CN113589686B - GSA-IFCM-based unit cycle time sequence self-adaptive extraction method - Google Patents
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Abstract
本发明公开了基于GSA‑IFCM的单位周期时间序列自适应提取方法,包括步骤S1.在舰炮供输弹机构运转过程中,利用传感器首先获得舰炮供输弹机构的原始振动信号;S2.利用GSA‑IFCM算法对原始振动信号包络线的极大值进行聚类处理,提取原始振动信号中的单位周期时间序列的中心点;S3.获取原始振动信号中单位周期时间序列的中心点后,利用t‑MSV对中心点进行处理,向中心点前后方向获取单位周期时间序列的长度,通过设定阈值寻找最终波底以确定单位周期时间序列的起止位置,进而提取到单位周期时间序列;经验证,本方法能够有效克服数据噪声的影响,提高聚类结果的准确性,精确提取单位周期时间序列。
The present invention discloses an adaptive extraction method of unit period time series based on GSA-IFCM, which includes steps S1. During the operation of the naval gun bomb supplying mechanism, the sensor is used to first obtain the original vibration signal of the naval gun bomb supplying mechanism; S2. Use the GSA‑IFCM algorithm to cluster the maximum values of the envelope of the original vibration signal and extract the center point of the unit period time series in the original vibration signal; S3. After obtaining the center point of the unit period time series in the original vibration signal , use t‑MSV to process the center point, obtain the length of the unit period time series in the forward and backward direction of the center point, find the final wave bottom by setting a threshold to determine the start and end positions of the unit period time series, and then extract the unit period time series; It has been verified that this method can effectively overcome the influence of data noise, improve the accuracy of clustering results, and accurately extract unit period time series.
Description
技术领域Technical field
本发明涉及机械装备健康状态检测方法技术领域,具体涉及基于GSA-IFCM的单位周期时间序列自适应提取方法。The invention relates to the technical field of mechanical equipment health status detection methods, and specifically relates to an adaptive extraction method of unit period time series based on GSA-IFCM.
背景技术Background technique
中大口径舰炮供输弹机构在运转过程中通常作循环往复式运动,过程复杂且常伴有剧烈的冲击、摩擦和振动,其工作健康状态一直是制约供输弹机构性能和实用性的障碍,也成为机械装备状态监测与故障诊断领域的焦点;对其健康状态进行评估的前提是状态监测数据的采集,在严格的数学意义上监测数据是非周期、非平稳的随机信号,但是从宏观角度考虑工作原理及过程,在连续运行时,监测数据表现出明显的近似周期性,因此,供输弹机构的振动信号是典型的近似周期信号,近似周期信号是一种特殊的近似周期时间序列;The ammunition supply and delivery mechanism of medium and large-caliber naval guns usually performs cyclic reciprocating motion during operation. The process is complex and often accompanied by severe impact, friction and vibration. Its working health has always restricted the performance and practicality of the ammunition supply and delivery mechanism. Obstacles have also become the focus in the field of mechanical equipment condition monitoring and fault diagnosis; the prerequisite for assessing its health status is the collection of condition monitoring data. In a strict mathematical sense, monitoring data are non-periodic and non-stationary random signals, but from a macro perspective Considering the working principle and process, during continuous operation, the monitoring data shows obvious approximate periodicity. Therefore, the vibration signal of the bomb supply mechanism is a typical approximate periodic signal, and the approximate periodic signal is a special approximate periodic time series. ;
目前,对于近似周期时间序列的周期估计和提取问题,吴述金等首次分析了近似周期时间序列,给出了详细的数学定义,并提出了运用矩估计法对时间序列的周期进行估计;洪淑慧等采用拟合估计法对已有时间序列数据提取能够反映时间变换的二维数据,更加真实的反映了近似周期时间序列的周期性变化;以上方法对于变化范围小的近似周期时间序列效果较好,而供输弹机构循环往复、工作节拍不一且瞬间冲击较大,其信号振幅瞬变且变化范围大,导致以上方法无法有效提取单位周期时间序列;陈仁祥等运用相位差频谱校正—互相关法对谐波减速器的近似周期振动信号分割构造出单位周期数据样本以准确刻画减速器的运行状态信息,但是该方法只针对包络线近似为正弦曲线的振动信号,而由于近似周期冲击信号无法通过计算有效构建包络线;Currently, regarding the problem of period estimation and extraction of approximate periodic time series, Wu Shujin et al. analyzed the approximate periodic time series for the first time, gave a detailed mathematical definition, and proposed the use of moment estimation method to estimate the period of the time series; Hong Shuhui et al. used The fitting estimation method extracts two-dimensional data that can reflect time transformation from existing time series data, and more truly reflects the periodic changes of approximately periodic time series; the above method is better for approximate periodic time series with a small change range, and The ammunition feeding mechanism reciprocates, the working rhythm is inconsistent, and the instantaneous impact is large. The signal amplitude is transient and has a large change range, which makes the above method unable to effectively extract the unit period time series. Chen Renxiang et al. used the phase difference spectrum correction-cross-correlation method to The approximately periodic vibration signal of the harmonic reducer is segmented to construct unit period data samples to accurately depict the operating status information of the reducer. However, this method only targets vibration signals whose envelope is approximately a sinusoidal curve, and the approximately periodic impact signal cannot pass through Compute and efficiently construct envelopes;
且目前对于近似周期时间序列提取的自适应提取方法研究甚少,多数还需要人工截取单位周期时间序列,依赖于专家经验且效率低下。At present, there is little research on adaptive extraction methods for approximate periodic time series extraction. Most of them require manual interception of unit period time series, which relies on expert experience and is inefficient.
