Fuzzy Neural Network based on Particle Swarm Optimization in Intermittent Pumping--Chen Weishi

Application of a Fuzzy Neural Network based on Particle Swarm Optimization inIntermittent PumpingZhang He,Chen Weishi(Electromechanic Engineering College,Southwest Petroleum University;Chengdu, Sichuan province, 610500, China)Abstract:In the intermittent pumping, due to the complexity and uncertainty of oil produc-tion process, it is difficult to accurately determine the pumping running status, result-ing in pumping unit start-stop cannot match the downhole oil quantity change. In or-der to more effectively evaluate the pumping running status, this paper presents an improved fuzzy neural network evaluation model. The model has used particle swarm optimization to optimize the membership function and the final output layer connec-tion weights of the fuzzy neural network, improving the traditional fuzzy neural net-work parameter selection randomness, reducing the possibility of falling into local optimal solution, enhancing the learning ability and generalization ability of model as well as the accuracy and the convergence speed.By comparison with the traditional fuzzy neural network, fuzzy neural network based on particle swarm optimization model has higher accuracy and faster convergence rate. Finally,the model is applied to the evaluation of the running status of a on-site well and it turns out that the evalua-tion results of the model are consistent with the actual situation, verifing the feasibili-ty of the model.Key words: Intermittent Pumping; PSO; Fuzzy Neural Network1.IntroductionIn the oil field exploitation,beam pumping plays a decisive role in oil ex-ploitation machinery because of its sim-ple structure, reliability, practicability and handiness. But on account that beam pumping rated extraction capacity is greater than oil well’s actual load and that there are different degrees of empty pumping , it makes electric motor light relatively and its power factor low, and makes pumping backlash increasing and energy waste[1]. If the motor can stop when it works lightly and the oil storing is less, and start up when the oil storing increases to the degree to which that the pumping can full pumping continuously, intermittent pumping can be realized, thus it can save energy, reduce wear, and improve economic benefit. In intermit-tent pumping, evaluating the running status of pumping, such as accurate judgement of full pumping and empty pumping, is the key to determine the start-stop interval of pumping. However power supply of each well, weight and position of counterbalance, motor power and suspension center’s load are diffe r-ent, and these factors are interconnected, which makes it difficult to have a clear criterion to judge the state of full and empty pumping. So how to use limited information to judge operation status of pumping is of practical significance forformulating reasonable intermittent pumping control plan.At present, intelligent control for pumping has become a hot spot. Among that, neural networks control, fuzzy log-ic control and expert control are typical control methods. However due to the complexity, randomness and nonlineari-ty of oil extraction systems, there isn’t a unified approach so far.Fuzzy neural network has been widely applied with good approximation ability of nonlinear function and learning ca-pacity. The article [1] proposed rule self-tuning RL fuzzy neural network, and has applied it to the intermittent pumping control with power-saving rate of 30%. The article [2] proposed a sim-plified fuzzy neural network intelligent control programme and has ener-gy-saving result. The article [3] pro-posed self-adapting fuzzy control system and has applied it to the energy saving retrofit of pumping oil production suc-cessfully. However, it still exists ran-domness of fuzzy neural network’s p a-rameter selecting and local optimal solu-tions when modeling with fuzzy neural network.In view of this, this paper improves fuzzy neural network using Particle Swarm Optimization algorithm through combinatorial optimization of center value and width value of membership function and the connection weights of final output layer of the fuzzy neural network.Particle Swarm Optimization algorithm improves fuzzy neural net-work’s learning ability and generaliza-tion ability. Through using this for eva-luating of operation state and being veri-fied by the actual data, the modified method improves the evaluation model’s accuracy and convergence rate. 2 T - S fuzzy neural networkFuzzy neural network is the com-bination of fuzzy logic and neural net-work, which has the advantages of rea-soning process is easily unders-tood,sample requirement is low,and stronger ability of self-learning. Howev-er, when modeling by fuzzy neural net-work,the relationship between learning ability and generalization ability of fuzzy nervous system is not direct ratio, only when the fuzzy neural network has moderate complexity, it has good gene-ralization ability [4].Moreover, when parameters of the network front section arbitrarily selected, improper selection will result in the convergence speed of fuzzy neural network slower, and falling into the local optimum.