CN115267446A - Power equipment partial discharge detection method based on multi-signal classification positioning algorithm - Google Patents
Power equipment partial discharge detection method based on multi-signal classification positioning algorithm Download PDFInfo
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Abstract
本发明公开了一种基于多信号分类定位算法的电力设备局放检测方法,包括如下步骤:S1、通过八元圆形麦克风阵列传感器对电力设备发出的局部放电信号进行接收;S2、将接收到的带有声源信息的时域数字信号进行傅里叶变换,将其由时域转化为频域;S3、对S2步骤中得到的频域放电信号进行特征频域提取,找到最能够代表接收到的放电信号的频率值;S4、利用一种适用于小信噪比和小快拍数情况下的多信号分类的声源定位算法,结合S3步骤中得到的信号特征频率值,对接收到的放电信号进行分析定位;本发明提出的检测方法采用了多参数联合估计,有利于更精确定位电力设备的局部放电位置,达到有效检测局部放电的目的。
The invention discloses a partial discharge detection method for power equipment based on a multi-signal classification and positioning algorithm, comprising the following steps: S1. Receive the partial discharge signal sent by the power equipment through an eight-element circular microphone array sensor; S2, receive the partial discharge signal sent by the power equipment. Fourier transform is performed on the time-domain digital signal with sound source information, and it is converted from the time domain to the frequency domain; S3. Extract the characteristic frequency domain of the frequency-domain discharge signal obtained in step S2, and find the best representative of the received signal. The frequency value of the discharge signal; S4, using a sound source localization algorithm suitable for multi-signal classification under the condition of small signal-to-noise ratio and small snapshot number, combined with the signal characteristic frequency value obtained in step S3, to the received signal The discharge signal is analyzed and located; the detection method proposed by the present invention adopts multi-parameter joint estimation, which is beneficial to more accurately locate the partial discharge position of the power equipment and achieve the purpose of effectively detecting partial discharge.
Description
技术领域technical field
本发明涉及电力设备局部放电检测领域,具体是一种基于多信号分类定位算法的电力设备局放检测方法。The invention relates to the field of partial discharge detection of electric power equipment, in particular to a partial discharge detection method of electric power equipment based on a multi-signal classification and positioning algorithm.
背景技术Background technique
局部异常放电是导致电力设备运行寿命减少的重要因素,也是各种电力设备最常见的异常运行状态。局部放电的定位检测是一项关键工程技术,是判断众多电力设备运行状态是否正常的重要依据。及时发现异常放电并对其进行准确定位对于防止电力设备发生严重故障具有重要的意义。Abnormal partial discharge is an important factor leading to the reduction of the operating life of power equipment, and it is also the most common abnormal operating state of various power equipment. The location detection of partial discharge is a key engineering technology and an important basis for judging whether the operating status of many power equipment is normal. Timely detection of abnormal discharge and its accurate location are of great significance to prevent serious failures of power equipment.
目前检测局部放电的方法主要有:电学,光学,光-声学以及特高频方法。其中超声波本身具有频率高且波长短的特点,且对信号的传输具有较强的方向感,因此检测过程相对较为简单。同时超声波测量方法也由于具有易于实现在线检测,便于空间定位,受电气干扰小等特点而被广泛研究。At present, the methods for detecting partial discharge mainly include: electrical, optical, photo-acoustic and UHF methods. Among them, the ultrasonic wave itself has the characteristics of high frequency and short wavelength, and has a strong sense of direction for signal transmission, so the detection process is relatively simple. At the same time, the ultrasonic measurement method has been widely studied because it is easy to realize on-line detection, convenient for spatial positioning, and less affected by electrical interference.
本发明提出一种基于多信号分类定位算法的电力设备局放检测方法,该检测方法采用了多参数联合估计,有利于更精确定位电力设备的局部放电位置,达到有效检测局部放电的目的。The invention proposes a partial discharge detection method for electric equipment based on a multi-signal classification and positioning algorithm. The detection method adopts multi-parameter joint estimation, which is beneficial to more accurately locate the partial discharge position of the electric equipment, and achieves the purpose of effectively detecting partial discharge.
