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Method of GIL partial discharge localization based on natural neighbour interpolation and ECOC‐MLP‐SVM using optical simulation technology

2021; Institution of Engineering and Technology; Volume: 6; Issue: 3 Linguagem: Inglês

10.1049/hve2.12071

2096-9813

Yiming Zang, Yong Qian, Hui Wang, Antian Xu, Gehao Sheng, Xiuchen Jiang,

Plasma Diagnostics and Applications

High VoltageVolume 6, Issue 3 p. 514-524 ORIGINAL RESEARCH PAPEROpen Access Method of GIL partial discharge localization based on natural neighbour interpolation and ECOC-MLP-SVM using optical simulation technology Yiming Zang, orcid.org/0000-0002-1370-8820 Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorYong Qian, Corresponding Author qian_yong@sjtu.edu.cn Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China Correspondence Yong Qian, Department of Electrical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road Minhang, Shanghai, 200240, China. Email: qian_yong@sjtu.edu.cnSearch for more papers by this authorHui Wang, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorAntian Xu, Department of Light Sources and Illuminating Engineering, Fudan University, Shanghai, ChinaSearch for more papers by this authorGehao Sheng, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorXiuchen Jiang, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this author Yiming Zang, orcid.org/0000-0002-1370-8820 Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorYong Qian, Corresponding Author qian_yong@sjtu.edu.cn Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China Correspondence Yong Qian, Department of Electrical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road Minhang, Shanghai, 200240, China. Email: qian_yong@sjtu.edu.cnSearch for more papers by this authorHui Wang, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorAntian Xu, Department of Light Sources and Illuminating Engineering, Fudan University, Shanghai, ChinaSearch for more papers by this authorGehao Sheng, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this authorXiuchen Jiang, Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, ChinaSearch for more papers by this author First published: 22 March 2021 https://doi.org/10.1049/hve2.12071 Associate Editor: Chuanyang Li AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Partial discharge (PD) is one of the main causes rendering the deterioration of the insulation state in gas-insulated transmission line (GIL). Accurate and timely localization of the PD source is essential to ensure the safe and stable operation of the GIL. At present, optical PD detection technology shows advantages in terms of high sensitivity and strong anti-interference performance. Therefore, an optical PD localization method based on optical simulation fingerprint database is proposed. The introduction of simulation conquers the difficulty of obtaining a PD fingerprint database in field experiments. This method constructs a simulation fingerprint database by performing PD simulation in a GIL simulation model of the same size as the actual GIL. The natural neighbour interpolation algorithm is applied to expand the simulation fingerprint database to cover all locations in the GIL. The two-level localization method proposed is to match the PD fingerprint to be tested with the expanded fingerprint database, which can reduce the amount of calculation while maintaining the localization accuracy. The experimental results show that the average localization error of this method is only 9.7 mm, and the localization time is reduced by about 11 times compared with the normal one-level localization method. 1 INTRODUCTION To meet the large-scale power transmission need and reduce transmission loss, gas-insulated transmission line (GIL) has been widely utilized worldwide since the 1970s [1-3]. During the operation of the GIL, the defects and deterioration of the insulation pose a significant threat to its safety [4], while partial discharge (PD) serves as a harbinger and manifestation of insulation degradation [5, 6]. Therefore, the localization of PD in the GIL functions as an important measure to improve the efficiency of maintenance and ensure a stable operation. Till date, the PD localization for the GIL has mainly been based on the detection of ultra–high frequency (UHF) signals and ultrasonic signals [7-9–7-9]. By contrast, the optical-only PD localization method performs with high sensitivity, no electromagnetic interference and no mechanical vibration interference [10, 11], which has promising research prospects and application value. Nevertheless, little research on optical-only PD localization for