CN109446625B - A Bayesian Inference-Based Dynamic Threshold Calculation Method for Helicopter Moving Parts - Google Patents
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Abstract
本发明公开了一种基于贝叶斯推理的直升机动部件动态阈值计算方法，该方法包括步骤：1)数据预处理，滤除数据中的噪声；2)特征提取，分别提取正常数据和故障数据的特征；3)动态阈值计算，采用贝叶斯推理方法计算正常数据与故障数据的动态阈值。本发明的优点是：在特征提取方法中，分别采用内圈特征频率能量提取、外圈特征频率能量提取、滚珠特征频率能量提取和M6A提取四种方法，对正常数据和不同类型故障数据进行特征提取，可以有效反映出正常和故障数据的振动特性；在动态阈值计算中，采用贝叶斯推理方法，不仅考虑了正常数据的概率密度，而且考虑了不同类型故障数据的概率密度，提高了动态阈值的计算准确度。
The invention discloses a dynamic threshold calculation method for helicopter moving parts based on Bayesian reasoning. The method comprises the steps of: 1) data preprocessing, filtering out noise in the data; 2) feature extraction, extracting normal data and fault data respectively 3) Dynamic threshold calculation, using Bayesian inference method to calculate the dynamic threshold of normal data and fault data. The advantages of the present invention are: in the feature extraction method, four methods are respectively used to extract the inner ring characteristic frequency energy, the outer ring characteristic frequency energy extraction, the ball characteristic frequency energy extraction and the M6A extraction, to carry out the characteristics of the normal data and different types of fault data. Extraction can effectively reflect the vibration characteristics of normal and fault data; in the dynamic threshold calculation, the Bayesian inference method is used, which not only considers the probability density of normal data, but also considers the probability density of different types of fault data, which improves dynamic performance. The calculation accuracy of the threshold.
Description
技术领域technical field
本发明涉及直升机健康监测与故障诊断领域，尤其涉及一种基于贝叶斯推理的直升机动部件动态阈值计算方法。The invention relates to the field of helicopter health monitoring and fault diagnosis, in particular to a method for calculating dynamic thresholds of helicopter moving parts based on Bayesian reasoning.
背景技术Background technique
相对于固定翼飞机，直升机能垂直起降，具有更好的机动性、快速反应能力和不受地形地貌限制的特点，可广泛应用于民用和军事领域。Compared with fixed-wing aircraft, helicopters can take off and land vertically, have better maneuverability, quick response capabilities and are not limited by terrain and landforms, and can be widely used in civil and military fields.
随着直升机的应用越来越广泛，它的安全性越来越受到人们的重视。直升机健康与使用监控系统(health and usage monitoring system,HUMS)，是当今世界保障直升机安全运行的重要技术和系统。为了减少事故，实时监测直升机关键部件特别是动部件的工作状态，是HUMS的重要内容。HUMS中常采用在试验台环境下通过故障植入试验，采集正常和故障数据，通过计算获得动态阈值，再用于直升机真实环境，实时监测动部件的健康状态。With the more and more extensive application of helicopters, its safety has been paid more and more attention by people. Helicopter health and usage monitoring system (HUMS) is an important technology and system to ensure the safe operation of helicopters in today's world. In order to reduce accidents, real-time monitoring of the working status of key parts of helicopters, especially moving parts, is an important part of HUMS. In HUMS, fault implantation tests are often used in the test bench environment to collect normal and fault data, obtain dynamic thresholds through calculation, and then use them in the real environment of helicopters to monitor the health status of moving parts in real time.
