CN102629243B - End effect suppression method based on neural network ensemble and B-spline empirical mode decomposition (BS-EMD) - Google Patents

End effect suppression method based on neural network ensemble and B-spline empirical mode decomposition (BS-EMD) Download PDF

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CN102629243B
CN102629243B CN201210053046.0A CN201210053046A CN102629243B CN 102629243 B CN102629243 B CN 102629243B CN 201210053046 A CN201210053046 A CN 201210053046A CN 102629243 B CN102629243 B CN 102629243B
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孟宗
顾海燕
李姗姗
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Yanshan University
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Abstract

本发明公开了一种基于神经网络集成和BS-EMD的端点效应抑制方法,包括以下步骤:A、利用速度传感器测量获取振动信号;B、采用神经网络集成对所述信号进行左延拓和右延拓;C、利用B样条均值函数得到所述信号的均值曲线;D、进行经验模式分解,抛弃两端数据,得到与原始信号相对应的若干IMF分量;E、分析各IMF分量,提取故障特征。本发明可以有效抑制端点效应,解决了端点效应对BS-EMD分解结果的影响。

The invention discloses an endpoint effect suppression method based on neural network integration and BS-EMD, which comprises the following steps: A, using a speed sensor to measure and obtain a vibration signal; Continuation; C, using the B-spline mean function to obtain the mean value curve of the signal; D, performing empirical mode decomposition, discarding the data at both ends, and obtaining some IMF components corresponding to the original signal; E, analyzing each IMF component, extracting failure characteristics. The invention can effectively suppress the endpoint effect and solve the influence of the endpoint effect on the BS-EMD decomposition result.

Description

基于神经网络集成和BS-EMD的端点效应抑制方法Endpoint Effect Suppression Method Based on Neural Network Ensemble and BS-EMD

技术领域 technical field

本发明涉及信号处理技术领域,特别涉及一种基于神经网络集成和BS-EMD(B-spline empirical mode decomposition,B样条经验模式分解)的端点效应抑制方法。 The invention relates to the technical field of signal processing, in particular to an endpoint effect suppression method based on neural network integration and BS-EMD (B-spline empirical mode decomposition, B-spline empirical mode decomposition).

背景技术 Background technique

大型旋转机械是现代冶金、电力、石油等部门的关键设备。受工作环境、使用寿命等限制,该机械设备中的某些部件容易出现一些故障,从而影响整个设备的正常工作,严重时甚至会导致机毁人亡,造成重大经济损失。在旋转机械出现故障或者发生异常时的振动信号多表现为非线性、非平稳特征,这些非平稳信号往往包含有大量的故障特征信息。因此,旋转机械的故障诊断与监测对避免重大的机械事故,促进经济发展有着重要的意义。目前,国内外学者已经取得了一定的成绩,但是对于旋转机械仍然需要不断进一步的研究和完善。 Large rotating machinery is the key equipment of modern metallurgy, electric power, petroleum and other departments. Limited by the working environment and service life, some parts of the mechanical equipment are prone to some failures, which will affect the normal operation of the entire equipment, and even lead to machine crash and death, resulting in major economic losses. When the rotating machinery breaks down or is abnormal, the vibration signals are mostly nonlinear and non-stationary, and these non-stationary signals often contain a large amount of fault characteristic information. Therefore, fault diagnosis and monitoring of rotating machinery is of great significance to avoid major mechanical accidents and promote economic development. At present, scholars at home and abroad have made some achievements, but the rotating machinery still needs to be further researched and perfected.

EMD(Empirical Mode Decomposition,经验模态分解)方法是近年来发展起来的一种新的时间序列信号分析方法,该方法把复杂的信号分解为一系列的IMF(Intrinsic Mode Function,本征模函数)分量之和。由于EMD是自适应的,因此该方法适用于非线性和非平稳信号的分析。 EMD (Empirical Mode Decomposition, Empirical Mode Decomposition) method is a new time series signal analysis method developed in recent years, which decomposes complex signals into a series of IMF (Intrinsic Mode Function, Intrinsic Mode Function) sum of components. Since EMD is adaptive, this method is suitable for the analysis of nonlinear and non-stationary signals.