[5]Thus, accord-ing to the performance requirements of model, select the best combination val-ues of fuzzy neural network parameters.In this paper, T-S fuzzy neural network model structure shown in Fig-ure 1, the model is divided into five le-vels, namely input layer, fuzzification layer , fuzzy inference layer, normaliza-tion layer and defuzzification layer. The first layer and the second layer represent the predictor of fuzzy rules,namely the input space division of fuzzy sys-tems;the left three parts represent the consequent of fuzzy rules , namely completing fuzzy inference rules of the system.Fig. 1five-layer fuzzy neural networkstructureThe input layer is the first layer in graph 1,and its nodes are the entrance of fuzzy information. The input layer transfers the information to the next layer,and each node represent input message()ii=1,2,...,n x respective-ly.Therefore,the number of input layer nodes depend on dimensions of input message,1n N=.There are three input quantities inthis paper,such as current I of pumping unit motor,differential value dI /dt and integral value ∫Idt,so n=3.The second is fuzzification layer,where each node represents a lan-guage variable value. The layer is used to calculate the membership function of each input component which belongs to the fuzzy set of linguistic variables()1,2,...;1,2,...iji n j m μ==.We select thegaussian function as the membership function,as shown in the equation (1).()22ij iji ij =exp c x μσ⎡⎤⎢⎥-⎢⎥⎢⎥⎢⎥⎣⎦- i=0,1,…n ; j=1，2，…m （1）ijcand ij σrepresent center and width ofmembership function in this equa-tion,respectively.n is dimension of in-put,m is number of fuzzy rules.In this article,we select n=3 and m=5. So the total number of this layer nodes isn2i=1=m N ∑=15 The third is fuzzy inference layer,where each node represents a fuzzy rule and used to match premis-es of fuzzy rules,and calucate fitness value of each rule.And it will be nor-malized by the fourth layer that is nor-malization layer. Normalized fitness value is calculated as follow:1,1,2,...,j m jii j m ααα===∑（2）There are equal numbers of nodes between the third layer and the fourth layer,that isn34i=1==m N N ∏，n=3 and m=5 in this paper ,so there are equal node numbers between fuzzy in-ference layer and normalization layer,that is 125.The fifth is output layer,also known as defuzzification layer,which realizes clear calculate in fuzzy neural network as shown in the equation (3)[6]mijjij=1=y ωα∑ i=1，2，…r （3）Where ，ij ωrepresent the connecting weigh between the ith output node andjth inference layer node.r is the node numbers of output layer ,there is only one output in this paper,therefore r=1. By the above analysis ，there are two kinds of learning parameters in Fuzzy neural network: one is the central value and width value of membership func-tion,which are ij c and ij σ,respectively;another one is the output weights ij ωin the last layer. 3. The realization of fuzzy neural network based on PSO algorithmFirst, the population of particles must be encoded and then the optimiza-tion for central values and width values of membership function and the final output layer connection weights of the fuzzy neural network are con-ducted again and again.The optimiza-tion stops until it has reached the pre-scribed scope of mean square error func-tion and outputs its optimal parameters.The particle population is com-posed by n vectors with D-dimension. The position vector X of the particle in the population represents the center val-ue ij c , the width value ij σof the mem-bership function of the fuzzy neural network, and final output layer connec-tion weights ij ω. Initialization of the particle swarm and updating the velocity and position of the particle according to the formula (4), (5).