目前，直升机动部件的动态阈值计算是采用加权平均方法，此类方法只利用了正常数据的特征均值和方差，计算得到动态阈值，具有计算简单的优点，但没有利用故障数据的特征，存在动态阈值准确度不高的问题。At present, the dynamic threshold calculation of helicopter moving parts adopts the weighted average method. This method only uses the characteristic mean and variance of normal data to calculate the dynamic threshold, which has the advantage of simple calculation, but does not use the characteristics of fault data, there is dynamic The problem of low threshold accuracy.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供基于贝叶斯推理的直升机动部件动态阈值计算方法，旨在解决针对不同类型故障数据时，现有技术计算得到的动态阈值存在准确度不高的问题。本发明的方法包括以下主要步骤：The purpose of the present invention is to provide a method for calculating dynamic thresholds of helicopter moving parts based on Bayesian reasoning, which aims to solve the problem of low accuracy of dynamic thresholds calculated in the prior art for different types of fault data. The method of the present invention comprises the following main steps:
1)数据预处理，具体包括以下步骤：1) Data preprocessing, which specifically includes the following steps:
(1.1)采集正常数据、内圈故障数据、外圈故障数据、滚珠故障数据；(1.1) Collect normal data, inner ring fault data, outer ring fault data and ball fault data;
(1.2)利用数据预处理方法对步骤(1.1)中采集到的所有数据进行预处理，滤除数据中的噪声，得到去噪后数据。(1.2) Using the data preprocessing method to preprocess all the data collected in step (1.1), filter out the noise in the data, and obtain the denoised data.
所述数据预处理方法为奇异值分解方法、小波去噪方法、小波包去噪方法、滑动平滑处理方法、基本形态滤波方法或差值形态滤波方法。The data preprocessing method is a singular value decomposition method, a wavelet denoising method, a wavelet packet denoising method, a sliding smoothing method, a basic morphological filtering method or a difference morphological filtering method.
2)特征提取，具体包括以下步骤：2) Feature extraction, which specifically includes the following steps:
(2.1)将步骤1)得到的去噪后正常数据、内圈故障数据、外圈故障数据、滚珠故障数据进行分组；(2.1) Group the normal data, inner ring fault data, outer ring fault data, and ball fault data obtained in step 1) after denoising;
(2.2)利用特征提取方法对步骤(2.1)中分组后的所有数据进行特征提取。(2.2) Use the feature extraction method to perform feature extraction on all the data grouped in step (2.1).
所述特征提取方法为内圈特征频率能量提取、外圈特征频率能量提取、滚珠特征频率能量提取和M6A提取。The feature extraction methods are inner ring characteristic frequency energy extraction, outer ring characteristic frequency energy extraction, ball characteristic frequency energy extraction and M6A extraction.
3)动态阈值计算，是通过计算步骤2)提取的特征的概率密度，并根据概率密度绘制概率密度曲线，最后通过贝叶斯推理方法计算得出动态阈值。具体包括以下步骤：3) The dynamic threshold calculation is to calculate the probability density of the features extracted in step 2), draw the probability density curve according to the probability density, and finally calculate the dynamic threshold by the Bayesian inference method. Specifically include the following steps:
(3.1)利用步骤2)提取的特征，分别计算正常数据特征、内圈故障数据特征、外圈故障数据特征、滚珠故障数据特征的概率密度；(3.1) Using the features extracted in step 2), calculate the probability density of normal data features, inner ring fault data features, outer ring fault data features, and ball fault data features respectively;
(3.2)在同一坐标系上，分别画出正常数据特征和内圈故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和内圈故障数据的动态阈值，并计算正确率和误报率来判断该动态阈值计算的有效性；(3.2) On the same coordinate system, draw the probability density curves of the normal data characteristics and the inner ring fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic of the normal data and the inner ring fault data. Threshold, and calculate the correct rate and false alarm rate to judge the validity of the dynamic threshold calculation;
(3.3)在同一坐标系上，分别画出正常数据特征和外圈故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和外圈故障数据的动态阈值，并计算正确率和误报率来判断该动态阈值计算的有效性；(3.3) On the same coordinate system, draw the probability density curves of the normal data characteristics and the outer ring fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic of the normal data and the outer ring fault data. Threshold, and calculate the correct rate and false alarm rate to judge the validity of the dynamic threshold calculation;
(3.4)在同一坐标系上，分别画出正常数据特征和滚珠故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和滚珠故障数据的动态阈值，并计算正确率和误报率来判断该动态阈值计算的有效性。(3.4) On the same coordinate system, draw the probability density curves of the normal data characteristics and the ball fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic threshold of the normal data and the ball fault data, And calculate the correct rate and false alarm rate to judge the validity of the dynamic threshold calculation.