发明内容Contents of the invention
本发明的目的在于提供一种基于多信号分类定位算法的电力设备局放检测方法,以便于在检测电力设备局部放电定位过程中获得更好的检测效果。The purpose of the present invention is to provide a partial discharge detection method of electric power equipment based on a multi-signal classification and positioning algorithm, so as to obtain better detection effect in the process of detecting and locating the partial discharge of electric power equipment.
为实现上述目的,本发明提供如下技术方案:To achieve the above object, the present invention provides the following technical solutions:
一种基于多信号分类定位算法的电力设备局放检测方法,包括如下步骤:A partial discharge detection method for electrical equipment based on a multi-signal classification and positioning algorithm, comprising the following steps:
S1、通过八元圆形麦克风阵列传感器对电力设备发出的局部放电信号进行接收;S1. Receive the partial discharge signal sent by the power equipment through the eight-element circular microphone array sensor;
S2、将接收到的带有声源信息的时域数字信号进行傅里叶变换,将其由时域转化为频域;S2. Perform Fourier transform on the received time-domain digital signal with sound source information, and convert it from time domain to frequency domain;
S3、对S2步骤中得到的频域放电信号进行特征频率提取,找到最能够代表接收到的放电信号的频率值;S3. Extracting the characteristic frequency of the frequency-domain discharge signal obtained in step S2, and finding the frequency value that best represents the received discharge signal;
S4、利用一种适用于小信噪比和小快拍数情况下的多信号分类的声源定位算法,结合S3步骤中得到的信号特征频率值,对接收到的放电信号进行分析定位;S4. Using a sound source localization algorithm suitable for multi-signal classification in the case of a small signal-to-noise ratio and a small number of snapshots, combined with the signal characteristic frequency value obtained in step S3, analyzing and locating the received discharge signal;
作为本发明进一步的方案:在步骤S1中,采用的八元圆形阵列是一种平面形麦克风传感器阵列。As a further solution of the present invention: in step S1, the eight-element circular array used is a planar microphone sensor array.
作为本发明进一步的方案:步骤S1中八元圆形阵列可以接收信号的俯仰角以及方位角两个位置参数,通过这两个参数的联合估计可以实现,空间三维有效定位。As a further solution of the present invention: in step S1, the eight-element circular array can receive two position parameters of the signal, the pitch angle and the azimuth angle, and the joint estimation of these two parameters can realize three-dimensional effective positioning in space.
作为本发明进一步的方案:在步骤S2中,傅里叶变换针对的对象是接收到的放电数字信号的时域状态,其中单个麦克风传感器接收到的信号数据量与快拍数相关联,并且是傅里叶变换中的信号长度参数。As a further solution of the present invention: in step S2, the object of Fourier transform is the time-domain state of the received discharge digital signal, wherein the amount of signal data received by a single microphone sensor is associated with the number of snapshots, and is Signal length parameter in the Fourier transform.
作为本发明进一步的方案:在步骤S2中,转化为频域以后的信号强度通过纵坐标的大小来表示,信号强度大的部分对应的频率应该在步骤S3中更多的被考虑。As a further solution of the present invention: in step S2, the signal strength converted into the frequency domain is represented by the size of the ordinate, and the frequency corresponding to the part with high signal strength should be more considered in step S3.
作为本发明进一步的方案:在步骤S4中,适用于小信噪比和小快拍数情况下的多信号分类的声源定位算法的应用条件是信号可以被认为是窄带信号时,对于窄带信号Sk(t)可以表示为:As a further scheme of the present invention: in step S4, the application condition of the sound source localization algorithm applicable to the multi-signal classification under the situation of small signal-to-noise ratio and small number of snapshots is that when the signal can be considered as a narrowband signal, for the narrowband signal Sk(t) can be expressed as:
Sk(t-t1)≈Sk(t)S k (tt 1 )≈S k (t)
其中,t1为阵列麦克风单元之间延迟所需时间。Wherein, t1 is the required delay time between array microphone units.
