JP2008151560A - Vibration characteristic estimation method and vibration characteristic estimation device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate simply and accurately a vibration characteristic of an object architecture. <P>SOLUTION: This vibration characteristic estimation method, which is a vibration characteristic estimation method for estimating a vibration characteristic of a structure to be estimated including a unit structure expressed by a plurality of physical quantities, includes the first measuring step wherein the structure to be estimated to which an additional structure expressed by a plurality of physical quantities including a reference physical quantity set at the first value is attached is vibrated into the first vibration state, and an element showing the first vibration state is measured; the second measuring step wherein the structure to be estimated to which the additional structure having the reference physical quantity set at the second value is attached is vibrated into the second vibration state, and an element showing the second vibration state is measured; and a determination step for determining the plurality of physical quantities for expressing the unit structure by solving an equation of motion wherein a motion of the structure to be estimated to which the additional structure is attached is expressed by a plurality of physical quantities, by using the first equation generated by the element showing the first vibration state and the second equation generated by the element showing the second vibration state. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a vibration characteristic estimation method and a vibration characteristic estimation apparatus that estimate vibration characteristics (that is, mass, rigidity, and damping coefficient) of a building.

  Currently, many buildings are left with a risk of collapse due to earthquakes. Therefore, it is necessary to perform such repairs (earthquake retrofits) to ensure earthquake resistance. Such seismic retrofitting involves first estimating the vibration characteristics of the target building (target building), that is, the mass, stiffness and damping coefficient, and then based on these estimated vibration characteristics. This is implemented by identifying the part to be reinforced by grasping the state of deterioration of the object and then actually renovating this part.

  Here, the estimation of the vibration characteristics of the target building is specifically performed by the following method. That is, first, by subjecting the target building to vibration, a period (natural period) at which the target building is easily shaken is extracted for each eigenmode of the target building. Here, this natural period has a property expressed by the ratio between the mass distribution of each level of the building and the stiffness distribution of each level. Therefore, by estimating the mass of the hierarchy using a predetermined calculation, the rigidity of the hierarchy is also estimated from the ratio. As a result, the mass and rigidity of each layer are estimated.

  However, when the vibration characteristic estimation method according to the related art as described above is used, the accuracy of rigidity depends on the estimated accuracy of mass. Usually, in a building, various objects are distributed and distributed throughout each level, and the arrangement changes with time. In such a building, it is impossible to accurately estimate the mass of each floor in advance by calculation. Therefore, the accuracy of the mass estimated by such calculation, and hence the accuracy of the rigidity, is also lowered. As a result, since the portion to be reinforced in the target building is not accurately specified, it is impossible to appropriately carry out the seismic retrofit of the target building.

  In addition, the method described in Unexamined-Japanese-Patent No. 2005-249687 is known as a method of estimating the vibration characteristic of object building. In this method, a test object with a variable part whose physical characteristics are variable is vibrated, and the vibration characteristics of the test object that change according to changes in the physical characteristics are attached to the test object. Using the measured and changed physical characteristics and measured vibration characteristics of the sensor, a linear matrix equation for identifying the structural matrix containing the unknown structural parameters of the DUT is constructed, and this linear matrix equation is solved. Can calculate unknown structural parameters (rigidity, damping, etc.) of the DUT. However, when this method is used, in order to measure the vibration characteristics of the DUT, it is necessary to prepare a plurality of displacement sensors and angle sensors, and attach them to appropriate positions on the DUT. Therefore, with this method, the vibration characteristics of the device under test cannot be estimated easily and efficiently.

  The present invention has been made in view of such problems, and an object thereof is to provide a vibration characteristic estimation method and a vibration characteristic estimation apparatus that easily and accurately estimate the vibration characteristics of a target building (estimated structure). And

A vibration characteristic estimation method according to the present invention is a vibration characteristic estimation method for estimating a vibration characteristic of an estimated structure including at least one unit structure represented by a plurality of physical quantities, and is set to a first value. A first measurement step of vibrating the estimated structure to which the additional structure represented by a plurality of physical quantities including a reference physical quantity is attached to a first vibration state and measuring an element indicating the first vibration state; A second measurement step of vibrating the estimated structure to which the additional structure having the reference physical quantity set to a second value is attached to a second vibration state and measuring an element indicating the second vibration state; The motion of the estimated structure to which the additional structure is attached using the first equation generated by the element indicating the first vibration state and the second equation generated by the element indicating the second vibration state The compound By solving the equation of motion is expressed by the physical quantity, and determining step of determining a plurality of physical quantities representing said at least one unit structure,
It is characterized by including.
A vibration characteristic estimation apparatus according to the present invention is a vibration characteristic estimation apparatus that estimates vibration characteristics of an estimated structure including at least one unit structure represented by a plurality of physical quantities, and is set to a first value. An element indicating the first vibration state of the estimated structure to which an additional structure represented by a plurality of physical quantities including a reference physical quantity is attached, and an additional structure in which the reference physical quantity is set to a second value are attached. An input means for inputting an element indicating the second vibration state of the estimated structure, a first equation generated by the element indicating the first vibration state, and a first element generated by the element indicating the second vibration state The at least one unit structure is solved by solving a motion equation expressing the motion of the estimated structure to which the additional structure is attached using the two physical quantities using two equations. Characterized by comprising processing means for determining a plurality of physical quantities to represent, the.

  According to the present invention, by generating a plurality of equations using elements indicating each of a plurality of vibration states of the target building (estimated structure), in the generated plurality of equations, Since the total number can be greater than or equal to the total number of unknowns included, the equation of motion expressing the motion of the target building can be solved, that is, the unknowns can be determined simultaneously. Thereby, the vibration characteristic of the target building can be accurately estimated.

(Embodiment 1)
It is proved that the vibration characteristic of the structure to be estimated can be estimated by using the vibration characteristic estimation algorithm according to the first embodiment of the present invention (identification algorithm based on the change in the natural circular frequency due to the variable stiffness). Hereinafter, in order to easily understand the vibration characteristic estimation algorithm according to the present embodiment, first, when the structure to be estimated is represented by a one-degree-of-freedom system, that is, the structure to be estimated has three physical quantities. It is proved that the vibration characteristic of this estimated structure can be estimated when it is expressed by one unit structure expressed by Next, when the estimated structure is expressed by an n-degree-of-freedom system, that is, when the estimated structure is expressed by n unit structures expressed by three physical quantities, this estimated structure It is proved that the vibration characteristics of can be estimated.

  First, proof is given for the case where the structure to be estimated is represented by a one-degree-of-freedom system. FIG. 1 is a schematic diagram conceptually showing an estimated structure (one-degree-of-freedom system) whose vibration characteristics are estimated by the vibration characteristic estimation algorithm according to Embodiment 1 of the present invention.

As shown in FIG. 1, the estimated structure 100 is represented by one unit structure 101 represented by three physical quantities (mass, stiffness, and attenuation). Specifically, the estimated structure 100 is conceptually configured such that, for example, an object having a mass m ₁ corresponding to a floor or furniture arranged on the floor is formed on a wall or a pillar on the ground 103. It is represented by one unit structure 101 represented by the form provided via the corresponding rigid body k ₁ and damping c ₁ . Here, the mass m is the most basic physical quantity related to the weight and difficulty of movement of the object, and the stiffness k means a physical quantity called a restoring force generated in proportion to the amount of interlayer deformation of the building, The damping c means a physical quantity called a restoring force that is generated in proportion to the interlayer deformation speed of the building.

