Research ArticleCavitation Detection in Centrifugal Pump Based on InteriorFlow-Borne Noise Using WPD-PCA-RBF

Liang Dong ,1,2 KanWu,1 Jian-cheng Zhu,1 Cui Dai ,3 Li-xin Zhang,1 and Jin-nan Guo1

1Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang 212013, China2Sichuan Provincial Key Lab of Process Equipment and Control, Sichuan University of Science & Engineering,Zigong 643000, China3School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Cui Dai; daicui@ujs.edu.cn

Received 18 March 2019; Accepted 21 April 2019; Published 12 May 2019

Academic Editor: Adam Glowacz

Copyright © 2019 Liang Dong et al. )is 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.

Cavitation detection is particularly essential for operating efficiency and stability of pumps. In this work, to improve the accuracyand efficiency of identification, an approach combining wavelet packet decomposition (WPD) with principal component analysis(PCA) and radial basic function (RBF) neural network is introduced to detect the cavitation status for centrifugal pumps. )ecavitation performance and interior flow-borne noise are measured under three different flow conditions. )en, time-frequencydomain analysis is performed on the interior flow-borne noise signal using WPD, and the energy coefficient of each node iscalculated to determine the optimal decomposition frequency band. Six-feature parameters are extracted based on frequency-division statistics, including three time-domain features and three wavelet packet features. After that, the PCA is applied fordimensionality reduction. Finally, three cavitation statuses of noncavitation, inception cavitation, and serious cavitation areidentified adopting RBF neural network. )e results show that the comprehensive identification rate of the proposed method forthree cavitation statuses reaches 98.2% with low identification error. )e method based on interior flow-borne noise analysis canbe well applied for on-line monitoring and diagnosis of pump industry.

1. Introduction

As the most widely used general machinery, pump plays avital role in the fields of hydraulic transportation, waterirrigation, flood control and drainage, and hydropowergeneration. However, for centuries, the cavitation within apump has been restricting the development of the pumpindustry, which not only limits the efficient operating rangeof the pump but also affects the operational reliability of thepump system. )e cavitation can appear within the entirerange of operating conditions in pumps. )erefore, it isnecessary to detect the cavitation status to avoid spreading toother parts of the pump system.

)e signal-based approaches, such as vibration, acousticemission, electrical currents, and interior flow-borne noise,are common approaches in cavitation detection in centrif-ugal pumps [1]. Wang and Chen [2] presented a method for

a centrifugal pump based on vibration signals. In themethod, a wavelet transform was used to extract featuresfrom measured vibration signals, and a linearized neuralnetwork was utilized to distinguish cavitation types. Sak-thivel et al. [3] carried out condition monitoring of amonoblock centrifugal pump using vibration signals. )estatistical features were transformed using dimensionalityreduction techniques and then the reduced set was applied toa decision tree to classify different modes of the pump.Alfayez et al. [4] presented a case study where acousticemission has been applied for detecting incipient cavitationand determining the best efficiency point (BEP) of a 60 kWcentrifugal pump. Farokhzad and Ahmadi [5] concentratedon a procedure for prediction of cavitation using acousticsignals and multilayer perceptron neural network. Durocherand Feldmeier [6] used stator currents to detect cavitationstatus in a centrifugal pump. Hernandez-Solis and Carlsson

HindawiShock and VibrationVolume 2019, Article ID 8768043, 12 pageshttps://doi.org/10.1155/2019/8768043

[7] measured motor current and voltage signals for differentoperating points of the pump and studied the correlationbetween the cavitation phenomena and the power of themotor. )e main challenge of using vibration, acousticemission, and electrical current signals is that the measuredsignals are so complex to identify the relationship betweencharacteristic parameters and cavitation status due to thecomplexity of the pump.

In fact, the interior flow-borne noise induced by cavi-tation in the pump is mainly a monopole noise source withstrong radiation efficiency and impact characteristic. Andthe centrifugal pump presents particular cavitation noisecharacteristics in normal operating condition comparedwith that upon inception cavitation. Chudina [8] utilized theinterior cavitation noise spectra to detect the onset ofcavitation in a centrifugal pump. )e results show that thereis a discrete frequency component, which is strongly de-pendent on the cavitation process and its development, andthe noise spectra can also be used to determine the NPSHrequired or the critical value, representing the upper limit ofpermissible pump operation without cavitation. In order tostudy the change rules of interior flow-borne noise with thedevelopment of cavitation, Dong et al. [9] optimized thecalculation accuracy using computational fluid dynamicscombined with the Lighthill acoustic analogy. )e resultsshow that, with the development of cavitation, the soundpressure level (SPL) at axial passing frequency (APF) and thefrequency bands of 10Hz∼100Hz and 1000Hz∼3000Hzshow an increasing trend, while it decreases at blade passingfrequency (BPF) and its harmonics. At the initial cavitation,the frequency band between 1000Hz and 3000Hz shows thehighest sensitivity for cavitation status detection.

However, the cavitation noise in pumps is a high-frequency continuous spectrum signal, and the frequencyspectrum analysis based on Fourier transform has in-surmountable limitations for cavitation detection withstrong shock catastrophe and nonstationary characteristics[10]. Wang et al. [11] conducted the cavitation noise eval-uation using wavelet packet decomposition (WPD) anddescribed the singular characteristics of cavitation noisesusing the extreme amplitude values in the transformeddomain. Two new parameters were suggested to describe thecharacteristics of cavitation noises under different cavitationdegrees. Application to real data analysis shows that thepresented method provides more information on abruptchanges in cavitation noises signals, and is useful in iden-tification of cavitation development stage. Wang and Chen[12] proposed a sequential diagnosis method using fuzzyneural network method to distinguish at an early stage onthe basis of the possibilities of symptom parameters.