发明内容Contents of the invention
针对上述存在的问题,本发明旨在提供基于GSA-IFCM的单位周期时间序列自适应提取方法,在中大口径舰炮供输弹机构在运转过程中,本方法首先通过改进的模糊C-均值聚类算法,将其与遗传模拟退火算法相结合,提取近似周期信号极大值的聚类中心;然后运用时间窗能量法,提取单位周期时间序列,本方法能够有效克服数据噪声的影响,提高聚类结果的准确性,精确提取单位周期时间序列。In view of the above existing problems, the present invention aims to provide an adaptive extraction method of unit period time series based on GSA-IFCM. During the operation of the medium and large caliber naval gun supply and delivery mechanism, this method first uses improved fuzzy C-means The clustering algorithm is combined with the genetic simulated annealing algorithm to extract the cluster center of the maximum value of the approximate periodic signal; then the time window energy method is used to extract the unit period time series. This method can effectively overcome the influence of data noise and improve Accuracy of clustering results, accurate extraction of unit period time series.
为了实现上述目的,本发明所采用的技术方案如下:In order to achieve the above objects, the technical solutions adopted by the present invention are as follows:
基于GSA-IFCM的单位周期时间序列自适应提取方法,包括步骤Adaptive extraction method of unit period time series based on GSA-IFCM, including steps
S1.在舰炮供输弹机构运转过程中,利用传感器首先获得舰炮供输弹机构的原始振动信号;S1. During the operation of the naval gun's bomb supply and transport mechanism, the sensor is first used to obtain the original vibration signal of the naval gun's bomb supply and transport mechanism;
S2.利用GSA-IFCM算法对原始振动信号包络线的极大值进行聚类处理,提取原始振动信号中的单位周期时间序列的中心点;S2. Use the GSA-IFCM algorithm to perform clustering processing on the maximum values of the envelope of the original vibration signal, and extract the center point of the unit period time series in the original vibration signal;
S3.获取原始振动信号中单位周期时间序列的中心点后,利用t-MSV对中心点进行处理,向中心点前后方向获取单位周期时间序列的长度,通过设定阈值寻找最终波底以确定单位周期时间序列的起止位置,进而提取到单位周期时间序列。S3. After obtaining the center point of the unit period time series in the original vibration signal, use t-MSV to process the center point, obtain the length of the unit period time series in the forward and backward directions of the center point, and find the final wave bottom by setting the threshold to determine the unit. The starting and ending positions of the periodic time series are then extracted to the unit period time series.
优选的,步骤S2所述的单位周期时间序列中心点的获取过程包括:Preferably, the process of obtaining the unit period time series center point in step S2 includes:
S201.利用MATLAB软件中envelope函数计算原始振动信号的有效包络线;S201. Use the envelope function in MATLAB software to calculate the effective envelope of the original vibration signal;
S202.提取振动信号包络线的极大值,进而求得原始振动信号的有效极大值点;S202. Extract the maximum value of the vibration signal envelope, and then obtain the effective maximum value point of the original vibration signal;
S203.以极大值点的横纵坐标作为输入向量,同时设定类别个数,通过GSA-IFCM算法迭代计算并不断修正聚类中心,直至得到最优聚类中心,从而得到单位周期时间序列中心点。S203. Use the horizontal and vertical coordinates of the maximum value point as the input vector, and set the number of categories at the same time. Iteratively calculate and continuously correct the clustering center through the GSA-IFCM algorithm until the optimal clustering center is obtained, thereby obtaining the unit period time series. center point.
优选的,步骤S203所述的单位周期时间序列中心点的获得过程包括:Preferably, the process of obtaining the unit period time series center point in step S203 includes:
S2031.装定聚类数目c和长度为n的时间样本数据X={x1,x2,…,xn},{A1,A2,…,Ac}表示此时间序列的c个类别;S2031. Set the number of clusters c and the time sample data of length n category;
S2032.初始化遗传退火算法控制参数:种群个体大小sizepop,最大进化次数MAXGEN,交叉概率P,变异概率Pm,退火初始温度T0,温度冷却系数k,终止温度Tend;S2032. Initialize the genetic annealing algorithm control parameters: population size sizepop, maximum number of evolutions MAXGEN, crossover probability P, mutation probability P m , annealing initial temperature T 0 , temperature cooling coefficient k, termination temperature T end ;
S2033.初始化加权参数b,设置加权参数步长bs;S2033. Initialize the weighting parameter b and set the weighting parameter step size b s ;
S2034.随机初始化c个聚类中心,并生成初始种群Po,对每个聚类中心用式(3)计算各样本的隶属度,以及每个个体的适应度值fi,其中i=1,2,…,sizepop;S2034. Randomly initialize c clustering centers and generate the initial population Po. For each clustering center, use equation (3) to calculate the membership degree of each sample and the fitness value fi of each individual, where i=1, 2,…,sizepop;
S2035.设循环计数变量gen=0;S2035. Set the loop count variable gen=0;
S2036.对群体Po实施选择、交叉和变异遗传操作,对新产生的个体用式(3)和式(4)计算c个聚类中心、各样本的隶属度、每一个体的适应度值fi',以及各聚类中心横坐标的方差值Var;若fi'>fi,则以新个体替换旧个体,否则,以概率P=exp((fi-fi')T)接受新个体,舍弃旧个体;S2036. Implement selection, crossover and mutation genetic operations on the population Po, and use formula (3) and formula (4) to calculate c cluster centers, the membership degree of each sample, and the fitness value f of each individual for the newly generated individuals. i ', and the variance value Var of the abscissa of each cluster center; if f i '>f i , replace the old individual with the new individual, otherwise, use probability P=exp(( fi -fi ')T) Accept the new individual and discard the old;
S2037.检测gen是否到达最大进化次数MAXGEN;若gen<MAXGEN,则gen=gen+1,转至S2038;否则,转至S2036;S2037. Check whether gen reaches the maximum number of evolutions MAXGEN; if gen<MAXGEN, then gen=gen+1, go to S2038; otherwise, go to S2036;
S2038.检测T是否到达终止温度Tend;若Ti<Tend,则转至S2039;否则,执行降温操作Ti+1=kTi,转至S2035;S2038. Detect whether T reaches the end temperature T end ; if Ti <T end , go to S2039; otherwise, perform the cooling operation Ti +1 = kT i , go to S2035;
S2039.检测方差值Var是否到达终止方差Varend;若Var<Varend,则算法成功结束,返回全局最优解;否则,加权参数增加步长b=b+bs,转至S2034。S2039. Detect whether the variance value Var reaches the termination variance Var end ; if Var < Var end , the algorithm ends successfully and returns the global optimal solution; otherwise, the weighted parameters increase the step size b=b+b s and go to S2034.