A sensor expressed by three physical quantities (mass m ₂ , stiffness k _2, and attenuation c ₂ ) with respect to the estimated structure 100 expressed in this way, and at least one physical quantity among these three physical quantities A variable sensor (variable structure; additional structure) 102 capable of changing (reference physical quantity) to a plurality of values is attached. As a result, the entire structure including the variable sensor 102 and the unit structure 101 is a two-degree-of-freedom system. In the present embodiment, as an example, the variable sensor 102 that can change the stiffness k ₂ into two values k _L and k _H is attached to the upper end of the structure to be estimated 100.
Here, m ₁ = 10, k ₁ = 125, c ₁ = 2.5, m ₂ = 10, k ₂ = (k _L = 100, k _H = 150), and c ₂ = 2.5.

When such an estimated structure 100 is vibrated with the stiffness k ₂ of the variable sensor 102 set to k _L , the natural period ω _1L and the damping constant h _{1L of the} primary mode are observed, and the variable sensor 102 is observed. When the natural period ω _1H and the damping constant h _1H of the first-order mode are observed when the vibration is applied in a state where the stiffness k ₂ is k _H , unknown parameters m ₁ , k ₁ , and c ₁ are identified. Think about it. Note that the vibration to the estimated structure 100 is realized by, for example, a vibration exciter 106 attached to, for example, a side surface of the estimated structure 100 vibrating the estimated structure 100. The vibration exciter 106 gives vibration to the estimation target structure 100 according to the waveform generated by the waveform generator 104 and amplified by the amplifier 105.

f(t)は、加振機１０６による加振力である。また、Ｍ、Ｃ及びＫは、それぞれ、質量、減衰及び剛性マトリクスである。
（固有方程式）
上記（１）の運動方程式に対応する固有方程式は、次の式（３）となる。

この式（３）を上記式（２）と合わせて考えると、式（３）は次の式（４）となる。

ここで、（ｍ₂λ²＋ｃ₂＋ｋ₂）＝Ａ、（ｃ₂λ＋ｋ₂）＝Ｂとおき、（ｃ₁＋ｃ₂）＝ｄとすると、上記式（４）は、次の式（４’）となる。

(Equation of motion)
The equation of motion when the one-degree-of-freedom unit structure 101 is added to the structure to be estimated 100 shown in FIG. 1 is the following expression (1).

f (t) is the excitation force by the shaker 106. M, C, and K are mass, damping, and stiffness matrices, respectively.
(Eigen equation)
An eigen equation corresponding to the equation of motion of (1) is expressed by the following equation (3).

When this equation (3) is considered together with the above equation (2), the equation (3) becomes the following equation (4).

Here, assuming that (m ₂ λ ² + c ₂ + k ₂ ) = A, (c ₂ λ + k ₂ ) = B, and (c ₁ + c ₂ ) = d, the above equation (4) can be expressed by the following equation (4 ').

複素固有値λと円振動数ω及び減衰定数ｈとの関係は、次の式（６ａ）及び式（６ｂ）により表現される。

よって、上記式（６ｂ）より、次の式（７）が得られる。

(Eigenvalue and mode natural period / damping constant)
When the above equation (3) is solved, the complex eigenvalue λ becomes the following equation (5).

The relationship between the complex eigenvalue λ, the circular frequency ω, and the damping constant h is expressed by the following equations (6a) and (6b).

Therefore, the following equation (7) is obtained from the above equation (6b).

When the vibration test is performed on the estimated structure 100 as described above and the stiffness k ₂ of the variable sensor 102 is set to each of the two values k _L and k _H , Assuming that the natural periods ω _L1 and ω _{H1 of the} mode and the damping constants h _L1 and h _H1 are obtained, unknown parameters m ₁ , c ₁ , and k ₁ are obtained.
ω _L1 = 2.1113 [rad / s], h _L1 = 0.0229
ω _H1 = 2.2361 [rad / s], h _H1 = 0.0215
Here, it is assumed that the physical parameters m ₂ = 10, c ₂ = 2.5, k _L = 100, and k _H = 150 are known.

From the above equation (6a), the following equations (8) and (9) are obtained.

The above equation (9) is substituted into the above equation (4 ′). First, A, Aλ, Aλ ² and B are calculated.
From A = (m ₂ λ ² + c ₂ λ + k ₂ ) and B = (c ₂ λ + k ₂ ), the following equation (10) is obtained.

A _L1 = 10 × (-0.0484 ± 2.1108i) ² + 2.5 × (-0.0484 ± 2.1108i) + 100 = 55.3477 ± 3.2337i
∴A _L1 × λ _L1 = (55.8477 ± 3.2337i) × (-0.0484 ± 2.1108i) =-9.5046 ± 116.67i
∴A _L1 × λ _L1 ² = -245.81 ± 25.709, B _L1 = {2.5 × (-0.0484 ± 2.1108i) +100} ² = 9948.0 ± 1054.1i
∴B _L1 -A _L1 k _L = 4413.2 ± 730.75i (10)

When the same calculation is performed for the case of k ₂ = k _H1 , the following equation (11) is obtained.
A _H1 = 99.9238 ± 3.4384i, A _H1 λ _H1 = -12.493 ± 223.22i, A _H1 λ _H1 ² = -498.44 ± 38.667i,
B _H1 = 22433 ± 1675.4i, B _H1 -A _H1 k _H = 7444.1 ± 1159.6i (11)

上記式（１２’）では、３つの未知数m₁,d,k₁に対して、２つの式しか存在しないので、これらの未知数を決定することができない。しかしながら、ｋ₂＝ｋ_Hの場合の上記（１１）式を上記（４’）に代入することにより、次の式（１３）に示す新たな固有方程式のマトリクス表示が得られる。

上記式（１２’）及び上記式（１３）とを連立させることにより、次の式（１４）が得られる。

上記式（１４）を解くと、ｍ₁＝１０．０、ｄ＝５．０、ｋ₁＝１２５．０が得られる。
また、ｃ₁＋ｃ₂＝ｄにおいて、ｃ₂＝２．５は既知であるので、ｃ₁＝ｄ−ｃ₂＝２．５となる。以上より、ｍ₁＝１０．０、ｃ₁＝２．５、ｋ₁＝１２５．０を求めることができる。
以上、被推定構造体が１自由度系により表現される場合について証明した。 Substituting the above equation (10) into the above equation (4) yields the following equation (12).
(-245.81 ± 25.709i) m ₁ + (-9.5046 ± 116.67i) d + (55.3477 ± 3.2337i) k ₁
= 4413.2 ± 730.75i (12)
Since the real part and the imaginary part are equal in the above formula (12), the following formula (12 ′) is obtained when these are divided and displayed in a matrix.

In the above equation (12 ′), since there are only two equations for the three unknowns m ₁ , d, and k ₁ , these unknowns cannot be determined. However, by substituting the above equation (11) in the case of k ₂ = k _H into the above (4 ′), a matrix display of a new eigen equation shown in the following equation (13) can be obtained.

The following equation (14) is obtained by combining the above equation (12 ′) and the above equation (13).

Solving the above equation (14) yields m ₁ = 10.0, d = 5.0, and k ₁ = 125.0.
Since c ₂ = 2.5 is known when c ₁ + c ₂ = d, c ₁ = d−c ₂ = 2.5. From the above, m ₁ = 10.0, c ₁ = 2.5, and k ₁ = 125.0 can be obtained.
As described above, the case where the structure to be estimated is expressed by a one-degree-of-freedom system has been proved.