Moreover, it is still one difficult problem that how todetect cavitation status in pumps more efficiently. )e ei-genvalues, such as the average, root mean square, andstandard deviation, were widely used in the feature ex-traction. However, the cavitation characteristics are dis-tributed over a wide frequency range and the characteristicsof different frequency bands varies. )e use of single ei-genvalue in a full-frequency band cannot reflect the changerule of the signal at different frequency bands before and

after cavitation. So, it is difficult to determine the eigenvaluesand their thresholds that can accurately identify the cavi-tation states [13].

In this paper, to overcome these difficulties, a multi-resolution cavitation status detection method for a centrifugalpump is proposed based on the interior cavitation noise signal.First, the wavelet packet decomposition (WPD) is employedto extract the decomposition frequency band characteristics.)e principal component analysis (PCA) is applied to reducedimensionality and remove redundancy. )en, three cavita-tion statuses including noncavitation, inception cavitation,and serious cavitation are identified using radial basic function(RBF) neural network. Finally, the classification and recog-nition effect of the proposed method for the three cavitationstatuses in centrifugal pumps are analyzed.

2. Theory of WPD-PCA-RBF

To improve the recognition accuracy and efficiency ofcavitation status in pumps, a cavitation detection methodbased on wavelet packet decomposition (WPD), principalcomponent analysis (PCA), and radial basic function (RBF)neural network is proposed. )e structure of the proposedmethod is presented in Figure 1 by means of a flow diagram,which describes the different stages of the methodology.

)e algorithmic details for each major step in themethod are as follows:

(1) Detect different types of cavitation status by cavi-tation performance experiment.

(2) Collect original liquid-borne noise data under dif-ferent cavitation status.

(3) Solve the energy coefficient on each node and de-termine the research nodes with larger energy co-efficients by WPD.

(4) Extract the eigenvalue of each research node andcompose the eigenvalue matrix. Normalize the ei-genvalue matrix due to large magnitude differencebetween eigenvalue elements.

(5) To improve the recognition speed, PCA is employedto obtain the principal component matrix with di-mensionality reduction.

(6) Input the principal component matrix of trainingsample into RBF as an input layer, determine thenumber of hidden layer nodes and RBF structure, andthen obtain the cavitation status recognition result onthe output layer. Calculate the error between thedesired output and actual output until the trainingsamples are fully trained and meet the network ac-curacy requirement or the iteration number isreached. Eventually, establish an ideal RBF network.

(7) Input the principal component matrix of testingsample into the ideal RBF network and output thediagnosis result.

2.1.WPD. WPD is a mathematical method that can providea multiscale time-frequency analysis by transforming signals

2 Shock and Vibration

from time domain into equal-width sub-band frequencydomain. With orthogonal transform, the WPD has theadded bene�t that the energy in the signals can be preservedand partitioned among the coe�cients.

Given the sampling frequency of the signal, f(t){ } be-comes f(s). Based on the sampling theorem, the maximumanalysis frequency of the signal is f(s)/2. After the j-layerwavelet packet transform applied on the signal, the fre-quency band 0− (f(s)/2){ } is divided into 2j{ } equal-widthsegments, that is, the width of each sub-band isf(s)/(2 × 2j). Correspondingly, the coe�cient at each layerCi,k,n is obtained, where i � 2, 3, . . . , j, k � 0, 1, 2, . . . , 2i − 1and n is the location index. According to Parseval energyequation, the signal energy can be expressed as the integral ofamplitude square over the entire time domain.�e coe�cientis used to represent the similarity between the wavelet packetfunction and the real signal. �erefore, the coe�cient Ci,k,ncan be used to represent the signal energy as follows [14]:

f(t)2 � ∑2j−1

k�0Cj,k∣∣∣∣∣

∣∣∣∣∣2, (1)

where j and k are the number of decomposition layer andfrequency band, respectively.

In the present study, after appropriate determination ofwavelet basis function and decomposition scale j, a j-layerwavelet packet transform was then applied on the signal.Because the orders of magnitude of the eigenvalue elementsdi�er greatly, normalization is performed to make sure thatthe input data are within an appropriate range. �e waveletpacket energy of the signal on all frequency bands is cal-culated by formula (1), and the wavelet packet energy oneach frequency band is normalized, that is

Tj,k � ∑n�1

Cj,k,n∣∣∣∣∣

∣∣∣∣∣2,

Tj,k′ �Tj,k

∑2j−1k�1 Tj,k

,

(2)

where Tj,k is the wavelet packet energy value on the kthfrequency band and Tj,k′ is the normalized feature vector.

2.2. PCA. PCA is a statistical procedure that uses an or-thogonal transformation to convert a set of observations ofpossibly correlated variables into a set of values of linearlyuncorrelated variables called principal components. It can beused to reduce the data dimensionality and eliminate someirregularities from the data. �e reduction process is asfollows [15].

Given a set ofm dimension feature vectors xi (i� 1, 2, . . .,n), normallym< n, the mean vector μ and covariance matrixC are calculated by

μ �1n∑n

i�1xi,

C �1n∑n

i�1xi − μ( ) xi − μ( )T.

