Because the forming mechanism of underwater acoustic signal is complex, it is difficult to establish the accurate predicting model. In this paper, we propose a nonlinear predicting modeling method of ship radiated noise based on genetic algorithm. Three types of ship radiated noise are taken as real underwater acoustic signal. First of all, a basic model framework is chosen. Secondly, each possible model is done with genetic coding. Thirdly, model evaluation standard is established. Fourthly, the operation of genetic algorithm such as crossover, reproduction, and mutation is designed. Finally, a prediction model of real underwater acoustic signal is established by genetic algorithm. By calculating the root mean square error and signal error ratio of underwater acoustic signal predicting model, the satisfactory results are obtained. The results show that the proposed method can establish the accurate predicting model with high prediction accuracy and may play an important role in the further processing of underwater acoustic signal such as noise reduction and feature extraction and classification

Guohui Li

Hong Yang

Mathematical Problems in Engineering

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Predicting Modeling Method of Ship Radiated Noise Based on Genetic Algorithm

Because the forming mechanism of underwater acoustic signal is complex, it is difficult to establish the accurate predicting model. In this paper, we propose a nonlinear predicting modeling method of ship radiated noise based on genetic algorithm. Three types of ship radiated noise are taken as real underwater acoustic signal. First of all, a basic model framework is chosen. Secondly, each possible model is done with genetic coding. Thirdly, model evaluation standard is established. Fourthly, the operation of genetic algorithm such as crossover, reproduction, and mutation is designed. Finally, a prediction model of real underwater acoustic signal is established by genetic algorithm. By calculating the root mean square error and signal error ratio of underwater acoustic signal predicting model, the satisfactory results are obtained. The results show that the proposed method can establish the accurate predicting model with high prediction accuracy and may play an important role in the further processing of underwater acoustic signal such as noise reduction and feature extraction and classification.</jats:p

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Research ArticlePredicting Modeling Method of Ship Radiated Noise Based onGenetic AlgorithmGuohui Li and Hong YangSchool of Electronic Engineering, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi 710121, ChinaCorrespondence should be addressed to Guohui Li; lghcd@163.comReceived 10 March 2016; Revised 20 May 2016; Accepted 29 May 2016Academic Editor: Yaguo LeiCopyright © 2016 G. Li and H. Yang. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Because the forming mechanism of underwater acoustic signal is complex, it is difficult to establish the accurate predicting model.In this paper, we propose a nonlinear predicting modeling method of ship radiated noise based on genetic algorithm. Three typesof ship radiated noise are taken as real underwater acoustic signal. First of all, a basic model framework is chosen. Secondly, eachpossible model is done with genetic coding. Thirdly, model evaluation standard is established. Fourthly, the operation of geneticalgorithm such as crossover, reproduction, and mutation is designed. Finally, a prediction model of real underwater acoustic signalis established by genetic algorithm. By calculating the root mean square error and signal error ratio of underwater acoustic signalpredicting model, the satisfactory results are obtained. The results show that the proposed method can establish the accuratepredicting model with high prediction accuracy and may play an important role in the further processing of underwater acousticsignal such as noise reduction and feature extraction and classification.1. IntroductionUnderwater acoustic signal processing is a major branch ofsignal processing. As road