优选的,步骤S2034所述的聚类中心的计算过程包括:Preferably, the calculation process of the cluster center in step S2034 includes:
(1)适应度值采用排序的适应度分配函数求得:Fint V=ranking(Jb),Jb越小,个体的适应度就越高,目标函数Jb为:(1) The fitness value is obtained by using the ranking fitness distribution function: Fint V=ranking(J b ). The smaller J b is, the higher the individual fitness is. The objective function J b is:
其中,在式(1)中:dik是欧几里得距离,用来度量第i样本xi与第k类中心点的距离;m是样本的特征数;b是加权参数,取值范围是1≤b≤∞;uk(xi)是样本xi对于类Ak的隶属度(简写为uik),其计算公式为:Among them, in formula (1): d ik is the Euclidean distance, used to measure the distance between the i-th sample x i and the k-th category center point; m is the feature number of the sample; b is a weighting parameter, the value range is 1≤b≤∞; u k ( xi ) is the membership degree of sample x i to class A k (abbreviated as u ik ), and its calculation formula is:
其中,在式(2)中,一个样本对于各个聚类的隶属度值和为1,即Among them, in formula (2), the sum of the membership values of a sample for each cluster is 1, that is
(2)设Ik={i|2≤c≤n;dik=0},对于所有的i类,i∈Ik,uik=0;则更新聚类中心vij的迭代方程为:(2) Assume I k ={i|2≤c≤n;d ik =0}, for all i categories, i∈I k , u ik =0; then the iteration equation for updating the cluster center v ij is:
优选的,步骤S3所述的利用t-MSV对中心点进行处理,提取到单位周期时间序列的具体过程包括Preferably, the specific process of using t-MSV to process the center point and extracting the unit period time series in step S3 includes:
S301.设置宽度较小的时间窗,以时间窗宽为步长,以聚类中心为起点向前循环计算窗内时间序列的能量值,表征信号能量值的参数均方值计算公式为:S301. Set a time window with a smaller width, use the time window width as the step size, and use the cluster center as the starting point to circularly calculate the energy value of the time series in the window. The calculation formula of the parameter mean square value that represents the signal energy value is:
其中,在式(5)中:Xi(t)为长度为N的时间序列的能量值,Yx 2为均方根;当均方值单调递增时,说明信号的能量在升高,处于冲击震荡阶段,当均方值单调递减时,说明信号的能量在下降,当均方值稳定在某一个值后,说明信号的能量趋于平稳,因此每个波峰对应的波底是冲击信号起始与结束的位置; Among them, in equation (5): X i (t) is the energy value of a time series of length N, and Y In the shock and oscillation stage, when the mean square value decreases monotonically, it means that the energy of the signal is declining. When the mean square value stabilizes at a certain value, it means that the energy of the signal tends to be stable. Therefore, the wave bottom corresponding to each wave peak is the starting point of the impact signal. start and end positions;
S302.计算时间窗能量曲线图波底对应的时间,设定相应阈值,若时间窗能量在阈值内未能检测到能量上升,则判定此波底为最终波底,此波底对应的时间即为周期时间序列的最优起始位置,其计算公式为:S302. Calculate the time corresponding to the wave bottom of the time window energy curve, and set the corresponding threshold. If the energy in the time window fails to detect an increase in energy within the threshold, it is determined that this wave bottom is the final wave bottom, and the time corresponding to this wave bottom is is the optimal starting position of the periodic time series, and its calculation formula is:
xf=max(xm)+xh (6)x f =max(x m )+x h (6)
s.t.f(x+ε)′≤0 (7)s.t.f(x+ε)′≤0 (7)
其中,在式(6)和式(7)中,xm为信号波峰对应的时间,xh为该波的波宽,xf为前方向最终波底对应的时间;Among them, in equations (6) and (7), x m is the time corresponding to the signal peak, x h is the wave width of the wave, and x f is the time corresponding to the final wave bottom in the forward direction;
S303.向后获取样本长度同步骤S302,获得后方向最终波底对应的时间,确定单位周期序列的起止位置,进而提取单位周期起止序列。S303. Obtaining the sample length backward is the same as step S302, obtaining the time corresponding to the final wave bottom in the backward direction, determining the start and end positions of the unit period sequence, and then extracting the start and end sequence of the unit period.