  Next, a case where the structure to be estimated is represented by an n-degree-of-freedom system is proved with reference to FIG. FIG. 2 is a schematic diagram conceptually showing an estimated structure (n-degree-of-freedom system) whose vibration characteristics are estimated by the vibration characteristic estimation algorithm according to the first embodiment of the present invention. 2 that are the same as those shown in FIG. 1 are assigned the same reference numerals as those in FIG. 1 and detailed descriptions thereof are omitted.

As shown in FIG. 2, the estimated structure 200 includes a plurality of unit structures (unit structures 201-1 to 201-n) each represented by three physical quantities (mass, stiffness, and attenuation). Expressed by the body. Specifically, the estimated structure 200 is conceptually a unit structure in which an object of mass m ₁ is expressed in a form in which the object is provided on the ground 103 via a rigid body k ₁ and an attenuation c _1. and 201-1, a unit structure 201-2 represented by the form provided through the rigid k ₂ and damping c ₂ over the unit structures 201-1, similarly unit structures 201- (n on the -1) and a rigid k _n and the unit structure 201-n represented by the format provided through the damping c _n, represented by n unit structure.

A structure represented by three physical quantities (mass m _k , stiffness k _k and damping c _k ) with respect to the estimated structure 200 represented in this way, and at least one of these three physical quantities A variable sensor 102 is attached which can be changed to a plurality of values. As a result, the entire structure including the variable sensor 102 and the n unit structures is an n + 1 degree of freedom system.

The equation of motion when a one-degree-of-freedom system (variable sensor 102) having variable rigidity is added to the estimated structure 200 shown in FIG. 2 is the following equation (15).

f (t) is the excitation force by the shaker 106. M, C, and K are mass, damping, and stiffness matrices, respectively, and are represented by the following equation (17) in the case of FIG.

In the above formula (17), the element whose suffix is k is that of the variable sensor 102 and is a known value. Therefore, the unknown physical parameters included in the matrix are n m, c, and k, respectively, and the total number of unknowns is 3n. Here, assuming that the stiffness of the variable sensor is k _k = k ₁ , r (up to n + 1) damped natural circular frequencies _i ω and damping constants _i h of the i-th mode are obtained by an excitation experiment or the like. Suppose. Then, the relationship between the natural value λ, the damped natural circular frequency ω, and the damping constant h of the system of the above formula (15) is expressed by the following formulas (18a) to (18c).

Of the above formulas (18a) to (18c), r sets of conjugate complex eigenvalues iλ can be determined from formula (18b). By substituting this value into the characteristic equation of the eigenvalue shown in the following equation (19), r sets of equations can be obtained.

  The above equation (19) is an equation of only the stiffness matrix K, the damping matrix C, and the mass matrix M, and the unknown parameters related thereto are n m, k, c, that is, 3n. On the other hand, the complex eigenvalue calculated by the above equation (18) from the r (maximum n + 1) damped natural circular frequencies ω and the damping constant h obtained in the excitation experiment is expressed by the above equation (19). Since the substituted r expressions are complex numbers, the real part and the imaginary part are considered separately, and actually 2r expressions. Since the maximum value of r is n + 1, the number of expressions eventually becomes 2 (n + 1) at the maximum. Therefore, when the degree of freedom n is 2 or more, 3n> 2 (n + 1) is always satisfied, and the total number of unknowns exceeds the total number of equations, so the unknowns cannot be determined.

Therefore, the stiffness of the variable sensor 102 is changed to k _k = k ₂ , a new excitation experiment is added, and the natural circular frequency _j Ω of s (the maximum value of s is also n + 1) j-order mode and A damping constant _j H is obtained, and s sets of complex complex eigenvalues _j λ can be determined therefrom. As characteristic equations for new eigenvalues corresponding thereto, the following equation (20) is expressed as s sets. Obtainable.

Thus, m, k, c can be determined by making the number of characteristic equations of eigenvalues larger than 3n of the total number of unknown parameters m, k, c related to the characteristic equations. .
As described above, the case where the structure to be estimated is expressed by an n-degree-of-freedom system has been proved.

  Next, a vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the present embodiment will be described with reference to FIG. 3 in addition to FIG. FIG. 3 is a flowchart showing a vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the first embodiment of the present invention. In FIG. 3, the estimation target structure 200 shown in FIG. 2 is an estimation target.

First, in step (hereinafter referred to as “ST”) 301, i which is a variable indicating the rigidity of the variable sensor 102 is set to 1, and t which is a variable indicating the total number of characteristic equations obtained by substituting eigenvalues. Set to zero. In ST302, k _i, that is, k ₁ (first value) is used as the stiffness k _k of the variable sensor 102 here.

  In ST303, the vibration exciter 106 performs vibration on the estimated structure 200. Specifically, the shaker 106 performs sweep excitation (excitation that gives a sinusoidal wave ranging from a high period to a low period to the estimated structure 200) or white noise excitation (having a wide range of frequency components). (Vibration giving vibration to the estimated structure 200) is performed on the estimated structure 200.

  In ST304, the r natural circular frequencies ω and the damping constant h (that is, the first vibration state is shown) of the estimated structure 200 in the state of being vibrated by the applied vibration (first vibration state). Element) is measured. That is, the natural circular frequency ω and the damping constant h corresponding to each of the unit structures 201-1 to 201-n are measured.

The measurement of the natural circular frequency ω and the damping constant h can be performed by the following method, for example. That is, first of all, for the frequency response obtained from the input / output relationship of the excitation experiment result, the natural period is directly read from each frequency peak, and the response shape around the peak is attenuated (from the slope of the mountain). A half power method for reading a constant or a curve fitting method for fitting a theoretical frequency response function by a least square method to obtain a natural period and an attenuation constant can be used.
Here, “input” in “input / output relationship of excitation experiment result” is a signal f (t) input from the amplifier 105 to the shaker 106.
Also, "output" in the "input-output relationship of the Loading Test Results" is most preferably, at least one of the absolute acceleration of the relative displacement (x _k -x _n) and mass m _k to the mass m _n of the mass m _k It is. Details of the relative displacement and the absolute acceleration will be described in detail in a second embodiment described later. As another example of “output” in “input / output relationship of excitation experiment result”, there are a relative displacement, a relative speed, a relative acceleration, and the like between a certain layer and another layer.
Obtaining the frequency response using the “input” and “output” given in this way is a well-known matter for those skilled in the art, and therefore detailed description thereof will be omitted.

  Secondly, a method for extracting a free vibration waveform from the input / output data by performing processing on the input / output data obtained in the vibration experiment and reading the mode characteristics from the extracted automatic vibration waveform. Can be used. This method includes a correlation method that uses the property that the autocorrelation function of the response resembles a free vibration waveform when the input is white noise, or a large number of small regions where the time history waveform of the response peaks at time zero. Random Decrement method that extracts the free vibration component by removing the forced vibration component due to random external force by dividing and superimposing these can be applied.

In ST305, r sets of conjugate complex eigenvalues λ are calculated from the above equation (18) using the natural circular frequency ω and the damping constant h measured in ST304.
In ST306, a characteristic equation of r sets of eigenvalues for the r sets of conjugate complex eigenvalues λ calculated in ST305 is obtained from the above equation (19).

In ST307, the total number 2r of characteristic equations obtained in ST306 is added to t which is a variable indicating the total number of characteristic equations obtained by substituting eigenvalues.
In ST308, it is determined whether or not the condition that the total number of characteristic equations currently obtained is equal to or greater than the total number of unknowns 3n related to this characteristic equation is satisfied.