(3)

By matrix manipulation, we obtain Cyj� λjyj, where λj(j� 1, 2, . . ., m) is the eigenvalue sorted in descending orderand yj (j� 1, 2, . . .,m) is the corresponding eigenvector. �ematrixes of eigenvalues and eigenvectors can be constructedas A� diag [λ1, λ2, . . ., λm] (λ1> λ2> . . .>λm) and Y� [y1, y2,. . ., ym]. To eliminate redundancy, k (k≤m) eigenvectorscorresponding to k largest eigenvalues are selected. Athreshold θ is introduced to decide the number k bycomputing the proportion of k largest eigenvalues in alleigenvalues.

∑kj�1λj∑mj�1λj≥ θ. (4)

Given the parameter θ, the number k can be determined.�en, the principal components with low dimensions aredecided as P� [y1, y2, . . ., yk]Txi.

2.3. RBF. RBF neural network is a particular type of arti�cialneural network (ANN) that uses radial basis functions asactivation functions. In principle, it could be employed inany sort of model, and particularly suitable for solving thestatus recognition problems with abrupt change in signals. Itconsists of an input layer, a hidden layer of RBF neurons,and an output layer with one node per category or class ofdata [16, 17].

�e RBF neurons store an available set of input-outputpairs of vectors, called training set. Each RBF neuron willcompute a measure of the similarity between the input andits training vector. �e input vectors which are more similarto the training sets will return a result closer to 1. �e outputof RBF neural network consists of a set of nodes, one percategory that we are trying to classify. Each output nodecomputes a sort of score for the associated category. �escore is computed by taking a weighted sum of the activationvalues from every RBF neuron. Determining the RBFweights is called training. After training, the RBF can be

Wavelet packet decomposition in time-frequency domain

Feature extraction based on frequency division statistics

Collecting internal noise data underdifferent cavitation numbers

Cavitation status determination

Principal component analysis for dimension reduction

Establishment of RBF neural network

Cavitation status recognition

Result output

Figure 1: Flow chart of the cavitation detection method.

Shock and Vibration 3

implemented with data whose underlying statistics is similarto that of the training set.

�e interpolation of a set of N data points in a multi-dimensional space requires every one of the D dimensionalinput vectors xp � xp: i � 1, . . . , D{ } to be mapped onto thecorresponding target output tp. �e goal is to �nd a functionf(x) such that f(xp) � tp∀p � 1, . . . , N. �e radial basisfunction method introduces a set of N basis functions, onefor each data point, which takes the form ϕ‖x − xp‖, whereϕ(·) is some nonlinear function. �us, the pth functiondepends on the distance ‖x− xp‖, usually taken to be Eu-clidean, between x and xp. �e output of the mapping istaken to be a linear combination of basic functions,i.e., f(x) � ∑Np�1wpϕ(‖x − xp‖). �e idea is to �nd the“weights” wp such that the function goes through the datapoints. It is easy to determine equations for the weights bycombining the above equations, that is, f(xq) � tq. Byde�nition, t � tp{ },w � wp{ }, andΦ � Φpq �{ ϕ(‖xq − xp‖)}.�e above equation can be simpli�ed in matrix form asΦw � t. �en, provided the inverse of Φ exists, we can useany standard matrix inversion technique to givew � Φ−1t. Itcan be shown, for a large class of basic function ϕ(·), thematrix Φ is indeed nonsingular (and invertable) providingthe data points are distinct. Once we have the weights, wehave a function f(x) that represents a continuous di�er-entiable surface that passes exactly through each data point.

Gaussian function is one of the most commonly usedbasic functions [18].

ϕ(r) � exp −r2

2σ2( ), (5)

where r> 0 represents a distance from a data point x to acentre c and the variable σ is the width parameter thatcontrols the smoothness of the interpolating function whichis always greater than zero.

3. Experimental Investigation

3.1. Experiment Model. �e experimental model is a low-speci�c speed centrifugal pump with a spiral volute in [19].�e design parameters of the centrifugal pump are design¡ow rate Qd� 12.5m3/h, design head Hd� 74m, rotatingspeed n� 2950 r/min, and speci�c speed ns� 25. �e maingeometry parameters of the centrifugal pump are given inTable 1.�e axial passing frequency (APF) and blade passingfrequency (BPF) of the centrifugal pump are, 49Hz and295Hz, respectively.

3.2. Test Rig. �e experimental test rig was designed andconstructed in the National Engineering and TechnologyResearch Centre of Pump and Pumping System, JiangsuUniversity, as illustrated in Figure 2. �e experimentalsystem mainly consists of a centrifugal pump, a vacuumpump, a cavitation tank, a pressure stabilizer, an exhaustport, inlet and outlet pipes, inlet and outlet valves, a variable-frequency driving motor, and others. Installed at the pumpoutlet, there is a pressure stabilizer for stabilizing the ¡uidpressure in the system and preventing the temperature rise

due to the thermodynamic e�ect caused by cavitation. Be-sides, during the testing of interior cavitation noise, thepressure stabilizer can play the role of sound insulation andnoise elimination with improved acoustic impedance. Also,it can solve the resonance and frequency-interferenceproblems between the noise generated by the change of¡owmeter and valve opening in the downstream of pressurestabilizer and the cavitation-induced noise of the pump. Toreduce the interference from the system vibration, the testedpump and the motor are �xed on the huge base, and thethick rubber gaskets are used at the connections between thepipeline and the pump.