本发明的有益效果是:本发明公开了基于GSA-IFCM的单位周期时间序列自适应提取方法,与现有技术相比,本发明的改进之处在于:The beneficial effects of the present invention are: the present invention discloses an adaptive extraction method of unit period time series based on GSA-IFCM. Compared with the existing technology, the improvements of the present invention are:
(1)针对表征供输弹机构往复运动过程中近似周期信号的单位周期时间序列难以提取的问题,本发明提出了一种基于GSA-IFCM的单位周期时间序列自适应提取方法,本方法首先通过改进的模糊C-均值聚类算法,将其与遗传模拟退火算法相结合,提取近似周期信号极大值的聚类中心;然后运用时间窗能量法,提取单位周期时间序列;(1) Aiming at the problem that it is difficult to extract the unit period time series representing the approximately periodic signal during the reciprocating motion of the bomb feeding mechanism, the present invention proposes an adaptive extraction method of unit period time series based on GSA-IFCM. This method first adopts The improved fuzzy C-means clustering algorithm is combined with the genetic simulated annealing algorithm to extract the cluster center of the maximum value of the approximate periodic signal; then the time window energy method is used to extract the unit period time series;
(2)本方法利用GSA与IFCM相结合的方法,可有效克服数据噪声的影响,聚类结果具有更强的稳定性和更优的目标函数值,对于随机分布且包含噪声的数据聚类有明显的优越性;(2) This method uses the combination of GSA and IFCM to effectively overcome the impact of data noise. The clustering results have stronger stability and better objective function values. It is effective for clustering randomly distributed data containing noise. Obvious superiority;
(3)本方法通过时间窗求取信号的时域特征参数均方值可表征信号的能量趋势,相比于其他时域特征参数可有效展现出原始信号的振动规律,能够准确提取出单位周期时间序列,具有能够有效克服数据噪声的影响,提高聚类结果的准确性,精确提取单位周期时间序列的优点。(3) This method uses the time window to obtain the mean square value of the time domain characteristic parameters of the signal, which can represent the energy trend of the signal. Compared with other time domain characteristic parameters, it can effectively show the vibration pattern of the original signal and can accurately extract the unit period. Time series has the advantage of being able to effectively overcome the influence of data noise, improve the accuracy of clustering results, and accurately extract unit period time series.
附图说明Description of the drawings
图1为本发明基于GSA-IFCM的单位周期时间序列自适应提取方法的算法流程图。Figure 1 is an algorithm flow chart of the adaptive extraction method of unit period time series based on GSA-IFCM of the present invention.
图2为本发明GSA-IFCM算法的算法流程图。Figure 2 is an algorithm flow chart of the GSA-IFCM algorithm of the present invention.
图3为本发明t-MSV算法的算法流程图。Figure 3 is an algorithm flow chart of the t-MSV algorithm of the present invention.
图4为本发明实施例1供输弹机构试验台架图。Figure 4 is a diagram of the test bench for the bomb feeding mechanism according to Embodiment 1 of the present invention.
图5为本发明实施例1加速度信号的时域波形图。Figure 5 is a time domain waveform diagram of an acceleration signal in Embodiment 1 of the present invention.
图6为本发明实施例1原始信号和包络线图。Figure 6 is the original signal and envelope diagram of Embodiment 1 of the present invention.
图7为本发明实施例1原始信号和极大值点图。Figure 7 is a diagram of the original signal and the maximum value point in Embodiment 1 of the present invention.
图8为本发明实施例1极大值点和聚类中心图。Figure 8 is a diagram of maximum value points and cluster centers in Embodiment 1 of the present invention.
图9为本发明实施例1原始信号加窗图。Figure 9 is a windowed view of the original signal in Embodiment 1 of the present invention.
图10为本发明实施例1能量曲线图。Figure 10 is an energy curve diagram of Embodiment 1 of the present invention.
图11为本发明实施例1提取到的单位周期时间序列。Figure 11 is the unit period time series extracted in Embodiment 1 of the present invention.
图12为本发明实施例1标准的FCM算法、基于GSA的FCM算法以及基于GSA-IFCM算法状态下时间距离曲线图。Figure 12 is a time distance curve diagram of the standard FCM algorithm, the GSA-based FCM algorithm and the GSA-IFCM algorithm in Embodiment 1 of the present invention.
图13为本发明实施例1时域特征时间窗曲线图。Figure 13 is a time domain characteristic time window curve diagram of Embodiment 1 of the present invention.
其中:在图12中,图(a)表示舰炮供输弹机构正常状态下标准的FCM算法、基于GSA的FCM算法以及基于GSA-IFCM算法状态下时间距离曲线图;图(b)表示表示舰炮供输弹机构产生滚轮裂纹下标准的FCM算法、基于GSA的FCM算法以及基于GSA-IFCM算法状态下时间距离曲线图;图(c)表示表示舰炮供输弹机构产生滑板磨损时标准的FCM算法、基于GSA的FCM算法以及基于GSA-IFCM算法状态下时间距离曲线图。Among them: in Figure 12, Figure (a) shows the standard FCM algorithm, GSA-based FCM algorithm and GSA-IFCM algorithm-based time distance curve under normal conditions; Figure (b) shows The standard FCM algorithm, GSA-based FCM algorithm and GSA-IFCM algorithm-based time distance curve when roller cracks occur in the naval gun bomb supply mechanism; Figure (c) shows the standard when the naval gun bomb supply mechanism produces slide wear. FCM algorithm, GSA-based FCM algorithm and time distance curve chart based on GSA-IFCM algorithm.
具体实施方式Detailed ways
为了使本领域的普通技术人员能更好的理解本发明的技术方案,下面结合附图和实施例对本发明的技术方案做进一步的描述。In order to enable those of ordinary skill in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention are further described below in conjunction with the accompanying drawings and examples.