()()11212c c t t ttttttsisissgsisisis VV r P X r P X +=+-+-（4）11t t t isis is V XX ++=+ （5）Where,1c 、2c both are learning factors;1r，2r are uniform random numberswhich values from zero to one. tis V is the speed oftimes dimension in ttimes iterations for particle i, t isXis thecurrent position,t isPis individual op-timal position, andt gsPis global op-timal position of s times dimension in t times iterations for the entire population.In this paper, the output mean square error of the fuzzy neural network is used as the fitness function of the par-ticle swarm algorithm, and the outputmean square error function of the fuzzy neural network is expressed as follows:()k2i=11di i 2k -y y SE =∑ （6）Where , di y and i y represent ex-pected output and actual output respec-tively, and K is the total number of thesample.Parameter optimization of fuzzy neural network: the output mean square error of the fuzzy neural network is used as the fitness function of the particle swarm optimization algorithm. The maximum error is 0.005 and the maxi-mum number of iterations is 800. When the error reaches the specified range or reaches the maximum number of itera-tions, the optimization stops and net-work model achieves the best. Optimi-zation steps of PSO algorithm for fuzzy neural network are shown in figure 2.Fig.2 optimization steps of PSO algo-rithm for fuzzy neural network4 PSO-FNN evaluation model con-structionSince the oil pumping controlsys-tem has the characteristics of model un-certainty, highly nonlinear, and the sys-tem main equipment is placed under-ground, the measurable state variable are quite less. The most convenient, reliable and relatively low-cost method deter-mining whether the pumping unit is empty or not is to detect current. [3] Therefore, the evaluation model established in this paper has three inputs and one output.The inputs include the current I, differential value dI / dt and the integral value ∫Idt of motor of pumping unit, namely the load current, load changes, the load accumulated.The output stands for the levels of pumping unit operating status, that are full pump-ing, half pumping and empty pumping and the corresponding values are 0,1,2. Table 1 shows input and output data of two representative wells [7].According to the data of Table 1, it can be seen the trends of current, current changes and current accumulation of motor of pumping unit, the running sta-tus of the pumping unit could be eva-luated in turn.(1)Full pumping phaseAfter pumping starts, current has increased and current change will be larger and current accumulation will be small ,these datas show that pumping unit is in "full pumping " state.However,during the downtime to start ,oil pump should be filled in a short time as oil flow from the pump back to the oil wells.(2)Stable full pumping phaseAfter pumping start-up, current I remains stable, current change dI/dt is smaller.(3)Half pumping transitional phaseThe current decreases slowly and the load of oil pumping reduces since the pump suction capacity is greater than the oil seepage ability of oil well.(4)Empty pumping phaseAt oil production later period，the current stabilizes at a lesser extent, cur-rent change is small and current integra-tion reaches the maximum, indicating the pumping unit to "empty pumping".［8］4.1 network training and evaluation model(1) Sample dataAs table 1 shows, input and output data of two representative wells have been given ,then selecting 32 sets of da-tas in group A as the training sample data are used for training the model and another 32 sets of datas in group B as the testing sample for model testing and inspection.Due to the large differences between datas, data normalization has done beforehand.(2)Network structureAccording to the characteristics of current parameters, the first layer has three input variables and theirs fuzzy division numbers by the second layer are selected as 5, i.e., m = 5, whereby the second layer has 15 nodes, and the number of membership functions cor-responding for 15. By the second section analysis, the number of nodes in the fuzzy inference layer is same with the normalized layer’s and the number is 125.And output layer node number is 1, which can determine the topology of the fuzzy neural network based on PSO for the 3-15-125-125-1 type.(3) Determination of model para-metersThe determination of model para-meters is done through fuzzy neural network training process. Further para-meters adjustment through continuoustraining of the model, actually the train-ing process is correction procedure for the parameters.In this paper, the learning rate of the network is set as 0.2η=,the maximum number of iterations is set to 800, the error is set to 0.005. 