If this condition is not satisfied, these unknowns cannot be determined. Therefore, after 1 is added to the variable i to change the stiffness of the variable sensor, the process returns to ST302 described above. Thereafter, the same processing as described above is performed in ST302 to ST306, whereby k _{i + 1,} that is, k ₂ (second value) is used as the stiffness k _k of the variable sensor 102, and a new r The natural circular frequency ω and the damping constant h (that is, the element indicating the second vibration state) are measured, and r sets of conjugate complex eigenvalues λ are calculated, thereby obtaining new r sets of characteristic equations. At this time, the total number of obtained characteristic equations is doubled compared to the previous time (when k _k = k ₁ ) (ST307).

Here, when the condition shown in ST308 is satisfied, since the unknown can be determined, the process moves to ST309.
In ST309, the unknowns m, k, and c can be determined from an equation in which all the characteristic equations obtained at present are combined. As a result, in ST310, the mass matrix M, the stiffness matrix K, and the attenuation matrix C can be determined from the above equation (17).

Next, an example of a vibration characteristic estimation apparatus that can be used in the vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the present embodiment will be described.
The vibration characteristic estimation device according to the present embodiment is stored in, for example, an input unit that inputs setting values and measurement values, a storage unit that stores setting values and measurement values input by the input unit, and a storage unit. And a processing unit that determines the vibration characteristic of the structure to be estimated 200 by executing the vibration characteristic estimation algorithm according to the present embodiment using the set value and the measurement value.

In the vibration characteristic estimation apparatus having such a configuration, the input unit inputs a plurality of stiffnesses k _k that can be used for the variable sensor 102 as set values. Further, the input unit inputs the mass m _k and the attenuation c _k of the variable sensor 102 as set values. Furthermore, the input unit sets, as a set value, the degree of freedom of the structure 200 to be estimated, that is, the number of unit structures included in the structure 200 to be estimated (in the case of the structure 200 to be estimated, the degree of freedom n). ). These set values are input through a keyboard by an operator of the vibration characteristic estimation apparatus, for example. Thus, the setting value input by the input unit is stored in the storage unit.

Furthermore, regarding the measured value, the input unit is connected to the shaker 106, and the signal (f (t)) input from the amplifier 105 to the shaker 106 is used as the shaker input (input data). input. In addition, the input unit includes, as a measurement value, an absolute acceleration response of the mass m _k of the variable sensor 102 and a unit structure (unit structure 201-n in FIG. 2) to which the variable sensor 102 is attached and the variable sensor 102. At least one of the relative displacements (x _k −x _n ) is input. The absolute acceleration response and the relative displacement will be described in detail in a second embodiment described later.
These measured values are also stored by the storage unit.

  After the setting values and measurement values as described above are stored in the storage unit or in parallel with the storage in the storage unit, the processing unit performs the processing in ST304 to ST310 described in FIG. All unknowns can be determined by executing according to the computer program stored in the storage unit.

  In addition, the extraction of the natural circular frequency and the damping constant described in ST304 may be configured to be extracted outside the vibration characteristic estimation device. In this case, the vibration characteristic estimation apparatus may input the natural circular frequency and the damping constant extracted outside from the input unit and store them in the storage unit.

  As described above, according to the vibration characteristic estimation algorithm according to the present embodiment, first, a variable sensor represented by three physical quantities including a reference physical quantity (in this embodiment, “rigidity”) is attached to the estimated structure. In addition, the estimated structure to which the variable sensor having the reference physical quantity set to the first value is vibrated to be in the first vibration state, and the natural circular frequency and the damping constant that are elements indicating the first vibration state And substituting the eigenvalue obtained by using this natural circular frequency and damping constant into the characteristic equation of the eigenvalue corresponding to the equation of motion representing the motion of the estimated structure to which the variable sensor is attached. One equation is obtained. In the first equation, when the unknowns cannot be determined due to the total number of unknowns regarding the three physical quantities being larger than the total number of equations, a variable in which the reference physical quantity is set to the second value is further set. The estimated structure to which the sensor is attached is vibrated to the second vibration state, and the natural circular frequency and the damping constant, which are elements indicating the second vibration state, are measured, and the natural circular frequency and the damping constant are used. A new equation (second equation) is obtained by substituting the obtained eigenvalue into the characteristic equation of the eigenvalue corresponding to the equation of motion representing the motion of the estimated structure to which the variable sensor is attached. Therefore, in an equation in which the first equation and the second equation are combined, the unknown number can be determined by making the total number of equations larger than the total number of unknowns related to the equation. If the total number of equations is still smaller than the total number of unknowns related to this equation, the total number of equations in the equation that combines the x-1 equation and the xth equation is the number of unknowns related to this equation. By oscillating the estimated structure to which the variable sensor having the reference physical quantity set to the x-th value is attached until it becomes larger than the total number, the same process is performed by changing the state to the x-th vibration state. Unknowns can be determined. As described above, this is not limited to the case where the structure to be estimated is a one-degree-of-freedom system, and also applies to the case where the structure to be estimated is an n-degree-of-freedom system. As described above, the vibration characteristics of the structure to be estimated can be estimated.

  If there are many unknowns to be identified due to the high degree of freedom of the structure to be estimated, by further changing the rigidity of the variable sensor added to the structure to be estimated and performing a new vibration experiment, or By adding a plurality of variable sensors to the structure to be estimated, changing the rigidity of these variable sensors in sequence, and performing an excitation experiment, the required number of eigenvalue characteristic equations are obtained, and the object is estimated The vibration characteristics of the structure can be estimated.

  In the above embodiment, as the most preferable mode, the case where the natural circular frequency and the damping constant of the estimated structure in a state where the vibration is applied by the vibrator is measured has been described. The present invention can also be applied to the case of measuring the natural circular frequency and the damping constant of a structure to be estimated in a state where excitation is given by an actually occurring earthquake.

In the above-described embodiment, as the most preferable mode, in a state where the additional structure (variable structure) 102 is attached to the estimated structure 200, the reference physical quantity in the additional structure 102 is changed from, for example, the rigidity k ₁ to the rigidity k. _The case of changing to ₂ has been described. However, a plurality of additional structures that differ only in the reference physical quantity (for example, rigidity) and have the same other physical quantities are prepared, and the plurality of additional structures are sequentially attached to the estimated structure 200, and vibration is applied in each case. Similar results can be obtained by carrying out the above.

(Embodiment 2)
In the present embodiment, a case will be described in which the vibration characteristics of the structure to be estimated are estimated using a vibration characteristic estimation algorithm different from that used in the first embodiment.

First, it is proved that the vibration characteristic of the structure to be estimated can be estimated by using the vibration characteristic estimation algorithm according to the second embodiment (identification algorithm using a time history response and a state space model).
FIG. 4 is a schematic diagram conceptually showing an estimated structure whose vibration characteristics are estimated by the vibration characteristic estimation algorithm according to the second embodiment of the present invention. 4 that are the same as those shown in FIG. 2 are assigned the same reference numerals as in FIG. 2 and detailed descriptions thereof are omitted.

As shown in FIG. 4, the estimated structure 200 has a plurality of unit structures (unit structures 201-1) each represented by three physical quantities (mass, stiffness, and attenuation), as in the first embodiment. ~ 200-n) represented by the included structure. Here, the distance between the mass m ₁ of the unit structure 201-1 and the ground 103 is represented by x ₁ , and the distance between the mass m ₂ of the unit structure 201-2 and the ground 103 is represented by x _2. Similarly, the distance between the mass m _n of the unit structure 201- _n and the ground 103 is represented by x _n .