参照附图1-3所示的基于GSA-IFCM的单位周期时间序列自适应提取方法,其特征在于:包括步骤Referring to the adaptive extraction method of unit period time series based on GSA-IFCM shown in Figures 1-3, it is characterized by: including steps
S1.在舰炮供输弹机构运转过程中,在舰炮供输弹机构上安装传感器,利用传感器首先获得舰炮供输弹机构的原始振动信号;S1. During the operation of the naval gun bomb supply and transport mechanism, install a sensor on the naval gun bomb supply and transport mechanism, and use the sensor to first obtain the original vibration signal of the naval gun bomb supply and transport mechanism;
S2.利用GSA-IFCM算法对原始振动信号包络线的极大值进行聚类处理,提取原始振动信号中的单位周期时间序列的中心点,其具体包括:S2. Use the GSA-IFCM algorithm to perform clustering processing on the maximum values of the envelope of the original vibration signal, and extract the center point of the unit period time series in the original vibration signal, which specifically includes:
S201.在MATLAB软件中,利用MATLAB软件中envelope函数计算原始振动信号的有效包络线;S201. In the MATLAB software, use the envelope function in the MATLAB software to calculate the effective envelope of the original vibration signal;
S202.提取振动信号包络线的极大值,进而求得原始振动信号的有效极大值点;S202. Extract the maximum value of the vibration signal envelope, and then obtain the effective maximum value point of the original vibration signal;
S203.以极大值点的横纵坐标作为输入向量,同时设定类别个数,通过GSA-IFCM算法迭代计算并不断修正聚类中心,直至得到最优聚类中心,从而得到单位周期时间序列中心点,由上述步骤可以看出,GSA-IFCM算法是获取聚类中心点的关键,其流程图如图2所示,其包括步骤:S203. Use the horizontal and vertical coordinates of the maximum value point as the input vector, and set the number of categories at the same time. Iteratively calculate and continuously correct the clustering center through the GSA-IFCM algorithm until the optimal clustering center is obtained, thereby obtaining the unit period time series. Center point, as can be seen from the above steps, the GSA-IFCM algorithm is the key to obtaining the clustering center point. Its flow chart is shown in Figure 2, which includes the steps:
S2031.装定聚类数目c和长度为n的时间样本数据X={x1,x2,…,xn},{A1,A2,…,Ac}表示此时间序列的c个类别;S2031. Set the number of clusters c and the time sample data of length n category;
S2032.初始化遗传退火算法控制参数:种群个体大小sizepop,最大进化次数MAXGEN,交叉概率P,变异概率Pm,退火初始温度T0,温度冷却系数k,终止温度Tend;S2032. Initialize the genetic annealing algorithm control parameters: population size sizepop, maximum number of evolutions MAXGEN, crossover probability P, mutation probability P m , annealing initial temperature T 0 , temperature cooling coefficient k, termination temperature T end ;
S2033.初始化加权参数b,设置加权参数步长bs;S2033. Initialize the weighting parameter b and set the weighting parameter step size b s ;
S2034.随机初始化c个聚类中心,并生成初始种群Po,对每个聚类中心用式(3)计算各样本的隶属度,以及每个个体的适应度值fi,其中i=1,2,…,sizepop;其具体过程包括:S2034. Randomly initialize c clustering centers and generate the initial population Po. For each clustering center, use equation (3) to calculate the membership degree of each sample and the fitness value fi of each individual, where i=1, 2,…,sizepop; its specific process includes:
(1)适应度值采用排序的适应度分配函数求得:FintV=ranking(Jb),Jb越小,个体的适应度就越高,目标函数Jb为:(1) The fitness value is obtained by using the ranking fitness distribution function: FintV=ranking(J b ). The smaller J b is, the higher the individual fitness is. The objective function J b is:
其中,在式(1)中:dik是欧几里得距离,用来度量第i样本xi与第k类中心点的距离;m是样本的特征数;b是加权参数,取值范围是1≤b≤∞;uk(xi)是样本xi对于类Ak的隶属度(简写为uik),其计算公式为:Among them, in formula (1): d ik is the Euclidean distance, used to measure the distance between the i-th sample x i and the k-th category center point; m is the feature number of the sample; b is a weighting parameter, the value range is 1≤b≤∞; u k ( xi ) is the membership degree of sample x i to class A k (abbreviated as u ik ), and its calculation formula is:
其中,在式(2)中,一个样本对于各个聚类的隶属度值和为1,即Among them, in formula (2), the sum of the membership values of a sample for each cluster is 1, that is
设Ik={i|2≤c≤n;dik=0},对于所有的i类,i∈Ik,uik=0;则更新聚类中心vij的迭代方程为:Assume I k ={i|2≤c≤n;d ik =0}, for all i categories, i∈I k , u ik =0; then the iterative equation for updating the cluster center v ij is:
S2035.设循环计数变量gen=0;S2035. Set the loop count variable gen=0;
S2036.对群体Po实施选择、交叉和变异等遗传操作,对新产生的个体用式(3)和式(4)计算c个聚类中心、各样本的隶属度、每一个体的适应度值fi',以及各聚类中心横坐标的方差值Var;若fi'>fi,则以新个体替换旧个体,否则,以概率P=exp((fi-fi')T)接受新个体,舍弃旧个体;S2036. Perform genetic operations such as selection, crossover, and mutation on the population Po, and use equation (3) and equation (4) to calculate c cluster centers, the membership degree of each sample, and the fitness value of each individual for the newly generated individuals. f i ', and the variance value Var of the abscissa of each cluster center; if f i '>f i , replace the old individual with the new individual, otherwise, use the probability P=exp(( fi -fi ')T ) accept new individuals and abandon old ones;
S2037.检测gen是否到达最大进化次数MAXGEN;若gen<MAXGEN,则gen=gen+1,转至S2038;否则,转至S2036;S2037. Check whether gen reaches the maximum number of evolutions MAXGEN; if gen<MAXGEN, then gen=gen+1, go to S2038; otherwise, go to S2036;
S2038.检测T是否到达终止温度Tend;若Ti<Tend,则转至S2039;否则,执行降温操作Ti+1=kTi,转至S2035;S2038. Detect whether T reaches the end temperature T end ; if Ti <T end , go to S2039; otherwise, perform the cooling operation Ti +1 = kT i , go to S2035;