categories of underwater acousticsignal, ship radiated noise is generated by the nonlinearity ofthe marine environment and hull structure together, whichcontains a large amount of ship target’s position, distance,and depth information [1]. The complex forming mechanismof underwater acoustic signal makes it difficult to establishthe accurate predicting model. The modeling of underwateracoustic signal is the foundation of the underwater acousticsignal processing. Research shows that underwater acousticsignal not only has the characteristics such as being nonlinear,non-Gaussian, and nonstationary, but also has the charac-teristics of being chaos, fractal, and so on [2–5]. In suchcases, it is possible to model the behaviour of the systemand get short-term prediction of the system evolution. Thepotential usefulness of this approach is enormous becausea wide variety of physical systems show a chaotic nature. Aphysical example of the above-mentioned situation is givenby the physical nature of ship radiated noise.Modeling effect has a direct impact on the result ofsubsequent processing. In order to establish the model ofunderwater acoustic signal effectively, some modeling meth-ods are proposed. Modeling and prediction of underwateracoustic signal based on PSO and RBF neural network [6]are proposed. Experimental results show this algorithm hasbetter performance in terms of training accuracy and conver-gence rate and also supports the modeling, prediction, anddynamic analysis of underwater acoustic signals. Predictionof underwater acoustic signals based on neural network [7] isproposed. Predictions of both simulated data and real shipradiated noise data are made using BP and RBF network.But those prediction methods do not give an accurate math-ematical expression of underwater acoustic signal. In recentyears, genetic algorithm is widely used in signal modeling.Fuel flow-rate modelling of transport aircraft for the climbflight using genetic algorithms is proposed [8]. Predictingunderwater ocean noise with genetic algorithms is proposed[9]. There are few reports on the modeling of ship radiatednoise using genetic algorithm. In view of this, this paper triesto propose a predicting modeling method of ship radiatednoise based on genetic algorithm.2. Predicting Modeling Method of ShipRadiated Noise Based on Genetic AlgorithmStudies have found that some seemingly similar randomsignals can be described by the deterministic nonlinearHindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 3429034, 5 pageshttp://dx.doi.org/10.1155/2016/34290342 Mathematical Problems in Engineeringdynamic system [10]. Volterra series model is the mostbasic model of nonlinear dynamic system [11]. In theory,any nonlinear dynamical system can be characterized byVolterra series model. In particular, when the Volterra seriesmodel is used to represent a nonlinear dynamical system,it not only has clear physical meaning, but also has stronguniversality. Research shows that ship radiated noise has adefinite nonlinear dynamic characteristic [2–5]. This conclu-sion provides a theoretical basis for the nonlinear dynamicmodeling of underwater acoustic signal and provides a newapproach for the prediction of underwater acoustic signal.The genetic algorithm has already shown itself to be robustapproaches to determining the functional form. In orderto get an accurate mathematical expression of underwateracoustic signal, the modeling method of ship radiated noisewith genetic algorithm is proposed. First of all, a basic modelframework is chosen. Secondly, each possible model is donewith genetic coding. Thirdly, model evaluation standard isestablished. Fourthly, the operation of genetic algorithm suchas crossover, reproduction, andmutation is designed. Finally,a prediction model of real underwater acoustic signal isestablished by genetic algorithm. Detailed procedure is asfollows.2.1. Selection of Basic Model. The Volterra series model isgiven by𝑦 = 𝑓 (𝑥1, 𝑥2, . . . , 𝑥𝑁)= 𝑤0+𝑁∑𝑖=1𝑤𝑖𝑥𝑖+𝑁∑𝑖1,𝑖2=1𝑤𝑖1𝑖2𝑥𝑖1𝑥𝑖2+ ⋅ ⋅ ⋅+𝑁∑𝑖1,𝑖2,...,𝑖𝑀=1𝑤𝑖1𝑖2⋅⋅⋅𝑖𝑀𝑥𝑖1𝑥𝑖2⋅ ⋅ ⋅ 𝑥𝑖𝑀,(1)where𝑀 is Volterra model order and 𝑁 is variable number.A total