the GIL and even other gas-insulated equipment could be found, and available ones mainly focus on two aspects of research. One is using an optical array for PD localization; yet, the optical array can only detect PD in a rather small area and does not work when confronted with the GIL with a long-distance structure [12]. The other is applying fingerprint database and machine learning into the optical PD localization. The Biswendu Chatterjee team conducted a series of optical PD experiments at different locations in the actual experiment device to assemble data. They put the optical PD fingerprint database containing location information into machine learning algorithms for training, which is used for the PD localization by fingerprints matching [13-15–13-15]. However, this method is limited due to several factors such as the huge size of the actual equipment and the complexity of the field situation. In this way, difficulty in obtaining training data for machine learning through a large number of field PD experiments could be seen. Moreover, this method can only identify the PD source generated at the specific location where the PD experiment was performed, which results in substantial impacts on localization accuracy. Therefore, we propose a novel optical PD localization method based on natural neighbour interpolation (NNI) and the Error Correcting Output Codes-Multilayer Perceptron-Support Vector Machine model (ECOC-MLP-SVM) applying optical simulation technology, designed to improve the detection range, accuracy and efficiency of the GIL PD localization. This method builds a GIL simulation model in Tracepro software [16] that is exactly the same as the actual GIL size and sensor layout, which can adjust according to the actual size. In the simulation model, the optical PD simulation is performed to obtain optical PD fingerprints at different locations in the GIL, in order to get over the difficulty of obtaining PD data in field experiments. To a certain extent, the higher the density of the fingerprint the database shows, the higher the localization accuracy is. Due to the large size of the GIL, it is impractical to simulate the PD signals at all locations. Therefore, a fingerprint expansion method to expand the limited optical PD fingerprints to PD fingerprints at all locations in the GIL through the NNI algorithm is proposed, which will boost the database density and make up for the defect that only a few specific PD locations can be identified. Meanwhile, in order to eliminate the impact of the actual PD signal intensity changes, the principal component analysis (PCA) algorithm is used to extract the feature of the difference between each optical signal irradiance as the PD fingerprint feature. In this process, however, the large size of the GIL and the expanded fingerprint database aiming to improve localization accuracy will drastically increase the number of learning samples, resulting in a significant drop in fingerprint matching efficiency. Therefore, we propose a two-level PD localization method to reduce the amount of calculation in the location process, solving the problem of the dimensionality curse caused by too many fingerprints. In the first level (pre-localization), the improved ECOC-MLP algorithm is used to match on a fingerprint database with a large range but low density to obtain the approximate area where the PD source is located. Since the ECOC-MLP algorithm can simplify the multi-classification problem into multiple two-classification problems, the dimensionality curse problem can be settled by using the two-classification method [17]. Furthermore, the low-density fingerprint database used in the first level reduces the amount of calculation rather than directly using a normal density fingerprint database for localization. In the second level (final localization), a small-range fingerprint database that contains a limited number of fingerprints is established in the approximate small area confirmed in the first level. Finally, the SVM algorithm is used to match the detected PD fingerprint in the second-level fingerprint database to obtain the specific location of the PD source. Optical PD simulation is applied instead of conducting an experiment to obtain PD fingerprint data. Then, the NNI algorithm is used to perform fingerprint expansion on the limited simulated fingerprint data, thereby establishing an optical PD fingerprint database covering all locations in the GIL. Finally, through the two-level matching model based on the ECOC-MLP-SVM, the PD source is accurately and efficiently located. The feasibility of this method is verified by the laboratory GIL experimental model. 