S2039.检测方差值Var是否到达终止方差Varend;若Var<Varend,则算法成功结束,返回全局最优解;否则,加权参数增加步长b=b+bs,转至S2034;S2039. Check whether the variance value Var reaches the end variance Var end ; if Var < Var end , the algorithm ends successfully and returns the global optimal solution; otherwise, the weighted parameter increases by the step size b=b+b s and goes to S2034;
S3.获取原始振动信号中的近似周期信号极大值的聚类中心后,利用t-MSV对中心点进行处理,向中心点前后方向获取单位周期时间序列的长度,通过设定阈值寻找最终波底以确定单位周期时间序列的起止位置,进而提取到单位周期时间序列,其具体过程包括:S3. After obtaining the clustering center of the maximum value of the approximate periodic signal in the original vibration signal, use t-MSV to process the center point, obtain the length of the unit period time series in the forward and backward direction of the center point, and find the final wave by setting the threshold The bottom is used to determine the starting and ending positions of the unit period time series, and then the unit period time series is extracted. The specific process includes:
S301.设置宽度较小的时间窗,以时间窗宽为步长,以聚类中心为起点向前循环计算窗内时间序列的能量值,表征信号能量值的参数均方值计算公式为:S301. Set a time window with a smaller width, use the time window width as the step size, and use the cluster center as the starting point to circularly calculate the energy value of the time series in the window. The calculation formula of the parameter mean square value that represents the signal energy value is:
其中,在式(5)中:Xi(t)为长度为N的时间序列的能量值,Yx 2为均方根;当均方值单调递增时,说明信号的能量在升高,处于冲击震荡阶段,当均方值单调递减时,说明信号的能量在下降,当均方值稳定在某一个值后,说明信号的能量趋于平稳,因此每个波峰对应的波底是冲击信号起始与结束的位置; Among them, in equation (5): X i (t) is the energy value of a time series of length N, and Y In the shock and oscillation stage, when the mean square value decreases monotonically, it means that the energy of the signal is declining. When the mean square value stabilizes at a certain value, it means that the energy of the signal tends to be stable. Therefore, the wave bottom corresponding to each wave peak is the starting point of the impact signal. start and end positions;
S302.计算时间窗能量曲线图波底对应的时间,设定相应阈值,若时间窗能量在阈值内未能检测到能量上升,则判定此波底为最终波底,此波底对应的时间即为周期时间序列的最优起始位置,其计算公式为:S302. Calculate the time corresponding to the wave bottom of the time window energy curve, and set the corresponding threshold. If the energy in the time window fails to detect an increase in energy within the threshold, it is determined that this wave bottom is the final wave bottom, and the time corresponding to this wave bottom is is the optimal starting position of the periodic time series, and its calculation formula is:
xf=max(xm)+xh (6)x f =max(x m )+x h (6)
s.t.f(x+ε)′≤0 (7)s.t.f(x+ε)′≤0 (7)
其中,在式(6)和式(7)中,xm为信号波峰对应的时间,xh为该波的波宽,xf为前方向最终波底对应的时间;Among them, in equations (6) and (7), x m is the time corresponding to the signal peak, x h is the wave width of the wave, and x f is the time corresponding to the final wave bottom in the forward direction;
S303.向后获取样本长度同步骤S302,获得聚类中心前后方向样本长度,即准确提取单位周期时间序列,计算公式如下:S303. Obtaining the sample length backward is the same as step S302. Obtain the sample length in the forward and backward direction of the cluster center, that is, accurately extract the unit period time series. The calculation formula is as follows:
x=xf+xb (8)x=x f +x b (8)
其中,在式(8)中,xb为后方向最终波底对应的时间,x为单位周期时间序列。Among them, in equation (8), x b is the time corresponding to the final wave bottom in the backward direction, and x is the unit period time series.
实施例1:如图4-13所示:本发明所述基于GSA-IFCM的单位周期时间序列自适应提取方法的算法还包括步骤Embodiment 1: As shown in Figure 4-13: the algorithm of the unit period time series adaptive extraction method based on GSA-IFCM of the present invention also includes steps
S4.试验及结果分析过程S4. Test and result analysis process
S401.试验介绍S401. Test introduction
本试验数据采集自某型供输弹机构试验台架,如图4所示;This test data is collected from a certain type of ammunition supply and delivery mechanism test bench, as shown in Figure 4;
试验在台架装置的摆动机滑板、位于滚轮上方的压板机附近布置了6个振动加速度传感器,传感器类型为ICP加速度传感器,采样频率为10kHz,采用32通道的LMS信号采集系统;分别采集正常工作、滚轮裂纹和滑板磨损三种状态下共24组振动加速度信号,每组信号包含20个循环动作,三种状态振动加速度信号的时域波形如图5所示;In the test, 6 vibration acceleration sensors were arranged near the swinging machine slide of the bench device and the plate press located above the rollers. The sensor type was an ICP acceleration sensor, the sampling frequency was 10kHz, and a 32-channel LMS signal acquisition system was used. The normal operation of the samples was collected separately. There are a total of 24 sets of vibration acceleration signals in three states: roller crack and skateboard wear. Each set of signals contains 20 cyclic actions. The time domain waveforms of the vibration acceleration signals in the three states are shown in Figure 5;
由图5可知,供输弹机构测得的振动加速度信号有较大的冲击振动,其中滚轮裂纹状态下冲击最为显著;同时,仅从原始振动加速度信号来看,每一个单位周期时间序列的周期长度和最大幅值均不为固定值,且相邻周期的间隔均不相等,所以无法使用一个固定周期循环提取单位周期时间序列;It can be seen from Figure 5 that the vibration acceleration signal measured by the bomb delivery mechanism has large impact vibration, among which the impact is most significant when the roller is cracked. At the same time, only from the original vibration acceleration signal, the period of each unit period time series Neither the length nor the maximum amplitude are fixed values, and the intervals between adjacent periods are not equal, so a fixed period cycle cannot be used to extract the unit period time series;
S402.试验台架振动信号自适应提取方法S402. Adaptive extraction method of test bench vibration signal