Before the testing, the cavitation tank was �lled withwater through the injection hole with all valves open in theclosed loop system. And they were closed when there waswater ¡owing out from the exhaust port. �en, with the inletvalve kept fully open, the air valve was open to connect thecavitation tank to the atmosphere. And, the system wasstabilized after discharging the air in the system driven byvariable-frequency motor. Under the rotating speed, thepump was stably operated at some ¡ow conditions byadjusting the outlet valve in the downstream of pressurestabilizer. Further at some ¡ow condition, the vacuum pumpwas turned on to reduce the pressure in the cavitation tank,and then the cavitation performance and liquid-borne noisemeasurements were synchronously performed.

For the liquid-borne noise measurement, a INV3020Chigh-performance data acquisition system combined with a

Table 1: Main geometry parameters of model pump.

Parameter Value

Impeller

Inlet diameter, D1 (mm) 68Outlet diameter, D2 (mm) 228

Number of blades, z 6Wrapping angle, θ/r 145Outlet width, b2 (mm) 7

VoluteBasic diameter, D3 (mm) 245Inlet width, b3 (mm) 18

Discharge nozzle diameter, d4 (mm) 32

13 1 2 3 4 5 6 7 8 9 10 11 12

14 15 16

Figure 2: Schematic of test rig: (1) vacuum pump; (2) cavitationtank; (3, 4, 8, 10) brake valves; (5) electromagnetic ¡owmeter; (6)pressure transducers; (7) model pump; (9) variable-frequencymotor; (11) pressure stabilizer; (12, 13) ball valve; (14) hydrophone.

4 Shock and Vibration

RHSA-10 hydrophone was used. Owing to easy influencefrom the pressure fluctuation of pump outlet, the hydro-phone was flush-mounted at 8 times the outlet diameterfrom the discharge flange. Different from the spectrumdistribution of mechanical failure signal, the broadbandfeature under cavitation reflects both in low- and high-frequency bands. To ensure the spectral precision in low-frequency band and reflect the changing trend in high-frequency band, the vibration and noise signals were col-lected for 30 s with a sampling frequency of 10.24 kHz. )einstruments used in the measuring system are given inTable 2.)e installation locations of the sensors are shown inFigure 3.

3.3. Cavitation Status Determination. Johann [20] pointedout that the NPSH1 (1% head drop) and NPSH3 (3% headdrop) can be used as standards for detecting the cavitationstatus in pumps. Based on these, the whole cavitation processis normally divided into three stages [13]: the noncavitationstage (head drop is less than 1%), the inception cavitationstage (head drop is between 1% and 3%), and the severecavitation stage (head drop is higher than 3%). To accuratelyobtain the cavitation numbers corresponding to 1% and 3%drop of head, the multimeasurement method was adoptedduring the test. Eventually, the average cavitation perfor-mance curves of the centrifugal pump under three typicalflow rates were obtained, as shown in Figure 4. )e cor-responding cavitation numbers for different stages areshown in Table 3.

)e frequency spectrum of liquid-borne noise underdifferent cavitation stages after Fourier transform is shown inFigure 5 at a rated flow rate of 12.5m3/h. )e logarithmicform is adopted in the abscissa, which can both reflect thevariation law of discrete eigenvalues in low-frequency bandand the overall change trend in high-frequency band. At thenoncavitation stage (σ � 0.048), the noise energy is mainlyconcentrated in the middle- and low-frequency bands below1000Hz. Moreover, it exhibits obvious discrete characteristicsof APF, BPF, and their harmonics. A small number of ei-genvalues appear in the frequency band of 1000∼3000Hz, andthe energy fluctuates with the increase of frequency. Com-pared with the noncavitation stage, the frequency spectrum atthe inception cavitation stage (σ � 0.021) shows no obviouschange, whereas the wideband SPL above 1000Hz increasesslightly. In this stage, the pressure pulsation in two-phase flowvaries somewhat due to the sound energy generated by thecollapse of a small amount of cavitation bubbles. However,due to the small volume and number of the cavitationbubbles, the variation is small. )e main changes are con-centrated in higher frequency band, which presents broad-band characteristics. At the severe cavitation stage (σ � 0.018),the SPL of cavitation noise increases obviously. When thenumber of cavitation increases to a certain extent, the flowpassage is partially blocked.)erefore, the SPLs of BPF and itsharmonics caused by rotor-stator interaction decreaseslightly. )e high-frequency discrete signals are graduallysubmerged in the wide frequency band, resulting in the re-duction of spectrum width.

4. Cavitation Status Recognition

4.1. Wavelet Packet Decomposition in Time-FrequencyDomain. From Figure 5, we can see the frequency spec-trums of cavitation noise under different cavitation condi-tions are mainly characterized by broadband. Simplystudying the amplitude at a certain characteristic frequencyor the overall energy value cannot accurately reflect thecharacteristics of cavitation noise. )erefore, the time-frequency characteristic analysis in sub-bands is of greatsignificance for cavitation status determination. Comparedwith the Fourier transform, the wavelet transform can finelyobserve the signal detail in time-frequency domain bydecomposing the time-domain signals into independentfrequency bands on the basis of multiscale orthogonal re-finement. Moreover, the wavelet packet transform canfurther decompose the high-frequency part, which is notsubdivided in the wavelet transform. Considering the APFand sampling frequency are 49Hz and 10.24 kHz, re-spectively, the db4 basis function was employed to proceed6-layer wavelet packet decomposition for interior cavitationnoise signals. After that, the cavitation noise signals weredecomposed into 64 frequency bands, that is, the frequencybandwidth of each node is 80Hz including APF. )e time-frequency of cavitation noise under different cavitationstages at the rated flow rate is shown in Figure 6.