为了验证动态阈值计算的有效性，可以按以下步骤进行动态阈值测试。In order to verify the validity of the dynamic threshold calculation, the dynamic threshold test can be performed according to the following steps.
4)动态阈值测试，具体包括以下步骤：4) Dynamic threshold test, which specifically includes the following steps:
(4.1)采集用于测试的正常数据、内圈故障数据、外圈故障数据、滚珠故障数据；(4.1) Collect normal data, inner ring fault data, outer ring fault data and ball fault data for testing;
(4.2)采用步骤(1.2)中相同的预处理方法对数据进行预处理，滤除数据中的噪声，得到去噪后数据；(4.2) using the same preprocessing method in step (1.2) to preprocess the data, filter out the noise in the data, and obtain the denoised data;
(4.3)将步骤(4.2)中得到的去噪后正常数据、内圈故障数据、外圈故障数据、滚珠故障数据进行分组；(4.3) Group the normal data, inner ring fault data, outer ring fault data and ball fault data obtained in step (4.2) after denoising;
(4.4)采用步骤(2.2)中相同的特征提取方法对分组后的所有数据进行特征提取；(4.4) Use the same feature extraction method in step (2.2) to perform feature extraction on all the grouped data;
(4.5)利用步骤(4.4)提取的特征，分别计算正常数据特征、内圈故障数据特征、外圈故障数据特征、滚珠故障数据特征的概率密度；(4.5) Using the features extracted in step (4.4), calculate the probability density of normal data features, inner ring fault data features, outer ring fault data features, and ball fault data features respectively;
(4.6)在同一坐标系上，分别画出正常数据特征和内圈故障数据特征的概率密度曲线，并将步骤(3.2)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性；(4.6) On the same coordinate system, draw the probability density curves of the normal data feature and the inner ring fault data feature respectively, and display the dynamic threshold calculated in step (3.2) on the coordinate system, and calculate the correct rate and false alarm rate to judge the validity of dynamic threshold calculation;
(4.7)在同一坐标系上，分别画出正常数据特征和外圈故障数据特征的概率密度曲线，并将步骤(3.3)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性；(4.7) On the same coordinate system, draw the probability density curves of the normal data characteristics and the outer ring fault data characteristics respectively, and display the dynamic threshold calculated in step (3.3) on the coordinate system, and calculate the correct rate and false alarm. rate to judge the validity of dynamic threshold calculation;
(4.8)在同一坐标系上，分别画出正常数据特征和滚珠故障数据特征的概率密度曲线，并将步骤(3.4)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性。(4.8) On the same coordinate system, draw the probability density curves of the normal data characteristics and the ball fault data characteristics respectively, and display the dynamic threshold calculated in step (3.4) on the coordinate system, and calculate the correct rate and false alarm rate. to judge the validity of dynamic threshold calculation.
本发明的优点是：在特征提取方法中，分别采用内圈特征频率能量提取、外圈特征频率能量提取、滚珠特征频率能量提取和M6A提取四种方法，对正常数据和不同类型故障数据进行特征提取，可以有效反映出正常和故障数据的振动特性；在动态阈值计算中，采用贝叶斯推理方法，不仅考虑了正常数据的概率密度，而且考虑到了不同类型故障数据的概率密度，提高了动态阈值的计算准确度。The advantages of the present invention are: in the feature extraction method, four methods are respectively used to extract the inner ring characteristic frequency energy, the outer ring characteristic frequency energy extraction, the ball characteristic frequency energy extraction and the M6A extraction, to carry out the characteristics of the normal data and different types of fault data. Extraction can effectively reflect the vibration characteristics of normal and fault data; in the dynamic threshold calculation, the Bayesian inference method is used, which not only considers the probability density of normal data, but also considers the probability density of different types of fault data, which improves dynamic performance. The calculation accuracy of the threshold.
附图说明Description of drawings
图1为本发明的工作流程图。Fig. 1 is the working flow chart of the present invention.