A structure represented by three physical quantities (mass m _k , stiffness k _k and damping c _k ) with respect to the estimated structure 200, and at least one physical quantity (reference physical quantity) among these three physical quantities A variable sensor 401 that can change the value to a plurality of values is attached. As a result, the entire structure including the variable sensor 401 and the n unit structures is an n + 1 degree-of-freedom system. Here, the distance between the variable sensor 401 and the ground 103 is represented by x _k .
The variable sensor 401 has basically the same configuration as the variable sensor 102 in the first embodiment described above, but a measurement unit that measures the relative displacement (x _k −x _n ) of the mass m _k with respect to the mass m _n , and in that it includes a measuring unit for measuring the absolute acceleration of mass m _k, which differs from the variable sensor 102.
4 is not shown for simplicity, but has the same configuration as that of the vibrator 106 in the first embodiment, and is generated by the waveform generator 104. A vibration corresponding to the waveform amplified by the amplifier 105 is applied to the estimation target structure 200.

ここで、図４に示した可変センサ４０１を取り付けた被推定構造体２００は、図２に示した被推定構造体２００と同一の構造を有するので、実施の形態１で用いた式（１５）〜（１７）は、図４に示した可変センサ４０１を取り付けた被推定構造体２００についても成り立つ。
よって、上記式（２１）に示す状態方程式は、次の式（２２）により表現される。

なお、上記式（２３）における₁f(t)は、加振機１０６に対する入力（すなわち、被推定構造体に与えられる振動を表現する関数）である。
可変センサ４０１での観測条件に応じて、次の式（２４）に示す観測方程式をたてる。

First, when the stiffness of the variable sensor 401 is k _k is k ₁ , the state quantity is set as in the following equation (21).

Here, the structure to be estimated 200 to which the variable sensor 401 shown in FIG. 4 is attached has the same structure as the structure to be estimated 200 shown in FIG. 2, and therefore, the equation (15) used in the first embodiment is used. (17) holds true for the estimated structure 200 to which the variable sensor 401 shown in FIG. 4 is attached.
Therefore, the state equation shown in the above equation (21) is expressed by the following equation (22).

Note that ₁ f (t) in the above equation (23) is an input to the shaker 106 (that is, a function expressing vibration given to the estimated structure).
In accordance with the observation condition with the variable sensor 401, an observation equation shown in the following equation (24) is established.

If the observation amount is only the sensor response of the variable sensor 401 and the response acceleration of the mass of the variable sensor 401 and the relative displacement with respect to the installation position, the observation equation shown in the above equation (24) is expressed by the following equation (25). Is done.

状態方程式は、次の式（２８）により表現される。

上記式（２９）における₂f(t)は、加振機１０６に対する入力（すなわち、被推定構造体に与えられる振動を表現する関数）である。
観測方程式は、次の式（３０）により表現される。

Normally, model parameters are identified by various identification algorithms using the state space model equations (22) and (24) created in this way. In this problem, as described in the first embodiment, In addition, since the number of these relational expressions is small with respect to the number of identification parameters, individual parameters cannot be determined.
Therefore, a new vibration experiment is performed by changing the rigidity of the variable sensor 401 (additional one degree of freedom system) from k ₁ to k ₂ . In this case, the state quantity is expressed by the following equation (27).

The state equation is expressed by the following equation (28).

₂ f (t) in the above equation (29) is an input to the vibrator 106 (that is, a function expressing vibration given to the structure to be estimated).
The observation equation is expressed by the following equation (30).

ここに、状態量及び観測量は、次の式（３４）により表現される。

状態空間モデルの各マトリクスは、次の式（３５）により表現される。

Next, a new state space model obtained by combining the state space model represented by the equations (22) and (24) and the state space model represented by the equations (28) and (30) will be considered. And this new state space model is expressed by the following equation (33).

Here, the state quantity and the observed quantity are expressed by the following equation (34).

Each matrix of the state space model is expressed by the following equation (35).

  The state space model shown in the equation (33) is expressed by the state space model expressed by the equation (22) and the equation (24), and the equation (28) and the equation (30). It has the same number of unknown parameters as the state space model, but the number of expressions is doubled so that a larger number of unknowns can be determined. In this state, when the number of unknown parameters is still large and the number of equations is insufficient, the rigidity of the variable sensor 401 can be further changed to create a state space model with a larger number of equations. From the state space model created in this way, rigidity, damping, and mass can be estimated simultaneously by various identification algorithms.

  Next, a vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the present embodiment will be described with reference to FIG. 5 in addition to FIG. FIG. 5 is a flowchart showing a vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the second embodiment of the present invention. In FIG. 5, the estimation target structure 200 shown in FIG. 4 is an estimation target.

First, in ST501, k ₁ (first value) is used as the stiffness k _k of the variable sensor 401. In ST502, as in the first embodiment (ST303 in FIG. 3), the shaker 106 vibrates the estimated structure 200. Thereby, the to-be-estimated structure 200 to which the variable sensor 401 is attached shifts to the first vibration state. In ST503, the signal ( ₁ f (t)) given to the estimated structure 200 by the shaker 106 and the sensor response (that is, the response acceleration of the mass m _k of the variable sensor 401 and the variable the relative displacement with respect to the mass m _n of the mass m _k of the sensor 401) are collected for a predetermined time. That is, vibrator input and sensor response time history data (elements indicating the first vibration state) are collected.

In ST504, the state space model of the estimation target structure 200 (with the variable sensor 401 attached) in a state where the stiffness k _k of the variable sensor 401 is k ₁ is based on the above formula (22) and the above formula (24). Created.

In the state space model created in ST504, since the total number of equations included in this model is smaller than the total number of unknowns (m, k, c) included in this model, these unknowns cannot be determined. Therefore, in order to increase the number of equations included in the obtained state space model so that these unknowns can be determined, a state in which the stiffness k _k of the variable sensor 401 is changed from k ₁ to k ₂ , for example. Then, a new excitation experiment is performed as shown below.

In ST505, k ₂ (second value) is used as the stiffness k _k of the variable sensor 401 instead of k ₁ . In ST506, as in ST502, the exciter 106 performs excitation on the estimated structure 200. Thereby, the to-be-estimated structure 200 to which the variable sensor 401 is attached shifts to the second vibration state. In ST507, the signal ( ₂ f (t)) given to the estimated structure 200 by the shaker 106 and the sensor response (that is, the response acceleration of the mass m _k of the variable sensor 401 and the variable the relative displacement with respect to the mass m _n of the mass m _k of the sensor 401) are collected for a predetermined time. That is, vibrator input and sensor response time history data (elements indicating the second vibration state) are collected.

In ST508, the state space model of the estimation target structure 200 (with the variable sensor 401 attached) in a state where the stiffness k _k of the variable sensor 401 is k ₂ is based on the above formula (28) and the above formula (30). Created.
In ST509, the state space model created in ST504 and the state space model created in ST508 are combined to create a new state space model as shown in the above equation (33). In this new state space model, the total number of equations included in this model is increased to twice the total number of equations included in the state space model created in ST504. Therefore, in this new state space model, the total number of equations included in this model is greater than or equal to the total number of unknowns included in this model. As a result, in ST510, stiffness, damping, and mass are simultaneously estimated from this new state space model according to various identification algorithms.

  As described above, even in the new state space model created in ST509, if the total number of equations included in this model is still smaller than the total number of unknowns included in this model, it is newly created. In the state space model, the above-described ST506 to ST509 are repeatedly executed until the total number of equations included in the model is equal to or greater than the total number of unknowns included in the model. can do.