It can be seen in the time domain the cavitation noisesignal presents an obvious periodicity at APF, BPF, and theirharmonics with similar amplitude for different periodsunder the noncavitation stage. With decreasing cavitationnumber, the sound pressure amplitude increases, the APFbecomes more difficult to identify, and the amplitude be-tween different periods varies greatly. )at is to say, thecavitation not only leads to an increase of the sound pressureamplitude but also worsens the signal periodicity and ag-gravates the confusion degree. In the frequency domain, asmaller peak value appears at 1000Hz under the non-cavitation stage. At the inception cavitation stage, the fullband energy goes up, the discrete eigenvalues at BPF and itsharmonics caused by rotor-stator interaction decline, andthe side lobe sound pressure of discrete eigenvalue increases.In the severe cavitation stage, the energy of the frequencyband below 2APF lowers, the band energy between 2APFand 2BPF ascents obviously, and a large number of char-acteristic frequency with peak value appears. )ese fre-quencies are induced by the pressure fluctuation radiated bythe collapse of bubble groups and the vibration generated onthe pipe wall. At 1000Hz, the peak value shows broadbandcharacteristic and the energy increases at higher frequencieswith no apparent peak.

4.2. Feature Extraction Based on Frequency-DivisionStatistics. )e frequency band studied directly affects theaccuracy of subsequent feature extraction. )e wider fre-quency range will lower the frequency resolution. On thecontrary, more eigenvalues would appear for a narrowfrequency range, which will lead to more analysis time andeasy data redundancy. Obviously, the 64 frequency bands

Shock and Vibration 5

decomposed by the 6-layer wavelet packet are too �ne to beused as the feature frequency band. To further accuratelydivide the frequency bands, the energy values of each fre-quency band was calculated and normalized into energycoe�cients. If the energy coe�cient of a node is higher, itmeans that the node takes a larger proportion of the wholesignal and contains more cavitation characteristic in-formation. �e energy coe�cients under di�erent cavitationnumbers at rated ¡ow rate are shown in Figure 7.

As can be seen, the peak energy coe�cient for all fre-quency bands is mainly concentrated in the �rst 15 nodes onthe sixth level, and other nodes account for a smaller amountof energy. �erefore, the discrete nodes on the 6th layer withlarger energy coe�cient ((6, 0)–(6, 7), (6, 12), and (6, 13))were selected as research subject. In addition, merged withthe nodes with smaller energy ratios, the upper layer nodeswere chosen, eventually the nodes (4, 2), (5, 7), (2, 1), and (1,1) were studied too. �e optimal wavelet tree and corre-sponding frequency bands for each node are obtained bycombining Shannon entropy, as shown in Figure 8. �etime-domain feature parameters (the mean value, the rootmean square, and the standard deviation) and the waveletpacket feature parameters (the energy value, the energycoe�cient, and the energy entropy) extracted from theobtained cavitation noise signals at rated ¡ow rate are usedfor pattern recognition in this paper. �ese six-feature pa-rameters on 14 nodes (denoted as one set) constitute theinputs to the RBF neural network, and the output valuesrepresent the classi�cation and recognition results of thecavitation status.

4.3. FeatureReductionBased onPCA. Due to large di�erenceexisting between eigenvalue elements, the 6 × 14 eigenma-trix obtained by the wavelet packet decomposition is notconducive for RBF neural network establishment. At themeantime, in this work, 600 sets of ¡ow-borne noise dataunder di�erent ¡ow conditions were selected, and 84 ei-genvalues were prepared for establishing the RBF network.�e dimensionality reduction was carried out by the PCAmethod, as shown in Figure 9. After the normalized 600 × 84eigenvalues were input into PCA, the eigenvectors arrangingfrom largest to smallest were obtained, that is, λ�(141.1170369, 76.39322079, 62.269420261, . . ., 0.000204067,0.000175016, 0.00012405). �e contribution rate of eacheigenvalue Pλ was calculated according to formula (7). �ethreshold θ is usually equal or greater than 0.9 by experience.Here, θ was selected as 97%.When the sum of k contributionrates is greater than 97%, it is considered that it can betterexpress the characteristics of all original data. �e original

Table 2: Instruments in the measuring system.

Device Range Resolution Locations

Electromagnetic ¡owmeter 1–50m3/h ±0.5% �e length of straight pipe before and after the¡owmeter is 10 times of its internal diameter

Pressure transducer at inlet −0.1–0.1MPa ±0.5% 2 times of pipe diameter from inlet ¡angePressure transducer at outlet 0–0.1MPa ±0.5% 2 times of pipe diameter from outlet ¡angeHydrophone 20Hz–100 kHz ±2 dB 8 times of pipe diameter from outlet ¡ange

Hydrophone

Figure 3: Positions for ¡ow-borne noise measurement.

Table 3: Cavitation numbers for di�erent cavitation stages.

Flow rate(m3/h)

Cavitation stage

Noncavitation Inceptioncavitation Severe cavitation

10 >0.020 0.018–0.020 <0.01812.5 >0.022 0.019–0.022 <0.01915 >0.022 0.020–0.022 <0.020

1.0 Qd = 12.5m3/h1.25Qd = 15m3/h

0.75Qd = 10m3/h

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Hea

d co

effic

ient

0.05 0.10 0.15

0.018 0.020 0.022

0.200.00Cavitation number

Figure 4: Cavitation performance curves under three ¡ow rates.