作为本发明进一步的方案:在步骤S4中,接收到的放电信号会首先通过获得协方差矩阵,再进行后续的信号分类。As a further solution of the present invention: in step S4, the received discharge signal will first pass through to obtain a covariance matrix, and then perform subsequent signal classification.
其中,X(i)为接收到的第i个信号数据,,XH(i)为X(i)的厄尔米特矩阵,N为总共的接收到的数据个数。Wherein, X(i) is the received i-th signal data, X H (i) is the Hermitian matrix of X(i), and N is the total number of received data.
作为本发明进一步的方案:由于是平面阵列,因此在步骤S4中,算法涉及到的时延τm,k,应为:As a further solution of the present invention: since it is a planar array, in step S4, the time delay τ m, k involved in the algorithm should be:
其中,τm,k是信号源k与阵元m相对阵列中心的相对延时,θk和为信号源k的俯仰角和方位角,r为圆形阵列的半径,M为阵元数目。Among them, τ m,k is the relative delay between signal source k and array element m relative to the center of the array, θ k and is the pitch angle and azimuth angle of the signal source k, r is the radius of the circular array, and M is the number of array elements.
作为本发明进一步的方案:由于是平面阵列,因此在步骤S4中,算法涉及到的方向矩阵A,应为:As a further solution of the present invention: since it is a planar array, in step S4, the direction matrix A involved in the algorithm should be:
其中,为阵列接收第i个信号源信息而产生的方向向量。in, The direction vector generated for the array receiving the i-th signal source information.
作为本发明进一步的方案:在步骤S4中,决定多信号分类算法最终搜索结果的谱函数为:As a further solution of the present invention: in step S4, the spectral function that determines the final search result of the multi-signal classification algorithm is:
其中,为传统谱函数P对方位角求二阶偏导的结果,为传统谱函数P对俯仰角θk求二阶偏导的结果。in, For the traditional spectral function P versus azimuth Find the result of the second order partial derivative, It is the result of calculating the second-order partial derivative of the traditional spectral function P with respect to the pitch angle θ k .
与现有技术相比,本发明的有益效果是:Compared with prior art, the beneficial effect of the present invention is:
1、采用八元十字麦克风阵列来接收放电信号,其平面阵列结构使得对声源位置的估计可以拓展为俯仰角和方位角两个参数,多参数的联合估计方法有益于更准确地确定放电声源的位置信息,有效完成局部放电的空间三维定位。1. The eight-element cross microphone array is used to receive the discharge signal. Its planar array structure enables the estimation of the position of the sound source to be extended to the two parameters of pitch angle and azimuth angle. The joint estimation method of multiple parameters is beneficial to more accurately determine the discharge sound. The location information of the source can effectively complete the spatial three-dimensional positioning of partial discharge.
2、通过对接收信号的傅里叶变换,获得放电信号的频谱信息,并从中提取主要的特征频率作为定位算法中频率参数的数值,精化了多信号分类算法中频率参数的取值,有利于加强信号的定位可靠性。2. Through the Fourier transform of the received signal, the spectrum information of the discharge signal is obtained, and the main characteristic frequency is extracted from it as the value of the frequency parameter in the positioning algorithm, which refines the value of the frequency parameter in the multi-signal classification algorithm. It is beneficial to strengthen the positioning reliability of the signal.
3、在所述步骤S4中,采用一种新的空间谱估计函数作为全局搜索后的峰值确定依据,相对于传统空间谱函数,这种方法在信号小信噪比和小快拍数情况下,对于电力设备的局部放电有更好的定位检测效果。3. In the step S4, a new spatial spectrum estimation function is used as the basis for determining the peak value after the global search. Compared with the traditional spatial spectrum function, this method has a small signal-to-noise ratio and a small number of snapshots. , it has a better positioning and detection effect for the partial discharge of power equipment.
附图说明Description of drawings
图1为本发明的算法流程图。Fig. 1 is the algorithm flowchart of the present invention.
图2为本发明采用的八元圆形传感器阵列接收远场放电信号时的模拟图。FIG. 2 is a simulation diagram of the eight-element circular sensor array used in the present invention when receiving far-field discharge signals.
