JPH09257634A - Device for analyzing vibration characteristic - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce FRF(Frequency Correspondence Function) number into a mode number by multiplying +1 or -1 by polarity of an imaginary number corresponding to an inherent mode selected by FRF, superimposing FRF which is made positive polarity, and finding FRF corresponding to the mode. SOLUTION: The FRF matrix of a 2N line and m row found in experiment is made [P], and matrix arranging an imaginary part on the direction of lines corresponding to the resonant peak of each inherent mode out of the matrix [P] is prepared. Negative and positive symbols of reach component of the matrix is same to make 1 of the size, and it is inverted to make another matrix [K]. The matrix [P] and the other matrix [K] are multiplied to prepare the reduced FRF matrix [Q]. The whole FRF is superimposed so as to arrange the symbol of the imaginary part of a inherent mode. In other words, a vibration point is made a response point at the time when the RFR matrix measured, the direction of force of each point is adjusted so that the inherent mode is most excited, and at the same time FRF is measured at the time of shock and vibration. Thus, FRF number can be reduced for the mode number.

Description

Detailed Description of the Invention

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vibration characteristic analyzing apparatus, and more particularly to a vibration characteristic analysis for obtaining a response by exciting a test object such as an engine block and identifying a mode characteristic of the test object from a response function. It concerns the device.

In order to analyze the dynamic characteristics of an actual mechanical structure, it is necessary to identify the dynamic characteristics of the structure from the vibration response characteristics obtained by performing a vibration test on the structure. In this case, it is a parameter that directly expresses the vibration phenomenon, and it is easy to understand the phenomenon directly, and the method of identifying modal parameters (modal parameters such as natural frequency, mode damping ratio, and natural mode shape) with good convergence is currently used. It has become mainstream.

[0002]

2. Description of the Related Art FIG. 1 schematically shows the structure of a conventionally known vibration characteristic analyzing apparatus.
And an impulse hammer 2 for exciting the DUT 1 are prepared.

A force detecting load cell 3 is attached to the hammer 2, and the vibration response due to the vibration of the hammer 2 is three-dimensional (x, y, z) at an arbitrary position of the DUT 1.
An acceleration sensor 4 for detecting directional acceleration is attached.

Then, the output signal of the acceleration sensor 4 and the output signal of the load cell 3 are given to the arithmetic unit 5 to perform FFT processing to obtain frequency response function data (FRF: compliance) and calculate and output a mode characteristic. Have

[0005] In this case, the vibration experiment is usually performed with the vibration place of the DUT 1 fixed by the hammer 2, and the acceleration sensor 4 is sequentially moved to give a plurality of response functions to the arithmetic unit 5. . The DUT 1 is fixed by a soft spring (not shown) or the like.

[0006] Many algorithms have been proposed as algorithms for the arithmetic unit (experimental mode analyzer) 5 of such a vibration characteristic analyzer. Among them, the "variation iterative method" in the frequency domain has a high accuracy. Currently widely used for its goodness.

However, the above-mentioned biased iteration method has the following two drawbacks.

Particularly, when there are a plurality of response functions, the parameter {γ} to be obtained also increases as the response function increases.
The calculation time of the inverse matrix in the expression for obtaining the correction vector {Δγ} that corrects the parameter {γ} will increase sharply.

Since the number of variables increases, iterative calculations are less likely to converge and more likely to diverge, and calculation may become impossible on the way.

Therefore, the inventor of the present invention discloses in Japanese Patent Application Laid-Open No. 8-5450 that the arithmetic unit 5 uses actual measurement data for the purpose of improving the problem related to the essence of the algorithm that it is easy to diverge and takes a long calculation time. Even if the linear term and the non-linear term change, the divisional iterative method in which the parameter is repeatedly changed until the residual with the theoretical value due to the modal characteristic parameter is minimized is calculated separately for the linear term and the non-linear term. It is proposed to identify the mode characteristic by providing a condition that the residual does not diverge.

A brief description of this improved biased iterative method follows.

The desired mode characteristic is represented by {γ}. The theoretical formula of the frequency response function FRF at the frequency point ω = ω _i is f
_i , and the corresponding experimental data are represented by y _i . When the number of FRFs to be referred to at the same time is represented by m and the number of frequency points is represented by N, the total number of data is 2Nm because the FRF is a complex number.

