CN108898117A - A kind of self-adapting random abnormal signal extracting method for sliding threshold value - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及一种提取随机信号异常的方法，具体地说，涉及一种滑动阈值的自适应随机信号异常提取方法。The invention relates to a method for extracting random signal anomalies, in particular to an adaptive random signal anomaly extraction method with a sliding threshold.
背景技术Background technique
在现实生活和科学研究中，随机信号是一种十分常见的数字序列，在现代信息处理技术中应用广泛，如气象数据分析、地震前兆异常提取、地下水位监测处理等领域广泛使用。目前随机信号异常信息提取有多种方法，包括设定阈值法、2σ法、可拓法以及小波分析法等。In real life and scientific research, random signal is a very common digital sequence, which is widely used in modern information processing technology, such as meteorological data analysis, earthquake precursor anomaly extraction, groundwater level monitoring and processing and other fields. At present, there are many methods for extracting abnormal information of random signals, including setting threshold method, 2σ method, extension method and wavelet analysis method, etc.
第一种阈值法。这种方法通过分段求取随机信号采集数据的均值后，人为增加一个阈值，计算公式如下：The first threshold method. This method calculates the average value of the random signal acquisition data in sections, and artificially increases a threshold. The calculation formula is as follows:
首先计算均值：First calculate the mean:
其中x(i)为一组长度为n的随机数据序列。Where x(i) is a set of random data sequences of length n.
其次在均值基础上添加一个人为给定的阈值T，如下：Secondly, add an artificially given threshold T on the basis of the mean value, as follows:
μ±Tμ±T
超过上下边界的数据被认为是异常数据。Data beyond the upper and lower boundaries are considered abnormal data.
第二种2σ法。这里σ是均方差，公式如下：The second 2σ method. Here σ is the mean square error, the formula is as follows:
其中x(i)为一组长度为n的随机数据序列。Where x(i) is a set of random data sequences of length n.
均方差σ是方差的算术平方根，反映一个数据集的离散程度。The mean square error σ is the arithmetic square root of the variance, which reflects the degree of dispersion of a data set.
2σ法是将均方差代替第一种方法的阈值T，如下：The 2σ method is to replace the mean square error with the threshold T of the first method, as follows:
μ±2σμ±2σ
这样阈值就可以通过求均方差而获取。In this way, the threshold can be obtained by calculating the mean square error.
第三种可拓法。可拓法解决问题的量化方法是建立关联函数，根据有关的可拓学理论和方法，简单关联函数定义如下：The third extension method. The quantitative method of extension method to solve problems is to establish correlation function. According to relevant extension theory and method, simple correlation function is defined as follows:
其中X＝<a，b>称作物元经典域，MIX。Among them, X=<a, b> is called the matter-element classical field, MIX.
在实际工作中，经典域的确定一般采用标准或者规范中的数据范围，但在没有规范的情况下，可以采用“2-8原则”来加以确定。如图1所示。In actual work, the determination of the classic domain generally adopts the data range in the standard or specification, but in the absence of a specification, the "2-8 principle" can be used to determine it. As shown in Figure 1.
第四种为小波分析法。小波变换是信号分析中最常用的方法，可在时间域和频率域上对信号进行深入分析，是一种分析非平稳信号的有效方法。小波分解能将信号分解为不同分辨率下的低频成分(近似成分)和高频成分(细节成分)，低频成分能表现出信号的大致趋势，高频成分展示了不同层次的细节信息，高频成分包含噪声信息，是信号异常存在区。例如地震前兆观测数据属于非平稳信号，通过小波分解，可实现信噪分离，从而能够更加有效地提取出异常信息。The fourth is the wavelet analysis method. Wavelet transform is the most commonly used method in signal analysis, which can analyze signals in depth in time domain and frequency domain, and is an effective method for analyzing non-stationary signals. Wavelet decomposition can decompose the signal into low-frequency components (approximate components) and high-frequency components (detail components) at different resolutions. The low-frequency components can show the general trend of the signal, and the high-frequency components show different levels of detail information. Contains noise information and is an area where signal anomalies exist. For example, earthquake precursor observation data is a non-stationary signal. Through wavelet decomposition, signal-to-noise separation can be achieved, so that abnormal information can be extracted more effectively.