但是,发明人在实现本发明时,发现现有技术存在端点效应的问题,即在EMD过程中,当以极值点为节点作样条插值来构造包络线时,不能确保数据序列左右两端点恰为极值点,从而使得样条曲线在端点处的插值精度很差,容易发生“过冲”或“欠冲”现象,并通过循环迭代将这种不良影响逐步“污染”整个数据序列,最终导致EMD的分解结果严重失真。 However, when the inventor realizes the present invention, he finds that there is a problem of endpoint effect in the prior art, that is, in the EMD process, when the extreme point is used as the node for spline interpolation to construct the envelope, it cannot ensure that the left and right sides of the data sequence The end point is exactly the extreme point, so that the interpolation accuracy of the spline curve at the end point is very poor, and the phenomenon of "overshoot" or "undershoot" is prone to occur, and this adverse effect will gradually "pollute" the entire data sequence through loop iterations , which eventually leads to serious distortion of the decomposition results of EMD.

发明内容 Contents of the invention

(一)要解决的技术问题 (1) Technical problems to be solved

本发明所要解决的问题是提供一种基于神经网络集成和BS-EMD的端点效应抑制方法,以克服现有技术在EMD过程中出现端点效应的缺陷。 The problem to be solved by the present invention is to provide an endpoint effect suppression method based on neural network integration and BS-EMD, so as to overcome the defect of the endpoint effect in the EMD process in the prior art.

(二)技术方案 (2) Technical solutions

为达到上述目的,本发明提供一种基于神经网络集成和BS-EMD的端点效应抑制方法,所述方法包括以下步骤: To achieve the above object, the present invention provides a method for suppressing endpoint effects based on neural network integration and BS-EMD, said method comprising the following steps:

A、利用速度传感器测量获取振动信号; A. Use the speed sensor to measure and obtain the vibration signal;

B、采用神经网络集成对所述信号进行左延拓和右延拓; B. Using neural network integration to carry out left extension and right extension of the signal;

C、利用B样条均值函数得到所述信号的均值曲线; C, utilize B-spline mean value function to obtain the mean value curve of described signal;

D、进行经验模式分解,抛弃两端数据,得到与原始信号相对应的若干IMF分量; D. Decompose the empirical mode, discard the data at both ends, and obtain some IMF components corresponding to the original signal;

E、分析各IMF分量,提取故障特征。 E. Analyze each IMF component and extract fault features.

优选的,所述步骤B具体包括: Preferably, said step B specifically includes:

B1、在只有一层神经网络时,对所述神经网络进行学习,得到权值和阈值的确定值; B1. When there is only one layer of neural network, learn the neural network to obtain the determined values of weight and threshold;

B2、根据公式                                                得到单层神经网络的输出;其中,为单个神经元的输出,为权值,为阈值,为输入样本。 B2. According to the formula Get the output of the single-layer neural network; where, is the output of a single neuron, is the weight, is the threshold, is the input sample.

B3、采用加权平均进行集成,采用个神经网络组成的集成对进行近似,网络的权值满足下式 B3, using weighted average for integration, using An ensemble pair of neural networks For approximation, the weight of the network satisfies the following formula

;

其中,表示从n维空间到一维空间的映射。 in, Represents a mapping from n- dimensional space to one-dimensional space.

B4、按照分布随机抽取,得到训练集;其中,在网络下,当输入为时,输出为B4. According to the distribution Randomly selected to get the training set; among them, in the network Next, when the input is , the output is ;

根据公式获取神经网络集成的输出; According to the formula Get the output of the neural network ensemble;

根据公式获取神经网络的泛化误差; According to the formula Get the generalization error of the neural network;

根据公式 获取神经网络集成的泛化误差; According to the formula Get the generalization error of the neural network ensemble;

根据公式获取各网络泛化误差的加权平均; According to the formula Obtain the weighted average of the generalization errors of each network;

根据公式获取神经网络的差异度; According to the formula Obtain the difference degree of the neural network;

根据公式 获取集成的差异度; According to the formula Obtain the integrated difference degree;

由此可得神经网络集成的泛化误差From this, the generalization error of the neural network ensemble can be obtained .

优选的,所述步骤C具体包括: Preferably, said step C specifically includes:

C1、假定有限区间[],给定划分: 代表节点值,根据公式 计算次B样条基函数,其中, 。规定当公式中的分母为0时,该函数的值为0。第个B样条函数的局部支撑性为 C1. Assuming a finite interval [ ], given the division: , Represents the node value, according to the formula calculate sub-B-spline basis functions, where, . Specifies that when the denominator in the formula is 0, the value of the function is 0. No. The local support of a B-spline function is

 ;  ;

C2、利用B样条,根据公式获取信号的均值曲线。为B 样条的控制点, 可由信号的极值点滑动平均得到,为第j个B 样条函数的局部支承性。 C2, using B-spline, according to the formula Get the mean curve of the signal. is the control point of the B-spline, which can be obtained from the moving average of the extreme points of the signal, is the local support of the jth B-spline function.