Next, an example of a vibration characteristic estimation apparatus that can be used in the vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the present embodiment will be described.
The vibration characteristic estimation device according to the present embodiment is stored in, for example, an input unit that inputs setting values and measurement values, a storage unit that stores setting values and measurement values input by the input unit, and a storage unit. And a processing unit that determines the vibration characteristic of the structure to be estimated 200 by executing the vibration characteristic estimation algorithm according to the present embodiment using the set value and the measurement value.

In the vibration characteristic estimation apparatus having such a configuration, the input unit inputs a plurality of stiffnesses k _k that can be used for the variable sensor 401 as set values. Further, the input unit inputs the mass m _k and the attenuation c _k of the variable sensor 401 as set values. Further, the input unit inputs the number of degrees of freedom of the structure to be estimated 200 as the setting value (degree of freedom n in the case of the structure to be estimated 200 in FIG. 4). These set values are input through a keyboard by an operator of the vibration characteristic estimation apparatus, for example. Thus, the setting value input by the input unit is stored in the storage unit.

Furthermore, regarding the measured value, the input unit is connected to the shaker 106, and inputs a signal (f (t)) input from the amplifier to the shaker 106 as a shaker input. In addition, the input unit displays the sensor response (that is, the response acceleration of the mass m _k of the variable sensor 401 and the relative displacement of the mass m _k of the variable sensor 401 with respect to the mass _mn ) measured by the variable sensor 401 in a predetermined time. , Input as sensor response time history data. These measured values are also stored by the storage unit.

  After the setting values and measurement values as described above are stored in the storage unit or in parallel with the storage in the storage unit, the processing unit performs the processes in ST504 and ST508 to ST510 described in FIG. For example, all unknowns can be determined by executing according to a computer program stored in the storage unit. This processing unit determines whether or not the total number of equations included in this model in the new state space model created in ST509 is equal to or greater than the total number of unknowns included in this model, and this condition is satisfied. The processing in ST508 and ST509 can be executed until it is satisfied.

Next, experimental results regarding the vibration characteristic estimation method using the vibration characteristic estimation algorithm according to the present embodiment will be described.
An experiment was conducted in the case where the variable sensor 401 was added to the structure to be estimated of the one-degree-of-freedom model (that is, the structure to be estimated in which n is 1 in FIG. 4). The natural period ω is 1 second, and the attenuation constant h is 0.02. The input by the shaker is a random wave input.
Under such conditions, an experiment was conducted in the case where noise was mixed in the observation data, assuming that the variable sensor according to the present embodiment was actually added to the structure. The results of this experiment are as shown in Table 1 below.

表１において、可変センサ４０１の相対変位（すなわちｘ_k−ｘ₁）、及び、可変センサ４０１の絶対加速度が、観測量として観測された。横軸には、混入されるノイズのレベルがＳＮ比１％、ＳＮ比５％及びＳＮ比１０％である場合の３パターンが、示されている。さらに、これら３パターンの各々について、ノイズを可変センサ４０１の入力データ（入力部）のみに混入した場合（表中において「入力」と表示）、ノイズを可変センサ４０１の応答データ（出力部）のみに混入した場合（表中において「出力」と表示）、及び、ノイズを可変センサ４０１の入力データ及び応答データの両方に混入した場合（表中において「入出力」と表示）における推定値の精度が示されている。 Note that the criteria shown in Table 2 below are used as evaluation criteria for the accuracy of the estimated values in Table 1 above.

In Table 1, the relative displacement (that is, x _k −x ₁ ) of the variable sensor 401 and the absolute acceleration of the variable sensor 401 were observed as observed quantities. The horizontal axis shows three patterns in the case where the level of noise to be mixed is an SN ratio of 1%, an SN ratio of 5%, and an SN ratio of 10%. Furthermore, for each of these three patterns, when noise is mixed only in the input data (input unit) of the variable sensor 401 (displayed as “input” in the table), the noise is only the response data (output unit) of the variable sensor 401. Of the estimated value when it is mixed in (displayed as “output” in the table) and when noise is mixed into both the input data and response data of the variable sensor 401 (displayed as “input / output” in the table) It is shown.

When the variable sensor 401 having a natural period shorter than the natural period of the structure to be estimated is used on the vertical axis (displayed as “short period” in the table), the natural period is longer than the natural period of the structure to be estimated. When using a variable sensor 401 having a characteristic period (indicated as “long period” in the table) and using a variable sensor 401 having substantially the same natural period as the structure to be estimated (“tuned” in the table) 3 patterns of display) are shown. Further, for each of these three patterns, the accuracy of the estimated value is shown when the mass ratio (m _k / m ₁ ) of the variable sensor to the estimated structure is four patterns of 0.1, 0.01, 0.001, and 0.0001. .

As is clear from this table, first, the greater the mass ratio, that is, the closer the mass of the variable sensor 401 is to the mass of the structure to be estimated, the higher the accuracy of the estimated value. Therefore, it is desirable to configure the variable sensor so that its mass is close to the mass of the structure to be estimated. In particular, the variable sensor is preferably configured such that its mass is about 0.01 times or more of the mass of the estimated structure, and further, its mass is about 0.1 or more of the mass of the estimated structure. More preferably, it is configured.
Second, in the case of short period or tuning, that is, when the natural period of the variable sensor 401 is shorter than the natural period of the structure to be estimated, or the natural period of the variable sensor 401 is substantially the same as the natural period of the structure to be estimated. In this case, the accuracy of the estimated value is higher than when the natural period of the variable sensor 401 is longer than the natural period of the structure to be estimated. Therefore, the variable sensor 401 is configured so that its natural period is shorter than the natural period of the structure to be estimated, or so that its natural period is substantially the same as the natural period of the structure to be estimated. Is desirable.
Third, it is desirable to minimize the noise mixed in the variable sensor 401 as a whole. Furthermore, when the amount of noise with respect to the signal is small, the estimated value when the noise is mixed in the input data input to the variable sensor 401, and the noise is mixed in the response data from the variable sensor 401 There is no significant difference between these estimates. However, as the amount of noise with respect to the signal increases, the estimated value when the noise is mixed into the input data input to the variable sensor 401 is the estimated value when the noise is mixed into the response data from the variable sensor 401. There is a tendency for the accuracy to be lower than the estimated value. Therefore, it is desirable to prevent noise (particularly large noise) from being mixed into the input data input to the variable sensor.

  As described above, according to the vibration characteristic estimation algorithm according to the present embodiment, first, a variable sensor represented by three physical quantities including a reference physical quantity (in this embodiment, “rigidity”) is attached to the estimated structure. In addition, the estimated structure to which the variable sensor having the reference physical quantity set to the first value is vibrated to be in the first vibration state, and the object in the first vibration state, which is an element indicating the first vibration state. The relative displacement of the additional structure with respect to the estimated structure and the absolute acceleration of the additional structure in the first vibration state are measured, and using these elements and the function expressing the vibration applied to the estimated structure, the first A first equation representing a state space model in the vibration state is generated. In the first equation, if the unknowns cannot be determined due to the total number of unknowns regarding the three physical quantities being larger than the total number of equations, the reference physical quantity is further set to the second value. The estimated structure to which the variable sensor is attached is vibrated to the second vibration state, the above-described elements indicating the second vibration state are measured, and these elements and a function expressing the vibration applied to the estimated structure are The second equation representing the state space model in the second vibration state is generated. Therefore, in the equation in which the first equation and the second equation are coupled, it is possible to determine these unknowns by making the total number of equations included in the coupled equations equal to or greater than the total number of unknowns related to the equation. it can. If the total number of equations is still smaller than the total number of unknowns related to this equation, the total number of equations in the equation that combines the x-1 equation and the xth equation is greater than or equal to the unknowns related to this equation. Until the estimated physical body to which the variable sensor having the reference physical quantity set to the x-th value is attached is vibrated to the x-th vibration state and finally the same processing is performed, so that all unknowns are finally obtained. Can be determined. As described above, this is not limited to the case where the structure to be estimated is a one-degree-of-freedom system, and also applies to the case where the structure to be estimated is an n-degree-of-freedom system. As described above, the vibration characteristics of the structure to be estimated can be estimated.