小波变换通过对母小波在不同尺度下进行伸缩和平移并与待分析信号作内积运算得到小波序列，实现对非平稳信号的小波变换，从而实现对信号的多尺度分解。小波基可以选取具有紧支撑性和近对称性的Daubechies族小波(dbN)，其阶数为N。小波分解层数的选择要综合考虑小波函数的光滑度和运算力大小，分解层数与小波光滑度和运算大小成正比，一般小波分解层数不宜过高。图2是选用db4小波对地震前兆信号进行二层小波分解，其中图2A为尺度函数，图2B为小波函数。Wavelet transform stretches and translates the mother wavelet at different scales and performs inner product operation with the signal to be analyzed to obtain the wavelet sequence, so as to realize the wavelet transform of the non-stationary signal, thereby realizing the multi-scale decomposition of the signal. The wavelet base can choose the Daubechies family wavelet (dbN) with compact support and near symmetry, and its order is N. The choice of wavelet decomposition layers should consider the smoothness of wavelet function and the size of computing power. The number of decomposition layers is proportional to wavelet smoothness and computing power. Generally, the number of wavelet decomposition layers should not be too high. Figure 2 shows the two-layer wavelet decomposition of earthquake precursor signals using db4 wavelet, in which Figure 2A is the scale function, and Figure 2B is the wavelet function.
在上述四种异常数据提取方法中，前两种具有很大的不确定性，阈值是否合理在学界存在较大分歧；第三种可拓学方法，需要对数据进行排序从而利用“2-8原则”求取经典域，但这样对于大量数据或者动态数据来说具有不确定性，难于推广。小波分解法在对长时间段的随机信号数据研究时，从原始数据中往往只能看出明显的突跳、阶变、上升、下降等异常变化，而小波高频成分在消除信号趋势变化的同时又突出了信号的异常信息，有利于采用阈值的方法对信号进行定量提取异常。但并非所有的突出点都是异常点，需要对包含异常的高频成分进行异常提取。Among the above four abnormal data extraction methods, the first two have great uncertainty, and there are great differences in the academic circles whether the threshold is reasonable; the third extension method needs to sort the data so as to use "2-8 "Principle" to obtain the classical domain, but this is uncertain for a large amount of data or dynamic data, and it is difficult to promote. When the wavelet decomposition method studies long-term random signal data, only obvious abnormal changes such as sudden jumps, step changes, rises, and drops can often be seen from the original data, while the wavelet high-frequency components can eliminate the signal trend changes. At the same time, it highlights the abnormal information of the signal, which is beneficial to the quantitative extraction of abnormal signals by using the threshold method. But not all salient points are outliers, and it is necessary to extract anomalies from high-frequency components containing anomalies.
总之，现有的随机信号异常数据提取方法存在精度不高、不确定性高等缺点。以上述提到阈值法和2σ法，很明显太随意，导致精度欠佳；在可拓学方法中，尽管采用了关联函数计算的关联度，但仍然出现精度问题，甚至于常常出现误判。而且可拓学方法，需要对数据进行排序从而利用“2-8原则”求取经典域，但这样对于大量数据或者动态数据来说具有不确定性，难于推广；小波分析法在对长时间段的随机信号数据研究时，从原始数据中往往只能看出明显的突跳、阶变、上升、下降等异常变化，而小波高频成分在消除信号趋势变化的同时又突出了信号的异常信息，尽管这有利于采用阈值的方法对信号进行定量提取异常，但并非所有的突出点都是异常点，这就出现了矛盾性，因此需要对包含异常的高频成分进行异常提取。In short, the existing random signal anomaly data extraction methods have shortcomings such as low precision and high uncertainty. The threshold method and 2σ method mentioned above are obviously too random, resulting in poor accuracy; in the extension method, although the correlation degree calculated by the correlation function is used, there are still problems with accuracy, and even misjudgments often occur. Moreover, the extenics method needs to sort the data so as to use the "2-8 principle" to obtain the classical domain, but this is uncertain for a large amount of data or dynamic data, and it is difficult to promote; the wavelet analysis method is used for long-term When researching random signal data, only obvious abnormal changes such as sudden jump, step change, rise, and fall can be seen from the original data, while the wavelet high-frequency components can eliminate signal trend changes while highlighting the abnormal information of the signal. , although this is beneficial to quantitatively extract abnormalities from the signal by using the threshold method, not all prominent points are abnormal points, which leads to contradictions, so it is necessary to extract abnormalities from high-frequency components containing abnormalities.
发明内容Contents of the invention
本发明的目的在于克服现有技术中存在的缺陷，提出了一种滑动阈值的自适应随机信号异常提取方法，一方面解决阈值由主观决定导致不客观问题，不同的个人因为经历、阅历、经验、学识等若干方面因素，造成阈值确定的不一致；另一方面，也克服了“2-8原则”计算阈值需要小样本数据或者静态数据，对于动态数据和大数据问题难于适应的问题；第三，解决了小波分析方法中提取异常信号时常常出现误判和冗余问题，尤其是提高了计算效率和精度。The purpose of the present invention is to overcome the defects existing in the prior art, and proposes an adaptive random signal anomaly extraction method with a sliding threshold. , knowledge and other factors, resulting in inconsistencies in determining the threshold; on the other hand, it also overcomes the problem that the "2-8 principle" requires small sample data or static data to calculate the threshold, and it is difficult to adapt to dynamic data and big data problems; the third , which solves the misjudgment and redundancy problems that often occur when extracting abnormal signals in the wavelet analysis method, especially improves the calculation efficiency and precision.