将本发明提出的提取方法应用于上述试验数据,选取正常工作状态下的振动信号,具体步骤如下:The extraction method proposed by the present invention is applied to the above test data to select the vibration signal under normal working conditions. The specific steps are as follows:
(1)计算原始振动信号的有效包络线如图6所示,图中深黑色曲线为原始振动信号,浅黑色为包络线;(1) Calculate the effective envelope of the original vibration signal as shown in Figure 6. The dark black curve in the figure is the original vibration signal and the light black curve is the envelope;
(2)提取包络线极大值,进而求得原始信号的有效极大值点,如图7所示,图中包络线的极大值点明显小于原始信号的极大值,以此来提高计算速度;(2) Extract the maximum value of the envelope, and then find the effective maximum point of the original signal. As shown in Figure 7, the maximum value point of the envelope in the figure is obviously smaller than the maximum value of the original signal. In this way to improve calculation speed;
(3)利用GSA-IFCM算法,以极大值点的横纵坐标作为输入向量,同时设定类别个数,通过不断迭代计算获得极大值点的最优聚类中心,以此来获取单位周期时间序列中心点,如图8所示;(3) Use the GSA-IFCM algorithm, take the horizontal and vertical coordinates of the maximum value points as the input vector, and set the number of categories at the same time, and obtain the optimal clustering center of the maximum value points through continuous iterative calculations to obtain the unit The center point of the periodic time series, as shown in Figure 8;
(4)通过不断试验,选取窗宽为0.01s的时间窗,由聚类中心向前循环累加时间窗,如图9所示;(4) Through continuous testing, select a time window with a window width of 0.01s, and cycle forward from the clustering center to accumulate time windows, as shown in Figure 9;
(5)通过对比采用其他时域特征方差和峰值,选取均方值以表征时间窗内时间序列的能量,获得能量曲线图,如图10所示,图中包含3个波峰,与中心点左侧存在三次冲击相对应;(5) By comparing the variance and peak value of other time domain features, the mean square value is selected to characterize the energy of the time series within the time window, and the energy curve is obtained, as shown in Figure 10. The graph contains 3 peaks, which are to the left of the center point. There are three impacts corresponding to the side;
(6)设定时间窗阈值k=100,若时间窗能量在阈值内未能检测到能量上升,则计算时间窗能量曲线图最后一个波峰波底对应的时间(如图10圈所示),即为单位周期时间序列的起始位置;(6) Set the time window threshold k = 100. If the time window energy cannot detect an increase in energy within the threshold, calculate the time corresponding to the last peak and bottom of the time window energy curve (as shown in the 10th circle in the figure). That is, the starting position of the unit period time series;
按照上述步骤以聚类中心为起点向右计算单位周期时间序列的结束位置,即可提取整个单位周期时间序列,如图11所示;Follow the above steps to calculate the end position of the unit period time series to the right starting from the cluster center, and then extract the entire unit period time series, as shown in Figure 11;
试验中一个完整的往复运动时间约为6.8s,每个波峰分别对应动作为:复进—起摆—回摆—关闩,采用本方法可以有效实现机构运动状态的准确复现。In the test, a complete reciprocating motion takes about 6.8 seconds, and each wave peak corresponds to the following actions: re-advance - starting swing - back swing - closing latch. This method can effectively achieve accurate reproduction of the mechanism's motion state.
S403.试验结果分析S403. Test result analysis
(1)每项状态下采集到的近似周期振动信号利用本发明方法均可有效提取出单位周期时间序列;试验中SA算法设置冷却系数q=0.8,初始温度T0=100,终止温度Tend=1;GA算法的相关初始参数如表1所示;(1) The unit period time series can be effectively extracted from the approximately periodic vibration signals collected in each state using the method of the present invention; in the experiment, the SA algorithm set the cooling coefficient q = 0.8, the initial temperature T 0 = 100, and the end temperature T end =1; The relevant initial parameters of the GA algorithm are shown in Table 1;
表1:GA算法相关参数表Table 1: GA algorithm related parameter table
为验证本发明所述方法的有效性,分别通过使用标准的FCM算法、基于GSA的FCM算法以及基于GSA的IFCM算法分别对三种健康状态下的1组近似周期振动信号极大值进行聚类,每种状态下振动信号聚类中心与单位时间序列中心点的时间距离曲线图如图12所示;若距离小于单位时间序列的一半(图12浅黑色直线),则认为该聚类结果正确;In order to verify the effectiveness of the method described in the present invention, a group of approximate periodic vibration signal maximum values in three health states were clustered by using the standard FCM algorithm, the GSA-based FCM algorithm and the GSA-based IFCM algorithm respectively. , the time distance curve between the vibration signal cluster center and the center point of the unit time series in each state is shown in Figure 12; if the distance is less than half of the unit time series (light black straight line in Figure 12), the clustering result is considered correct ;
观察图12可知,采用标准的FCM算法对大规模数据进行聚类处理,由于其对初始中心选取较为敏感,更加容易收敛到局部最优解,不能有效的对原始信号的极大值进行均匀聚类;利用基于GSA的FCM算法对三种振动信号极大值进行聚类,虽然聚类中心近似均匀分布,但由于加权参数取值模糊,仍有陷入局部极小点的可能性,例如图11中有2个聚类中心点异常;而运用GSA-IFCM算法可有效克服数据噪声的影响,准确提取各周期时间序列的中心点,出现过早收敛的可能性极小,所获得的聚类结果具有更强的稳定性和更优的目标函数值,对于随机分布的数据聚类有明显的优越性;Observing Figure 12, we can see that the standard FCM algorithm is used to cluster large-scale data. Since it is more sensitive to the initial center selection, it is easier to converge to the local optimal solution and cannot effectively uniformly cluster the maximum values of the original signal. Class; the FCM algorithm based on GSA is used to cluster the maximum values of the three vibration signals. Although the cluster centers are approximately uniformly distributed, there is still the possibility of falling into local minimum points due to the fuzzy values of the weighting parameters, such as Figure 11 There are 2 clustering center points that are abnormal; the use of GSA-IFCM algorithm can effectively overcome the impact of data noise and accurately extract the center points of each periodic time series. The possibility of premature convergence is extremely small. The obtained clustering results It has stronger stability and better objective function value, and has obvious advantages for randomly distributed data clustering;