图2为滚动轴承结构示意图。Figure 2 is a schematic diagram of the structure of the rolling bearing.
图3为正常和故障数据的概率密度曲线图。Figure 3 is a graph of probability density for normal and fault data.
具体实施方式Detailed ways
本发明采用如图1所示的基于贝叶斯推理的直升机动部件动态阈值计算方法的工作流程图，实现动态阈值的计算，其具体实施步骤如下：The present invention adopts the working flow chart of the method for calculating dynamic thresholds of helicopter moving parts based on Bayesian reasoning as shown in FIG. 1 to realize the calculation of dynamic thresholds, and the specific implementation steps are as follows:
1)数据预处理1) Data preprocessing
(1.1)采集正常数据、内圈故障数据、外圈故障数据、滚珠故障数据。(1.1) Collect normal data, inner ring fault data, outer ring fault data, and ball fault data.
本发明实施例中，实验数据是通过故障植入方式采集正常和故障的数据。In the embodiment of the present invention, the experimental data is normal and faulty data collected by means of fault implantation.
(1.2)利用数据预处理方法对步骤(1.1)中采集到的所有数据进行预处理，滤除数据中的噪声，得到去噪后数据。(1.2) Using the data preprocessing method to preprocess all the data collected in step (1.1), filter out the noise in the data, and obtain the denoised data.
所述数据预处理方法为奇异值分解方法、小波去噪方法、小波包去噪方法、滑动平滑处理方法、基本形态滤波方法或差值形态滤波方法。The data preprocessing method is a singular value decomposition method, a wavelet denoising method, a wavelet packet denoising method, a sliding smoothing method, a basic morphological filtering method or a difference morphological filtering method.
2)特征提取2) Feature extraction
(2.1)将步骤1)得到的去噪后正常数据、内圈故障数据、外圈故障数据、滚珠故障数据进行分组。(2.1) Group the denoised normal data, inner ring fault data, outer ring fault data, and ball fault data obtained in step 1).
本发明实施例中，根据轴承转动一周的数据点数为1369个，对去噪后的数据进行分组。In the embodiment of the present invention, the denoised data are grouped according to the number of data points in one rotation of the bearing being 1369.
(2.2)利用特征提取方法对步骤(2.1)中分组后的所有数据进行特征提取。(2.2) Use the feature extraction method to perform feature extraction on all the data grouped in step (2.1).
所述特征提取方法为内圈特征频率能量提取、外圈特征频率能量提取、滚珠特征频率能量提取和M6A提取。The feature extraction methods are inner ring characteristic frequency energy extraction, outer ring characteristic frequency energy extraction, ball characteristic frequency energy extraction and M6A extraction.
本发明实施例中，内圈特征频率能量提取、外圈特征频率能量提取、滚珠特征频率能量提取的具体实施步骤如下：In the embodiment of the present invention, the specific implementation steps of the inner ring characteristic frequency energy extraction, the outer ring characteristic frequency energy extraction, and the ball characteristic frequency energy extraction are as follows:
(2.2.1)根据式(1)、式(2)、式(3)分别计算得到轴承的内圈特征频率、外圈特征频率、滚珠特征频率；(2.2.1) According to formula (1), formula (2) and formula (3), calculate the inner ring characteristic frequency, outer ring characteristic frequency and ball characteristic frequency of the bearing respectively;
滚动轴承结构如图2所示，d为滚珠直径；α为接触角；D为轴承节径；n为转速，单位为转/分钟。根据轴承发生故障部件的不同，常见的故障频率有内圈故障频率、外圈故障频率、滚珠故障频率，其分别对应的特征频率计算公式如下：The rolling bearing structure is shown in Figure 2, where d is the diameter of the ball; α is the contact angle; D is the pitch diameter of the bearing; n is the rotational speed, in revolutions per minute. According to the different components of the bearing, the common fault frequencies include the inner ring fault frequency, the outer ring fault frequency, and the ball fault frequency. The corresponding characteristic frequency calculation formulas are as follows:
内圈故障频率：Inner ring fault frequency:
外圈故障频率：Outer ring fault frequency:
滚珠故障频率：Ball failure frequency:
其中，N为滚珠数，fr为滚动轴承的转轴基频，计算公式如下：Among them, N is the number of balls, and f r is the fundamental frequency of the shaft of the rolling bearing. The calculation formula is as follows:
fr＝n/60 (4)fr = n /60 (4)
本发明实施例中，d取值为9.525mm，α取值为30度，D取值为374.326mm，n取值为209rpm，N取值为95个。In the embodiment of the present invention, the value of d is 9.525 mm, the value of α is 30 degrees, the value of D is 374.326 mm, the value of n is 209 rpm, and the value of N is 95.