2 OPTICAL PD SIMULATION MODEL OF THE GIL 2.1 Simulation settings of optical PD signals In the optical PD simulation, the typical needle-plate defect is used to simulate the generation of PD, and other types of PD defect are also applicable. In the simulation, a spherical point light source is set as the PD source, located on the head of the needle defect. It is assumed that the optical PD signals emitted by the PD source are perpendicular to the PD source surface and are evenly distributed [18]. The optical radiation flux of the PD source is 100 watts. The total number of optical rays is 250,000. The insulating medium in the GIL simulation model is set to SF6, whose optical refractive index is 1.000783. The absorption spectrum of SF6 is mainly concentrated in the mid-infrared band, while the wavelength of the PD light radiation in SF6 is mainly concentrated at approximately 500 nm. Thus, the absorption of light by SF6 can be negligible, and we set the PD light source to green light with a wavelength of 546.1 nm [19]. In order to effectively simulate the received intensity of the optical sensor, the concept of light irradiance E0 is proposed: E o = d I o d S (1)where Io is the light radiation flux received by the optical sensor and S is the receiving area of the sensor. On the condition that the PD localization method is based on the distribution of optical signals between different sensors rather than the direct use of actual intensity, the relative irradiance Eo can fully represent the characteristics of optical PD signals between each sensor. 2.2 Simulation settings of GIL model material The material parameters of the GIL simulation model exert a pivotal influence on the propagation and scattering of PD optical signals. The diffuse reflection model of the simulation GIL surface material is a bidirectional reflection distribution function (BRDF) [20]. In Figure 1, this model determines the reflection and scattering law of the PD light signal on the inner surface of the GIL model. where αr, θr and ϕr represent the solid angle, elevation angle and azimuth angle of the reflected light, respectively. αi, θi and ϕi represent the solid angle, elevation angle and azimuth angle of the incident light, respectively. FIGURE 1Open in figure viewer Schematic diagram of the BRDF The definition of the BRDF model is f ( θ i , ϕ i , θ r , ϕ r ) = d L ( θ r , ϕ r ) d E ( θ i , ϕ i ) (2)where dE is the incident light irradiance in a direction per unit area and dL is the reflecting light irradiance in a direction per unit area. The material of this simulation model is set to aluminum consistent with the experimental GIL tank material. Considering aluminum is a non-transmissive metal material, only the absorption, specular reflection and diffuse reflection of the tank need to be taken into account during the propagation of PD light in this simulation model. The relationship of these three parameters satisfies the following relationship: α + R + D = 1 (3)where α represents the absorption coefficient, R represents the specular reflection coefficient and D represents the diffuse reflectance coefficient [18]. The GIL material used is polished and oxidized medium-smooth aluminium. Among them, the corresponding parameters of the polished and oxidized medium-smooth aluminum used in the GIL model are α = 0.3, R = 0.2 and D = 0.5 [21]. 2.3 Simulation settings of GIL structure Owing to the fact that long-distance GIL equipment currently in operation cannot be used for PD testing and lacks reserved optical sensor installation locations and allowing for the main structural characteristics of GIL, a test GIL tank was built in the laboratory and a GIL simulation model of the same size was built in the Tracepro software. The simulation model with the same size as the experimental GIL tank is shown in Figure 2. FIGURE 2Open in figure viewer Structure diagram of GIL simulation tank The specific dimensions of the experimental GIL are as follows: the wall thickness is 10 mm, the inner radius is 90 mm, the internal height of the GIL tank is 310 mm and the inner conductor diameter of the axis is 25 mm. The axis conductor post is connected to a needle-plate defect model that can change the angle and radial length. The distance among the needle plates is always 6 mm, the angle of the tip cross section is 30°, the length of the needle tip is 25 mm and the radius of the grounding disk below is 10 mm. The occurrence of PD at different locations in the GIL is simulated by changing the location of the needle-plate defect. For the collection of optical PD signals, according to the distribution of optical sensors on the experimental GIL simulation tank, nine optical signal