CN113204739A - Frequency response function quality line optimization method based on K-means clustering - Google Patents

Abstract

The invention discloses a frequency response function quality line optimization method based on K-means clustering, which is characterized in that a frequency response function frequency band measured by a test mode is divided into corresponding data sets and standardized; determining an initial clustering center and a clustering number of each data set; defining an iteration index and an iteration formula of the algorithm, and repeatedly iterating a clustering center and a clustering number until the index is optimal; defining weight coefficients, and calculating the mean value of the selected frequency response function quality line according to different clusters and the corresponding weight coefficients. The method combines the advantages of a mass line mean value calculation formula and a K-mean value clustering algorithm, mainly determines the initial clustering number and clustering center method, a K-mean value iteration index and the weight coefficient of the class, proves that the calculation precision is obviously optimized by compiling program simulation, and simultaneously greatly improves the efficiency of a mass line inertia parameter identification method based on test modes.

Description

Frequency response function quality line optimization method based on K-means clustering

Technical Field

The invention relates to the field of inertia parameter identification of complex components such as electromechanical manufacturing, vehicles and ships, aerospace, navigation, military industry and the like, in particular to a frequency response function quality line optimization method based on K-means clustering.

Background

The method for identifying the inertia parameters by the mass line based on the test mode has very important significance in engineering technology and scientific research of electromechanical manufacturing, vehicles and ships, aerospace, navigation, military industry and the like. The processing of the frequency response function mass line data is a very important link for accurately identifying the inertial parameters. However, in the process of calculating the inertia parameters by using the method based on the frequency response function mass line, the arithmetic mean value is generally directly adopted for calculating the mean value, the influence of fluctuation and the most value of data in a frequency band is ignored, the frequency response function mass line of an actual test result is not ideal and smooth, and errors are accumulated more in the test process, so that the test result needs to be refined, and the efficiency and the precision of the test technology can be improved better.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a frequency response function quality line optimization method based on K-means clustering.

The technical scheme for realizing the purpose of the invention is as follows:

a frequency response function quality line optimization method based on K-means clustering comprises the following steps:

1) m frequency response function frequency bands S determined by test mode_nPartitioning into m datasets T ═ S₁...S_mAnd (4) standardizing, wherein the specific steps are as follows:

1-1) frequency response function S_mIs a two-dimensional array, and the amplitude H (omega) of the ordinate is ═ H₁H₂…H_nAnd angular frequency ω ═ ω of abscissa₁ ω₂…ω_nThe values of two variables are established in a one-to-one mapping relation;

1-2) data normalization

1-2-1) optionally a number set S_mCalculating S_mArithmetic mean of amplitude H (omega)

1-2-2) calculating the residual absolute value of the amplitude H (omega)

Determining a set of residual absolute values as U_re＝{μ₁，μ₂，…，μ_n}；

1-2-3) calculating the amplitude H (omega) standard deviation

1-2-4) to reduce the effect of the fluctuating peak of the initial data on solving the overall mean, a normalization process is performed on each sample of the amplitude H (ω), where any sample is represented as

The amplitude set is H_BZi＝{h_BZ1，h_BZ2，…，h_BZnThe corresponding abscissa angular frequency ω ═ ω₁ ω₂…ω_nThe method is not changed;

2) determining the number of clusters K for each frequency response function data set₀And an initial clustering center C₀The method comprises the following steps:

2-1) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering number K₀

2-1-1) computing the set H_BZiExtreme difference Ra of_O＝max(H_BZi)-min(H_BZi)；

2-1-2) computing the set H_BZiArithmetic mean of

2-1-3) computing the set H_BZiResidual error of

Determining a set of residual absolute values as U_BZn＝{μ_BZ1，μ_BZ2，…，μ_BZn}；

2-1-4) computing the set H_BZiResidual mean of

2-1-5) calculating the number of initial classifications K₀Adding 1 to the integer of the residual error of the polar difference division, i.e.

2-2) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering center C₀；

2-2-1) A set H_BZiN samples divided into K₀Class i, i

And the corresponding abscissa angular frequency ω ═ ω₁ ω₂…ω_n}；

2-2-2) Each subset A₁，A₂，…A_j，

The number of samples in is

2-2-3) dividing the subset if

Then

2-2-4) calculating the center of the initial cluster, the value of the cluster center being the mean of each class subset, i.e.