(2.2.2)将步骤(2.1)中分组后的所有数据，通过快速傅里叶变换(FFT)，在频谱图中分别找到内圈特征频率、外圈特征频率、滚珠特征频率对应倍频(-1～+1)范围的幅值的最大值，并求得能量作为特征。(2.2.2) All the data grouped in step (2.1), through fast Fourier transform (FFT), find the inner ring characteristic frequency, outer ring characteristic frequency, ball characteristic frequency corresponding frequency octave ( The maximum value of the amplitude in the range of -1 to +1) is obtained, and the energy is obtained as a feature.
本发明实施例中，M6A提取的具体实施步骤如下：In the embodiment of the present invention, the specific implementation steps of M6A extraction are as follows:
将步骤(2.1)中分组后的所有数据，根据式(5)计算得到特征。All the data grouped in step (2.1) are calculated according to formula (5) to obtain features.
设振动信号为{xi},i＝1,2,3,…,N，M6A的计算公式为：Assuming that the vibration signal is {x i }, i = 1, 2, 3, ..., N, the calculation formula of M6A is:
式中，
3)动态阈值计算3) Dynamic threshold calculation
(3.1)利用步骤2)提取的特征，分别计算正常数据特征、内圈故障数据特征、外圈故障数据特征、滚珠故障数据特征的概率密度。(3.1) Using the features extracted in step 2), calculate the probability density of normal data features, inner ring fault data features, outer ring fault data features, and ball fault data features respectively.
本发明实施例中，概率密度计算的具体实施步骤如下：In the embodiment of the present invention, the specific implementation steps of the probability density calculation are as follows:
(3.1.1)定义最小区间的长度，把特征平均值和特征最小值的差，均分成m份，作为最小区间；(3.1.1) Define the length of the minimum interval, and divide the difference between the characteristic mean value and the characteristic minimum value into m parts as the minimum interval;
本发明实施例中，m取20～30效果最好；In the embodiment of the present invention, m taking 20 to 30 has the best effect;
(3.1.2)计算全部数据中每个最小区间所包含特征的数量。(3.1.2) Calculate the number of features included in each minimum interval in all data.
(3.1.3)根据各个区间的概率，计算得到各个区间的概率密度。(3.1.3) Calculate the probability density of each interval according to the probability of each interval.
(3.2)在同一坐标系上，分别画出正常数据特征和内圈故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和内圈故障数据的动态阈值，并计算正确率和误报率来判断该动态阈值计算的有效性。(3.2) On the same coordinate system, draw the probability density curves of the normal data characteristics and the inner ring fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic of the normal data and the inner ring fault data. Threshold, and calculate the correct rate and false alarm rate to judge the validity of the dynamic threshold calculation.