item in (1) is 1 + 𝑁 + 𝑁2 + ⋅ ⋅ ⋅ + 𝑁𝑀. In theseitems, not everyone can reflect the internal rule of time series.Too much model items will decline the model predictionperformance. So a new model is formed by selecting someitems based on the Volterra model. The selection of modelitem is accomplished by genetic algorithm.2.2. Genetic Code. In order to solve the model by geneticalgorithm, the right items are chosen as the components ofthe model, and each item is needed to code.The model item can have the general representationdefined by𝑀∏𝑖=1𝑥𝑖𝑛𝑖 𝑛𝑖≥ 0, (2)where ∑𝑁𝑖=1𝑛𝑖≤ 𝑀.Equation (2) can be represented by a vector 𝑎 =(𝑛1, 𝑛2, . . . , 𝑛𝑚)𝑇. Such vectors are composed of a matrixwhich means a model. Each column vector of the matrixrepresents an item of the model, and the column number ofthe matrix is the item number of the model.2.3. Model Evaluation Criteria. In the process of establishingthe prediction model of the measured underwater acousticsignal, the prediction accuracy can be used as the evaluationcriteria of the model. In this model, the model coefficientsare calculated by the least square method. So the predictionprecision of the model is increased with the model item. Butactually increased polynomial does not necessarily reflect theinherent laws of the data. In order to solve this problem, apart of data is selected as the training data, and the rest isused as the evaluation data. For a certain model, the modelcoefficients are calculated by the training data and the leastsquare method. The prediction error of the model which iscalculated by the evaluation data is used as the evaluationcriterion of the model.2.4. Genetic Operation. Cross breeding is as follows. Theseitems of the two models are sorted, respectively, according tocertain rules. In two sequences, a crossover point is randomlyselected; then the second half of the sequence is exchanged,so that two new models are obtained, which are the offspringof cross breeding.Genetic variation is as follows. Firstly, one item of themodel is randomly generated. Secondly, the original one ofthe model is randomly replaced. Lastly, genetic variation iscompleted.2.5. Establishing Prediction Model. Combined with the opti-mal individual encoding and these coefficients, the math-ematical expression of underwater acoustic signal is estab-lished.3. Modeling of Measured UnderwaterAcoustic SignalIn the South China Sea, three types of ship radiated noise aremeasured in the same sea condition. They are, respectively,the first type of ships, the second type of ships, and the thirdtype of ships, as shown in Figure 1. The sampling frequencyof the ship signals is 20 kHz. The sample length of the data is2048, and there are 50 samples for each type of ship data.In the prediction, 6 points are used, the time intervalbetween each point is 1, the population size is 60, thereproduction algebra is 20, and the alienation probability is0.03.The modeling process and results of three types ofmeasured underwater acoustic signal are given, respectively,as follows.3.1. Modeling of the First Type of Underwater Acoustic Signal.Optimal individual encoding is given by[[[[[[[[[1 0 0 0 1 0 00 1 0 0 1 0 10 0 1 0 0 1 10 0 0 1 0 2 00 0 0 0 1 0 1]]]]]]]]]. (3)Mathematical Problems in Engineering 3Measured signal−0.6−0.4−0.200.20.40.6x(n)500 1000 1500 20000n(a) Measured signal of the first typeMeasured signal−0.6−0.4−0.200.20.40.6x(n)500 1000 1500 20000n(b) Measured signal of the second typeMeasured signal500 1000 1500 20000n−0.8−0.6−0.4−0.200.20.40.60.8x(n)(c) Measured signal of the third typeFigure 1: Measured signal for the three types of ship radiated noise (2048 points).The first line to the fifth line represent, respectively, 𝑥(𝑛 −1), 𝑥(𝑛−2), 𝑥(𝑛−3), 𝑥(𝑛−4), and 𝑥(𝑛−5).The first column tothe seventh column represent that the mathematical expres-sion has seven components after modeling. The numericalvalue is 1 for its own, and the value is 2 for the square of itsown. For example, the sixth column is 0 0 1 2 0. That is,the sixth item of the mathematical expression after modelingis 𝑥(𝑛 − 3)𝑥(𝑛 − 4)2.These coefficients obtained by the least squares