amount consisting of those mass normalized reference mode shapes, in order to determine the value must know the normalization constant c _n. However, in order to determine the c _n, it is necessary either:.
(A) A high-precision mathematical model (such as a finite element model) of the entire structure,
(B) Dynamic response measurement covering the mass matrix of the entire structure and the entire structure with sufficient spatial density,
(C) Active vibration means for the structure, vibration force measurement means, and dynamic response measurement at the vibration point.
In any case, the realization of a low-cost, flexible and easy-to-use damage diagnostic apparatus is hindered.

Next, simplification of the evaluation method will be described. The right side of Equation (3) is the inner product of two vectors {a ₁ ,..., A _N } and {d ₁ ,..., D _N } in the N-dimensional vector space. Of these, {a ₁ ,..., A _N } is a vector formed by mass normalizing the reference mode shape of each mode, and includes a normalization constant, which is difficult to obtain as described above. By selecting the axial direction appropriately, it can be regarded as a vector that hardly changes due to local damage. On the other hand, {d ₁ ,..., D _N } is a vector composed of a quantity (mode shape that is not natural frequency and mass-normalized) that can be calculated from vibration measurement data, and local damage. It is a vector that varies greatly depending on. Therefore, instead of directly evaluating the local flexibility index LFI of the expression (3), the change of LFI is approximately evaluated by the change of the vector {d ₁ ,..., D _N }. In order to evaluate the change of the vector {d ₁ ,..., D _N }, one or a plurality of feature amounts may be extracted from the vector. For example, a method based on a vector norm or a method based on an inner product may be considered.

Here, in order to identify the mode shape, the acceleration response y (x _k , t) at the point x _k is used as a reference response. In general, any physical quantity at any point may be selected as a reference response, but it is desirable to select an amount that is less susceptible to damage for reasons described below. In some cases, the angular velocity response at either point x _i or point x _j can be adopted as the reference response, and in that case, the number of sensors can be reduced by one. However, in the experimental apparatus described later, since the point x _i and the point x _j show only the horizontal movement in the healthy state, both angular velocity responses are almost zero. For this reason, the acceleration response in the horizontal direction is separately measured and used as a reference response. In the following, the case _where the acceleration response at the point xk is used as the reference response will be described, but the same discussion can be made when another physical quantity is used as the reference response.

Next, the vector _{{d 1, ..., d N} } calculation method and the vector from the vibration measurement data _{{d 1, ..., d N} } shown below how to evaluate the changes in the. here,
(1) As means for calculating the vector {d ₁ ,..., D _N } from the vibration measurement data, the relative amount (difference) of the vibration response data at the two points x _i and x _j and the cross spectrum of the reference response data Adopting the method based on power spectrum ratio,
(2) The change of the vector {d ₁ ,..., D _N } is evaluated by the norm of the variation from the reference vector at the time of non-damage.

  There are various options for identifying the modal parameter. Here, the simplest method, that is, the method of reading the peak value of the spectrum of the steady random response is used. In this method, it is only necessary to install two or three sensors in the vicinity of the target site in order to evaluate one local flexibility, and two measurement channels are sufficient. For this reason, there exists an advantage that a measurement system and a calculation system can be comprised independently for every object site | part which is interested.

  However, the natural frequency and mode shape calculation means and the vector change evaluation method are not limited to these, and any one can be selected as appropriate.

ただしｆ_ｎ(ｔ)はモード外力であり、次式（６）で与えられる

The local flexibility index will be further described. The equation of motion in the nth order mode coordinate system is written as follows.

However, f _n (t) is a mode external force and is given by the following equation (6).

Here, it is assumed that the distributed external force f is a weak stationary process having a power spectrum S _f (x, y, ω) of the following equation (7).

ここで、ｐは０から２までの整数であり、点ｘ_ｉ、ｘ_ｊで変位または角度を計測する場合はｐ＝０、速度または角速度を計測する場合はｐ＝１、加速度または角加速度を計測する場合はｐ＝２である。同様に、点ｘ_ｋで変位または角度を計測する場合はｑ＝０、 速度または角速度を計測する場合はｑ＝１、加速度または角加速度を計測する場合はｑ＝２である。右上付きの＊は複素共役を表す。ここで、ＧおよびＨは、以下のように表される。

同様に、参照加速度応答y(ｘ_ｋ,ｔ)のパワースペクトルＳ_ｙは次式（１０）のようになる。

Then, the cross spectrum S _xy of the relative angular velocity response z (x _i , x _j , t) between the two points x _i and x _j and the reference response y (x _k , t) is expressed by the following equation (8). .