If the distribution of the error mixed in y _i is a normal distribution, the most probable mode characteristic is {γ} that minimizes the weighted residual sum of squares S in the following equation.

[0014]

[Equation 1]

Here, the weight coefficient W _i is proportional to the reciprocal of the population variance of y _i .

All variables {γ} are divided into linear terms {α} (element u) and non-linear terms {β} (element v). The concept of erasing {α} will be shown. In the entire variable space, only {β} is used as a variable to search an area in which the following equation holds.

[0017]

[Equation 2]

[0018] Equation (2) in the minimum area of the {alpha} satisfied, FRF theoretical formula _{f i ({α}, {} β}) of the variable {alpha} those expressed in {beta} a H _i Then, the following formula is obtained.

[0019]

(Equation 3)

Here, the following equation is obtained from the equation (1).

[0021]

(Equation 4)

If the differential coefficient of the equation (3) is determined, the correction vector {Δβ} can be obtained by the least square method by the linear approximation of the following equation.

[0023]

[C] ^T [W] [C] {Δβ} = [C] ^T [W] {y _i −f _i } ... Expression (5) [C]: ∂H _i / ∂β _k [W]: a diagonal matrix having W _i as diagonal elements

The matrix [C] in equation (5) is called the Jacobian matrix. The size of this Jacobian matrix [C] is v × 2 Nm, and increases with the number m of FRFs.

[0025]

Here, with the recent development of multi-channel data processing devices and multi-axis speed sensors,
This arithmetic unit 4 is capable of processing a large number of frequency response functions (F
It has become possible to obtain (RF) experimentally.

For example, in FIG. 1, the information of three channels of X, Y, Z from the triaxial acceleration sensor 4 and the information of one channel of the force detection load cell 3 for detecting the vibration input = the information of a total of four channels. Is entered. If a plurality of acceleration sensors 4 are provided in parallel in order to reduce the measurement time and the like, the number of channels will increase by the increase.

In this FRF, as shown in FIG. 20, the vertical axis represents frequency and the horizontal axis represents measurement points (point 1, point 2 ...).
Can be treated as a matrix of 2N rows and m columns in which the axis data X, Y, and Z are sequentially arranged, and for example, a memory capacity of 4 bytes is assigned to one data.

However, the number of frequency response functions referenced m
Since the amount of such information increases as the number of times increases, it is becoming difficult to obtain a quick result with the limited calculation speed and memory capacity of the computer and the conventional calculation method.

In order to solve this problem, since the data to be processed at the same time is given as an FRF matrix, this matrix may be reduced.

As a method of reducing this FRF matrix,
Conventionally, a singular value decomposition method has been proposed.

In this singular value decomposition method, the procedure for reducing the FRF matrix [P] (2N rows and m columns) obtained in the experiment by using the singular value decomposition is shown in FIGS. 21 (1) to 21 (4). explain.

The matrix [B] (m rows and m columns) is calculated by the following equation ((1) in the same figure).

[0033]

[B] = [P] ^T [P] Equation (6) [P] ^T : transposed matrix of matrix [P]

The eigenvalue λ and eigenvector {x} of the matrix [B] are obtained ((2) in the same figure).

The set of eigenvalue λ and eigenvector {x} is
Arrange in descending order of eigenvalue λ. Then, the one whose eigenvalue λ is smaller than the others is omitted. The number of eigenvalues of the matrix [B] is found, but here, the number is reduced to a set of n eigenvalues and eigenvectors {x _i } of the number of modes ((3) in the same figure).

From the n eigenvectors {x _i }, the FRF vectors {P _i } reduced to n by the following equation are calculated ((4) in the same figure).

[0037]

## EQU00007 ## {P _i } = [P] {x _i } i = 1 to n Equation (7)

Therefore, this method takes time to calculate the eigenvalues and eigenvectors of the equations (6) and (7). Further, in order to calculate the equations (6) and (7), the matrix [P] (2N rows m
Column) and matrix [B] (m rows and m columns) need to be stored.

Since the eigenvalues are calculated and arranged in descending order of eigenvalues and eigenvectors, the one with the smallest coefficient is truncated and compressed into the data with the number of modes n.
The physical meaning of the compressed information is unknown, and the compressed information is not stored as complete information, so that there is a problem that accurate mode characteristics cannot be obtained.