具体实施方式Detailed ways
下面结合附图对本专利的技术方案作进一步详细地说明。Below in conjunction with accompanying drawing, the technical scheme of this patent is described in further detail.
参照附图1,一种基于多信号分类定位算法的电力设备局放检测方法,包括以下步骤:Referring to accompanying drawing 1, a kind of electric equipment partial discharge detection method based on multi-signal classification positioning algorithm comprises the following steps:
S1、通过八元圆形麦克风阵列传感器对电力设备发出的局部放电信号进行接收;S1. Receive the partial discharge signal sent by the power equipment through the eight-element circular microphone array sensor;
检测电力设备局部放电时,首先将八元圆形麦克风阵列的大致方位朝向待检测电力设备,持续一段时间,接收电力设备的放电信号。When detecting partial discharge of electrical equipment, firstly, the general orientation of the eight-element circular microphone array is directed towards the electrical equipment to be detected, and lasts for a period of time to receive the discharge signal of the electrical equipment.
S2、将接收到的带有声源信息的时域数字信号进行傅里叶变换,将其由时域转化为频域;S2. Perform Fourier transform on the received time-domain digital signal with sound source information, and convert it from time domain to frequency domain;
将每个麦克风接收到的信号做傅里叶变换,将其由时域转化为频域进行分析。其中,傅里叶变换针对的对象是接收到的放电数字信号的时域状态,单个麦克风传感器接收到的信号数据量与快拍数相关联,并且是傅里叶变换中的信号的长度参数。The signal received by each microphone is Fourier transformed, and it is converted from the time domain to the frequency domain for analysis. Among them, the object of Fourier transform is the time domain state of the received discharge digital signal, the signal data volume received by a single microphone sensor is associated with the number of snapshots, and is the length parameter of the signal in Fourier transform.
S3、对S2步骤中得到的频域放电信号进行特征频率提取,找到最能够代表接收到的放电信号的频率值;S3. Extracting the characteristic frequency of the frequency-domain discharge signal obtained in step S2, and finding the frequency value that best represents the received discharge signal;
由于放电信号具有一定的波动性,以及周围噪声的干扰,即使是通过滤波处理之后,得到的频域信息仍然不会是某一特定频率,而是诸多频率信号不同强度的叠加。其中信号强度较大的就是放电信号部分,在信号幅值较大的区域内,选取合适的频率作为接收到的放电信号的主频率,并在接下来的步骤S4的算法中,将这一数值带入到算法涉及到的信号频率参数中。Due to the certain volatility of the discharge signal and the interference of surrounding noise, even after filtering, the obtained frequency domain information will not be a specific frequency, but the superposition of many frequency signals with different intensities. Among them, the larger signal strength is the part of the discharge signal. In the region where the signal amplitude is larger, select an appropriate frequency as the main frequency of the received discharge signal, and in the algorithm of the next step S4, use this value Bring it into the signal frequency parameters involved in the algorithm.
S4、利用一种适用于小信噪比和小快拍数情况下的多信号分类的声源定位算法,结合S3步骤中得到的信号特征频率值,对接收到的放电信号进行分析定位S4. Utilize a sound source localization algorithm suitable for multi-signal classification in the case of small signal-to-noise ratio and small number of snapshots, and combine the signal characteristic frequency value obtained in step S3 to analyze and locate the received discharge signal
本发明步骤S4中具体的改进多信号分类算法原理如下:The concrete improved multi-signal classification algorithm principle in step S4 of the present invention is as follows:
多信号分类算法具有高分辨率、高精度和高稳定性的特点,因此适用于电力巡检中的异常放电定位场景。The multi-signal classification algorithm has the characteristics of high resolution, high precision and high stability, so it is suitable for the abnormal discharge location scene in power inspection.