Here, p is an integer from 0 to 2, p = 0 when measuring displacement or angle at points x _i and x _j , p = 1 when measuring speed or angular velocity, and acceleration or angular acceleration as When measuring, p = 2. Similarly, q = 0 when measuring the displacement or angle at the point _xk , q = 1 when measuring the velocity or angular velocity, and q = 2 when measuring the acceleration or angular acceleration. * With an upper right represents a complex conjugate. Here, G and H are expressed as follows.

Similarly, the power spectrum S _y of the reference acceleration response y (x _k , t) is expressed by the following equation (10).

よって、ｎ次固有振動数ω_ｎでは、式（９）は次式（１２）のようになる。

Assuming that the natural frequencies of the respective modes are separated from each other and the mode damping ratio is sufficiently small, at the n- _th natural frequency ω _n , when n = m and n ≠ m, respectively, As shown above and below.

Therefore, at the n-th natural frequency ω _n , the equation (9) becomes the following equation (12).

From this, equations (8), and (10), the following equations (13) and (14) are obtained.

となり、次式（１６）を得る。

Taking the ratio of Equation (13) and Equation (14),

Thus, the following equation (16) is obtained.

From the equations (16), (3), and (4), the approximate evaluation equation (17) of the local flexibility index LFI is derived.

ここで添え字presentは現在の評価値を、添え字baselineは評価の基準となる初期状態（または健全状態）における評価値を表す。 The right side of equation (17) is the inner product of two vectors {a ₁ ,..., A _N } and {d ₁ ,..., D _N } in the N-dimensional vector space. Of these, the vector {a ₁ ,..., A _N } is obtained by mass normalizing the reference mode shape of each mode and includes a normalization constant, so that it is difficult to obtain as described above. By choosing appropriately (ie, choosing an amount that is less susceptible to damage as a reference response), it can be considered a vector that hardly changes with local damage. On the other hand, the vector {d ₁ ,..., D _N } is composed of a quantity that can be calculated from the vibration measurement data (a natural frequency and a mode shape that is not mass-normalized), and changes greatly due to local damage. Therefore, here, the local flexibility index LFI of Expression (17) is not directly evaluated, but the change in LFI is approximately evaluated by the change in the vector {d ₁ ,..., D _N }. Specifically, the change of the vector {d ₁ ,..., D _N } is evaluated by the norm of the fluctuation from the reference vector at the time of non-damage. That is, the damage index DI (i, j) is defined as in the following equation (18), and damage is detected by a change in the value of this index.

Here, the subscript present represents the current evaluation value, and the subscript baseline represents the evaluation value in an initial state (or a healthy state) that serves as a reference for evaluation.

Next, as an example of the local flexibility index LFI, the local flexibility index LFI for rotational deformation will be described. (The following description will also be repeated with respect to portions that overlap with the above-described general description.) The local flexibility index LFI is a pair of static values applied to two points x _i and x _j on the structure. This is a relative rotational angular displacement of deformation with respect to a typical unit moment load, and is calculated by Equation (31) using a modal parameter of the structure. Equation (31) is derived as follows.

ただしｆ_n(ｔ)はモード外力であり、次式（２０）で与えられる

The equation of motion in the nth order mode coordinate system is written as follows.

However, f _n (t) is a mode external force and is given by the following equation (20).

Here, it is assumed that the distributed external force f is a weak stationary process having the following power spectrum S _f (x, y, ω).

ここで、右上付きの＊は複素共役を表す。また、Ｇ，Ｈは以下のとおりである。

同様に、参照加速度応答Ｓ_y(ｘ_ｋ,ｔ)のパワースペクトルは次のようになる。

The installation points of the angular velocity sensor are x _i and x _j, and the ground point of the reference acceleration sensor is x _k . Then, the cross spectrum S _zy between the relative angular velocity response z (x _i , x _j , t) between the two points x _i and x _j and the reference response y (x _k , t) is expressed by the following equation (22). .

Here, * with an upper right represents a complex conjugate. G and H are as follows.

Similarly, the power spectrum of the reference acceleration response S _y (x _k , t) is as follows.

Assuming that the natural frequencies of the respective modes are separated from each other and the mode damping ratio is sufficiently small, at the n- _th natural frequency ω _n , when n = m and n ≠ m, the upper and lower sides of the right side of Expression (25) As shown.