本发明实施例中，贝叶斯推理方法描述先验信息以一种概率方式与样本信息结合在一起。Z表示特征，包括内圈特征频率能量、外圈特征频率能量、滚珠特征频率能量和M6A，X表示类别，包括正常和故障。当给定Z时，可以通过贝叶斯推理来计算X的后验概率密度函数：In the embodiment of the present invention, the Bayesian inference method describes that the prior information is combined with the sample information in a probabilistic manner. Z represents characteristics, including inner ring eigenfrequency energy, outer ring eigenfrequency energy, ball eigenfrequency energy, and M6A, and X represents categories, including normal and faulty. When given Z, the posterior probability density function of X can be computed by Bayesian inference:
式(6)中，p(X)表示正常数据和故障数据的概率，都为0.5；p(Z)表示正常数据或者故障数据在该特征下的概率；p(X|Z)是给定Z时X的条件概率，又称后验概率，表示在特征一定时，正常或者故障发生的概率；p(Z|X)是给定X时Z的条件概率，又称似然估计，表示在正常或者故障类别一定时，该特征发生的概率。贝叶斯推理统计中的基本概念是先验分布、似然函数和后验分布。由后验概率密度最大可知，为得到最大正确率，p(Z|X)两概率密度曲线交点，即为最优动态阈值t。In formula (6), p(X) represents the probability of normal data and faulty data, both of which are 0.5; p(Z) represents the probability of normal data or faulty data under this feature; p(X|Z) is the given Z The conditional probability of time X, also known as the posterior probability, represents the probability of normal or fault occurrence when the characteristics are fixed; p(Z|X) is the conditional probability of Z given X, also known as the likelihood estimate, which represents the normal Or the probability of occurrence of this feature when the fault category is certain. The basic concepts in Bayesian inferential statistics are prior distribution, likelihood function, and posterior distribution. It can be known from the maximum posterior probability density that in order to obtain the maximum correct rate, the intersection of the two probability density curves of p(Z|X) is the optimal dynamic threshold t.
本发明实施例中，概率密度曲线如图3所示，正确率是真正率类(true positiverate，TPR)，TPR＝TP/(TP+FN)，代表分类器预测的正类中实际实例占所有正实例的比例；误报率是负正类率(false positive rate，FPR)，FPR＝FP/(FP+TN)，代表分类器预测的正类中实际负实例占所有负实例的比例。In the embodiment of the present invention, the probability density curve is shown in FIG. 3 , the correct rate is the true positive rate (TPR), TPR=TP/(TP+FN), which means that the actual instances in the positive class predicted by the classifier account for all the The proportion of positive instances; the false positive rate is the false positive rate (FPR), FPR=FP/(FP+TN), which represents the proportion of actual negative instances in the positive class predicted by the classifier to all negative instances.
(3.3)在同一坐标系上，分别画出正常数据特征和外圈故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和外圈故障数据的动态阈值，并计算正确率和误报率来判断该动态阈值计算的有效性。(3.3) On the same coordinate system, draw the probability density curves of the normal data characteristics and the outer ring fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic of the normal data and the outer ring fault data. Threshold, and calculate the correct rate and false alarm rate to judge the validity of the dynamic threshold calculation.
(3.4)在同一坐标系上，分别画出正常数据特征和滚珠故障数据特征的概率密度曲线，通过贝叶斯推理方法计算可得，两曲线的交点为正常数据和滚珠故障数据的动态阈值，并计算正确率和误报率来判断动态阈值计算的有效性。(3.4) On the same coordinate system, draw the probability density curves of the normal data characteristics and the ball fault data characteristics respectively, which can be calculated by the Bayesian inference method. The intersection of the two curves is the dynamic threshold of the normal data and the ball fault data, And calculate the correct rate and false alarm rate to judge the effectiveness of dynamic threshold calculation.
4)动态阈值测试4) Dynamic threshold test
(4.1)采集用于测试的正常数据、内圈故障数据、外圈故障数据、滚珠故障数据。(4.1) Collect normal data, inner ring fault data, outer ring fault data, and ball fault data for testing.
(4.2)采用步骤(1.2)中相同的预处理方法对数据进行预处理，滤除数据中的噪声，得到去噪后数据。(4.2) Use the same preprocessing method in step (1.2) to preprocess the data, filter out the noise in the data, and obtain the denoised data.
(4.3)将步骤(4.2)中得到的去噪后正常数据、内圈故障数据、外圈故障数据、滚珠故障数据进行分组。(4.3) Group the normal data, inner ring fault data, outer ring fault data, and ball fault data obtained in step (4.2) after denoising.
(4.4)采用步骤(2.2)中相同的特征提取方法对分组后的所有数据进行特征提取。(4.4) Use the same feature extraction method in step (2.2) to perform feature extraction on all the grouped data.