6 Shock and Vibration

10 100Frequency (Hz)

1000 300080

100120140160180200

Soun

d pr

essu

re le

vel (

dB)

(a)

10 100Frequency (Hz)

100080

100120140160180200

Soun

d pr

essu

re le

vel (

dB)

(b)

10 100Frequency (Hz)

100080

100120140160180200

Soun

d pr

essu

re le

vel (

dB)

(c)

Figure 5: Frequency spectrum of cavitation noise at rated ¡ow rate: (a) noncavitation stage σ � 0.048; (b) inception cavitation stageσ � 0.021; (c) severe cavitation stage σ � 0.018.

0 20 40 60 80 100Time (ms)

120 140 160 180 20040

80

160

320

640

1280

2560

5120

Freq

uenc

y (H

z)

–2.4 –0.2 –0.1 0 0.2 0.5 0.8 2.8–0.4(μPa)

(a)

–2.4 –0.2 –0.1 0 0.2 0.5 0.8 2.8–0.4

40

80

160

320

640

1280

2560

5120

Freq

uenc

y (H

z)

20 40 60 80 100 120 140 160 180 2000Time (ms)

(μPa)

(b)

Figure 6: Continued.

Shock and Vibration 7

600 × 84 eigenvalues were then reduced to 600 × k principalelement eigenvalues. Here, the number of the reducedfeatures k after calculation equals to 20.

�e contribution rate of eigenvalue is calculated asfollows:

Pλ(i) �λi∑ λi

. (6)

�e space distribution of principal components of ¡uid-borne noise is shown in Figure 10. As can be seen, thebubbles under the stages of noncavitation, inception

cavitation, and serious cavitation are distributed in di�erentspatial regions with no overlap between them. It proves thatthe principal components obtained by PCA can be used as agood feature for di�erent cavitation stages.

4.4. Establishment of RBFNeuralNetwork. �e RBF networktypically has three layers: an input layer, a hidden layer, andan output layer. Obviously, the output nodes have beendetermined, which are noncavitation stage (0, 0, 1), in-ception cavitation stage (0, 1, 0), and severe cavitation (1, 0,0). In general, the number of hidden layer nodes m can be�rstly calculated as follows:

m ������n + 1

√+ α, (7)

where n is the number of input nodes and α is the constantbetween 1 and 10.

�e approximate range calculated is from 5 to 15. �en,after repeated attempts and veri�cation, the suitable numberof hidden layer nodes is �nally determined to be 10. Table 4shows the input samples and the arranged outputs.

5. Results and Discussion

In this work, 360 sets of feature data are randomly selected astraining samples, 120 sets of data are selected as veri�cationsamples, and the other 120 sets of data are used as testingsamples. �e identi�cation rate will vary due to randomselection of training and testing samples. In order to reducethe e�ect of selected samples, we run the program ten times.�e average identi�cation result is shown in Figure 11.

–2.4 –0.2 –0.1 0 0.2 0.5 0.8 2.8–0.4

40

80

160

320

640

1280

2560

5120

Freq

uenc

y (H

z)

20 40 60 80 100 120 140 160 180 2000Time (ms)

(μPa)

(c)

Figure 6: Time-frequency domain diagram of cavitation noise at rated ¡ow rate: (a) noncavitation stage σ � 0.048; (b) inception cavitationstage σ � 0.021; (c) severe cavitation stage σ � 0.018.

30

25

20

Ener

gy co

effic

ient

(%)

15

10

5

010

2030

40Node 5060 0.0487

0.0298

Cavitation number0.0212

0.01980.0194

0.0190

Figure 7: Energy coe�cient under di�erent cavitation numbers atrated ¡ow rate.

8 Shock and Vibration

As can be seen, from the perspective of the overallsample, the comprehensive identi�cation rate for all cavi-tation status is higher, that is 98.2%. It indicates that themethod based on WPD-PCA-RBF can accurately detect thecavitation status. �e identi�cation rate of noncavitationstatus under di�erent ¡ow rates is excellent, reaching amaximum of 100%. It indicates when the cavitation occurs,and it can be fully recognized by the method. �e identi-�cation rate of inception cavitation status is 83.3%. Four of�ve sets of wrong samples are misjudged as noncavitationstatus, and one set is misjudged as serious cavitation status. Itshows the inception cavitation stage cannot be completelydistinguished from the other two stages. �e identi�cationrate of serious cavitation status is 97.9%. Six wrong sets of290 sample data are misjudged as inception cavitation. Itshows that the serious cavitation stage is well separated from

the noncavitation status. �e distinction from inceptioncavitation status needs to be improved. From the perspectiveof training sets, the identi�cation rates of the three stages ofnoncavitation, inception cavitation, and serious cavitation

0.2

0.1

0.0

–0.1

–0.2–0.08

–0.040.00

0.040.08 –0.04

0.000.04

Principal component 2Principal component 1

Prin

cipa

l com

pone

nt 3

0.080.12

0.160.20

Before cavitation

Cavitation birth

Severe cavitation

Figure 10: Space distribution of principal components based onPCA.

Table 4: Input samples and arranged outputs.

Flow rate (m3/h) 10 12.5 15 Output resultNoncavitation 100 80 100 (0, 0, 1)Inception cavitation 10 10 10 (0, 1, 0)Serious cavitation 90 110 90 (1, 0, 0)

(0, 0)

(1, 0)

(2, 0)

(3, 0) (3, 1)

(4, 3)(4, 1)(4, 0)

(5, 0)

0–80

Hz

80–1

60H

z

160–

240H

z

240–

320H

z

320–

400H

z

400–

480H

z

480–

560H

z

560–

640H

z

640–

960H

z

960–

1040

Hz

1040

–112

0Hz

1120

–128

0Hz

1280

–256

0Hz

2560

–512

0Hz

(5, 1) (5, 2) (5, 3) (5, 6)

(1, 1)

(2, 1)

(5, 7)

(4, 2)

(6, 13)(6, 12)(6, 7)(6, 6)(6, 5)(6, 4)(6, 2)(6, 0) (6, 1) (6, 3)

Figure 8: Optimal wavelet tree and corresponding frequency bands for each node.