methodare 2.1129, −1.9148, 1.0187, −0.2583, −0.6330, −0.5970, and1.2200.Combined with the optimal individual encoding andthese coefficients, the mathematical expression of the firsttype of underwater acoustic signal is given by the nonlinearfunctional relation𝑥 (𝑛) = 2.1129𝑥 (𝑛 − 1) − 1.9148𝑥 (𝑛 − 2)+ 1.0187𝑥 (𝑛 − 3) − 0.2583𝑥 (𝑛 − 4)− 0.633𝑥 (𝑛 − 1) 𝑥 (𝑛 − 2) 𝑥 (𝑛 − 5)− 0.597𝑥 (𝑛 − 3) 𝑥 (𝑛 − 4)2+ 1.22𝑥 (𝑛 − 2) 𝑥 (𝑛 − 3) 𝑥 (𝑛 − 5) ,(4)where 𝑥(𝑛) is the signal amplitude.Measured signal and predicted signal for the first type ofreal ship radiated noise are shown in Figure 2. To facilitate4 Mathematical Problems in EngineeringPredicted signalMeasured signal−0.6−0.4−0.200.20.40.6x(n)50 100 150 2000nFigure 2: Measured signal and predicted signal for the first type ofreal ship radiated noise (200 points).comparison, only the first 200 points of the waveform aredrawn.In the same way, optimal individual encoding for thesecond type of underwater acoustic signal is given by[[[[[[[[[[[1 0 0 0 1 1 0 00 1 0 0 1 0 0 10 0 1 0 0 1 1 00 0 0 1 0 0 2 10 0 0 0 0 0 0 1]]]]]]]]]]]. (5)These coefficients are, respectively, 1.8801, −1.6157, 0.7905,−0.1650, 0.0931, −0.1155, −0.1167, and 0.0694.The mathematical expression of the second type is givenby the nonlinear functional relation𝑥 (𝑛) = 1.8801𝑥 (𝑛 − 1) − 1.6157𝑥 (𝑛 − 2)+ 0.7905𝑥 (𝑛 − 3) − 0.165𝑥 (𝑛 − 4)+ 0.0931𝑥 (𝑛 − 1) 𝑥 (𝑛 − 2)− 0.1155𝑥 (𝑛 − 1) 𝑥 (𝑛 − 3)− 0.1167𝑥 (𝑛 − 3) 𝑥 (𝑛 − 4)2+ 0.0694𝑥 (𝑛 − 2) 𝑥 (𝑛 − 4) 𝑥 (𝑛 − 5) ,(6)where 𝑥(𝑛) is the signal amplitude (Figure 3).Predicted signalMeasured signal−0.6−0.4−0.200.20.40.6x(n)50 100 150 2000nFigure 3: Measured signal and predicted signal for the second typeof real ship radiated noise (200 points).In the sameway, optimal individual encoding for the thirdtype of underwater acoustic signal is given by[[[[[[[[[1 0 0 0 3 1 0 00 1 0 0 0 0 1 00 0 1 0 0 2 1 10 0 0 1 0 0 0 00 0 0 0 0 0 1 2]]]]]]]]]. (7)These coefficients are, respectively, 1.8034, −1.6079,0.9540, −0.2238, −0.1592, 0.0138, 0.0290, and −0.1847.The mathematical expression of the third type is given bythe nonlinear functional relation𝑥 (𝑛) = 1.8034𝑥 (𝑛 − 1) − 1.6079𝑥 (𝑛 − 2)+ 0.954𝑥 (𝑛 − 3) − 0.2238𝑥 (𝑛 − 4)− 0.1592𝑥 (𝑛 − 1)3+ 0.0138𝑥 (𝑛 − 1) 𝑥 (𝑛 − 3)2+ 0.029𝑥 (𝑛 − 2) 𝑥 (𝑛 − 3) 𝑥 (𝑛 − 5)− 0.1847𝑥 (𝑛 − 3) 𝑥 (𝑛 − 5)2,(8)where 𝑥(𝑛) is the signal amplitude (Figure 4).In (1), Volterra series have a lot of items. By geneticalgorithm, some items are discarded, and others are kept.Then these coefficients are calculated by the least squaresmethod. Lastly, the mathematical expressions of underwateracoustic signal are obtained such as (4), (6), and (8).4. Results and DiscussionsIn order to quantitatively analyze the effect of underwateracoustic signal predicting modeling method with geneticMathematical Problems in Engineering 5Predicted signalMeasured signal50 100 150 2000n−0.8−0.6−0.4−0.200.20.40.60.8x(n)Figure 4: Measured signal and predicted signal for the third type ofreal ship radiated noise (200 points).Table 1: The root mean square error and signal error ratio ofunderwater acoustic signal prediction.Underwater acoustic signal classification RMSE SERThe first type of real ship radiated noise 0.0428 14.7The second type of real ship radiated noise 0.0660 10.1The third type of real ship radiated noise 0.0881 9.3algorithm, the root mean square error and the signal errorratio are used.The root mean square error (RMSE) and the signal errorratio (SER) are, respectively, defined byRMSE = √ 1𝑁𝑁∑𝑛=1(?̂? (𝑛) − 𝑥 (𝑛))2,SER = 10 log10[𝐸 (𝑥 (𝑛)2)𝐸 ((𝑥 (𝑛) − ?̂? (𝑛))2)] ,(9)where 𝑥(𝑛) represents the measured value at 𝑛 moment and?̂?