detection points are also set on the inner wall of the simulated GIL model. Nine detection points are divided into 3 columns at 120° around the tank. The distance between the centre of the 3 detection points on each column from the top surface of the tank is 70, 160 and 250 mm, respectively. The detection point has a radius of 10 mm and is a fully transmissive volume model, which would not generate any catadioptric reflection or absorption effect on the light emitted by the PD source. According to the aforementioned simulation settings, a PD source is randomly selected in the GIL simulation tank to perform an optical PD simulation experiment. The ray-tracing diagram and the light irradiance distribution through three cross sections are shown in Figure 3. FIGURE 3Open in figure viewer Schematic diagram of optical PD simulation 2.4 Establishment of optical PD fingerprint database On the basis of the aforementioned optical PD simulation, the optical PD fingerprint database is set up, which figures out the problem of obtaining the fingerprint database on site and improves the resolution of the fingerprint database. The construction process of the fingerprint database presents as follows. An optical PD simulation experiment is performed at N locations in the simulation tank. Let Lj be the location of PD sources (j = 1,2, …, N). In every simulation experiment, there are M detection probes for optical signal acquisition. Let Si be the detection probes (i = 1,2, …, M). When the simulated PD source is located at Lj, the PD light irradiance detected by the detection probes Si is expressed as φ'i,j. In order to highlight the strength difference and distribution law of the PD signals among the sensors, and to avoid the adverse effects caused by the fluctuation in the intensity of the optical signal between different PD sources, we use the detection signal after normalization and PCA feature extraction as PD fingerprint. First, the value of each detection probe is subtracted from each other. D = M ! ( M − 2 ) ! × 2 ! (4) δ h , N ′ = φ a , N ′ − φ b , N ′ s . t . { h = 1,2 , … , D a < b ; a , b ∈ Z ; a , b ∈ [ 1 , M ] . (5)where D stands for the fingerprint dimension after subtraction, φ'a,N and φ'b,N represent the light irradiance of the PD at N location detected by probes and δ' is the difference of the light irradiance between each two detection probes. Second, all the values δ' of the same PD source are normalized to [-1,1]. The rule of normalization is δ h , j = 2 × ( δ h , j ′ − min ( δ 1 , j ′ , δ 2 , j ′ , ⋯ , δ D , j ′ ) ) ( max ( δ 1 , j ′ , δ 2 , j ′ , ⋯ , δ D , j ′ ) − min ( δ 1 , j ′ , δ 2 , j ′ , ⋯ , δ D , j ′ ) ) − 1 (6)where δh,j is the normalized light irradiance value. Third, the first P principal components are extracted from N vector [δ1,j, δ2,j,…, δD,j]T by the PCA algorithm, obtaining N final PD fingerprint Ψj = [φ1,j,φ2,j,…,φP,j]T. Finally, all PD fingerprints Ψj are combined into an optical PD fingerprint database Ψ: ψ = [ φ 1,1 φ 1,2 ⋯ φ 1 , N φ 2,1 φ 2,2 ⋯ φ 2 , N ⋮ ⋮ ⋮ ⋮ φ P , 1 φ P , 2 ⋯ φ P , N ] (7)where P is the fingerprint dimension (P < D), N is the number of the simulated PD sources, the column vector Ψj= [φ1,j,φ2,j,…,φP,j]T in the matrix represents the optical PD fingerprint of the PD source Lj and φ is the transformed fingerprint feature after PCA. The simulated fingerprint database can be built in line with different structures and sizes of GIL equipment, replacing large-scale offline repetitive experiments and improving localization flexibility. In the fingerprint database, each PD fingerprint represents the feature information related to location of one PD source. We match the PD fingerprint to be located with the fingerprints in the fingerprint database through a matching algorithm proposed, so as to obtain a final fingerprint, the most similar to the fingerprint to be located. The location corresponding to the final fingerprint is recognized as the localization result. 3 PD FINGERPRINT EXPANSION: NNI In the optical PD simulation, although we select as many PD source locations as possible in the GIL simulation tank for simulation, in light of the simulation time and efficiency, it is impossible to traverse all locations in the GIL. Therefore, a PD fingerprint expansion method is proposed to solve the problem of limited location of simulated PD sources. In this manner, the scale of fingerprint samples in the fingerprint database is enlarged, improving the range and accuracy of localization. 