  According to the present invention, for example, without attaching a dedicated sensor to each of the unit structures included in the estimated structure, the relative displacement of the estimated structure with respect to the additional structure in each vibration state and the addition By only measuring the absolute acceleration of the structure, it is possible to accurately estimate the vibration characteristics of the structure to be estimated while reducing costs.

  Next, main differences between the present invention and the technique described in Japanese Patent Application Laid-Open No. 2005-249687 (hereinafter referred to as “conventional technique”) will be described.

一方、本発明では、このような基礎式は必要とされず、図３（実施の形態１）又は図５（実施の形態２）を示して説明したアルゴリズムを用いて、未知パラメターが同定される。すなわち、対象建築物の振動特性を推定するために、本発明と従来技術との間において、全く異なるアルゴリズムが用いられる。 First, in the prior art, unknown parameters are identified based on the basic equation shown in the following equation (A).

On the other hand, in the present invention, such a basic equation is not required, and an unknown parameter is identified using the algorithm described with reference to FIG. 3 (Embodiment 1) or FIG. 5 (Embodiment 2). . That is, a completely different algorithm is used between the present invention and the prior art in order to estimate the vibration characteristics of the target building.

Secondly, in the prior art, a plurality of displacement sensors and angle sensors (displacement sensors 4 and angles in FIG. 1) are measured with respect to the target building in order to measure vibration characteristics necessary for estimation of unknown parameters, that is, natural frequencies. It is necessary to attach the sensor 5, the displacement sensor 4) in FIG. Specifically, for example, when the target building is the estimated structure 200 as shown in FIG. 2, for each of the n unit structures constituting the estimated structure 200, It is necessary to attach a dedicated displacement sensor and angle sensor, respectively. As a result, when this prior art is used, it is difficult to estimate the unknown parameter easily and efficiently. This problem becomes more prominent as the structure of the target building becomes more complex (in the above example, the greater the number n of unit structures constituting the estimated structure 200).
On the other hand, in Embodiment 2 of the present invention, the sensor response required for estimating the unknown parameter, that is, the relative displacement of one variable sensor attached to an arbitrary location in the target building with respect to the target building. The absolute acceleration of the variable sensor can be measured by a sensor provided only in the variable sensor. Therefore, in Embodiment 2, it is not necessary to attach a plurality of sensors as in the prior art. This is true even if the structure of the target building becomes complex.
On the other hand, in Embodiment 1 of the present invention, the natural circular frequency and the damping constant required for estimating the unknown parameter are the input to the shaker and at least one of the relative displacement and the absolute acceleration. It is determined by measuring. Therefore, also in Embodiment 1, it is not necessary to attach a plurality of sensors as in the prior art. This is true even if the structure of the target building becomes complex.
As described above, according to the present invention, unknown parameters can be estimated easily and efficiently regardless of the structure of the target building.

  Thirdly, in the prior art, it is assumed that steady excitation is used as the excitation for the target building, that is, a sine wave is used as the excitation wave given to the target building. On the other hand, in this invention, there is no limitation about the excitation with respect to an object building, Arbitrary excitation waves can be used with respect to an object building.

Fourth, the technique shown in FIG. 6 of the prior art requires a variable viscosity device (labeled “21” in FIG. 6) that can change the viscosity coefficient. As shown in FIG. 6, the viscous device is installed at the end of the target building 2 so as to be positioned between the target building 2 and the fixed portion. Therefore, in order to identify an unknown parameter using such a method, a variable viscosity device having an appropriate specification is incorporated in advance between the target building 2 and the fixed part, or such a variable Work to install a viscous device is required. As a result, when using this technique of the prior art, it is difficult to identify unknown parameters simply and efficiently.
On the other hand, in the present invention, it is only necessary to attach the additional structure 102 (one-degree-of-freedom system) having variable rigidity as an example to an arbitrary position in the target building. Further, as is apparent from the experimental results shown in Table 1, when there is no noise, the size of the additional structure 102 is very small (for example, about 1 / 10,000 of the target building: in Table 1). Even with a mass ratio of “0.0001”), sufficiently accurate identification is possible. Furthermore, even when noise is mixed, if an appropriate additional structure 102 (for example, a mass ratio “0.001 to 0.01” or more in Table 1 or an appropriate natural period) is employed, sufficient accuracy can be obtained. It is possible to identify.
As described above, according to the present invention, unknown parameters can be estimated much more easily and efficiently than in the prior art.

The schematic diagram which shows notionally the to-be-estimated structure (1 degree-of-freedom system) by which a vibration characteristic is estimated by the vibration characteristic estimation algorithm which concerns on Embodiment 1 of this invention. The schematic diagram which shows notionally the to-be-estimated structure (n-degree-of-freedom system) by which a vibration characteristic is estimated by the vibration characteristic estimation algorithm which concerns on Embodiment 1 of this invention. The flowchart which shows the vibration characteristic estimation method using the vibration characteristic estimation algorithm which concerns on Embodiment 1 of this invention. The schematic diagram which shows notionally the to-be-estimated structure in which a vibration characteristic is estimated with the vibration characteristic estimation algorithm which concerns on Embodiment 2 of this invention. The flowchart which shows the vibration characteristic estimation method using the vibration characteristic estimation algorithm which concerns on Embodiment 2 of this invention.

Explanation of symbols

101, 201-1 to 201-n Unit structure 102, 401 Variable sensor (additional structure, variable structure)
106 Exciter

Claims (18)