Therefore, according to the present invention, a force detecting load cell attached to an impulse hammer for vibrating the DUT, and the impulse hammer attached to an arbitrary position of the DUT are attached. The frequency response function data is obtained by receiving the acceleration sensor for measuring the vibration response due to the load, the output signal of the load cell and the output signal of the sensor, and the frequency response function data and the residual of the theoretical formula of the frequency response function are obtained. In a vibration characteristic analysis device provided with an arithmetic device for identifying the mode characteristic of the DUT by calculating the mode characteristic parameter by dividing into a linear term and a non-linear term in the least squares method of minimizing the sum of squared differences, The purpose is to compress the information that is handled correctly, instead of the singular value decomposition method.

[0041]

[Means for Solving the Problems]

[1] With respect to the present invention, a method for reducing the FRF while preserving the information contained in the input data and having a simple and clear physical meaning will be described below.

F in which the FRF of each point is arranged as a column vector
The RF matrix [P] is reduced by the following equation.

[0043]

[Q] = [P] [K] Equation (8) where [P]; 2N rows m of the FRF matrix obtained in the experiment
Column [Q]; Reduced FRF matrix 2N rows n columns [K]; Reduction matrix m rows n columns n; Number of adopted eigenmodes (5 to 10) (m> n)

To create the matrix [K], first of all, the matrix [P]
Only the imaginary part corresponding to the resonance peak of each eigenmode is taken out of (2N rows and m columns) to create a matrix arranged in the row direction. Next, the positive and negative signs of each element of this matrix are the same, and only the magnitude is changed to 1 (FIG. 2 (1)).

The matrix [K] ^T thus created is transposed to create a matrix [K] ((2) in the same figure).

Then, a reduced FRF matrix [Q] is created based on the FRF matrix [P] and the matrix [K] by the equation (8) ((3) in the same figure).

In the calculation of the equation (8), all the FRFs are superposed so that the signs of the imaginary numbers near the resonance peak of a certain eigenmode are the same.

This means that the excitation point at the time of measuring the FRF matrix is used as the response point (measurement point), the direction of the force at each point is adjusted so that a certain eigenmode is excited most, and the shock is applied at the same time. This corresponds to measuring the FRF when shaking. Therefore, the number of FRFs equal to the number of eigenmodes becomes
You can shrink the matrix.

In fact, it is very difficult to correctly excite each point so that a certain mode is excited most. But,
If a large number of FRFs are acquired by a hit test or the like for each point, the measurement result corresponding to simultaneous impact vibration can be easily obtained by using the formula (8).

The processing of equation (8) is -1 or + for each FRF.
Multiply by 1 and add. The absolute value of the addition coefficient is 1
Therefore, in the FRF after addition, the random noise is canceled and reduced.

Even if the number of FRFs is large, the number of FRFs can be reduced to the same number as the number of eigenmodes to be extracted by the formula (8). The calculation time and memory capacity for that are much shorter than the method by singular value decomposition or principal component analysis.

The above principle will be described more specifically with reference to FIGS.

The FRF matrix is, as shown in FIG.
The upper half is arranged as real part data and the lower half is arranged as imaginary part data. This state is the state before compression and the amount of information for m columns.

A method of compressing this into the information amount of the adopted eigenmode number n columns will be described.

The number of eigenmodes adopted is the number of eigenmodes within the range when the user divides the frequency region in the technical field in which the DUT is to be observed, as shown in FIG. is there.

In the figure, for example, from 0 Hz to 100
If the observation range is 0 Hz, the number of eigenmodes is two. Generally, it is 5 to 10.

Focusing on this eigenmode, the procedure for reducing the number of FRFs will be described with reference to FIGS.

In FIGS. 4 (1) to 4 (4), the DUT 1 is
When the waveforms at the measurement points (1) to (4) (see FIG. 1) are simply added, the shape of the eigenmode does not have a desired resonance peak, as shown in FIG. 5, for example.

Therefore, as shown in FIG. 6 (2), when the phase is +, the amplitude value is the same as it is, and when the phase is −, the amplitude value obtained by multiplying it by −1 is used to obtain the positive polarity. By adding these, a desired waveform is obtained as shown in FIG.