优选的,所述步骤D具体包括: Preferably, said step D specifically includes:

D1、假定原始信号为无限长,根据公式获取信号的均值,并根据公式得到插值函数; D1. Assuming the original signal is infinitely long, according to the formula Get the mean of the signal , and according to the formula Get the interpolation function;

D2、根据IMF判据,若不是一个IMF,则将作为代入公式重复上述过程,直到为一个本征模函数; D2. According to the IMF criterion, if is not an IMF, the as Into the formula Repeat the above process until is an eigenmode function;

重复上述过程,得到各个IMF分量及残余函数,根据公式得到被分解为个本征模函数和一个趋势项的信号,其中为第i个本征模函数,r为趋势项; Repeat the above process to get each IMF component and residual function, according to the formula gets broken down into A signal of eigenmode functions and a trend term ,in is the i -th eigenmode function, r is the trend item;

D3、对得到的IMF进行处理,截去延长部分的数据,得到与原始信号相对应的IMF分量。 D3. Process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal.

优选的,所述步骤D1具体包括: Preferably, the step D1 specifically includes:

D11、找出转子故障振动速度信号所有的局部极值点,用B样条曲线将所有的局部极大值点连接起来形成上包络线,用B样条曲线将所有的局部极小值点连接起来形成下包络线; D11. Find out the rotor fault vibration speed signal For all local extreme points, connect all local maximum points with B-spline curves to form an upper envelope, and use B-spline curves to connect all local minimum points to form a lower envelope;

D12、所述上包络线、下包络线的平均值记为,求出D12, the average value of the upper envelope and the lower envelope is denoted as , find .

优选的,所述步骤D2具体包括: Preferably, the step D2 specifically includes:

D21、判断是否满足IMF的条件,如果是,则为信号的第一个满足IMF条件的分量; D21. Judgment Is the condition of the IMF met, and if so, then for the signal The first component of satisfying the IMF condition;

如果不是,则将作为原始数据,重复步骤D11和D12,再利用B样条函数得到上下包络的平均值,判断是否满足IMF条件,重复上述过程,直到得到满足IMF条件的;记,则为信号的第一个满足IMF条件的分量; If not, the As the original data, repeat steps D11 and D12, and then use the B-spline function to obtain the average value of the upper and lower envelopes ,judge Whether the IMF condition is met, repeat the above process until the IMF condition is met ;remember ,but for the signal The first component of satisfying the IMF condition;

D22、将从速度信号中分离出来,得到D22. Will from the speed signal separated from the ;

作为原始数据重复步骤D11、 D12和D21,得到的第2个满足IMF分量条件的;重复循环次,得到速度信号个满足IMF条件的分量Will Repeat steps D11, D12 and D21 as raw data to get The second one that satisfies the IMF component condition ;repeat loop times, get the speed signal of A component that satisfies the IMF condition ;

成为单调函数时,循环结束,得到速度信号when When it becomes a monotonic function, the loop ends and the speed signal is obtained .

(三)有益效果 (3) Beneficial effects

1、本发明采用神经网络集成和BS-EMD方法结合,提出了一种解决端点效应的新方法; 1. The present invention adopts the combination of neural network integration and BS-EMD method, and proposes a new method to solve the endpoint effect;

2、采用B样条插值方法求取信号的上下包络,解决了三次样条包络曲线法造成的过冲和欠冲问题; 2. The B-spline interpolation method is used to obtain the upper and lower envelopes of the signal, which solves the overshoot and undershoot problems caused by the cubic spline envelope curve method;

3利用神经网络集成通过训练将多个神经网络的结论合成,显著提高了学习系统的泛化能力; 3 Using neural network integration to synthesize the conclusions of multiple neural networks through training, which significantly improves the generalization ability of the learning system;

4、解决了端点效应对BS-EMD分解结果的影响。 4. Solved the influence of endpoint effect on BS-EMD decomposition results.

附图说明 Description of drawings

图1是本发明实施例的一种基于神经网络集成和BS-EMD的端点效应抑制方法的流程图; Fig. 1 is a flow chart of an endpoint effect suppression method based on neural network integration and BS-EMD according to an embodiment of the present invention;

图2是本发明实施例的利用BS-EMD方法对振动信号进行分解的流程图; Fig. 2 is the flow chart that utilizes BS-EMD method to decompose vibration signal in the embodiment of the present invention;

图3是现有技术的EMD分解结果示意图; Fig. 3 is the schematic diagram of the EMD decomposition result of prior art;

图4是本发明实施例的分解结果示意图。 Fig. 4 is a schematic diagram of decomposition results of an embodiment of the present invention.