3) Defining iteration index, determining iteration formula, and repeatedly iterating and clustering center C_nAnd the number of clusters K_nUntil the index is optimal, the specific steps are as follows:

3-1) defining an iteration index, K₀Number of classes

3-1-1) defining an iteration index

Where Sd is the internal standard deviation of class

Rn is like internal pole difference Rn ═ max (A)_j)-min(A_j)，

Is the difference in the mean values between the classes,

p，

is the arithmetic mean value of the interior of the class,

the mean value of the minimum value of the difference between the intra-class element and the mean value between the classes is

3-1-2) calculating the sum of absolute values of various internal slopes

Wherein the slope inside each subclass is k, and setting the linear function inside the subclass by minimum multiplication

Then

The difference between the minimum and maximum values of the mean value of the class RN ═ max (A)_j)-min(A_j)；

3-2) determining an iterative equation and an iterative algorithm

3-2-1) iterative equation as ordinate H_BZiDistance between, i.e. Yd ═ h_BZn-C₀|；

3-2-2) calculating each amplitude h in turn_BZnTo respectively K₀The distance Yd of the initial clustering center is the h corresponding to the minimum Yd_BZnAttributing to the initial class corresponding to the corresponding initial clustering center, and repeating the steps until each amplitude value h is assigned_BZnAfter all the classes are classified, determining the clustering center of the new class according to the new number set class, calculating indexes of the new class, comparing the indexes of the new class, and stopping iteration until the minimum index is found;

3-2-3) pairs of other S within the data set T_mRepeating step 1-2-1) to step 3-2-2) until the index of each number set is minimumDetermining a clustering center, a clustering number and a point set of each class;

3-2-4) mapping to original amplitude according to the abscissa corresponding to the optimal class to form a new set H (omega)^finally＝{B₁B₂…B_K0}＝{(H₁...H_a)(H_d...H_e)...(H_g...H_n)}，d＜e＜g＜n

4) Defining a weight coefficient, and calculating the average value of the frequency band selected by the frequency response function quality line, wherein the specific steps are as follows:

4-1) calculating the S_mSmoothing coefficient ph of frequency response function number set_all＝Arm_all×k_all×sd_allWherein

k_all、sd_allAre respectively S_mArithmetic mean, slope, standard deviation of the frequency response function number set;

4-2) calculation of removal of S_mCalculating the amplitude of the J-th class in the frequency response function number set, and calculating the arithmetic mean value of the remaining K-1 classes

Slope k_K-1And standard deviation sd_K-1Smoothing coefficient of (d):

ph_K-1＝Arm_K-1×k_K-1×sd_K-1

4-3) defining the weight as according to steps 4-1), 4-2)

4-4) calculating S_mThe weight coefficients of K classes in the frequency response function number set are normalized,

5) calculating an average value: the class formed by the original amplitude value H (omega) corresponding to the class classified according to each frequency response function and the class corresponding to the normalized classWeight, calculating Average value B₁δ₁ ^gy+B₂δ₂ ^gy...B_K0δ_r ^gy。

According to the method for optimizing the frequency response function mass line based on the K-means clustering, the identification precision of the frequency response function mass line inertial parameters based on the test mode is optimized, and the identification efficiency of the frequency response function mass line inertial parameters based on the test mode is improved.

Drawings

FIG. 1 is a flow chart of a frequency response function quality line optimization method based on K-means clustering;

FIG. 2 is a diagram showing the method for dividing the initial frequency band of the mean value of the single frequency response function data of the test;

FIG. 3 is a diagram showing the result of the method dividing the mean value of a single frequency response function;

Detailed Description

The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.

Example (b):

a frequency response function quality line optimization method based on K-means clustering is disclosed, as shown in figure 1, and comprises the following steps:

1) m frequency response function frequency bands S determined by test mode test_nPartitioning into m datasets T ═ S₁...S_mAnd (4) standardizing, wherein the specific steps are as follows:

1-1) frequency response function S_mIs a two-dimensional array, and the amplitude H (omega) of the ordinate is ═ H₁ H₂…H_nAnd angular frequency ω ═ ω of abscissa₁ ω₂…ω_nThe values of two variables are established in a one-to-one mapping relation;

1-2) data normalization

1-2-1) optionally a number set S_mCalculating S_mArithmetic mean of amplitude H (omega)

1-2-2) calculating amplitudeResidual absolute value of value H (omega)

Determining a set of residual absolute values as U_re＝{μ₁，μ₂，…，μ_n}；

1-2-3) calculating the amplitude H (omega) standard deviation

1-2-4) to reduce the effect of the fluctuating peak of the initial data on solving the overall mean, a normalization process is performed on each sample of the amplitude H (ω), where any sample is represented as

The amplitude set is H_BZi＝{h_BZ1，h_BZ2，…，h_BZnThe corresponding abscissa angular frequency ω ═ ω₁ ω₂…ω_nThe method is not changed;

2) determining the number of clusters K for each frequency response function data set₀And an initial clustering center C₀The method comprises the following steps:

2-1) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering number K₀

2-1-1) computing the set H_BZiExtreme difference Ra of_O＝max(H_BZi)-min(H_BZi)；

2-1-2) computing the set H_BZiArithmetic mean of

2-1-3) computing the set H_BZiResidual error of

Determining a set of residual absolute values as U_BZn＝{μ_BZ1，μ_BZ2，…，μ_BZn}；

2-1-4) computing the set H_BZiResidual mean of

2-1-5) calculating the number of initial classifications K₀Adding 1 to the integer of the residual error of the polar difference division, i.e.