However, in this operation, the desired result can be obtained only for the eigenmode, but it is not known what the waveform will be after the next eigenmode.

Therefore, next, the same operation is performed in the eigenmode portion (see FIG. 7).

This operation is sequentially executed for the number of adopted peculiar modes.

As a result, the FRF having the total number of data m is reduced to the FRF having the number of adopted eigenmodes n (n <m) with accurate information for each eigenmode.

[2] On the other hand, the equation (5) is the FRF as described above.
Since the number increases with the number m, it imposes a heavy load on both the storage capacity and the calculation time of the computer. In order to reduce such a load, the calculation method of the equation is improved as follows.

As a method of solving the equation (5), (1) a method of solving as a simultaneous equation of v elements and v rows called a normal equation, and (2) orthogonal transformation of the Jacobian matrix [C] by the Householder method etc. Solving methods have been known so far, and it is generally said that the latter (2) has better calculation accuracy.

As a result of actual calculation, both calculation results were the same in the double precision calculation in this case. Moreover, in terms of calculation time and storage capacity, the former (1) which solves the normal equation was more advantageous.

Therefore, in the present invention, attention is focused on improving the calculation method by using a normal equation.

First, the normal equation of the equation (5) can be rewritten as the following equation.

[0069]

[G] {Δβ} = {d} Equation (9)

When calculating [G] and {d} in the equation (9) from the Jacobian matrix [C], the differential coefficient of the theoretical equation H _i of the frequency response function is used in the Newton method and the residual sum of squares S is used. Convert to the differential coefficient of.

When the equation (3) is substituted into the equation (5), the right side of the equation (9) becomes the following equation.

[0072]

(Equation 10)

The formula (10) is developed and arranged as follows.

[0074]

[Equation 11]

Since {α} satisfies the minimum condition at a certain stage in the iterative calculation, ∂S / ∂α _s = 0.
(S = 1 to u) is established. Therefore, the following equation is obtained.

[0076]

(Equation 12)

Next, the amount obtained by omitting the second differential term in the equation (4) will be represented by the following equation.

[0078]

(Equation 13)

The component G of the coefficient matrix [G] on the left side of the equation (9)
_jk is obtained from the equation (5) as follows.

[0080]

[Equation 14]

By substituting equation (3) into equation (14), the following equation is obtained.

[0082]

(Equation 15)

The right side of the equation (15) is expressed as A + B + C, and by substituting the equations (1) and (9) for rearranging, the following equations relating to A, B, and C are obtained.

[0084]

(Equation 16)

[0085]

[Equation 17]

[0086]

(Equation 18)

Here, {x} ^T , {a}, and {b} are defined by the following equations.

[0088]

[Equation 19]

Substituting equation (19) into equation (18), the following equation holds.

[0090]

(Equation 20)

Therefore, equations (16), (17) and (20)
Is substituted into G _jk = A + B + C, the following equation is obtained.

[0092]

(Equation 21)

Until now, the number of multiplications of the matrix [F] ⁻¹ of the second term on the right side of the equation (3) is large, which is a burden on the calculation time. Moreover, the calculation of the second term on the right side is v × 2 Nm
Had been going around.

However, in the equation (21), since Σ has been removed to calculate G _jk , the necessary calculation is 3 times, and the whole [G] is 3v ² times.

The nonlinear term is a common term of all FRFs, and the number v thereof is smaller than the normal frequency point N and the reference FRF number m, so that the calculation time can be shortened. Further, until now, the matrix [C] of 2Nm rows and v columns was stored as it is, but it is sufficient to store [G] of v rows and v columns and {d} of v rows, and the required storage capacity is reduced. To do.

That is, in order to calculate the equation (21), S
It suffices to calculate the differential coefficients of α and S ′ with respect to α _s and β _k .

[0097]

BEST MODE FOR CARRYING OUT THE INVENTION The vibration characteristic analyzing apparatus according to the present invention may have the same structure as that of the conventional example shown in FIG. 1 described above, but the difference from the conventional example is the arithmetic processing in the arithmetic unit 5. Is. The calculation process will be described below with reference to the flowchart shown in FIG.