具体实施方式 Detailed ways

下面结合附图和实施例,对本发明的具体实施方式作进一步详细描述。以下实施例用于说明本发明,但不用来限制本发明的范围。 The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

本发明实施例的一种基于神经网络集成和BS-EMD的端点效应抑制方法如图1所示,包括以下步骤: An endpoint effect suppression method based on neural network integration and BS-EMD in an embodiment of the present invention is shown in Figure 1, including the following steps:

步骤s101,利用速度传感器测量获取振动信号。 Step s101, using a speed sensor to measure and acquire a vibration signal.

步骤s102,采用神经网络集成对所述信号进行左延拓和右延拓。利用神经网络集成对信号进行延拓,包括以下步骤: Step s102, performing left extension and right extension on the signal by neural network integration. Extending the signal using neural network ensembles involves the following steps:

(1)只有一层神经网络的情况时,利用神经网络进行数据序列延拓主要分为两步进行:学习,延拓。神经网络学习过程的目的就是为了得到权值和阈值的确定值。 (1) When there is only one layer of neural network, the data sequence extension using neural network is mainly divided into two steps: learning and extension. The purpose of the neural network learning process is to obtain certain values of weights and thresholds.

(2)单层神经网络的输出可以表示为 (2) The output of a single-layer neural network can be expressed as

                        (1) (1)

其中,为单个神经元的输出,为权值,为阈值,为输入样本。 in, is the output of a single neuron, is the weight, is the threshold, is the input sample.

(3)集成采用加权平均,采用个神经网络组成的集成对进行近似,网络的权值满足下式 (3) Integration adopts weighted average, using set of neural networks Approximating in pairs, the weight of the network satisfies the following formula

                                 (2) (2)

                               (3) (3)

其中,表示从n维空间到一维空间的映射。 in, Represents a mapping from n- dimensional space to one-dimensional space.

(4)训练集按照分布随机抽取,在网络下当输入为时,输出为,此时神经网络集成的输出为 (4) The training set is distributed according to randomly selected from the network When the input is , the output is , the output of the neural network integration at this time is

                       (4) (4)

神经网络的泛化误差和集成的泛化误差分别为 Generalization Error of Neural Networks and the generalization error of the ensemble respectively

                  (5) (5)

                    (6) (6)

各网络泛化误差的加权平均为 The weighted average of the generalization errors of each network is

                              (7) (7)

神经网络的差异度和集成的差异度分别是 The degree of variance of the neural network and integrated difference respectively

                   (8) (8)

                             (9) (9)

神经网络集成的泛化误差为 The generalization error of the neural network ensemble is

                               (10) (10)

式(10)中的显示了神经网络集成各网络的相关程度,因此,只有尽可能使集成中各网络的误差互不相关,才能增强神经网络的泛化能力。 In formula (10) It shows the correlation degree of each network integrated by the neural network. Therefore, only by making the errors of each network in the integration uncorrelated as much as possible can the generalization ability of the neural network be enhanced.

步骤s103,利用B样条均值函数得到所述信号的均值曲线: Step s103, using the B-spline mean function to obtain the mean value curve of the signal:

(1)计算次B样条基函数为: (1) calculation The sub-B-spline basis functions are:

           (11) (11)

其中, in,

           (12) (12)

规定当式(11)中的分母为0时即出现的情况时,此时定义其值为0。第个B样条函数的局部支撑性为 It is stipulated that when the denominator in formula (11) is 0, it will appear In the case of , define its value as 0 at this time. No. The local support of a B-spline function is

                      (13) (13)

(2)B样条基函数具有递推性、局部支撑性和线性无关性等性质。利用B样条计算信号的均值曲线为 (2) B-spline basis functions have the properties of recursion, local support and linear independence. Using B-spline to calculate the mean curve of the signal is

                        (14) (14)

步骤s104,进行经验模式分解,抛弃两端数据,得到与原始信号相对应的若干IMF分量。具体的分解过程如下: Step s104, perform empirical mode decomposition, discard the data at both ends, and obtain several IMF components corresponding to the original signal. The specific decomposition process is as follows:

s1041,假定原始信号为无限长的,根据式(14)求信号的均值,则插值函数为 s1041, assuming the original signal is infinitely long, according to formula (14) to find the mean value of the signal , then the interpolation function is

                          (15) (15)

s1042,根据IMF判据,若不是一个IMF,则将作为代入式(15)重复上述过程,直到是一个本征模函数,直至得到各个IMF分量及残余函数。此时信号被分解为个本征模函数和一个趋势项,即 s1042, according to the IMF criterion, if is not an IMF, the as Substitute into formula (15) and repeat the above process until is an eigenmode function until each IMF component and residual function are obtained. signal at this time is broken down into eigenmode functions and a trend term, namely

                        (16) (16)

s1043,对得到的IMF进行处理,截去延长部分的数据,得到与原始信号相对应的IMF分量。 S1043, process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal.