其技术方案如下：Its technical scheme is as follows:
一种滑动阈值的自适应随机信号异常提取方法，包括以下步骤：An adaptive random signal anomaly extraction method with a sliding threshold, comprising the following steps:
第一步：需要计算滑动平均值，以表示，则计算的公式如下：The first step: need to calculate the moving average to Indicates that the calculation formula is as follows:
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
公式中，为随机信号观测数据序列中第i到第(i+s-1)个数形成的滑动平均值，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据，∑为求和符号。formula, is the sliding average formed by the number i to (i+s-1) in the random signal observation data sequence, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the circular variable, and x j is The jth data, ∑ is the summation symbol.
第二步：需要计算滑动均方差，以σ表示，公式如下：The second step: need to calculate the sliding mean square error, represented by σ, the formula is as follows:
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
公式中，σ(i:i+s-1)为随机信号观测数据序列中第i到第(i+s-1)个数形成的滑动均方差，为滑动平均值，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据，∑为求和符号。In the formula, σ (i:i+s-1) is the sliding mean square error formed by the number i to (i+s-1) in the random signal observation data sequence, is the moving average, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the loop variable, x j is the jth data, and ∑ is the summation symbol.
第三步：计算滑动阈值Step 3: Calculate the sliding threshold
在上述的第一步、第二步都是常用的一些算法，也比较简单。在本步中，需要计算确定阈值的上确界和下确界，具体计算式如下：The first and second steps above are commonly used algorithms, and they are relatively simple. In this step, it is necessary to calculate the supremum and infimum of the determination threshold, and the specific calculation formula is as follows:
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
TU(i:i+s-1)为阈值上界；TL(i:i+s-1)为阈值下界；N正整数，可以取值2,3,4等，需要根据采样频率调整，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据。在前人的随机信号异常提取算法中，阈值的确定是一个固定值，不能适应随机信号的正常幅度变化。而本方法采用均方差的倍数作为自动适应信号幅度变化的数值，能够较好地突出异常。TU (i:i+s-1) is the upper bound of the threshold; TL (i:i+s-1) is the lower bound of the threshold; N is a positive integer, which can be 2, 3, 4, etc., and needs to be adjusted according to the sampling frequency, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the loop variable, and x j is the jth data. In previous random signal anomaly extraction algorithms, the determination of the threshold is a fixed value, which cannot adapt to the normal amplitude variation of random signals. However, this method uses the multiple of the mean square error as the value to automatically adapt to the change of signal amplitude, which can better highlight the abnormality.
第四步：确定随机信号异常数据Step 4: Determine the random signal anomaly data
利用第三步计算的阈值上、下确界，通过下式来确定哪些属于随机信号异常数据：Using the threshold upper and lower bounds calculated in the third step, the following formula is used to determine which data belong to the random signal abnormal data:
xj＞TL(i:i+s-1)或xj＜TU(i:i+s-1)为异常x j >TL (i:i+s-1) or x j <TU (i:i+s-1) is abnormal
TL(i:i+s-1)≤xj≤TU(i:i+s-1)为正常TL (i:i+s-1) ≤x j ≤TU (i:i+s-1) is normal
TU(i:i+s-1)为阈值上界；TL(i:i+s-1)为阈值下界；N正整数，可以取值2,3,4等，需要根据采样频率调整，s为滑动窗口大小，i为循环变量，xj为第j个数据。TU (i:i+s-1) is the upper bound of the threshold; TL (i:i+s-1) is the lower bound of the threshold; N is a positive integer, which can be 2, 3, 4, etc., and needs to be adjusted according to the sampling frequency, s is the size of the sliding window, i is the loop variable, and x j is the jth data.
本发明的有益效果为：The beneficial effects of the present invention are:
本发明面对多分辨率、多测项向的随机信号数据，采用滑动均值±2倍均方差作为阈值提取异常，是合理的，能够快速地定量提取前兆数据异常信号，对研究异常天气、地震预测、海啸预警等自然灾害发生意义重大。In the face of random signal data with multiple resolutions and multiple observations, the present invention uses the sliding mean ± 2 times the mean square error as the threshold to extract anomalies, which is reasonable and can quickly and quantitatively extract anomalous signals of precursory data, which is useful for studying abnormal weather and earthquakes. Prediction, tsunami warning and other natural disasters are of great significance.