Therefore, at the n-th natural frequency ω _n , G and H are expressed by the following equation (26).

From this, equations (22) and (24), the following equations (27) and (28) are obtained.

となり、次式（３０）を得る。

When the ratio of Expression (27) and Expression (28) is taken, Expression (29)

Thus, the following formula (30) is obtained.

From the expressions (30), (3), and (4), the approximate evaluation expression (31) of the local flexibility index LFI is derived.

ここで添え字presentは現在の評価値を、添え字baselineは評価の基準となる初期状態（または健全状態）における評価値を表す。 Two vectors on the right side of the equation (31) is an N-dimensional vector space _{{a 1, ..., a N} } and _{{d 1, ..., d N} } has become inner product of. Of these, the vector {a ₁ ,..., A _N } is obtained by mass normalizing the reference mode shape of each mode and includes a normalization constant, so that it is difficult to obtain as described above. By choosing appropriately, it can be regarded as a vector that hardly changes due to local damage. On the other hand, the vector {d ₁ ,..., D _N } consists of a quantity that can be calculated from vibration measurement data (a natural frequency and a mode shape that is not mass-normalized), and changes greatly due to local damage. Therefore, instead of directly evaluating the LFI of the equation (31), the change of the LFI is approximately evaluated by the change of the vector {d ₁ ,..., D _N }. Specifically, the change of the vector {d ₁ ,..., D _N } is evaluated by the norm of the fluctuation from the reference vector at the time of non-damage. That is, the damage index DI is defined as in the following equation (32), and damage is detected by a change in the value of this index.

Here, the subscript present represents the current evaluation value, and the subscript baseline represents the evaluation value in an initial state (or a healthy state) that serves as a reference for evaluation.

  Furthermore, it is also possible to use the above-described damage index evaluation for evaluating flexibility regarding translational deformation. In that case, displacement, speed, acceleration, etc. may be selected as the measurement amount of the sensor.

  FIG. 1 shows a damage diagnosis system according to an embodiment of the present invention. This diagnostic system includes two angular velocity sensor units 20 installed with a monitoring target part (for example, a joint connected by welding or bolts) 10 interposed therebetween, 1 connected to these parts by wire and installed in the vicinity of the monitoring target part. The host computer 40 includes a single wireless sensor node 30 and a wireless access point 42. The wireless sensor node 30 transmits the data processing result wirelessly, and the wireless access point 42 receives the data processing result from the wireless sensor node 30. A wired connection may be used without using the wireless interface 38 (FIG. 2). Further, the access point 42 need not be directly connected to the host computer 40, and may be connected via a LAN or the like.

  FIG. 2 conceptually shows a signal processing system in this diagnostic system. An angular velocity sensor (for example, a gyro sensor) 22 incorporated in the angular velocity sensor unit 20 measures an angular velocity response at an installation point, and the signal is amplified by an amplifier 24 and sent to the wireless sensor node 20. The acceleration sensor 32 built in the wireless sensor node 30 measures the acceleration response of the installation point as reference data. In the wireless sensor node 30, these response data are converted into digital data by the AD converter 34, and the processor 36 processes these digital data to calculate a damage index DI (formula (18)). The processor 36 has a configuration similar to that of a normal computer, stores the above-described evaluation value in a healthy state as a reference for evaluation, and performs calculation processing for calculating a damage index DI stored in a storage device (not shown). The program processes the input data and calculates the damage index DI. The obtained damage index DI is transmitted to the host computer 40 via the wireless interface 38, and is presented to the user through appropriate post-processing. Any wireless interface 38 can be used.

FIG. 3 is a flowchart of signal processing performed by the processor 36 of the wireless sensor node 30. The sound state vector {d ₁ ,..., D _N } is obtained by using the following procedure, and is stored in advance as an evaluation value in the sound state as a reference for evaluation. First, measurement data from each sensor is input from the AD converter 34 (S10). Next, the natural frequency and the mode shape are obtained. For this reason, the FFT of the relative angular velocity data and the reference acceleration data is performed, the ratio of the cross spectrum data and the power spectrum of the relative angular velocity data and the reference acceleration data is obtained, and the natural frequency and the mode shape are obtained (S12). Then, a vector {d ₁ ,..., D _N } is calculated using the natural frequency and the mode shape (S14). Further, the change of the vector {d ₁ ,..., D _N } is evaluated by the norm of the variation from the reference vector at the time of non-damage (S16). Then, the damage index DI is obtained (S18) and transmitted to the host computer 40 (S20).