其中步骤s1041和步骤s1042具体过程如下: Wherein the specific process of step s1041 and step s1042 is as follows:

1)找出转子故障振动速度信号所有的局部极值点,用B样条曲线将所有的局部极大值点连接起来形成上包络线。再用B样条曲线将所有的局部极小值点连接起来形成下包络线,上、下包络线应该包括所有的数据点。 1) Find out the rotor fault vibration speed signal All the local extreme points are connected with B-spline curves to form the upper envelope. Then use the B-spline curve to connect all the local minimum points to form the lower envelope, and the upper and lower envelopes should include all the data points.

2)上、下包络线的平均值记为,求出 2) The average value of the upper and lower envelopes is recorded as , find

                             (17) (17)

理想地,如果满足IMF的条件,那么就是的第一个IMF分量。 Ideally, if satisfies the conditions of the IMF, then that is The first IMF component of .

3)如果不满足IMF的条件,把作为原始数据,重复步骤1)~2),再利用B样条函数得到上下包络的平均值,再判断是否满足IMF条件。记,则为信号的第一个满足IMF条件的分量。 3) if does not meet the conditions of the IMF, the As the original data, repeat steps 1)~2), and then use the B-spline function to get the average value of the upper and lower envelopes , and then judge Whether to meet the IMF conditions. remember ,but for the signal The first component of is that satisfies the IMF condition.

4)将从速度信号中分离出来,得到 4) Will from the speed signal separated from the

                            (18) (18)

作为原始数据重复步骤1)~3),得到的第2个满足IMF分量条件的,重复循环次,得到振动加速度信号各满足IMF条件的分量,即 Will Repeat steps 1)~3) as the original data to get The second one that satisfies the IMF component condition , repeating the loop times to get the vibration acceleration signal of Each component that satisfies the IMF condition, namely

                           (19) (19)

当满足终止条件(即成为单调函数不能再从中提取IMF分量)时,循环结束。此时速度信号可以表示为 When the termination condition is met (i.e. becomes a monotonic function from which IMF components can no longer be extracted), the loop ends. At this time, the speed signal can be expressed as

。                      (20) . (20)

式中,代表信号的平均趋势,是信号的残余分量。而各个IMF分量分别包含了信号的从高到低的各个不同频率段的成分,每一个频率段所包含的频率成分不同。而且各IMF分量随着振动信号本身的变化而变化。 In the formula, Represents the average trend of the signal and is the residual component of the signal. Each IMF component contains components of different frequency bands from high to low of the signal, and each frequency band contains different frequency components. Moreover, each IMF component changes with the change of the vibration signal itself.

步骤s105,分析各IMF分量,提取故障特征。 Step s105, analyzing each IMF component and extracting fault features.

本发明的BS-EMD通过B样条插值函数求取信号的上下包络曲线,避免了信号的欠冲和过冲问题,B样条插值具有良好的局部性质,被广泛应用于函数插值和拟合等。利用神经网络集成对转子试验数据进行左右延拓,利用B样条插值曲线对数据进行插值计算得到信号的均值曲线,再进行经验模式分解,最后抛弃两端延拓的数据,即得到与原始信号相对应的本征模函数。 The BS-EMD of the present invention obtains the upper and lower envelope curves of the signal through the B-spline interpolation function, avoiding the undershoot and overshoot problems of the signal, and the B-spline interpolation has good local properties, and is widely used in function interpolation and pseudo Together and so on. Use the neural network integration to extend the rotor test data left and right, and use the B-spline interpolation curve to interpolate the data to obtain the mean value curve of the signal, then decompose the empirical mode, and finally discard the extended data at both ends, that is, get the same as the original signal The corresponding eigenmode function.

本发明旨在利用神经网络集成对信号进行端点延拓来解决端点效应问题,通过理论研究和试验分析,对旋转机械的转子不平衡故障信号进行分析。首先,对信号进行神经网络集成的延拓,再分解得到信号的特征分量,通过对各分量的分析得到信号的频率特征,从而提取出该故障的信息。本发明实施例利用BS-EMD方法对振动信号进行分解的流程如图2所示。本发明通过测试信号说明该方法可以有效地抑制端点效应问题。 The invention aims at solving the problem of the endpoint effect by utilizing the neural network integration to extend the endpoint of the signal, and analyzes the unbalanced fault signal of the rotor of the rotary machine through theoretical research and test analysis. Firstly, the signal is extended by neural network integration, and then decomposed to obtain the characteristic components of the signal, and the frequency characteristics of the signal are obtained by analyzing each component, so as to extract the information of the fault. The process of decomposing the vibration signal by using the BS-EMD method in the embodiment of the present invention is shown in FIG. 2 . The present invention demonstrates that the method can effectively suppress the problem of endpoint effect through test signals.

