Using the curve moment and the PSO-SVM method to diagnose downhole conditions of a sucker rod pumping unit

Petroleum Science, Feb 2013

Downhole working conditions of sucker rod pumping wells are automatically identified on a computer from the analysis of dynamometer cards. In this process, extraction of feature parameters and pattern classification are two key steps. The dynamometer card is firstly divided into four parts which include different production information according to the “four point method” used in actual oilfield production, and then the moment invariants for pattern recognition are extracted. An improved support vector machine (SVM) method is used for pattern classification whose error penalty parameter C and kernel function parameter g are optimally chosen by the particle swarm optimization (PSO) algorithm. The simulation results show the method proposed in this paper has good classification results.

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Using the curve moment and the PSO-SVM method to diagnose downhole conditions of a sucker rod pumping unit

Journal of Petroleum Science and Engineering. Using the curve moment and the PSO-SVM method to diagnose downhole conditions of a sucker rod pumping unit Li Kun 0 Gao Xianwen 0 Tian Zhongda 0 Qiu Zhixue 0 0 College of Information Science and Engineering, Northeastern University , Shenyang, Liaoning 110819 , China computer from the analysis of dynamometer cards. In this process, extraction of feature parameters and include different production information according to the “four point method” used in actual oilfield only needs a small number of training samples and has good and classification performance. So, this study firstly uses the moment curve method to extract the features of typical method for pattern classification which is combined with - C and 1 Introduction g cards collected from the dynamometer measuring the force of the card shapes can encounter some problems, such as influence by subjective factors, no real-time analysis, and high cost. With the development of automation technology in petroleum production, many jobs relying on people have important to use the machine learning method to replace the advanced analytical methods have been used in diagnosis best error penalty factor C the expert system and the rough set have a single way of analysis have some limitations. The support vector machine 2 Downhole dynamometer card in sucker rod pumping wells of the subsurface pump as it may eliminate effects of the deformation, viscous resistance, vibration and inertia of the L 20 0 function and the displacement function of the polished rod are given in numerical forms, the Fourier coefficients may be determined by approximate numerical integration (Chen, 1988). The calculated result of the pump dynamometer card is shown in Fig. 1. Surface dynamomerer card Downhole dynamomerer card 0 0.5 1.0 3.0 3.5 4.0 1.5 2.0 2.5 Displacement, m 3 F e a t u r e e x t r a c t i o n o f t h e d o w n h o l e d y n a m o m e t e r c a r d b a s e d o n t h e c u r v e moment as the data precision and dimension of the dynamometer cards formula is as follows: x y xi xmax yi ymax xmin xmin ymin ymin where xi and yi represent the displacement and load data; x and y Known from the principle of the dynamometer card, the geometric features of all types of dynamometer cards are the four corners of the parallelogram. So, it is particularly important to determine the fully open and closed positions of the valve, which is the four-point method commonly used theoretical dynamometer card for example, its partition is shown in Fig. 2. Seen from the diagram, the dynamometer card is divided into four parts, lower left, upper left, upper right and lower right, respectively, which contains A, B, C and D points D Displacement l and m are: C l (3) (4) (5) (6) (1) (2) d a o L A 0 mpq pq where Lmax and Lmin represent the maximum load and the minimum load respectively; S The partition results of one dynamometer card are shown in Fig. 3. The curve moment theory (Chen, 1993) is introduced to extract the moment features of the dynamometer card in this paper. Geometric moment and geometric central moment of the M M i 1 li(s) i 1 li(s) x p yq d s (x x) p ( y y)q d s where M is the number of the curve segments; li(s) is t h e i s t c u r v e s e g m e n t ; x p, q 0, 1, 2, . m10 / m00 ; y m01 / m00 ; Research by Wolfson in 1995 proves that the central moment pq of the contour moment is not affected by improved form of the contour moment, so the central moment transformations. The feature extraction of the downhole dynamometer card is conducted as follows. Each part after partition is a curve composed of discrete points (xi, yi), i = 1, 2,···, N. Its p+q mpq is 1.0 mpq xi p yiq li pq 00 10 01 11 20 xm10 where xi yi is the vertical coordinate of the discrete point; i is the ist discrete point in the curve edge; N is the total number of the li is the straight-line distance between two adjacent discrete points, li (xi xi 1 )2 ( yi yi 1 )2 , p, q 0, 1, 2, . The corresponding p + q as: (xi x) p ( yi y)q li where point (x, y) is the barycentric coordinates of the curve. 4.0 1.5 (15) (16) (17) (18) Point B Point D 2.0 3.0 Displacement, m 0.5 1.0 Displacement, m 1.5 2.0 2.0 2.5 3.0 Displacement, m 3.5 Point C Point A 0.5 1.0 Displacement, m m30 m03 m12 m21 3xm20 3ym02 2 ym11 2xm11 2m10 x 2m01 y 2 2 xm02 ym02 2 2 y m10 2 2x m01 central moment 30 and 03 describe the graphic asymmetry. of deviation of the mean distribution. 