Matrix X standardization: each column has a mean of 0 and a variance of 1

�e obtained feature vectors are arranged in rows byeigenvalue λ (i = 1, 2, ..., k) from large to small.

Find the covariance matrix a�er X matrix normalization C

Arranging the eigenvalues of the sample into a matrix.X = n ∗ s

Number of raw data feature values = s, number of samples = n

Calculation Y = PX. Obtain an eigenvalue matrixthat is reduced by s eigenvalues into k principals

∑ni=1 Pλ(i) > 97% N

Y

Calculate the characteristic root contribution rate Pλ(i) = λi/∑ λi

Figure 9: Flow chart of PCA.

Shock and Vibration 9

1 2 3Target class

1

2

3Out

put c

lass

Training confusion matrix

17047.2%

00.0%

00.0%

100%0.0%

10.3%

164.4%

10.3%

88.9%11.1%

00.0%

30.8%

16946.9%

98.3%1.7%

99.4%0.6%

84.2%15.8%

99.4%0.6%

98.6%1.4%

(a)

1 2 3Target class

1

2

3Out

put c

lass

Validation confusion matrix

5142.5%

00.0%

00.0%

100%0.0%

10.8%

54.2%

00.0%

83.3%16.7%

00.0%

10.8%

6251.7%

98.4%1.6%

98.1%1.9%

83.3%16.7%

100%0.0%

98.3%1.7%

(b)

1 2 3Target class

1

2

3Out

put c

lass

Test confusion matrix

5949.2%

00.0%

00.0%

100%0.0%

21.7%

43.3%

00.0%

66.7%33.3%

00.0%

21.7%

5344.2%

96.4%3.6%

96.7%3.3%

66.7%33.3%

100%0.0%

96.7%3.3%

(c)

1 2 3Target class

1

2

3Out

put c

lass

All confusion matrix

28046.7%

00.0%

00.0%

100%0.0%

40.7%

254.2%

10.2%

83.3%16.7%

00.0%

61.0%

28447.3%

97.9%2.1%

98.6%1.4%

80.6%19.4%

99.6%0.4%

98.2%1.8%

(d)

Figure 11: Cavitation identi�cation result based on WPD-PCA-RBF.

0

400

200

800

600

1000

1600

1400

1200

Insta

nces

Errors = targets – outputs

–0.8

59

–0.7

674

–0.6

758

–0.5

843

–0.4

927

–0.4

011

–0.3

095

–0.2

18

–0.1

264

–0.0

3483

0.05

675

0.14

83

0.23

99

0.33

15

0.42

3

0.51

46

0.60

62

0.69

78

0.78

93

0.88

09

TrainingValidation

TestZero error

Figure 12: RBF neural network error distribution.

10 Shock and Vibration

are 100%, 88.9%, and 98.3%, respectively. It shows the ei-genvalues inputted into the RBF neural network can reflectthe difference of noise signals between cavitation andnoncavitation statuses. However, the difference of noisesignals between inception cavitation and serious cavitationstatuses is not obvious.

)e identification error is quantitative, and the errordistribution histogram is shown in Figure 12. )e redvertical line denotes zero error. )e farther away from thezero-error line indicates the larger error value and less ac-curate identification result. It can be seen from Figure 12that, most of the sample data are distributed in two adjacentintervals of the zero-error line (−0.035, 0.057). )e error of asmall amount of data reaches ±0.15. )e rest of the intervalsamples distribution is minimal. It shows that the identi-fication accuracy of cavitation status is high.

6. Conclusions

)is paper presents a cavitation status detection methodsuitable for centrifugal pump based on interior flow-bornenoise analysis. In this method, theWPDwas used to improvethe frequency domain resolution. Six-feature parameters oneach frequency band with higher energy coefficient wereextracted. )e PCA was applied to reduce dimensionality.600 × 84 eigenvalues obtained after wavelet packet de-composition were reduced to 600 × 20 principal compo-nents. With input samples and arranged outputs, the RBFneural network was finally used to detect cavitation status.)e interior flow-borne noise at three cavitation statusesunder three flow conditions was measured. Moreover, 360sets of feature data were randomly selected as trainingsamples, 120 sets were selected as verification samples, andthe other 120 sets were used as testing samples. From theperspective of overall samples, the comprehensive identifi-cation rate for cavitation status reaches 98.2%. From theperspective of training sets, the identification rates of thethree stages of noncavitation, inception cavitation, and se-rious cavitation are 100%, 88.9%, and 98.3%, respectively.)e error distribution shows high identification accuracy forcavitation status. )erefore, the presented method can beapplied for online monitoring and diagnosis of pump.

Data Availability

)e experimental data used to support the findings of thisstudy were supplied by the research group of JiangsuUniversity under license and so they still cannot be put itinto the system, and the requests for access to these datashould be made to the corresponding author.

Conflicts of Interest

)e authors declare that they have no conflicts of interest.