32 sets of sample data are input for model training, spe-cific training process is:First, enter a set of sample data namely data a, the output could be ob-tained after the gradual spread between the layers,and then calculate the change amount of neurons’ weight in each layer of the data a,including a ω∆, c a ∆andaσ∆;Second, repeat the first step process until completing the calculation of all the sample. According to a ωω∆=∑∆,a c c ∆=∑∆，a σσ∆=∑∆, the change of theconnection weight of this round training are calculated,as ω∆、c ∆、σ∆;Again, according to the output mean square error (mse), center value and width value of the membership function of network with network con-nection weights can be adjusted through iteration , if mse of the output is less than the preset value or the maximum number of iterations is reached, the ite-ration stops; otherwise it continues .Thus, the fuzzy neural network evaluation model based on particle swarm optimization is established and it can be used to evaluate the running state of pumping unit.4.2 Comparative Example simulation and evaluation results(1)Convergence speed comparison The training for the traditionalfuzzy neural network (called FNN) hasdone with the same sample data and consistent parameters,as the learning rate is 0.2η=, the maximum number of iterations is set to 800, error is set to 0.005.The FNN model reaches steady state after 583 iterations and the fuzzy neural network model based on particle swarm optimization (referred to as the PSO-FNN) after 352 iterations is stabi-lized.Training error curve are shown in Figure 3 and Figure 4. Table 2 is the performance analysis of two kinds of models. From the figures and the table, when the MSE objective value is 0.005, PSO-FNN model can meet the require-ments after 352 iterations,which is less 231 iterations than the FNN’s.Also the running time is shorter than the latter. Therefore, PSO-FNN model has the ad-vantages of less iteration number and faster convergence speed.Fig.3 Mean square error curve of FNN modelFig.4 Mean square error curve of PSO-FNN modelTab.2 The performance analysis of two modelsPerformance FNNPSO-FNNMSE 0.005 0.005 iterations 352 583run time/s 23.6 37.3 (2)Evaluation accuracy comparisonThe network is trained and tested by the normalized training sample and test sample data. Using the already trained fuzzy neural network,the model is tested by 32 sets of data of group B in table 1. In contrast the model actual output to the expected output, the accu-racy of the PSO - FNN model could be checked,furthermore,comparing with the output results of the FNN model. Figure 5 and Figure 6 represent the test output results from the FNN model and PSO-FNN model respectively. Table 3 shows output average error comparison of test data of two models.Comparison of the two methods by the figures and the table, the PSO-FNN has better fitting degree since the actual output of it is very close to the expected output and average error of its test out-put is 0.0083 contrasting the FNN mod-el’s is 0.0693. It is visible that PSO-FNN model is more accurate. Fig.5 FNN model test output diagram Fig.6 PSO-FNN model test output dia-gramTab.3 Comparison of average error oftwo model test dataAverage errorFNN PSO-FNN0.0693 0.0083Comparative Cases verification shows that the fuzzy neural network model based on PSO has significantly improved on the convergence rate and accuracy of the evaluation results in contrast to the traditional fuzzy neural network model. The improved pumping state evaluation model has a strong self-learning ability, good generalization ability and precision,so it will be more suitable for the pumping operating status evaluation.4.3 Application of pumping unit op-erating state evaluation modelA field well is selected as the re-search object and its basic situation is as follow: pumping speed is 3.52 min-1, the length of stroke is 3m and pump diameter is 28mm. Data acquisition time is on 2016/3/9 15:00:23. A stroke of the current acquisition curve is shown in Figure 7 and the blue curve of which represents the process of downstroke while the red part represents up-stroke.The indicator diagram curve of the well is shown in Figure 8.Fig.7 The current curve in a stroke of the wellFig.8 The indicator diagram in a stroke of the wellAccording to table 1, the current parameters of the downhole stroke is selected as the research object with ex-tracting 20 sets of current values from it, then corresponding calculation including differential current and current integra-tion have