In this embodiment, a local flexibility index for bending deformation is evaluated to detect damage in a rigidly connected joint. For this reason,
(1) Two angular velocity sensors are used for acquiring the relative mode shape, and one acceleration sensor is used for acquiring the reference mode shape.
(2) As a means for calculating the vector {d ₁ ,..., D _N } from the vibration measurement data, the ratio between the cross spectrum and the power spectrum of the relative angular velocity data and the reference acceleration data is used.
However, the target location and the deformation mode to be evaluated, the sensor configuration (measurement amount, arrangement and combination), the natural frequency and mode shape calculation means, and the vector change evaluation method are not limited to these. it can.

  For example, not the angular velocity but the angle or angular acceleration may be used as the sensor measurement amount. In some cases, one of two angular velocity data instead of acceleration can be used as reference data. In this case, the total number of sensors can be two. As a means for calculating the natural frequency and the mode shape, a NEXT + ERA method, a subspace method, or the like may be used. As an evaluation method of the vector change, an inner product with a vector at the time of non-damage may be used, or a more advanced pattern classification method may be used. These signal processes are performed in the wireless sensor node 30, but part or all of the signal processes may be performed by the host computer 40.

Measurement data from the vibration response detection sensor (for example, the angular velocity sensor 22) and the reference response detection sensor (for example, the acceleration sensor 32) is processed by the wireless sensor node 30 and the host computer 40. In the data processing procedure shown in FIG. The damage index is calculated by the processor in the wireless sensor node 30 installed at each damage monitoring location, and the result, that is, the “damage index value” is transmitted to the host computer 40. The host computer 40 records the damage indexes at a plurality of points together and presents them to the user. However, various forms of data processing in the wireless sensor node 30 and the host computer 40 are possible. In one example, the wireless sensor node 30 performs measurement data acquisition, transmits vibration measurement data via a wireless link, and the host computer 40 executes a data processing procedure similar to that in FIG. 3 to evaluate a damage index. In another example, the wireless sensor node 30 performs a part of the data processing procedure of FIG. 3 (for example, up to the calculation of the vector {d _n }), and transmits an intermediate result of the data processing to the host computer 40 via a wireless link. . In the host computer 40, the remaining data processing is executed to obtain the damage index. The damage index at a plurality of points is recorded and displayed together.

  Next, an example of damage diagnosis will be described. Experiments were performed using a four-layer shear structure model shown in FIG. In FIG. 4, the left side is an elevational view, and the right side is a top view of the first to third layers. In the model, the uppermost slab 42 is fixed to four upright aluminum thin plate columns 40 (2 mm thickness, 40 mm width), and the first to third layers are mounted on a support block 44 fixed to the columns at equal intervals. The four corners of the intermediate layer slabs 46a, 46b, 46c are each fixed with four M6 bolts 48 via a disc spring washer. A state in which all bolts are sufficiently tightened is defined as a healthy state. As shown in Table 1, the damage level is defined by the four bolt loosening angles. Bolt numbers 1-4 are shown in FIG. Loosen the bolts sequentially at three points in the four corners of the intermediate slab (damage level 0-3), then loosen the fixing bolts 48 in ten steps for the remaining one of the four corners of the intermediate slab. In order to create a damaged state, the fastening rigidity of the slab and column was changed. Table 1 shows the definition of the damage state. In Table 1, the loosening angle is an angle obtained by turning the bolt in the loosening direction from the fully tightened state. > 1800 means more than 5 revolutions and corresponds to a fully relaxed state.

Table 1 Definition of damage level

Since measuring actual relative speed response in a wide band is difficult, one by one gyro sensor (not shown) in this measurement is a type of angular velocity sensor on either side of the point x _i and the point x _j of sites Installed, and the necessary modal parameters are estimated from the difference z (x _i , x _j , t) of the angular velocity responses measured by these. As the gyro sensor, a small and inexpensive vibration gyro is used. Various types of vibratory gyros with an upper limit of about 50 Hz are available. For this measurement, ADXRS401 from Analog Devices Inc. was used. Table 2 shows the specifications of this sensor.