<Parameter division> When a plurality of response functions are considered simultaneously, if the number of response functions is m and the number of eigenmodes to be identified is n as in the above, the parameter {γ}
Is 2n + (2n + 4) m. Among the parameters {γ}, the nonlinear term is 2n and the linear term is (2n + 4) m.
It is. This parameter {γ} is divided into a linear term {α} and a non-linear term {β} as in the following equation.

[0099]

## _EQU22 ## {γ} ^T = {{α} ^T , {β} ^T } {α} ^T = {..., U _rj , V _rj , ..., C _j , D _j , E _j , F _j , ...} (R = 1 to n, j = 1 to m) {β} ^T = {..., σ _r , ω _dr , ...} (r = 1 to n) Equation (22)

Here, U _rj and V _rj in the linear term {α} represent the real and imaginary parts of the r-th residue with respect to the measurement point j,
1 / C _j and 1 / D _j are parameters introduced by taking into consideration the influence of the eigenmode that is not noted as a surplus mass, and 1 / E _j and 1 / F _j are similarly introduced as surplus stiffness.

Further, σ _r in the nonlinear term {β} indicates each peak (there are n peaks shown in FIG. 9 (2)), that is, the attenuation rate in each mode characteristic, and ω _dr indicates each peak. That is, the damping natural angular frequency in each mode characteristic is shown.

Since the response function (theoretical value) of the mode characteristics given to the arithmetic unit 5 when the DUT 1 is excited by the hammer 2 has amplitude and phase, the real part G _Rj A theoretical model represented by a complex number composed of (ω) and an imaginary part G _Ij (ω) is well known.

[0103]

(Equation 23)

The damping ratio σ _r and the natural frequency ω _dr do not change even if the response point (the mounting position of the acceleration sensor 4) changes. In other words, the number 2n of the parameter {β} of the nonlinear term is characterized in that it does not change even if the number m of the response functions increases, because the position (frequency) of the mountain shown in FIG. 9 (2) does not change, It can be seen that this does not affect the number of response functions.

If the nonlinear term is obtained, the linear term can be easily obtained by the linear least squares method without repeated calculation.

Therefore, it is devised to first obtain only the nonlinear term. Therefore, first, the weighting factor W _i in the equation (1) is calculated.
And initial values of the damping natural angular frequency ω _{d r} and the mode damping rate σ _r as the nonlinear term parameter {β} are set (see FIG. 8).
Step S1).

Since any initial value of the attenuation converges, the peak of the function obtained by summing the squares of the FRF amplitudes (see FIG. 9).
Only the initial value of the damping natural angular frequency may be obtained from (2)).

Then, the frequency response function y _i which is the experimental data is input (step S2).

Next, in order to reduce the following calculation load, the input frequency response function FRF is reduced using equation (8) (step S3). The reduction rate is n (number of adopted modes) / m (number of FRFs).

If the non-linear term parameter {β} is initialized, the linear term parameter {α} can be obtained by one calculation by the following equation (step S4).

[0111]

[Formula 24] {α} = ([D] ^T [W] [D]) ^-1 [D] ^T [W] {y _i } Equation (24) where D _ij = ∂f _i / ∂ α _j (i = 1 to 2p, j = 1 to (2
n + 4) m)

The theoretical value f _i of the frequency response function FRF is calculated by the equation (23) using the linear term {α} and the nonlinear term {β} thus obtained (step S5). The value of the first nonlinear term is the value initialized in step S1.

The residual sum of squares S of the theoretical value and the experimental value of the response function thus calculated is calculated according to the equation (1) (step S6).

Then, it is determined whether or not this residual sum of squares S is smaller than the previously obtained value (step S
7). In this case, the first residual sum of squares S may be set to a sufficiently large value.

As a result, when the residual sum of squares S is smaller than the previous value, it means that the residual sum of squares S has not reached the minimum value yet. Therefore, the residual sum of squares S is set to the minimum value. The following non-linear term parameter {β} for is obtained as follows.

That is, d _k is calculated using the equation (12),
The differential coefficients of α and β of S and S ′ are calculated by using the equations (4) and (13). Then, using Equation (21), G _jk
Is calculated (step S8).

By substituting the above result into the equation (9), the correction vector {Δβ} is calculated (step S9).