附图说明Description of drawings
图1是经典域的确定；Figure 1 is the determination of the classical domain;
图2是db4小波分解，其中，图2A为尺度函数，图2B为小波函数；Fig. 2 is db4 wavelet decomposition, wherein, Fig. 2A is scale function, Fig. 2B is wavelet function;
图3是实施例中地震前兆监测数据的滑动阈值自适应方法计算结果；Fig. 3 is the calculation result of the sliding threshold adaptive method of earthquake precursor monitoring data in the embodiment;
图4为图3中方框中的放大图。FIG. 4 is an enlarged view of the box in FIG. 3 .
具体实施方式Detailed ways
下面结合附图和具体实施方式对本发明的技术方案作进一步详细地说明。The technical solutions of the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.
本发明的具体原理如下：Concrete principle of the present invention is as follows:
由于均值±n倍均方差常作为异常提取的判定阈值，滑动窗口思想对数据处理有很好的自适应性，将两者结合，形成滑动均值±n倍均方差异常法，能够更好地判别信息异常。具体原理如下：Since the mean ± n times the mean square error is often used as the judgment threshold for abnormal extraction, the sliding window idea has a good adaptability to data processing. Combining the two forms a sliding mean ± n times the mean square difference normal method, which can better distinguish The information is abnormal. The specific principles are as follows:
1)计算滑动平均值 1) Calculate the moving average
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
公式中，为随机信号观测数据序列中第i到第(i+s-1)个数形成的滑动平均值，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据，∑为求和符号。formula, is the sliding average formed by the number i to (i+s-1) in the random signal observation data sequence, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the circular variable, and x j is The jth data, ∑ is the summation symbol.
2)计算滑动均方差(σ)2) Calculate the sliding mean square error (σ)
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
公式中，σ(i:i+s-1)为随机信号观测数据序列中第i到第(i+s-1)个数形成的滑动均方差，为滑动平均值，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据，∑为求和符号。In the formula, σ (i:i+s-1) is the sliding mean square error formed by the number i to (i+s-1) in the random signal observation data sequence, is the moving average, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the loop variable, x j is the jth data, and ∑ is the summation symbol.
3)计算滑动阈值3) Calculate the sliding threshold
(i＝1,2,……,n-s+1；j＝i,……,i+s-1)(i=1,2,...,n-s+1; j=i,...,i+s-1)
TU(i:i+s-1)为阈值上界；TL(i:i+s-1)为阈值下界；N正整数，可以取值2,3,4等，需要根据采样频率调整，n为随机信号观测数据的序列长度，s为滑动窗口大小，i为循环变量，xj为第j个数据。TU (i:i+s-1) is the upper bound of the threshold; TL (i:i+s-1) is the lower bound of the threshold; N is a positive integer, which can be 2, 3, 4, etc., and needs to be adjusted according to the sampling frequency, n is the sequence length of the random signal observation data, s is the size of the sliding window, i is the loop variable, and x j is the jth data.
4)随机信号数据异常判断4) Abnormal judgment of random signal data
xj＞TL(i:i+s-1)或xj＜TU(i:i+s-1)为异常 (5)x j >TL (i:i+s-1) or x j <TU (i:i+s-1) is abnormal (5)
TL(i:i+s-1)＜＜xj＜＜TU(i:i+s-1)为正常 (6)TL (i:i+s-1) ＜＜x j ＜＜TU (i:i+s-1) is normal(6)
TU(i:i+s-1)为阈值上界；TL(i:i+s-1)为阈值下界；N正整数，可以取值2,3,4等，需要根据采样频率调整，s为滑动窗口大小，i为循环变量，xj为第j个数据。TU (i:i+s-1) is the upper bound of the threshold; TL (i:i+s-1) is the lower bound of the threshold; N is a positive integer, which can be 2, 3, 4, etc., and needs to be adjusted according to the sampling frequency, s is the size of the sliding window, i is the loop variable, and x j is the jth data.
实施例Example
下面以某次地震前一段时间内的采集数据作为样本，展示本发明方法的前兆异常数据提取结果。Taking the collected data in a period of time before an earthquake as a sample, the extraction results of precursory anomaly data obtained by the method of the present invention are shown below.
图4为图3中方框中的放大图，从中可以看出，采用滑动均值±2倍均方差的阈值方法可以检测出异常点。Figure 4 is an enlarged view of the box in Figure 3, from which it can be seen that the abnormal point can be detected by using the threshold method of the sliding mean ± 2 times the mean square error.
以上所述，仅为本发明较佳的具体实施方式，本发明的保护范围不限于此，任何熟悉本技术领域的技术人员在本发明披露的技术范围内，可显而易见地得到的技术方案的简单变化或等效替换均落入本发明的保护范围内。The above is only a preferred specific embodiment of the present invention, and the scope of protection of the present invention is not limited thereto. Any person familiar with the technical field within the technical scope disclosed in the present invention can obviously obtain the simplicity of the technical solution. Changes or equivalent replacements all fall within the protection scope of the present invention.
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