done to ultimately form 20 groups of current data of the well’s downhole stroke, as shown in Table 4.Then these current data ,as the input of PSO-FNN model established in this pa-per, are used for pumping unit operation status evaluation and the model’s output is shown in Figure 9. The figure shows that there are 16 sets of data in 20 groups output is level 1 which stands for half pumping,while the remaining 4 sets is level 0 standing for full pumping. Taking into account a certain chrono-logical relationship of the 20 sets of da-ta,the output results of the model can be evaluated according to the overall trend. Therefore, it can be judged that the op-erating state of the well pumping unit is half pumping ,namely, liquid supply de-ficiencies and intermittent pumping measures need to be taken.The Figure 8 shows that the well has a "knife-type" indicator diagram that is typical characteristics for insufficient liquid supply of a well. Therefore, the well is currently in a state of insufficient supply.The results of the evaluation model consistent with the actual situa-tion.In addition, combined with the data and output evaluation results, the model not only can output the evaluation lev-el,but also can detail evaluation results through analysising data reflected in the level location. This would contribute to the analysis and accumulation of typical current parameters and provide more help to the decision makers.Fig.9 PSO - FNN model output evalua-tion results5. Conclusions(1) Improvement of fuzzy neural network uses PSO algorithm through combinatorial optimization of center value and width value of membership function and the connection weights of final output layer of the fuzzy neural network, enhancing the learning ability and the generalization ability of fuzzy neural network.(2) PSO-FNN model has good ge-neralization ability and has been im-proved both in the rate of convergence and the accuracy of evaluation results compared with traditional FNN model’s. And influences of some human factors may be avoided through this model's ability of evaluation and prediction, saving human and material resources and improving the intelligent degree of the running status evaluation of pumping unit.(3) The PSO-FNN model has been applied to a oil well and verified feasibly of the model as evaluation results are consistent with the actual situation. At the same time, detailing evaluation re-sults by the data location reflected in evaluating grade, contributes to analyz-ing and accumulating typical current parameters and providing arguments for qualitative and quantitative evaluation, which is of guiding significance of deci-sion in the field.Tab.1 data of two wellstime A BI dI/dt ∫Idt Output I dI/dt ∫Idt Output 12401031010 22512032220 32944032040 43127034240 53439035170 634012035080 7340140350100 834017035-1110 933-1180351130 1031-121034-2140………………………………………………27 20 1 37 2 27 0 35 128 21 1 38 2 26 -1 35 1 2919-2382260362 3018-138225-1362 31180382250372 321803822503726. References[1]Ding Bao,Zhang Yan-li,Sun Li-feng. RL Fuzzy Neural Network and its Applica-tion to Oil Pumping Control [J]. Control Engineering of China,2002,9(6):57-59.[2]Qi Wei-gui,Zhu Xue-li,Zhang Yan-li.A Study of Fuzzy Neural Network Controlof energy-saving of Oil Pump[J].Proceedings of the CSEE,2004,24(6):138-140.[3]Zhang Bingcheng.Application of energy saving control system of pumping unitintelligent control system[J].Energy Conservation,2010,336(7) :42-45.[4]Xue Qingsong.Reasearch on fuzzy neural network based on improved particleswarm optimization[D].Chongqing University,2008.[5]Xia Meijuan,Liang Xuechun,HanFengtao.Water quality comprehensive assess-ment approach based on T-S fuzzy neural network and improved FCM algo-rithm[J].Computers and Applied Chemistry, 2013,30（10）：1197-1201.[6]Sun Hui,Zhang Xueying,Ning Aiping.The Application of Fuzzy Neural Networkbased on PSO Algorithm in Speech Recognition System[J].Mathematics Practice and Theory,2010,40(6):113-117.[7]Zhang Xuhua. Pumping Unit Energy-Saving Algorithm Based on Neural Net-work [D].X i’an Shiyou University,2014,5.[8]Ding Bao, Qi Wei-gui,Zhu Xue-li. A Study of Energy-Saving Control of OilPump Based on Fuzzy Neural Network Prediction[J]. Acta Eletronic Sinica, 2004,32（10）：1742-1745.[9]Pan Feng,LiWeixing,GaoQi.Particle Swarm Optimizer and Multi-object Optimi-zation[M].Beijing:Beijing Institute of Technology Press,2013.[10]Zhou Runjing,Zhang Li-na. Design of fuzzy and neural network based onMATLAB and fuzzyTECH[M].Beijing:Publishing house of electronics indus-try,2010.。