<Setting of Side Constraints> The correction vector {Δβ} of the nonlinear term has been obtained as described above, but if it is used as it is, it may diverge. Therefore, further side constraints are set.

As a lateral constraint for preventing divergence, there is a method of applying a reduction factor to the correction vector to reduce the same size in that direction. In this method, each parameter is multiplied by the same coefficient. Here, a separate constraint of the following equation is set for each nonlinear term.

[0120]

[Expression 25] | Δω _dr / ω _dr | ≦ K ₁ | Δσ _r / σ _r | ≦ K ₂ , σ _r > 0 ... Expression (25)

If {Δβ} does not meet this condition, it is corrected by the equation (25) (step S11).

The correction vector {Δβ} thus obtained is added to the previous nonlinear term parameter {β} (initial value is the initial value) to calculate the new nonlinear term parameter {β ^* } this time (step S12).

[0123]

[Formula 26] {β ^* } = {β} + {Δβ} Equation (26)

Using the new non-linear term parameter {β ^* } thus obtained, the above steps S4 and thereafter are repeatedly executed. If the residual sum of squares S calculated in step S6 of this iterative loop is not smaller than the previous value, this means that this S has reached the minimum value.
Exit from the calculation loop of {β} (“N of step S7
o ”).

Then, the FRF that is not reduced is input again (step S13), and this FRF and the already determined {β} are substituted into the equation (24) to calculate the linear term {α} (step S14).

Since the linear least squares method can be applied to this process, iterative calculation is unnecessary.

Then, {α} and {β} indicating the optimum mode characteristics are output (step S15).

The computer load when the mode characteristics are extracted by simultaneously considering a large number of frequency response functions is the calculation time and the storage capacity required for identification. In order to identify using an inexpensive computer at the experiment site, it is necessary to greatly reduce both loads. Here, actual experimental data is used to verify the superiority of the present invention in terms of calculation time and storage capacity.

In FIG. 1, the object to be tested 1 with the impulse hammer 2
Is oscillated, and the modal characteristics are identified using the experimental data obtained by measuring the response with the triaxial acceleration sensor 4.

As input data for experimental identification of modal characteristics, the FRF matrix from 140 Hz to 736 Hz is first reduced and used. There are nine eigenmodes in this frequency domain. The response points are 63 points × 3 directions.

FIGS. 9A and 9B show the phase and amplitude of the FRF of the X-direction response at the point (1) before reduction, respectively. The solid line is the experimental FRF, and the thin broken line is the FRF constructed from the identified mode characteristics. Eigenmode exists 18
Random noise is mixed near 0 Hz.

FIGS. 10 (1) and 10 (2) show examples of the phase and amplitude obtained by simply superposing all the FRFs and reducing them into one FRF. Almost all the random noise is removed here, but the resonance peak corresponding to the eigenmode is unclear.

11 (1), 11 (2) to 19 (1),
(2) shows the FRF reduced by the FRF reducing means of the present invention so as to emphasize the eigenmodes. Here, eigenmode in FIG. 11, eigenmode in FIG. 12, eigenmode in FIG. 13, eigenmode in FIG. 14, eigenmode in FIG. 15, eigenmode in FIG. 16, eigenmode in FIG. 17, eigenmode in FIG. In FIG. 19, each targeted mode such as the eigenmode is emphasized, and the level of random noise is lowered, which shows the effectiveness of the reduction method of the present invention.

<Calculation Time> Table 1 shows a comparison of calculation times in the case of identifying the mode characteristics of five eigenmodes by using the data of 573 frequency points for each FRF.

As can be seen from Table 1, by improving the efficiency of the matrix calculation in the present invention, the calculation time can be reduced to about 1/3 of the conventional method. Input data (FRF matrix)
It can be seen that when is reduced, it becomes effective when the number of FRFs becomes equal to or more than the number of eigenmodes (5 in this case).

[0136]

[Table 1]

<Reduction of Storage Capacity> Table 2 shows the storage capacity of the computer used for the identification calculation in the conventional example and the present invention. The identification conditions are 300 simultaneous reference FRFs, 5 adopted eigenmodes, and 573 each FRF frequency point.