试验共采集三种状态下各8组振动加速度信号,每组20个循环动作,即三种状态下各160个循环动作;每组原始信号的聚类结果正确个数与准确度如表2所示:The test collected a total of 8 groups of vibration acceleration signals in each of three states, with 20 cyclic actions in each group, that is, 160 cyclic actions in each of the three states. The correct number and accuracy of the clustering results of each group of original signals are shown in Table 2 Show:
表2:聚类结果的准确度Table 2: Accuracy of clustering results
由表2可知,采用3种不同的方法,正常状态下的聚类准确度均高于滚轮裂纹和滑板磨损其原因是正常状态下振动信号的噪声较小,对算法的影响较小,滚轮裂纹状态下准确度未达到100%的原因是此状态下振动最为剧烈,峰—峰值可达900g,但运用GSA-IFCM算法依然可以达到较高的准确度;It can be seen from Table 2 that using three different methods, the clustering accuracy under normal conditions is higher than that for roller cracks and skateboard wear. The reason is that the noise of the vibration signal is smaller under normal conditions and has less impact on the algorithm. Roller cracks The reason why the accuracy does not reach 100% in this state is that the vibration is the most violent in this state, and the peak-to-peak value can reach 900g. However, high accuracy can still be achieved using the GSA-IFCM algorithm;
(2)为验证采用时域特征均方值来表征时间窗能量的优势,利用正常状态下的振动信号,分别对比采用其他归一化时域特征方差和峰值计算出的时间窗曲线图,如图13所示;当选取峰值特征参数时,如图13峰值曲线所示,发现在第二个波峰中出现一个波动,无法准确描述原始信号的波动过程,而且峰值仅描述信号值的变化范围,难以确定信号的起止范围;而选取方差特征参数,如图13方差曲线所示,可以看出波峰符合信号的振动规律,但是第一个和第三个波峰区分不明显,对信号离散程度小的区段描述较弱;选择均方值特征参数,如图13均方值曲线所示,可以看出该特征可以准确描述信号的振动过程,有效表征其能量变化规律,与中心点左侧存在三次冲击相对应;因此,与采用峰值、方差等其他的时域特征参数对信号进行提取相比较,利用均方值表征时间窗能量可以准确提取出单位周期时间序列。(2) In order to verify the advantage of using the mean square value of time domain characteristics to characterize the time window energy, the vibration signal in the normal state is used to compare the time window curves calculated by using other normalized time domain characteristic variances and peak values, such as As shown in Figure 13; when selecting the peak characteristic parameters, as shown in the peak curve in Figure 13, it is found that a fluctuation appears in the second peak, which cannot accurately describe the fluctuation process of the original signal, and the peak value only describes the changing range of the signal value. It is difficult to determine the starting and ending range of the signal; and by selecting the variance characteristic parameters, as shown in the variance curve in Figure 13, it can be seen that the wave peaks conform to the vibration pattern of the signal, but the distinction between the first and third wave peaks is not obvious, and the degree of discreteness of the signal is small The section description is weak; select the mean square value characteristic parameter, as shown in the mean square value curve in Figure 13. It can be seen that this feature can accurately describe the vibration process of the signal, effectively characterize its energy change pattern, and exists three times to the left of the center point. Corresponding to the impact; therefore, compared with extracting signals using other time domain characteristic parameters such as peak value and variance, using the mean square value to characterize the time window energy can accurately extract the unit period time series.
结论:针对表征供输弹机构往复运动过程中近似周期信号的单位周期时间序列难以提取的问题,本发明提出一种基于GSA-IFCM的单位周期时间序列自适应提取方法,试验表明该方法能够有效克服数据噪声的影响,提高聚类结果的准确性,精确提取单位周期时间序列;Conclusion: In order to solve the problem of difficulty in extracting the unit period time series representing the approximate periodic signal during the reciprocating motion of the bomb feeding mechanism, the present invention proposes an adaptive extraction method of unit period time series based on GSA-IFCM. Experiments show that this method can be effective. Overcome the impact of data noise, improve the accuracy of clustering results, and accurately extract unit period time series;
1)利用GSA与IFCM相结合的方法,可有效克服数据噪声的影响,聚类结果具有更强的稳定性和更优的目标函数值,对于随机分布且包含噪声的数据聚类有明显的优越性;1) The method of combining GSA and IFCM can effectively overcome the influence of data noise. The clustering results have stronger stability and better objective function values. It is obviously superior to clustering of randomly distributed data containing noise. sex;
2)通过时间窗求取信号的时域特征参数均方值可表征信号的能量趋势,相比于其他时域特征参数可有效展现出原始信号的振动规律,能够准确提取出单位周期时间序列。2) Obtaining the mean square value of the time domain characteristic parameters of the signal through the time window can represent the energy trend of the signal. Compared with other time domain characteristic parameters, it can effectively show the vibration pattern of the original signal and accurately extract the unit period time series.
以上显示和描述了本发明的基本原理、主要特征和本发明的优点。本行业的技术人员应该了解,本发明不受上述实施例的限制,上述实施例和说明书中描述的只是说明本发明的原理,在不脱离本发明精神和范围的前提下,本发明还会有各种变化和改进,这些变化和改进都落入要求保护的本发明范围内。本发明要求保护范围由所附的权利要求书及其等效物界定。The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have other aspects. Various changes and modifications are possible, which fall within the scope of the claimed invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.
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