Table 2 Specifications of gyro sensor

  One gyro sensor was mounted on the slab and one on the support block, and the detection axes were mounted in directions that were parallel to the direction of the acting axis of the column bending moment. Furthermore, one acceleration sensor (ADXL311) (not shown) for reference response measurement was attached so that the detection axis was parallel to the horizontal vibration direction of the slab.

  The entire structure model was installed on a horizontal shaking table, and the actuator was driven by steady pink noise to perform vibration. The measured response values for each sensor were recorded twice for each experimental condition with a sampling frequency of 500 Hz and a data length of 214 pieces. The data was divided into 1024 segments, a Hanning window was applied to each segment, a zero was added and the length was expanded 8 times, and fast Fourier transform was performed. The necessary power spectrum and cross power spectrum were calculated by multiplying these in an appropriate combination and then calculating the arithmetic average for all segments.

  Next, experimental results will be described. Experiments were conducted by setting the damage states shown in Table 1 for the fastening nodes between the first to third slabs 44a to 44c and the support block 42.

  First, FIGS. 5a to 5c show values of the natural frequencies read from the power spectrum of the acceleration response in each damage state. FIGS. 5a, 5b and 5c show the change in natural frequency in the first to third intermediate slabs 44a, 44b and 44c, respectively. Compare the healthy state (the state where the slab and support block are completely fastened at 4 locations) and the state of the most serious damage (the state where one of the 4 fastening joints between the slab and the support block is completely broken) However, it can be seen that there is no significant change in the natural frequency.

Next, FIGS. 6a to 6c show the results of obtaining the damage index. In calculating the damage index was obtained from the first try in healthy during vector _{{d 1, ..., d N} } to _{{d 1, ..., d N} } was taken as _baseline. The damage index values plotted at the damage level 0 (healthy state) in FIGS. 6a to 6c are {d ₁ ,..., D _N } obtained from the second trial in the healthy state, and {d ₁ ,. , d _N } _baseline . It can be seen from FIGS. 6a to 6c that the damage index increases as the damage progresses when any layer is damaged.

  Furthermore, it can be seen that the transition of the damage index is divided into three regions: (I) from a healthy state to a damage level 3, (II) damage level 4, and (III) damage level 5 and later. The value of the damage index in the area (I) is almost the same as the value in the healthy state, which means that the influence of the damage remains within the range of the variation of the damage index. That is, the damage level in this region cannot be detected. Since the bolt 4 remains in a completely fastened state in the range up to the damage level 3, it is considered that the rigidity of the fastened joint is not substantially lowered, so this result is considered to be appropriate. When entering the area (II), the damage index increases rapidly. This is because the remaining one bolt 4 starts to loosen, so that the rigidity of the fastening node starts to decrease substantially. The value of the damage index increases rapidly while the bolt 4 is half-rotated, and after the half-rotation (region (III)), there is a tendency to almost increase after saturation. It is thought that the bolt tightening force is almost lost after half rotation.

  In this experiment, even though some measures were taken, such as using a conical spring washer on the fastening bolt, the increase in damage index was discontinuous and abrupt. I could not investigate in detail. In order to investigate the detection limit, it is considered necessary to further devise the experimental apparatus to continuously control the damage state.

  As explained above, in the experiment using the shear structure model, we succeeded in detecting a decrease in the fastening rigidity between the slab and the column. In this diagnosis, it is only necessary to install two or three sensors in the vicinity of the target site in order to evaluate the local flexibility at one location, and the measurement system and the calculation system are configured independently for each target site of interest. There is an advantage that you can. For this reason, it is compatible with the wireless sensor network environment, and in the future, it can be expected to develop as a structural health monitoring technique by distributed processing using the wireless sensor network system.

  Further, in the example shown in FIG. 1, damage diagnosis is performed at one location. However, when performing diagnosis at a plurality of locations, as shown in FIG. 7, an angular velocity sensor unit and a wireless sensor node are arranged at each location. That's fine. Since the apparatus for diagnosis and the calculation process are independent from each other for each target part, addition / deletion of a monitoring part is easy.

In addition, the above-mentioned damage diagnosis system includes structural health monitoring for high-rise buildings and social infrastructure structures, dynamic precise seismic diagnosis for individual houses (such as wooden houses) and various facilities, monitoring for various stationary equipment in plants, wind power It can be applied to various fields such as power turbine blades, helicopter rotor damage monitoring, and aerospace structure health monitoring.