(4.5)利用步骤(4.4)提取的特征，分别计算正常数据特征、内圈故障数据特征、外圈故障数据特征、滚珠故障数据特征的概率密度。(4.5) Using the features extracted in step (4.4), calculate the probability density of normal data features, inner ring fault data features, outer ring fault data features, and ball fault data features respectively.
(4.6)在同一坐标系上，分别画出正常数据特征和内圈故障数据特征的概率密度曲线，并将步骤(3.2)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性。(4.6) On the same coordinate system, draw the probability density curves of the normal data feature and the inner ring fault data feature respectively, and display the dynamic threshold calculated in step (3.2) on the coordinate system, and calculate the correct rate and false alarm rate to judge the effectiveness of dynamic threshold calculation.
(4.7)在同一坐标系上，分别画出正常数据特征和外圈故障数据特征的概率密度曲线，并将步骤(3.3)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性。(4.7) On the same coordinate system, draw the probability density curves of the normal data characteristics and the outer ring fault data characteristics respectively, and display the dynamic threshold calculated in step (3.3) on the coordinate system, and calculate the correct rate and false alarm. rate to judge the effectiveness of dynamic threshold calculation.
(4.8)在同一坐标系上，分别画出正常数据特征和滚珠故障数据特征的概率密度曲线，并将步骤(3.4)中计算出来的动态阈值显示在坐标系上，计算正确率和误报率来判断动态阈值计算的有效性。(4.8) On the same coordinate system, draw the probability density curves of the normal data characteristics and the ball fault data characteristics respectively, and display the dynamic threshold calculated in step (3.4) on the coordinate system, and calculate the correct rate and false alarm rate. to judge the validity of dynamic threshold calculation.
本发明实施例中，将本发明基于贝叶斯推理的直升机动部件动态阈值计算方法与加权平均方法进行对比研究。动态阈值计算所用的正常数据、刻伤1.5的内圈故障数据、刻伤1.2的外圈故障数据、刻伤1.3的滚珠故障数据各为1200000个点，阈值测试所用的正常数据、刻伤1.5的内圈故障数据、刻伤1.2的外圈故障数据、刻伤1.3的滚珠故障数据各为300000个点。In the embodiment of the present invention, the method for calculating dynamic thresholds of helicopter moving parts based on Bayesian inference and the weighted average method are compared and studied. The normal data used for dynamic threshold calculation, the inner ring fault data of 1.5 nick, the outer ring fault data of 1.2 nick, and the ball fault data of 1.3 nick are each 1,200,000 points. The fault data of the inner ring, the fault data of the outer ring with a scratch 1.2, and the ball fault data with a scratch 1.3 are each 300,000 points.
正常数据和内圈故障数据动态阈值计算对比实验。(a)利用奇异值分解方法去除噪声，采用内圈特征频率能量进行特征提取，采用加权平均方法计算得到的动态阈值大小为4.44，通过测试数据得到的TPR和FPR分别为98.91％和47.70％；采用贝叶斯推理方法计算得到的动态阈值大小为3.10，通过测量数据得到的TPR和FPR分别为90.04％和22.35％。(b)利用奇异值分解方法去除噪声，采用M6A方法进行特征提取，采用加权平均方法计算得到的动态阈值大小为11.92，通过测试数据得到的TPR和FPR分别为98.82％和7.43％；采用贝叶斯推理方法计算得到的动态阈值大小为10.84，通过测试数据得到的TPR和FPR分别为96.67％和1.47％。Comparison experiment of dynamic threshold calculation between normal data and inner ring fault data. (a) The noise is removed by the singular value decomposition method, and the characteristic frequency energy of the inner circle is used for feature extraction. The dynamic threshold size calculated by the weighted average method is 4.44, and the TPR and FPR obtained by the test data are 98.91% and 47.70%, respectively; The dynamic threshold size calculated by the Bayesian inference method is 3.10, and the TPR and FPR obtained from the measured data are 90.04% and 22.35%, respectively. (b) Using the singular value decomposition method to remove noise, using the M6A method for feature extraction, the dynamic threshold size calculated by the weighted average method is 11.92, and the TPR and FPR obtained from the test data are 98.82% and 7.43%, respectively; The dynamic threshold size calculated by the inference method is 10.84, and the TPR and FPR obtained by the test data are 96.67% and 1.47%, respectively.