3.1 Natural neighbour coordinates The natural neighbour is based on the Voronoi tesselation (VT) and the Delaunay triangulation (DT). Although the problem of interpolation in three-dimensional (3D) coordinates is solved here, NNI has the same principle in two-dimensional (2D) and 3D, except that the 2D is extended to 3D Voronoi polyhedra and Delaunay tetrahedra [22]. Therefore, a more intuitive 2D theory is used here to explain. In the NNI, the VT and DT of the scattered point set correspond to each other. The VT partitions the plane (or space) into a disjoint set of polygons (or polytopes) called tiles. Each tile Ti encloses one given point xi in the scattered point set. The Ti represents the area (or volume) that is closer to the point xi than to any other points of the set: T i = { x ∈ R 2 | d ( x , x i ) ≤ d ( x , x j ) ∀ j = 1 , … , n } (8)where d (x, xi) represents the Euclidean distance between the points x and xi. If xi and xj have a common boundary or point of contact, the two points are called natural neighbour. Before NNI, the construction of VT and DT of the given scattered point set is a necessary preprocessing step. 3.2 Natural neighbour interpolation Based on the VT and DT constructed, the concept of natural neighbour can be adapted to a newly inserted point x that is not in the present point set. The new point x creates a new Voronoi cell by stealing area (or volume) from the existing and surrounding natural neighbours, as shown in Figure 4 [23]. FIGURE 4Open in figure viewer Voronoi diagram and Delaunay triangulation (DT) with insertion point x In Figure 4, bold lines represent the tile after the insertion of point x. The dotted lines indicate the old edges before the insertion of point x. The DT associated with the VT is shown by dashed lines, where the boundaries of the tile are the vertical bisector of the triangle boundaries. Therefore, the new tile of point defines as T ( x ) = { z ∈ R 2 | d ( z , x i ) ≤ d ( z , x j ) ∀ j = 1 , … , n } (9) The intersections of new tile and old tiles are T i ( x ) = T ( x ) ∩ T i (10) Thus, representing the area of a tile T by S(T), the NNI at the point x defines as f ( x ) = ∑ i h i ( x ) z i (11)where h i ( x ) = S [ T i ( x ) ] S [ T ( x ) ] ( 0 ≤ h i ( x ) ≤ 1 , ∑ i h i ( x ) = 1 ) (12) Through (6), it can show that the NNI is a weighted average of the natural neighbours of the interpolated point x. However, (6) is only C0 continuous. We must use a C1-continuous interpolant at each point in the set. Therefore, we denote the gradient ∇z(x) as the function z(x) at the point xi, and replace the zi in (6) by a first-degree polynomial gi(x) shown as g i ( x ) = z i + ∇ z ( x i ) T ( x − x i ) (13) According to (8), we combine the values zi and their corresponding gradients while using natural neighbour weights. Thus, the NNI value defines as f ( x ) = ∑ i w i ( x ) g i ( x ) = ∑ i h i ( x ) d ( x , x i ) − 1 ∑ i h i ( x ) d ( x , x i ) − 1 g i ( x ) (14)where w i ( x ) = ∑ i h i ( x ) d ( x , x i ) − 1 ∑ i h i ( x ) d ( x , x i ) − 1 (15) NNI is a method based on area-based weights, which is superior to distance-based weights, since NNI would compensate for the data density change, not just be sensitive to distance. Through NNI, the fingerprint database Ψ is expanded to the fingerprint database ΨNNI, which covers the PD fingerprints of all locations in the GIL tank. Finally, in response to the localization requirements of different accuracy, we use different sampling rates to sample fingerprints in ΨNNI, so as to build fingerprint databases with different degrees of density. 4 TWO-LEVEL PD LOCALIZATION METHOD: ECOC-MLP-SVM Although the accuracy and range of localization are improved by the NNI fingerprint expansion, it also increases the burden of calculation in the matching process. Moreover, in view of the large size of the actual GIL device, the number of fingerprints will increase simultaneously while constructing the simulated fingerprint database. Therefore, a two-level fingerprint matching method using ECOC-MLP-SVM is proposed, which can reduce the amount of calculation and avoid the dimensionality curse caused by a large number of PD fingerprints. 4.1 First-level PD localization: ECOC-MLP The first level of localization is for the entire area of the GIL tank, but the fingerprint database is constructed at a lower sampling rate from ΨNNI, that is, the low-density fingerprint database. This method can ease the burden of fingerprint calculation in the matching process and realize the pre-localization of the PD localization. Although it is devised for the low-density fingerprint database, due to the large size of the GIL and the accuracy of pre-localization, a certain number of fingerprints still remain in the first-level fingerprint database. Therefore, we use the ECOC-MLP algorithm that can simplify the multi-classification problem into multiple binary classification