2-2) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering center C₀；

2-2-1) A set H_BZiN samples divided into K₀Class i, i

And the corresponding abscissa angular frequency ω ═ ω₁ ω₂…ω_n}；

2-2-2) Each subset A₁，A₂，…A_j，

The number of samples in is

2-2-3) dividing the subset if

Then h is_BZj∈A_j，

2-2-4) calculating the center of the initial cluster, the value of the cluster center being the mean of each class subset, i.e.

3) Defining iteration index, determining iteration formula, and repeatingGeneration clustering center C_nAnd the number of clusters K_nUntil the index is optimal, the specific steps are as follows:

3-1) defining an iteration index, K₀Number of classes

3-1-1) defining an iteration index

Where Sd is the internal standard deviation of class

Rn is like internal pole difference Rn ═ max (A)_j)-min(A_j)，

Is the difference in the mean values between the classes,

p，

is the arithmetic mean value of the interior of the class,

the mean value of the minimum value of the difference between the intra-class element and the mean value between the classes is

3-1-2) calculating the sum of absolute values of various internal slopes

Wherein the slope inside each subclass is k, and setting the linear function inside the subclass by minimum multiplication

Then

The difference between the minimum and maximum values of the mean value of the class RN ═ max (A)_j)-min(A_j)；

3-2) determining an iterative equation and an iterative algorithm

3-2-1) iterative equation as ordinate H_BZiDistance between, i.e. Yd ═ h_BZn-C₀|；

3-2-2) calculating each amplitude h in turn_BZnTo respectively K₀The distance Yd of the initial clustering center is the h corresponding to the minimum Yd_BZnAttributing to the initial class corresponding to the corresponding initial clustering center, and repeating the steps until each amplitude value h is assigned_BZnAnd after classification, determining the clustering center of the new class according to the new number set class, calculating indexes of the new class, comparing the indexes of the new class, and stopping iteration until the minimum index is found.

3-2-3) pairs of other S within the data set T_mRepeating the step 1-2-1) and the step 3-2-2) until the index of each number set is minimum, and determining a clustering center, a clustering number and a point set of each class;

3-2-4) mapping to original amplitude according to the abscissa corresponding to the optimal class to form a new set H (omega)^finally＝{B₁B₂…B_K0}＝{(H₁...H_d)(H_d...H_e)...(H_g…H_n)}，d＜e＜g＜n

4) Defining a weight coefficient, and calculating the average value of the frequency band selected by the frequency response function quality line, wherein the specific steps are as follows:

4-1) calculating the S_mSmoothing coefficient ph of frequency response function number set_all＝Arm_all×k_all×sd_allWherein

k_all、sd_allAre respectively S_mArithmetic mean, slope, standard deviation of the frequency response function number set;

4-2) calculation of removal of S_mCalculating the amplitude of the J-th class in the frequency response function number set, and calculating the arithmetic mean value of the remaining K-1 classes

Slope k_K-1And standard deviation sd_K-1Smoothing coefficient of (d):

ph_K-1＝Arm_K-1×k_K-1×sd_K-1

4-3) defining the weight as according to steps 4-1), 4-2)

4-4) calculating S_mThe weight coefficients of K classes in the frequency response function number set are normalized,

5) calculating an average value: calculating Average value B according to the class formed by the original amplitude value H (omega) corresponding to the class of each frequency response function and the weight corresponding to the class after standardization₁δ₁ ^gy+B₂δ₂ ^gy...B_K0δ_r ^gy。

The matlab programming is performed on the method, the average value initial frequency band processing is performed on the single frequency response function data acquired in the test, and the result is shown in fig. 2. The final mean value calculation frequency band division result for the experimental data is shown in fig. 3.

Claims (1)

1. A frequency response function quality line optimization method based on K-means clustering is characterized by comprising the following steps:

1) m frequency response function frequency bands S determined by test mode_nPartitioning into m datasets T ═ S₁ ... S_mAnd (4) standardizing, wherein the specific steps are as follows:

1-1) frequency response function S_mIs a two-dimensional array, and the amplitude H (omega) of the ordinate is ═ H₁ H₂ … H_nAnd angular frequency ω ═ ω of abscissa₁ ω₂ … ω_nThe values of two variables are established in a one-to-one mapping relation;

1-2) data normalization

1-2-1) optionally a number set S_mCalculating S_mArithmetic mean of amplitude H (omega)

1-2-2) calculating the residual absolute value of the amplitude H (omega)