正常数据和外圈故障数据动态阈值计算对比实验。(a)利用奇异值分解方法去除噪声，采用外圈特征频率能量进行特征提取，采用加权平均方法计算得到的动态阈值大小为1.71，通过测试数据得到的TPR和FPR分别为99.01％和0；采用贝叶斯推理方法计算得到的动态阈值大小为11.42，通过测试数据得到的TPR和FPR分别为100％和0。(b)利用奇异值分解方法去除噪声，采用M6A方法进行特征提取，采用加权平均方法计算得到的动态阈值大小为11.92，通过测试数据得到的TPR和FPR分别为98.82％和0，采用贝叶斯推理方法计算得到的动态阈值大小为34.54，通过测试数据得到的TPR和FPR分别为100％和0。Comparison experiment of dynamic threshold calculation between normal data and outer ring fault data. (a) The noise is removed by the singular value decomposition method, and the characteristic frequency energy of the outer ring is used for feature extraction. The dynamic threshold size calculated by the weighted average method is 1.71, and the TPR and FPR obtained by the test data are 99.01% and 0, respectively; The dynamic threshold size calculated by the Bayesian inference method is 11.42, and the TPR and FPR obtained from the test data are 100% and 0, respectively. (b) The singular value decomposition method is used to remove noise, and the M6A method is used for feature extraction. The dynamic threshold size calculated by the weighted average method is 11.92, and the TPR and FPR obtained from the test data are 98.82% and 0, respectively. Bayesian The dynamic threshold size calculated by the inference method is 34.54, and the TPR and FPR obtained from the test data are 100% and 0, respectively.
正常数据和滚珠故障数据动态阈值计算对比实验。(a)利用奇异值分解方法去除噪声，采用滚珠特征频率能量进行特征提取，采用加权平均方法计算得到的动态阈值大小为2.14，通过测试数据得到的TPR和FPR分别为98.44％和50.53％；采用贝叶斯推理方法计算得到的动态阈值大小为1.23；通过测试数据得到的TPR和FPR分别为83.39％和16.12％。(b)利用奇异值分解方法去除噪声，采用M6A方法进行特征提取，采用加权平均方法计算得到的动态阈值大小为11.92，通过测试数据得到的TPR和FPR分别为98.82％和31.08％，采用贝叶斯推理方法计算得到的动态阈值大小为9.58，通过测试数据得到的TPR和FPR分别为90.29％和3.86％。Comparison experiment of dynamic threshold calculation between normal data and ball fault data. (a) The singular value decomposition method is used to remove noise, and the characteristic frequency energy of the ball is used for feature extraction. The dynamic threshold size calculated by the weighted average method is 2.14, and the TPR and FPR obtained by the test data are 98.44% and 50.53%, respectively; The dynamic threshold size calculated by the Bayesian inference method is 1.23; the TPR and FPR obtained by the test data are 83.39% and 16.12%, respectively. (b) The noise is removed by the singular value decomposition method, and the M6A method is used for feature extraction. The dynamic threshold size calculated by the weighted average method is 11.92, and the TPR and FPR obtained by the test data are 98.82% and 31.08%, respectively. The dynamic threshold size calculated by the inference method is 9.58, and the TPR and FPR obtained by the test data are 90.29% and 3.86%, respectively.
通过以上对比实验可知，总体来说贝叶斯推理方法计算得到的动态阈值比加权平均方法计算得到的动态阈值正确率略低一点，但是误报率却低很多，提高了动态阈值的计算准确度。It can be seen from the above comparative experiments that, in general, the dynamic threshold calculated by the Bayesian inference method has a slightly lower correct rate than the dynamic threshold calculated by the weighted average method, but the false alarm rate is much lower, which improves the calculation accuracy of the dynamic threshold. .
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