03 represents the asymmetry measurement of the curve about the vertical axis; 30 represents the asymmetry measurement of the curve about then value of the 30 and 03 =[ 1, 2,..., 28]. This moment which is from linear or nonlinear combinations geometric meaning; secondly, more importantly, 28 feature vectors by partition calculation can describe the details of the pump dynamometer card accurately. Seven invariant moment ranges vary greatly in their and the structural characteristic of the following pattern recognition, a total of 28 feature parameters in four parts of the downhole dynamometer card are revised to adjust its range. i ' lg i where i =1, 2, ···, 28. 4 P a t t e r n c l a s s i f i c a t i o n o f d o w n h o l e dynamometer cards based on PSO-SVM needs a small number of training samples, and has good dynamometer cards in oil rod pumping units. (19) For classification problems, parameters affecting parameter C g. The error penalty parameter C adjusts the ratio of the confidence g mainly affects the complexity of sample data distribution actually change the mapping function and thereby change the complexity (number of dimensions) of sample data dimensions, and limits the complexity of the constructed data subspace, and also determines the VC dimension (VC dimension is a measure of function class, and the higher VC dimension denotes the more complexity of a problem) of the algorithm to choose the best C and g which play important computational intelligence field, which was first proposed by Kennedy, Eberhart and Shi (Eberhart and Kennedy, 1995; Kennedy and Eberhart, 1995; Shi and Eberhart, 1998). Its basic concept comes from the research into birds’ predation and effective way of each bird to find food is to search the surroundings of the bird that has the shortest distance to food currently. Its algorithm steps are as follows: vector of each particle is a real number between 0 and 1,000. Determine c1, c2 and calculate k and the fitness of each as the particle’s personal optimal solution to search for the global optimal solution. 2) Calculate the update speed and the updated position of each particle. 3) Use the evaluation function to evaluate all of the particles. When a particle’s current evaluation value is better than its historical evaluation value, the current evaluation value is regarded as the historical optimal evaluation value, and the current position vector is credited as optimal position vector. 4) Search for the global optimal solution. If its value is better than the current historical optimal solution, update it; end the search if it satisfies the termination condition, otherwise go to step 2 to a new round of search. C and g based on PSO algorithm is shown in Fig. 4. 5 Simulation dynamometer cards, in which, fault type 1 stands for normal for gas influence, 20 samples; fault type 3 stands for feed viscosity, 10 samples; fault type 6 stands for travelling valve in bottom dead position, 10 samples; fault type 8 stands for pump bumping in top dead position, 10 samples; fault type 9 stands for sand production, 10 samples. The input of each sample is 28 invariant moments, the output is fault type, and the coding modes are respectively 1— fault type 1, 2—fault type 2, …, 10—fault type 10. C=2 and g=0.01 is used to do fault pattern classification. In this simulation, the sample set is divided into two parts, of which 88 dynamometer cards in the training set and 40 dynamometer cards in the testing set. The results are shown in Figs. 5 and 6. accuracy rates are not satisfactory. In order to improve the accuracy rate, the methods of cross validation (CV) and “grid search” are used to optimally select parameters C and g. The specific simulation is as follows: firstly according to the K-fold cross validation (K-CV) method the training samples are divided into four groups, then the “grid search” method is used to test different parameters C and g in the cross validation process in order to obtain different accuracy rates. Finally, the parameter which has the best accuracy rate is chosen as the optimal one. We use the exponential growth Li Z, Liu B, Liu T N, et al. The research on fault diagnoses of oil pump classify support vector machine. 2007 IEEE International Conference China International Conference on Evolutionary Computation Proceedings, support vector machines for fault diagnosis of induction motors. Petroleum Exploration and Development . 2011 . 38 ( 1 ): 109 - 115 (in Chinese) system. Paper SPE 26246 presented at SPE Petroleum Computer repair function for screw oil pump based on support vector machine . Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, December 15 - 18 , 2007b, Sanya, China Wang J P and Bao Z F. Study of pump fault diagnosis based on rough sets theory . 2008 3rd International Conference on Innovative Computing Information and Control (ICICIC) , June 18-20, 2008 , Dalian, Liaoning, China Sensing . 2011 . 66 ( 3 ): 247 - 259 Cybernetics, and Computer Engineering, November 19- 20 , 2011 , vector methods. Pattern Recognition . 2006 . 39 ( 8 ): 1473 -1480 September 23-26 , 1990 , New Orleans, Louisiana 33 ( 4 ): 46 - 48 (in Chinese)

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Kun Li, Xianwen Gao, Zhongda Tian, Zhixue Qiu. Using the curve moment and the PSO-SVM method to diagnose downhole conditions of a sucker rod pumping unit, Petroleum Science, 2013, 73-80, DOI: 10.1007/s12182-013-0252-y