(𝑛) represents the predicted value at 𝑛moment.The root mean square error and signal error ratio ofthe prediction are shown in Table 1. It can be seen fromTable 1 that modeling method of ship radiated noise withgenetic algorithm is feasible. When the ups and downs inthe time domain waveform change little, such as the firsttype of underwater acoustic signal, its modeling effect is best,because the root mean square error and the signal error ratioare 0.0428 and 14.7 dB, respectively.Three types of underwater acoustic signal are modeled,respectively, by genetic algorithm, and the correspondingmathematical expressions are given, which will play animportant role in the subsequent processing of underwateracoustic signal.5. ConclusionIn this paper, we employ recent developments on nonlin-ear physics and time series prediction to study the physi-cal characteristics of measured underwater acoustic signal.Specifically, we examine the predictability of a sample of shipradiated noise recorded in the South China Sea. To do that,an approach based on genetic algorithms has been employed.By calculating the root mean square error and signal errorratio, the satisfactory results are obtained.The results indicatethat the proposed modeling method has higher predictionaccuracy and is the foundation for the further processing ofunderwater acoustic signal such as noise reduction, featureextraction, and classification.Competing InterestsThe authors declare that they have no competing interests.References[1] Q. Leng, W. H. Song, C. M. Zhao, and G. Q. Wu, “Propagationcharacteristic of envelope line spectrum of ship radiating noisein shallow water channel,” Science China Physics, Mechanics &Astronomy, vol. 44, no. 2, pp. 134–141, 2014.[2] X. Zhang, X. Zhang, and L. Lin, “Researches on chaotic phe-nomena of noises radiated from ships,” Acta Acustica, vol. 23,no. 2, pp. 134–140, 1998.[3] A. G. Song and J. R. Lu, “Nonlinear feature analysis andextraction of ship noise signal based on limit cycle,” ActaAcustica, vol. 24, no. 4, pp. 407–415, 1999.[4] Y. A. Li, X. M. Zhang, and D. M. Xu, “The research on thechaotic characteristics of the signals of the target in the sea,”Journal of Detection & Control, vol. 22, no. 2, pp. 17–21, 2000.[5] G. H. Li and H. Yang, “A prediction method for underwateracoustic chaotic signal based on RBF neural network,” Journalof Software, vol. 9, no. 6, pp. 1581–1586, 2014.[6] Y. Y. He and H. D. Zhang, “Modeling and prediction ofunderwater acoustic signal based on PSO and RBF neural net-work,” Computer Engineering, vol. 34, no. 23, pp. 208–213, 2008.[7] J. N. Zhou, Y. A. Li, and Y. S. Wu, “Prediction of underwateracoustic signals based on neural network,” Technical Acoustics,vol. 25, no. 3, pp. 226–229, 2006.[8] T. Baklacioglu, “Fuel flow-rate modelling of transport aircraftfor the climb flight using genetic algorithms,”The AeronauticalJournal, vol. 119, no. 1212, pp. 173–183, 2015.[9] A. Alvarez, C. Harrison, andM. Siderius, “Predicting underwa-ter ocean noise with genetic algorithms,” Physics Letters A, vol.280, no. 4, pp. 215–220, 2001.[10] J. S. Zhang and X. C. Xiao, “Predicting low-dimensional chaotictime series using volterra adaptive filers,” Acta Physica Sinica,vol. 49, no. 3, pp. 407–408, 2000.[11] Q. F. Meng, Q. Zhang, and W. Y. Mu, “A novel multi-step adap-tive prediction method for chaotic time series,” Acta PhysicaSinica, vol. 55, no. 4, pp. 1666–1671, 2006.Submit your manuscripts athttp://www.hindawi.comHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical Problems in EngineeringHindawi Publishing Corporationhttp://www.hindawi.comDifferential EquationsInternational Journal ofVolume 2014Applied MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Mathematical PhysicsAdvances inComplex AnalysisJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014OptimizationJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Operations ResearchAdvances inJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Function SpacesAbstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014International Journal of Mathematics and Mathematical SciencesHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014AlgebraDiscrete Dynamics in Nature and SocietyHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Decision SciencesAdvances inDiscrete MathematicsJournal ofHindawi Publishing Corporationhttp://www.hindawi.comVolume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Stochastic AnalysisInternational Journal of

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Predicting Modeling Method of Ship Radiated Noise Based on Genetic Algorithm

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