Illustration of damage detection system Diagram showing data processing system Flow chart of signal processing program Illustration of a four-layer shear structure model Graph of natural vibration against damage level in the first layer Graph of natural vibration against damage level in the second layer Graph of natural vibration against damage level in the third layer Graph of damage index against damage level in the first layer Graph of damage index against damage level at layer 2 Graph of damage index against damage level at layer 3 Illustration of a modification of the damage detection system

Explanation of symbols

  20 angular velocity sensor unit, 22 angular velocity sensor, 30 wireless sensor node, 32 acceleration sensor, 36 processor, 40 host computer.

Claims (12)

A plurality of vibration response detection sensors installed at two points x _i and x _j sandwiching a monitoring target portion of the structure, and a reference response detection sensor installed at a reference point x _k different from the positions x _i and x _j ;
Vibration measurement data is acquired from the vibration response detection sensor and the reference response detection sensor. From the input vibration measurement data, the mode shape of the nth-order mode (1 ≦ n ≦ N) in each of the vibration modes of the number N of natural vibrations. Relative mode shape Ψ _n (x _i , x _j ), which is the relative displacement amount in the direction of the axis of interest between the extracted two points x _i , x _j , and the reference axis direction component of the mode shape of the nth-order mode at the reference point x _k The reference mode shape φ _n ^r (x _k ) and the natural frequency ω _n of the _n-th mode are obtained by the following equation:

In calculating the d _n to be defined, the following formula

Data (the evaluation values used herein subscript present current d _n, subscript baseline representing the evaluation value of d _n in the state of health as a reference for evaluation) assessing damage index DI is defined by A structure damage diagnosis system comprising a data processing device for executing at least a part of the processing. The reference point x _k is the position x _i, is the same position as the one of x _j, set forth in claim 1, one of said plurality of vibration response detecting sensor, characterized in that it is also used as the reference response detection sensor Diagnostic system.   The diagnostic system according to claim 1, wherein the vibration response detection sensor is a sensor that detects an angle, an angular velocity, or an angular acceleration.   The diagnostic system according to claim 1, wherein the vibration response detection sensor is a sensor that detects displacement, velocity, or acceleration.   The diagnostic system according to claim 1, wherein the reference response detection sensor is a sensor that detects displacement, velocity, or acceleration.   The diagnostic system according to claim 1, wherein the reference response detection sensor is a sensor that detects an angle, an angular velocity, an angular acceleration, or a distortion.   The diagnosis system according to claim 1, further comprising a host computer that receives a data processing result from the data processing device provided for each of a plurality of monitoring target portions.   The data processing device is a data processing device that executes a part of the data processing, and the host device executes the remaining part of the data processing based on a data processing result received from the data processing device. The diagnostic system according to claim 7, wherein:   9. The diagnosis system according to claim 7, wherein data is transmitted between the data processing device and the host computer wirelessly. Wherein the data processing device, two points x _i, the cross spectrum and the ratio of the power spectrum of the reference response data and the relative amount of vibrational response data (difference) in the x _j obtains the d _n, non-damaging changes in the d _n The diagnostic system according to any one of claims 1 to 9, wherein the evaluation is performed using a norm of fluctuation from a reference vector d _n (x _i , x _j ) | _{baseline of} time. Vibration measurement data from a plurality of vibration response detection sensors installed at two points x _i and x _j sandwiching a monitoring target location of the structure and a reference response detection sensor installed at a reference point x _k different from the positions x _i and x _j Get
Relative displacement in the direction of the axis of interest between the two points x _i and x _j extracted from the mode shape of the nth order mode (1 ≦ n ≦ N) in each of the vibration modes of the number N of natural vibrations from the input vibration measurement data The relative mode shape Ψ _n (x _i , x _j ) that is a quantity, the reference mode shape φ _n ^r (x _k ) that is the reference axial component of the mode shape of the n-th mode at the reference point x _k, and the characteristic of the n-th mode Find the frequency ω _n ,
The following formula

In calculating the d _n to be defined,
The following formula

(Letter present subscript here the evaluation value of the current d _n, subscript baseline represents the evaluation value of d _n in the state of health as a reference for evaluation) of the structure to evaluate the damage index DI defined in damage Diagnosis method. The _dn is obtained from the ratio of the relative amount (difference) of the vibration response data at the two points x _i and x _j and the cross spectrum and power spectrum of the reference response data,
Wherein d reference vector _{d n (x i, x j} ) changed in the non-damaged _n | diagnostic method according to claim 11, characterized in that the evaluation by the norm of variation from _baseline.

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