该场景下,其用于确定信号来波方向时,有以下优点:In this scenario, when it is used to determine the incoming wave direction of a signal, it has the following advantages:
1.可对多个声源进行定位;1. Can locate multiple sound sources;
2.检测效果具有高精度;2. The detection effect has high precision;
3.天线波束信号具有高分辨率;3. The antenna beam signal has high resolution;
4.适用于短数据情况。4. Applicable to short data situations.
为方便理论分析,我们做以下规定:For the convenience of theoretical analysis, we make the following provisions:
1.每个测试信号源具有相同但不相关的极化。1. Each test signal source has the same but unrelated polarization.
2.信号源是窄带,同时每个源具有相同的中心频率ω0。2. The signal sources are narrowband, while each source has the same center frequency ω0.
3.假设测试信号源的个数为D;3. Assume that the number of test signal sources is D;
采集阵列是由M(M>D)个阵元组成的圆形阵列;需要说明的是,本发明中M的值具体为8,即本发明采用八元圆形阵列对放电信号进行接收,但在原理叙述时,设阵列中阵元个数为M个。The acquisition array is a circular array composed of M (M>D) array elements; it should be noted that the value of M in the present invention is specifically 8, that is, the present invention uses an eight-element circular array to receive the discharge signal, but When describing the principle, let the number of array elements in the array be M.
每个元素具有相同的特性,并且在每个方向上都是各向同性的。Each element has the same properties and is isotropic in every direction.
4.麦克风阵元间距为d,且阵元间距不大于最高频率信号波长的一半。4. The distance between the microphone elements is d, and the distance between the elements is not greater than half of the wavelength of the highest frequency signal.
5.麦克风阵列属于远场场景,即收到的声源信号可以模拟为平面波;5. The microphone array belongs to the far-field scene, that is, the received sound source signal can be simulated as a plane wave;
6.阵列元素和测试信号都是不相关的;6. Both array elements and test signals are uncorrelated;
方差σ2为零平均高斯噪声nm(t);The variance σ 2 is zero mean Gaussian noise n m(t) ;
7.接收信号支路的特征相同。7. The characteristics of the receiving signal branches are the same.
假设传播到麦克风阵列的信号源数量为k(k=1,2,…,D),波前信号为Sk(t),我们假设其为窄带信号,由于窄带信号的简化条件,Sk(t)可以表示为:Assuming that the number of signal sources propagating to the microphone array is k (k=1,2,...,D), and the wavefront signal is S k (t), we assume it is a narrowband signal. Due to the simplified condition of the narrowband signal, S k ( t) can be expressed as:
Sk(t)=sk(t)exp[jωk(t)]S k (t) = s k (t) exp[jω k (t)]
其中,sk(t)是Sk(t)的复包络。where s k (t) is the complex envelope of S k (t).
ωk(t)是Sk(t)的角频率。ω k (t) is the angular frequency of S k (t).
所有信号的中心频率ω0相同。The center frequency ω 0 is the same for all signals.
因此therefore
其中,c为信号波速。Among them, c is the signal wave speed.
λ为波长。λ is the wavelength.
同时,at the same time,
λ=c/fλ=c/f
将本发明中步骤S3得到的频率值带入,c取340m/s,可以得到λ。Bring in the frequency value obtained in step S3 of the present invention, and c is 340m/s, and λ can be obtained.
设阵列麦克风单元之间延迟所需时间为t1。The time required for the delay between the array microphone units is assumed to be t 1 .
在信号为窄带条件下,有:Under the condition that the signal is narrowband, there are:
Sk(t-t1)≈Sk(t)S k (tt 1 )≈S k (t)
因此,延迟后的波前信号是Therefore, the delayed wavefront signal is
以本发明中的圆阵中心作为麦克风传感器参考点。The center of the circular array in the present invention is used as the reference point of the microphone sensor.
当时刻t时,阵元m(m=1,2,...,M)对第k个信号源的感应信号为At time t, the induction signal of the kth signal source by the array element m (m=1,2,...,M) is
其中,ak是阵元m对信号源k的影响系数。Among them, a k is the influence coefficient of array element m on signal source k.