A vibration characteristic estimation method for estimating a vibration characteristic of a structure to be estimated including at least one unit structure represented by a plurality of physical quantities,
The estimated structure to which the additional structure represented by a plurality of physical quantities including the reference physical quantity set to the first value is attached is vibrated to a first vibration state, and an element indicating the first vibration state is measured. A first measurement stage;
A second measurement step of vibrating the estimated structure to which the additional structure having the reference physical quantity set to a second value is attached to a second vibration state and measuring an element indicating the second vibration state;
Using the first equation generated by the element indicating the first vibration state and the second equation generated by the element indicating the second vibration state, the estimated structure to which the additional structure is attached is used. Determining a plurality of physical quantities representing the at least one unit structure by solving a motion equation expressing motion by the plurality of physical quantities;
A vibration characteristic estimation method comprising: The additional structure in which the reference physical quantity is set to the n-th value is attached until the total number of the generated equations from the first equation to the n-th equation is equal to or greater than the total number of unknown physical quantities included in the equation of motion. An n-th measurement step of vibrating the estimated structure to an n-th vibration state and measuring an element indicating the n-th vibration state;
The vibration characteristic estimation method according to claim 1, further comprising: The first measuring step includes a step of measuring a natural circular frequency and a damping constant in the first vibration state as an element indicating the first vibration state;
The second measuring step includes measuring a natural circular frequency and a damping constant in the second vibration state as an element indicating the second vibration state;
The determining step comprises:
Generating the first equation by substituting the eigenvalue calculated using the natural circular frequency and the damping constant in the first vibration state for the characteristic equation of the eigenvalue corresponding to the equation of motion;
Generating the second equation by substituting the eigenvalue calculated using the natural circular frequency and damping constant in the second vibration state for the characteristic equation of the eigenvalue;
Determining the plurality of physical quantities by solving a characteristic equation of the eigenvalue using the first equation and the second equation,
The vibration characteristic estimation method according to claim 1, wherein the vibration characteristic is estimated. In the first measurement step, as an element indicating the first vibration state, a relative displacement of the estimated structure relative to the additional structure in the first vibration state and an absolute of the additional structure in the first vibration state Measuring acceleration, and
In the second measurement step, as an element indicating the second vibration state, a relative displacement of the estimated structure with respect to the additional structure in the second vibration state and an absolute of the additional structure in the second vibration state Measuring acceleration, and
The determining step comprises:
A state space model in the first vibration state is expressed using the relative displacement, the absolute acceleration in the first vibration state, and a function expressing the vibration given to the estimated structure in the first vibration state. Generating the first equation;
A state space model in the second vibration state is expressed using the relative displacement, the absolute acceleration in the second vibration state, and a function expressing the vibration given to the estimated structure in the second vibration state. Generating the second equation.
The vibration characteristic estimation method according to claim 1, wherein the vibration characteristic is estimated. The additional structure is
The reference physical quantity can be changed to a plurality of values including the first value and the second value,
5. The device according to claim 1, wherein the first value is set to the first value and the second value is set to the second value in the second measurement step. 6. The vibration characteristic estimation method according to any one of the above. The additional structure is
A first additional structure in which the reference physical quantity is the first value; and a second additional structure in which the reference physical quantity is the second value;
In the first measurement stage, the first additional structure is attached to the estimated structure,
5. The vibration characteristic estimation method according to claim 1, wherein in the second measurement stage, the second additional structure is attached to the estimated structure. 6.   The vibration characteristic estimation method according to claim 1, wherein the reference physical quantity is rigidity.   The vibration characteristic estimation method according to claim 1, wherein the plurality of physical quantities include mass, rigidity, and damping.   The vibration according to any one of claims 1 to 8, wherein the additional structure is configured so that a mass thereof is approximately 0.01 times or more of a mass of the estimated structure. Characteristic estimation method.   The vibration characteristic estimation method according to claim 9, wherein the additional structure is configured so that a mass thereof is approximately 0.1 times or more of a mass of the estimated structure.   The vibration characteristic estimation method according to any one of claims 1 to 10, wherein the additional structure is configured such that a natural period thereof is shorter than a natural period of the structure to be estimated.   The vibration characteristic estimation according to any one of claims 1 to 10, wherein the additional structure is configured such that a natural period thereof is substantially the same as a natural period of the structure to be estimated. Method. A vibration characteristic estimation device that estimates vibration characteristics of an estimated structure including at least one unit structure represented by a plurality of physical quantities,
The element indicating the first vibration state of the estimated structure to which the additional structure represented by a plurality of physical quantities including the reference physical quantity set to the first value is attached, and the reference physical quantity set to the second value Input means for inputting an element indicating a second vibration state of the estimated structure to which the additional structure is attached;
Using the first equation generated by the element indicating the first vibration state and the second equation generated by the element indicating the second vibration state, the estimated structure to which the additional structure is attached is used. Processing means for determining the plurality of physical quantities representing the at least one unit structure by solving a motion equation representing motion by the plurality of physical quantities;
The vibration characteristic estimation apparatus characterized by comprising. The input means is
As an element indicating the first vibration state, a natural circular frequency and a damping constant in the first vibration state are input,
As an element indicating the second vibration state, a natural circular frequency and a damping constant in the second vibration state are input,
The processing means is
By substituting eigenvalues calculated using the natural circular frequency and damping constant in the first vibration state into the characteristic equation of the eigenvalue corresponding to the equation of motion, the first equation is generated, By substituting the characteristic value calculated using the natural circular frequency and damping constant in the second vibration state for the characteristic equation, the second equation is generated,
The plurality of physical quantities are determined by solving a characteristic equation of the eigenvalue using the first equation and the second equation.
The vibration characteristic estimation apparatus according to claim 13. The input means is
As elements indicating the first vibration state, relative displacement of the estimated structure with respect to the additional structure in the first vibration state, absolute acceleration of the additional structure in the first vibration state, and the first vibration A function that expresses vibration given to the estimated structure in a state,
As elements indicating the second vibration state, relative displacement of the estimated structure with respect to the additional structure in the second vibration state, absolute acceleration of the additional structure in the second vibration state, and the second vibration A function that expresses vibration given to the estimated structure in a state,
The processing means is
Using the relative displacement, the absolute acceleration, and the function in the first vibration state, the first equation expressing a state space model in the first vibration state is generated,
Using the relative displacement, the absolute acceleration, and the function in the second vibration state, the second equation expressing a state space model in the second vibration state is generated,
Determining the plurality of physical quantities using the generated first equation and the second equation;
The vibration characteristic estimation apparatus according to claim 13. A computer program that can be incorporated into a vibration characteristic estimation device that estimates vibration characteristics of an estimated structure including at least one unit structure represented by a plurality of physical quantities,
The element indicating the first vibration state of the estimated structure to which the additional structure represented by a plurality of physical quantities including the reference physical quantity set to the first value is attached, and the reference physical quantity set to the second value Input an element indicating the second vibration state of the estimated structure to which the additional structure is attached,
Using the first equation generated by the element indicating the first vibration state and the second equation generated by the element indicating the second vibration state, the estimated structure to which the additional structure is attached is used. In order to determine the plurality of physical quantities representing the at least one unit structure by solving a motion equation representing motion by the plurality of physical quantities,
A computer program for operating the vibration characteristic estimation apparatus. As an element indicating the first vibration state, a natural circular frequency and a damping constant in the first vibration state are input,
As an element indicating the second vibration state, a natural circular frequency and a damping constant in the second vibration state are input,
By substituting eigenvalues calculated using the natural circular frequency and damping constant in the first vibration state into the characteristic equation of the eigenvalue corresponding to the equation of motion, the first equation is generated, By substituting the characteristic value calculated using the natural circular frequency and damping constant in the second vibration state for the characteristic equation, the second equation is generated,
By using the first equation and the second equation to solve the characteristic equation of the eigenvalue, the plurality of physical quantities are determined.
The computer program according to claim 16, wherein the vibration characteristic estimation device is operated. As elements indicating the first vibration state, relative displacement of the estimated structure with respect to the additional structure in the first vibration state, absolute acceleration of the additional structure in the first vibration state, and the first vibration A function that expresses vibration given to the estimated structure in a state,
As elements indicating the second vibration state, relative displacement of the estimated structure with respect to the additional structure in the second vibration state, absolute acceleration of the additional structure in the second vibration state, and the second vibration A function that expresses vibration given to the estimated structure in a state,
Using the relative displacement, the absolute acceleration, and the function in the first vibration state, the first equation expressing a state space model in the first vibration state is generated,
Using the relative displacement, the absolute acceleration, and the function in the second vibration state, the second equation expressing a state space model in the second vibration state is generated,
In order to determine the plurality of physical quantities using the generated first equation and the second equation,
The computer program according to claim 16, wherein the vibration characteristic estimation device is operated.

Images