problems to avoid the dimensionality curse in pre-localization. The ECOC-MLP algorithm includes two main stages: training stage and test stage. For the training stage, we define a C × b code matrix, where C represents the number of classes. Each class label is encoded by the rows of the coding matrix. Using training samples to train each base classifier of the coding matrix, a classifier with b output nodes can be obtained. For the test stage, an incoming test sample x is applied to the trained classifier, creating an output vector: y = [ y 1 , y 2 , ⋯ , y b ] T (16)where yj is the output of jth (j = 1, 2, …, b) node. For each class, the ECOC calculates the distance between the output vector and each label of class: L i = ∑ j = 1 b | Z i j − Z j | (17)where Zij represents the value at ith row and jth column in code matrix. Therefore, the decoding rule for test sample x is i = A r g M i n ( L i ) (18) Using the aforementioned decoding rules, the MLP learning network is used to transform the determination of each codeword in the coding matrix into the process of weight learning in the MLP network, which is more adapted to the ECOC method [24]. During the construction of the MLP network, a weight ω is introduced to reflect the influence of error in the output vector produced by each incoming sample. By the adjustment of the weight ω, when the error on target codeword is high, produced error in each output node has more influence on the training cost function. This allows the weight parameters of the network to be effectively updated, reducing the error on total codeword by trained network. Therefore, we combine the weight with the MLP training form of minimizing the squared error cost function. The modified cost function F is F ( w ) = 1 N ∑ i = 1 N ω i ( y ( w , u i ) − d i ) 2 (19)where ωi represents the weight of error produced by ith sample, ui is the input vector, di is the desired network output and y(w,ui) is the actual network output of the ith training vector. The summation of total errors produced by the ith sample in target codeword is as follows: ω i = ∑ j = 1 b ( y i j ( w , u i ) − d i j ) 2 (20)where j is the number of output nodes, b is the length of codeword. Therefore, the first-level fingerprint database is matched by ECOC-MLP to get the first-level location of the PD source, which is prepared for the second-level localization. 4.2 Second-level PD localization: SVM The second level of localization is for a small range but a normal density PD fingerprint database. Although the density of the fingerprint database is higher than that in the first level, the fingerprint database covers a smaller range. Therefore, the number of fingerprints will be far less than in the first level. Centring on the cross section where the first-level localization result locates, extending a certain distance (depends on specific size) to both sides of the GIL is selected as the range of fingerprint matching. In this limited range, ΨNNI is sampled at a normal density to obtain the second-level fingerprint database. The selection of database range in two-level localization is shown in Figure 5. FIGURE 5Open in figure viewer Schematic diagram of two-level PD localization SVM minimizes confidence and empirical risk, so that it can achieve a good classification effect in the case of small samples, while it will have the curse of dimensionality when the number of samples is large. Thus, for the second-level fingerprint database, we use the SVM algorithm to match the actually detected PD fingerprints with the second-level fingerprint database, obtaining the fingerprint most similar to the detected one. The matching function of the SVM algorithm is f ( x ) = sgn ( ∑ i = 1 n λ i y i K ( x i , x ) + b ) ( i = 1,2 , ⋯ , n ) (21)where n is the number of training samples, λ is Lagrange multiplier, yi is the label of xi, b is threshold and K(xi,x) is the inner product kernel function. Here, the Radial Basis Function is used as the kernel function: K ( x i , x j ) = exp ( − ‖ x i − x j ‖ 2 2 σ 2 ) (22)where σ represents kernel function parameters. The parameters of SVM are determined through optimization. Through determining the spatial position corresponding to the PD fingerprint identified by SVM, the final location of the PD source can be obtained in the second-level PD localization. 5 EXPERIMENTAL VERIFICATION OF PD LOCALIZATION For the experimental verification, this PD localization method based on the optical simulation mainly includes two parts: experimental detection stage and optical fingerprint localization stage. The overall process of the PD localization is shown in Figure 6. FIGURE 6Open in figure viewer Overall proces