因为每个阵元不具备方向性,所以设ak=1;Because each array element does not have directionality, so set a k =1;
τm,k是信号源k与阵元m相对阵列中心的相对延时,可表示为τ m,k is the relative delay between signal source k and array element m relative to the center of the array, which can be expressed as
其中,r为阵列半径。Among them, r is the array radius.
和θk分别为信号源k的方位角和俯仰角。 and θ k are the azimuth and elevation angles of the signal source k, respectively.
为附图2中信号源与正x轴间的负角,范围在0°-360°。 It is the negative angle between the signal source and the positive x-axis in Fig. 2, and the range is 0°-360°.
θk是附图2中信号源与阵列中心法线正方向之间的夹角,范围在0°-90°。θ k is the angle between the signal source and the positive direction of the array center normal in Figure 2, and the range is 0°-90°.
考虑上噪声和所有信号源的来波,则第m个阵元的输出信号为:Considering the noise and incoming waves from all signal sources, the output signal of the mth array element is:
其中,nm(t)为测量噪声。where n m(t) is the measurement noise.
将上式写成向量形式,并令ak=l,则有Write the above formula in vector form, and let a k = l, then we have
X(t)=α(θk)Sk(t)+N(t)X(t)=α(θ k )S k (t)+N(t)
其中,in,
X(t)=[x1(t),x2(t),…xM(t)]T X(t)=[x 1 (t), x 2 (t), ... x M (t)] T
N(t)=[n1(t),n2(t),…,nM(t)]T N(t)=[n 1 (t), n 2 (t), ..., n M (t)] T
则,but,
X(t)=AS(t)+N(t)X(t)=AS(t)+N(t)
其中in
S(t)=[S1(t),S2(t),…,SD(t)]T S(t)=[S 1 (t), S 2 (t), ..., S D (t)] T
至此,问题就变成对xm(t)进行采样,然后从{xm(i),i=1,2,...,M}中估计信号源k的来波方向。So far, the problem becomes to sample x m (t), and then estimate the direction of arrival of signal source k from {x m (i), i=1, 2, . . . , M}.
对于阵列输出x(t),其协方差矩阵R为For the array output x(t), its covariance matrix R is
R=E[X(t)XH(t)]R=E[X(t)X H (t)]
信号和噪声是不相关的,噪声为零平均白噪声。The signal and noise are uncorrelated, and the noise is zero-mean white noise.
因此可以得到下列结果:Therefore the following results can be obtained:
R=E[(AS+N)(AS+N)H]R=E[(AS+N)(AS+N) H ]
=AE[SSH]AH+E[NNH]=AE[SS H ]A H +E[NN H ]
=APAH+RN= APAH +RN
其中,P为空间信号的相关矩阵,RN为噪声的相关矩阵,可分别表示如下Among them, P is the correlation matrix of the spatial signal, and R N is the correlation matrix of the noise, which can be expressed as follows
P=E[S(t)SH(t)]P=E[S(t)S H (t)]
RN=σ2IR N =σ 2 I
其中,σ2是噪声功率,I是M×M的单位矩阵。Among them, σ 2 is the noise power, and I is the identity matrix of M×M.
当θi≠θj,i≠j时,矩阵A是由上式定义的范德蒙德矩阵。When θ i ≠ θ j , When i≠j, matrix A is a Vandermonde matrix defined by the above formula.
由于A是范德蒙德矩阵,所以其每一列之间互相独立。Since A is a Vandermonde matrix, each column is independent of each other.
这样,若P为非奇异阵,既有:In this way, if P is a non-singular matrix, there are:
rank(APAH)=Drank(APA H )=D
由于P是正定的,因此矩阵APAH的特征值为正,即共有D个正的特征值。因此,R为满秩矩阵,有M个特征值。Since P is positive definite, the eigenvalues of the matrix APA H are positive, that is, there are D positive eigenvalues in total. Therefore, R is a full-rank matrix with M eigenvalues.
我们再将特征值降序排列,有We then arrange the eigenvalues in descending order, we have
λ1≥λ2≥…≥λM>0λ 1 ≥λ 2 ≥…≥λ M >0
这M个特征值中,较大的D个特征值对应于信号,而剩下的较小的M-D个特征值对应于噪声。Among the M eigenvalues, the larger D eigenvalues correspond to the signal, and the remaining smaller M-D eigenvalues correspond to the noise.