本实施例中,在旋转机械故障模拟平台上模拟转子不对中故障,其故障特征频率除工频外,还有二倍频。利用速度传感器提取垂直方向的振动信号,轴的转速为924r/min,采样频率为500Hz,采集点数为512点,对信号进行分解,提取信号的特征值。 In this embodiment, the rotor misalignment fault is simulated on the rotating machinery fault simulation platform, and its fault characteristic frequency has a double frequency in addition to the power frequency. The vibration signal in the vertical direction is extracted by the speed sensor. The rotational speed of the shaft is 924r/min, the sampling frequency is 500Hz, and the number of collection points is 512 points. The signal is decomposed and the characteristic value of the signal is extracted.

在上述情况下,现有技术的EMD分解结果示意图如图3所示,本发明实施例的分解结果示意图如图4所示。 Under the above circumstances, the schematic diagram of the EMD decomposition result in the prior art is shown in FIG. 3 , and the schematic diagram of the decomposition result in the embodiment of the present invention is shown in FIG. 4 .

参照图3,原始信号的波形为“signal”,直接采用EMD进行分解,从图中可以看出,IMF2,IMF3在端点处出现端点效应。 Referring to Figure 3, the waveform of the original signal is "signal", which is directly decomposed by EMD. It can be seen from the figure that IMF2 and IMF3 have endpoint effects at the endpoints.

参照图4,从图中的IMF2,IMF3中可以看出信号的端点效应得到了明显的抑制。在图中,IMF1都代表二倍频成分,IMF2代表工频成分。比较两者的IMF3,发现使用原始方法得到的IMF3在端点处出现起伏,尤其是在左端点处波动比较明显。而通过本发明实施例得到的端点处的值比较平坦,频率成分比较集中,能量泄露比较少。通过比较这两种分解方法,可以看出两种方法都能成功地揭示出信号的不对中故障,但是通过本发明实施例的信号分解在端点处有更好的表现,可以有效抑制端点效应,使故障特征更容易准确辨识。通过比较图3和图4,可以看出本发明提出的方法是一种十分有效的抑制端点效应的方法。 Referring to Fig. 4, it can be seen from IMF2 and IMF3 in the figure that the endpoint effect of the signal is obviously suppressed. In the figure, IMF1 represents the double frequency component, and IMF2 represents the power frequency component. Comparing the IMF3 of the two, it is found that the IMF3 obtained by the original method fluctuates at the endpoints, especially at the left endpoint. However, the values at the endpoints obtained by the embodiment of the present invention are relatively flat, the frequency components are relatively concentrated, and the energy leakage is relatively small. By comparing these two decomposition methods, it can be seen that both methods can successfully reveal the misalignment fault of the signal, but the signal decomposition in the embodiment of the present invention has a better performance at the end point, which can effectively suppress the end point effect, Make fault features easier to accurately identify. By comparing Fig. 3 and Fig. 4, it can be seen that the method proposed by the present invention is a very effective method for suppressing the endpoint effect.

本发明实施例的基于神经网络集成和BS-EMD的端点效应抑制方法具有以下有益效果: The endpoint effect suppression method based on neural network integration and BS-EMD in the embodiment of the present invention has the following beneficial effects:

1、本发明采用神经网络集成和BS-EMD方法结合,提出了一种解决端点效应的新方法; 1. The present invention adopts the combination of neural network integration and BS-EMD method, and proposes a new method to solve the endpoint effect;

2、采用B样条插值方法求取信号的上下包络,解决了三次样条包络曲线法造成的过冲和欠冲问题; 2. The B-spline interpolation method is used to obtain the upper and lower envelopes of the signal, which solves the overshoot and undershoot problems caused by the cubic spline envelope curve method;

3利用神经网络集成通过训练将多个神经网络的结论合成,显著提高了学习系统的泛化能力; 3 Using neural network integration to synthesize the conclusions of multiple neural networks through training, which significantly improves the generalization ability of the learning system;

4、解决了端点效应对BS-EMD分解结果的影响。 4. Solved the influence of endpoint effect on BS-EMD decomposition results.

以上所述仅是本发明的优选实施方式,应当指出,对于本技术领域的普通技术人员来说,在不脱离本发明技术原理的前提下,还可以做出若干改进和替换,这些改进和替换也应视为本发明的保护范围。 The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and replacements can also be made, these improvements and replacements It should also be regarded as the protection scope of the present invention.