Determining a set of residual absolute values as U_re＝{μ₁，μ₂，…，μ_n}；

1-2-3) calculating the amplitude H (omega) standard deviation

1-2-4) normalizing each sample of the amplitude H (ω), where any sample is represented as

The amplitude set is H_BZi＝{h_BZ1，h_BZ2，…，h_BZnThe corresponding abscissa angular frequency ω ═ ω₁ ω₂ … ω_nThe method is not changed;

2) determining the number of clusters K for each frequency response function data set₀And an initial clustering center C₀The method comprises the following steps:

2-1) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering number K₀

2-1-1) computing the set H_BZiExtreme difference Ra of_O＝max(H_BZi)-min(H_BZi)；

2-1-2) computing the set H_BZiArithmetic mean of

2-1-3) computing the set H_BZiResidual error of

Determining a set of residual absolute values as U_BZn＝{μ_BZ1，μ_BZ2，…，μ_BZn}；

2-1-4) computing the set H_BZiResidual mean of

2-1-5) calculating the number of initial classifications K₀Adding 1 to the integer of the residual error of the polar difference division, i.e.

2-2) set H of normalized amplitudes H (omega)_BZiDetermining an initial clustering center C₀；

2-2-1) A set H_BZiN samples divided into K₀Class i, i.e. H_BZj＝{A₁，A₂，…A_j，

And the corresponding abscissa angular frequency ω ═ ω₁ ω₂ … ω_n}；

2-2-2) Each subset A₁，A₂，…A_j，

The number of samples in is

2-2-3) dividing the subset if

Then h is_BZj∈A_j，

2-2-4) calculating the center of the initial cluster, the value of the cluster center being the mean of each class subset, i.e.

3) Defining iteration index, determining iteration formula, and repeatedly iterating and clustering center C_nAnd the number of clusters K_nUntil the index is optimal, the specific steps are as follows:

3-1) defining an iteration index, K₀Number of classes

3-1-1) defining an iteration index

Where Sd is the internal standard deviation of class

Rn is like internal pole difference Rn ═ max (A)_j)-min(A_j)，

Is the difference in the mean values between the classes,

is the arithmetic mean value of the interior of the class,

the mean value of the minimum value of the difference between the intra-class element and the mean value between the classes is

3-1-2) calculating various internal slopesSum of absolute values of rates

Wherein the slope inside each subclass is k, and setting the linear function inside the subclass by minimum multiplication

Then

The difference between the minimum and maximum values of the mean value of the class RN ═ max (A)_j)-min(A_j)；

3-2) determining an iterative equation and an iterative algorithm

3-2-1) iterative equation as ordinate H_BZiDistance between, i.e. Yd ═ h_BZn-C₀|；

3-2-2) calculating each amplitude h in turn_BZnTo respectively K₀The distance Yd of the initial clustering center is the h corresponding to the minimum Yd_BZnAttributing to the initial class corresponding to the corresponding initial clustering center, and repeating the steps until each amplitude value h is assigned_BZnAfter all the classes are classified, determining the clustering center of the new class according to the new number set class, calculating indexes of the new class, comparing the indexes of the new class, and stopping iteration until the minimum index is found;

3-2-3) pairs of other S within the data set T_mRepeating the step 1-2-1) and the step 3-2-2) until the index of each number set is minimum, and determining a clustering center, a clustering number and a point set of each class;

3-2-4) mapping to original amplitude according to the abscissa corresponding to the optimal class to form a new set H (omega)^{fin ly}＝{B₁ B₂ … B_K0}＝{(H₁ ... H_d) (H_d ... H_e) ... (H_g ... H_n)}，d＜e＜g＜n

4) Defining a weight coefficient, and calculating the average value of the frequency band selected by the frequency response function quality line, wherein the specific steps are as follows:

4-1) calculating the S_mSmoothing coefficient ph of frequency response function number set_all＝Arm_all×k_all×sd_allWherein

k_all、sd_allAre respectively S_mArithmetic mean, slope, standard deviation of the frequency response function number set;

4-2) calculation of removal of S_mCalculating the amplitude of the J-th class in the frequency response function number set, and calculating the arithmetic mean value of the remaining K-1 classes

Slope k_K-1And standard deviation sd_K-1Smoothing coefficient of (d):

ph_K-1＝Arm_K-1×k_K-1×sd_K-1

4-3) defining the weight as according to steps 4-1), 4-2)

4-4) calculating S_mThe weight coefficients of K classes in the frequency response function number set are normalized,

5) calculating an average value: calculating Average value B according to the class formed by the original amplitude value H (omega) corresponding to the class of each frequency response function and the weight corresponding to the class after standardization₁δ₁ ^gy+B₂δ₂ ^gy...B_K0δ_r ^gy。

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