因此,可以将R的特征值(特征向量)分解为信号特征值(特征向量)和噪声特征值(特征向量)。Therefore, the eigenvalues (eigenvectors) of R can be decomposed into signal eigenvalues (eigenvectors) and noise eigenvalues (eigenvectors).
设λi为矩阵R的第i个特征值,vi为对应于λi的特征向量,则:Let λi be the ith eigenvalue of matrix R, and vi be the eigenvector corresponding to λi, then:
Rvi=λivi Rv i =λ i v i
设λi=σ2是R的最小特征值,则有Let λ i = σ 2 be the minimum eigenvalue of R, then we have
Rvi=σ2vi,i=D+1,D+2,…,MRv i = σ 2 v i , i = D+1, D+2, ..., M
σ2vi=(APAH+σ2I)vi,i=D+1,D+2,…,Mσ 2 v i =(APA H +σ 2 I)v i , i=D+1, D+2, . . . , M
整理可得:Organized to get:
APAHvz=0APA H v z =0
因为AHA是D×D维满秩矩阵,所以(AHA)-1存在,P-1也存在。从上面看,同时在上式两边同乘P-1(AHA)-1AH,可得:Because A H A is a D×D dimensional full-rank matrix, (A H A) -1 exists, and so does P -1 . Seen from the above, multiplying P -1 (A H A) -1 A H on both sides of the above formula at the same time, we can get:
P-1(AHA)-1AHAP Hvi=0P -1 (A H A) -1 A H AP H v i =0
因此,therefore,
AHvi=0,i=D+1,D+2,…,MA H v i =0, i=D+1, D+2,..., M
即噪声特征向量与信号矩阵的列向量垂直。That is, the noise eigenvectors are perpendicular to the column vectors of the signal matrix.
也就是说我们找到与噪声子空间正交(或者最接近于正交的)向量,其方向就代表了波达方向。That is to say, we find the vector orthogonal to the noise subspace (or the closest to it), and its direction represents the direction of arrival.
使用噪声特征值作为每列,构造一个噪声矩阵:Construct a noise matrix using noise eigenvalues for each column:
En=[VD+1,VD+2,…,VM]E n =[V D+1 , V D+2 , . . . , V M ]
进而定义二维空间谱:Then define the two-dimensional spatial spectrum:
式中分母是信号矩阵和噪声矩阵的内积。where the denominator is the inner product of the signal matrix and the noise matrix.
理想状态下,分母的值为零。Ideally, the value of the denominator is zero.
但由于检测电力设备时环境中噪声的存在,分母只是存在最小值,因此有一个峰值。However, due to the presence of noise in the environment when detecting electrical equipment, the denominator only has a minimum value, so There is a peak.
对二维空间进行搜索,使θ和发生变化,寻找二维空间谱的峰值,进而来确定声源位置。Search the two-dimensional space such that θ and Change, find the peak of the two-dimensional spatial spectrum, and then determine the location of the sound source.
但当接收到的信号信噪比较低且信号数据个数不多时,上述的空间谱估计声源位置不能取得很好的效果,本发明提出一种对空间谱函数进行改进的多信号分类算法。However, when the signal-to-noise ratio of the received signal is low and the number of signal data is small, the above-mentioned spatial spectrum estimation of the sound source position cannot achieve good results. The present invention proposes a multi-signal classification algorithm that improves the spatial spectrum function .
本发明在谱峰处分别对俯仰角和方位角求二阶导数,构造新的空间谱函数,进而提高算法的分辨率。The invention calculates the second-order derivatives for the pitch angle and the azimuth angle respectively at the peak of the spectrum, constructs a new space spectrum function, and further improves the resolution of the algorithm.
假设方位角的范围为角的范围为搜索间隔为俯仰角θ的范围为Rθ,搜索间隔为△θ。Assume that the range of azimuth angles is angle in the range of The search interval is The range of the pitch angle θ is Rθ, and the search interval is Δθ.