Claims (5)

1.一种基于神经网络集成和BS-EMD的端点效应抑制方法,其特征在于,所述方法包括以下步骤:1. an endpoint effect suppression method based on neural network integration and BS-EMD, is characterized in that, described method comprises the following steps: A、利用速度传感器测量获取振动信号;A. Use the speed sensor to measure and obtain the vibration signal; B、采用神经网络集成对所述信号进行左延拓和右延拓;B. Using neural network integration to carry out left extension and right extension of the signal; C、利用B样条均值函数得到所述信号的均值曲线;C, utilize B-spline mean value function to obtain the mean value curve of described signal; D、进行经验模式分解,抛弃两端数据,得到与原始信号相对应的若干IMF分量;D. Decompose the empirical mode, discard the data at both ends, and obtain some IMF components corresponding to the original signal; E、分析各IMF分量,提取故障特征;E. Analyze each IMF component and extract fault features; 所述步骤B具体包括:Described step B specifically comprises: B1、在只有一层神经网络时,对所述神经网络进行学习,得到权值和阈值的确定值;B1. When there is only one layer of neural network, learn the neural network to obtain the determined values of weight and threshold; B2、根据公式ai=f(ωi×pm,i+bi)得到单层神经网络的输出;其中,ai为单个神经元的输出,ωi为权值,bi为阈值,pm,i为输入样本;B2. Obtain the output of the single-layer neural network according to the formula a i = f(ω i × p m, i + b i ); wherein, a i is the output of a single neuron, ω i is the weight, b i is the threshold, p m, i is the input sample; B3、采用加权平均进行集成,采用N个神经网络组成的集成对f:Rn→R进行近似,网络的权值ωα满足下式B3. Use the weighted average to integrate, and use the integration composed of N neural networks to approximate f:R n → R, and the network weight ω α satisfies the following formula &omega;&omega; &alpha;&alpha; >> 00 &Sigma;&Sigma; &alpha;&alpha; &omega;&omega; &alpha;&alpha; == 11 ;; 其中,f:Rn→R表示从n维空间到一维空间的映射;Among them, f:R n → R represents the mapping from n-dimensional space to one-dimensional space; B4、按照分布p(x)随机抽取,得到训练集;其中,在网络α下,当输入为X时,输出为Vα(X);B4. Randomly extract according to the distribution p(x) to obtain the training set; wherein, under the network α, when the input is X, the output is V α (X); 根据公式获取神经网络集成的输出;According to the formula Get the output of the neural network ensemble; 根据公式Eα=∫dxp(x)(f(x)-Vα(x))2获取神经网络的泛化误差;Obtain the generalization error of the neural network according to the formula E α =∫dxp(x)(f(x)-V α (x)) 2 ; 根据公式获取神经网络集成的泛化误差;According to the formula Get the generalization error of the neural network ensemble; 根据公式获取各网络泛化误差的加权平均;According to the formula Obtain the weighted average of the generalization errors of each network; 根据公式获取神经网络的差异度;According to the formula Obtain the difference degree of the neural network; 根据公式获取集成的差异度;According to the formula Obtain the integrated difference degree; 由此可得神经网络集成的泛化误差 From this, the generalization error of the neural network ensemble can be obtained 2.根据权利要求1所述的基于神经网络集成和BS-EMD的端点效应抑制方法,其特征在于,所述步骤C具体包括:2. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 1, is characterized in that, described step C specifically comprises: C1、假定有限区间[a,b],给定划分:Δa=t0<t1<...<tN-1<tN=b,tj代表节点值,根据公式 B j , k ( t ) = t - t j t j + k - 1 - t j B j , k - 1 ( t ) + t j + k - t t j + k - t j + 1 B j + 1 , k - 1 ( t ) 计算k次B样条基函数,其中,规定当公式中的分母为0时,该函数的值为0;第j个B样条函数的局部支撑性为C1. Assuming a finite interval [a,b], given the division: Δa=t 0 <t 1 <...<t N-1 <t N =b, t j represents the node value, according to the formula B j , k ( t ) = t - t j t j + k - 1 - t j B j , k - 1 ( t ) + t j + k - t t j + k - t j + 1 B j + 1 , k - 1 ( t ) Compute k-th B-spline basis functions, where, It is stipulated that when the denominator in the formula is 0, the value of the function is 0; the local support of the jth B-spline function is C2、利用B样条,根据公式获取信号的均值曲线;ωj为B样条的控制点,可由信号的极值点滑动平均得到,Bj,k(t)为第j个B样条函数的局部支承性。