From Table 2, the required storage capacity is reduced to about 1/7 by the improvement of the matrix calculation method according to the present invention. It can be seen that if the reduction of the input data is also used, it is further reduced to about 1/8, which is 1.7% of the conventional example. In the case of input data reduction, the required storage capacity does not change even if the number of FRFs increases.

That is, the amount of FRF up to the limit of the external storage capacity can be processed with this 600 Kbite.

[0140]

[Table 2]

[0141]

As described above, according to the vibration characteristic analyzer of the present invention, the polarity of the imaginary part corresponding to the selected eigenmode of the frequency response function is multiplied by +1 or -1 to make it positive. Since the frequency response functions corresponding to the eigenmodes are obtained by superposing the frequency response functions and the number of the frequency response functions is reduced to the number of eigenmodes, there is no reduction in accuracy due to data reduction. The calculation efficiency can be significantly improved.

Further, the normal matrix in the normal equation for obtaining the correction vector by the least square method by linear approximation is used to calculate the weighted residual sum of squares of the theoretical value and the experimental value of the frequency response function and its residual excluding its second derivative term. The calculation efficiency can be further improved by obtaining the differential coefficient related to the linear term and the nonlinear term of the sum of squares.

[0143]

[Brief description of drawings]

FIG. 1 is a block diagram showing a vibration characteristic analyzer common to the present invention and a conventional example.

FIG. 2 is an F used in the vibration characteristic analyzer according to the present invention.
It is a figure explaining data reduction of RF (frequency response function) matrix.

FIG. 3 is a graph showing the FRF phase and amplitude of vibration measurement data (one-time unidirectional component data of one point).

FIG. 4 is a graph showing amplitudes of four FRFs.

FIG. 5 is a graph diagram when each FRF amplitude in FIG. 4 is simply added.

FIG. 6 is an FRF when the FRF data reduction focusing on the eigenmode is performed by the vibration characteristic analyzer according to the present invention.
It is a graph figure for showing improvement of amplitude.

FIG. 7 is an FRF when FRF data reduction focusing on eigenmodes is performed by the vibration characteristic analyzer according to the present invention.
It is a graph figure for showing improvement of amplitude.

FIG. 8 is a flowchart showing an arithmetic algorithm stored and executed in the arithmetic unit in the vibration characteristic analyzing apparatus according to the present invention.

FIG. 9 is a graph showing the FRF phase and vibration of unreduced vibration measurement data.

FIG. 10 is a graph diagram when each FRF data of all vibration measurement data is simply added.

FIG. 11 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 12 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 13 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 14 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 15 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 16 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 17 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 18 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 19 is a graph diagram when each FRF data of all vibration measurement data is reduced by paying attention to an eigenmode.

FIG. 20 is a diagram showing an example of an FRF matrix.

FIG. 21 is a diagram showing an example of data reduction by a conventional singular decomposition method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 DUT 2 Impulse hammer 3 Load cell 4 Acceleration sensor 5 Arithmetic device In the drawings, the same reference numerals indicate the same or corresponding parts.

Claims (2)

[Claims] 1. A force detection load cell attached to an impulse hammer for vibrating an object to be tested, and an exciter of the impulse hammer attached to an arbitrary location of the object to be tested. The frequency response function data is obtained by receiving the acceleration sensor for measuring the response, the output signal of the load cell and the output signal of the sensor, and the residual sum of squares of the frequency response function data and the theoretical formula of the frequency response function is minimized. In a vibration characteristic analysis device including a calculation device that identifies a mode characteristic of the device under test by calculating a mode characteristic parameter by dividing into a linear term and a non-linear term in the least squares method, By superimposing the positive frequency response function by multiplying the polarity of the imaginary part corresponding to the selected eigenmode of the frequency response function by +1 or -1. Determined the frequency response function corresponding to the eigenmodes, the vibration characterization unit, characterized in that to reduce the number of the frequency response function of the number of eigenmodes. 2. The arithmetic unit according to claim 1, wherein a normal matrix in a normal equation for obtaining a correction vector by a least square method by linear approximation is used to calculate a weighted residual sum of squares of a theoretical value and an experimental value of a frequency response function and Part 2
An apparatus for analyzing vibration characteristics, which is obtained by a differential coefficient relating to a linear term and a non-linear term of a residual sum of squares without the secondary differential term.