则令order
则空间谱函数可表示为:Then the spatial spectral function can be expressed as:
由二元离散函数对变量求偏导数可得,在处离散函数P对自变量的一阶偏导数为:It can be obtained by calculating the partial derivative of the variable by the binary discrete function, in The discrete function P at the independent variable The first partial derivative of is:
记为P′φk。remember is P′ φk .
在处对的二阶导数为:exist right The second derivative of is:
记为P″φk。remember is P″ φk .
同理可得在处离散函数P对自变量θ的一阶导数和二阶导数分别为:in the same way The first and second derivatives of the discrete function P with respect to the independent variable θ are:
记与分别为 remember and respectively
由分析可知,原谱函数极大值点的二阶导数在方位角和俯仰角的到达角处构成尖锐的负向谱峰。It can be seen from the analysis that the second derivative of the maximum point of the original spectral function forms a sharp negative spectral peak at the arrival angle of the azimuth and elevation angles.
由此可对新谱函数进行整理:即将偏导数大于0的数值归为0,因此可得到新谱函数为:From this, the new spectral function can be sorted out: that is, the values with partial derivatives greater than 0 are classified as 0, so the new spectral function can be obtained as:
由于P对和θ求二阶偏导是相互独立的,所以可以将原谱函数的二阶导数P”表示为:Since P is right and θ are independent of each other, so the second derivative P" of the original spectral function can be expressed as:
由以上公式可构成新的空间谱函数;A new spatial spectrum function can be formed by the above formula;
在步骤S4中,通过算法对空间的角度进行遍历之后,找到新的空间谱函数的谱峰,其所对应的方位角和俯仰角就是估计出的电力设备放电声源的空间位置。In step S4, after traversing the spatial angles through the algorithm, a new spectral peak of the spatial spectral function is found, and its corresponding azimuth and elevation angles are the estimated spatial position of the electric equipment discharge sound source.
本发明的有益效果是:The beneficial effects of the present invention are:
1.采用八元十字麦克风阵列来接收信号,其平面阵列结构使得对声源位置的估计可以拓展为俯仰角和方位角两个参数,多参数的联合估计方法有益于更准确地确定放电声源的位置信息,有效完成局部放电的空间三维定位。1. An eight-element cross microphone array is used to receive signals. Its planar array structure enables the estimation of the position of the sound source to be extended to the two parameters of pitch angle and azimuth angle. The joint estimation method of multiple parameters is beneficial to more accurately determine the discharge sound source The location information of the device effectively completes the spatial three-dimensional positioning of partial discharge.
2.通过对接收信号的傅里叶变换,获得放电信号的频谱信息,并从中提取主要的特征频率作为定位算法中频率参数的数值,精化了多信号分类算法中频率参数的取值,有利于加强信号的定位可靠性。2. Through the Fourier transform of the received signal, the spectrum information of the discharge signal is obtained, and the main characteristic frequency is extracted from it as the value of the frequency parameter in the positioning algorithm, which refines the value of the frequency parameter in the multi-signal classification algorithm. It is beneficial to strengthen the positioning reliability of the signal.
3.在所述步骤S4中,采用一种新的空间谱估计函数作为全局搜索后的峰值确定依据,相对于传统空间谱函数,这种方法在信号小信噪比和小快拍数情况下,对于电力设备的局部放电有更好的定位检测效果。3. In the step S4, a new spatial spectrum estimation function is used as the basis for determining the peak value after the global search. Compared with the traditional spatial spectrum function, this method has a small signal-to-noise ratio and a small number of snapshots. , it has a better positioning and detection effect for the partial discharge of power equipment.
上述仅为本发明的具体实施方式,但本发明的设计构思并不局限于此,凡利用此构思对本发明进行非实质性的改动,均应属于侵犯本发明保护范围的行为。The above is only a specific embodiment of the present invention, but the design concept of the present invention is not limited thereto, and any non-substantial changes made to the present invention by using this concept should be an act of violating the protection scope of the present invention.
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