C2, using B-spline, according to the formula Obtain the mean value curve of the signal; ω j is the control point of the B-spline, which can be obtained from the moving average of the extreme points of the signal, and B j,k (t) is the local support of the jth B-spline function. 3.根据权利要求2所述的基于神经网络集成和BS-EMD的端点效应抑制方法,其特征在于,所述步骤D具体包括:3. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 2, is characterized in that, described step D specifically comprises: D1、假定原始信号x(t)为无限长,根据公式获取信号的均值m,并根据公式x(t)-m=h得到插值函数;D1. Assuming that the original signal x(t) is infinitely long, according to the formula Obtain the mean value m of the signal, and obtain the interpolation function according to the formula x(t)-m=h; D2、根据IMF判据,若h不是一个IMF,则将h作为x(t)代入公式x(t)-m=h重复上述过程,直到h为一个本征模函数;D2, according to the IMF criterion, if h is not an IMF, then use h as x (t) to substitute into formula x (t)-m=h and repeat the above-mentioned process, until h is an eigenmode function; 重复上述过程,得到各个IMF分量及残余函数,根据公式得到被分解为n个本征模函数和一个趋势项的信号x(t),其中ci(t)为第i个本征模函数,r为趋势项;Repeat the above process to get each IMF component and residual function, according to the formula Obtain the signal x(t) decomposed into n eigenmode functions and a trend item, where c i (t) is the i-th eigenmode function, and r is the trend item; D3、对得到的IMF进行处理,截去延长部分的数据,得到与原始信号相对应的IMF分量。D3. Process the obtained IMF, cut off the data of the extended part, and obtain the IMF component corresponding to the original signal. 4.根据权利要求3所述的基于神经网络集成和BS-EMD的端点效应抑制方法,其特征在于,所述步骤D1具体包括:4. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 3, is characterized in that, described step D1 specifically comprises: D11、找出转子故障振动速度信号x(t)所有的局部极值点,用B样条曲线将所有的局部极大值点连接起来形成上包络线,用B样条曲线将所有的局部极小值点连接起来形成下包络线;D11. Find out all the local extreme points of the rotor fault vibration speed signal x(t), connect all local maximum points with B-spline curves to form an upper envelope, and use B-spline curves to connect all local extreme points The minimum points are connected to form the lower envelope; D12、所述上包络线、下包络线的平均值记为m1,求出x(t)-m1=h1D12. The average value of the upper envelope and the lower envelope is denoted as m 1 , and x(t)-m 1 =h 1 is obtained. 5.根据权利要求4所述的基于神经网络集成和BS-EMD的端点效应抑制方法,其特征在于,所述步骤D2具体包括:5. the endpoint effect suppression method based on neural network integration and BS-EMD according to claim 4, is characterized in that, described step D2 specifically comprises: D21、判断h1是否满足IMF的条件,如果是,则h1为信号x(t)的第一个满足IMF条件的分量;D21, judge whether h 1 satisfies the condition of IMF, if yes, then h 1 is the first component that satisfies the IMF condition of signal x(t); 如果不是,则将h1作为原始数据,重复步骤D11和D12,再利用B样条函数得到上下包络的平均值m11,判断h11=h1-m11是否满足IMF条件,重复上述过程,直到得到满足IMF条件的h1k;记c1=h1k,则c1为信号x(t)的第一个满足IMF条件的分量;If not, take h 1 as the original data, repeat steps D11 and D12, and then use the B-spline function to obtain the average value m 11 of the upper and lower envelopes, judge whether h 11 = h 1 -m 11 satisfies the IMF condition, and repeat the above process , until h 1k satisfying the IMF condition is obtained; record c 1 =h 1k , then c 1 is the first component of the signal x(t) satisfying the IMF condition; D22、将c1从速度信号x(t)中分离出来,得到r1=x(t)-c1D22. Separate c 1 from the speed signal x(t), and obtain r 1 =x(t)-c 1 ; 将r1作为原始数据重复步骤D11、D12和D21,得到x(t)的第2个满足IMF分量条件的c2;重复循环n次,得到速度信号x(t)的n个满足IMF条件的分量Repeat steps D11, D12 and D21 using r 1 as the original data to obtain the second c 2 of x(t) that meets the IMF component condition; repeat the cycle n times to obtain n components of the velocity signal x(t) that meet the IMF condition weight rr 11 -- cc 22 == rr 22 .. .. .. rr nno -- 11 -- cc nno == rr nno ;; 当rn为单调函数时,循环结束,得到速度信号 When r n is a monotone function, the loop ends and the speed signal is obtained
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