Acknowledgments

)is work was supported by the National Natural ScienceFoundation of China (Nos. 51879122 and 51779106); theZhenjiang Key Research and Development Plan (GY2017001

and GY2018025); the Open Research Subject of Key Lab-oratory of Fluid and Power Machinery; Ministry of Edu-cation, Xihua University (szjj2017-094); Sichuan ProvincialKey Lab of Process Equipment and Control (GK201614 andGK201816); the Advanced Talent Foundation of JiangsuUniversity (15JDG052); and a project funded by the PriorityAcademic Program Development of Jiangsu Higher Edu-cation Institutions (PAPD).

References

[1] P. Samanipour, J. Poshtan, and H. Sadeghi, “Cavitation de-tection in centrifugal pumps using pressure time-domainfeatures,” Turkish Journal of Electrical Engineering & Com-puter Sciences, vol. 25, no. 5, pp. 4287–4298, 2017.

[2] H. Wang and P. Chen, “Intelligent diagnosis method for acentrifugal pump using features of vibration signals,” NeuralComputing and Applications, vol. 18, no. 4, pp. 397–405, 2009.

[3] N. R. Sakthivel, B. B. Nair, M. Elangovan, V. Sugumaran, andS. Saravanmurugan, “Comparison of dimensionality re-duction techniques for the fault diagnosis of mono blockcentrifugal pump using vibration signals,” Engineering Scienceand Technology, an International Journal, vol. 17, no. 1,pp. 30–38, 2014.

[4] L. Alfayez, D. Mba, and G. Dyson, “)e application of acousticemission for detecting incipient cavitation and the best effi-ciency point of a 60 kW centrifugal pump: case study,”NDT&E International, vol. 38, no. 5, pp. 354–358, 2005.

[5] S. Farokhzad and H. Ahmadi, “Acoustic based cavitationdetection of centrifugal pump by neural network,” Journal ofMechanical Engineering and Technology, vol. 1, no. 1, pp. 1–5,2013.

[6] D. B. Durocher and G. R. Feldmeier, “Predictive versuspreventive maintenance-future control technologies in motordiagnosis and system wellness-future control technologies inmotor diagnosis and system wellness,” IEEE Industry Ap-plications Magazine, vol. 10, no. 5, pp. 12–21, 2004.

[7] A. Hernandez-Solis and F. Carlsson, “Diagnosis of submersiblecentrifugal pumps: a motor current and power signature ap-proaches,” EPE Journal, vol. 20, no. 1, pp. 58–64, 2010.

[8] M. Chudina, “Noise as an indicator of cavitation in a cen-trifugal pump,” Acoustical Physics, vol. 49, no. 4, pp. 463–474,2003.

[9] L. Dong, Y. Q. Zhao, D. Cui, and Y. Wang, “Research oncavitation acoustic characteristics of centrifugal pump basedon fluid-acoustic field coupling method,” Advances in Me-chanical Engineering, vol. 10, no. 5, pp. 1–13, 2018.

[10] Y. Liu, Y. Y. He, and D. R. Chen, “Water entropy basedcondition test and identification of cavitation,” Journal ofMechanical Strength, vol. 1, no. 31, pp. 19–23, 2009.

[11] J. Wang, L. Pan, and S. Cao, “Wavelet transforms applied tocavitation noise analysis for hydro-turbine,” Journal of Hy-droelectric Engineering, vol. 32, no. 4, pp. 215–220, 2013.

[12] H. Q. Wang and P. Chen, “Sequential condition diagnosis forcentrifugal pump system using fuzzy neural network,” NeuralInformation Processing, vol. 11, no. 3, pp. 41–50, 2007.

[13] G. He, Y. Cao, T. Ming et al., “Cavitation state recognition ofcentrifugal pump based on features of modified octavebands,” Journal of Harbin Engineering University, vol. 38,no. 8, pp. 1263–1267, 2017.

[14] X. G. Yang, “Pattern recognition of engine abnormal soundbased on wavelet packet and bispectrum,”Noise and VibrationControl, vol. 38, no. 6, pp. 146–149, 2018.

Shock and Vibration 11

[15] L. Su, T. Shi, Z. Liu, H. Zhou, L. Du, and G. Liao, “Non-destructive diagnosis of flip chips based on vibration analysisusing PCA-RBF,” Mechanical Systems and Signal Processing,vol. 85, pp. 849–856, 2017.

[16] G. L. Liao, L. Du, L. Su, M. Zeng, L. Nie, and T. Shi, “UsingRBF networks for detection and prediction of flip chip withmissing bumps,” Microelectronics Reliability, vol. 55, no. 12,pp. 2817–2825, 2015.

[17] S. Chang, M. Leng, H. Wu, and J. )ompson, “Aircraft iceaccretion prediction using neural network and wavelet packettransform,” Aircraft Engineering and Aerospace Technology,vol. 88, no. 1, pp. 128–136, 2016.

[18] M. A. Halali, V. Azari, M. Arabloo, A. H. Mohammadi, andA. Bahadori, “Application of a radial basis function neuralnetwork to estimate pressure gradient in water-oil pipelines,”Journal of the Taiwan Institute of Chemical Engineers, vol. 58,pp. 189–202, 2016.

[19] L. Dong, Y. Q. Zhao, and C. Dai, “Detection of inceptioncavitation in centrifugal pump by fluid-borne noise di-agnostic,” Shock and Vibration, vol. 2019, Article ID 9641478,15 pages, 2019.

[20] F. G. Johann, Centrifugal Pump, Springer, Berlin, Heidelberg,Germany, 2014.

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwww.hindawi.com Volume 2018

RoboticsJournal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Shock and Vibration

Hindawiwww.hindawi.com Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwww.hindawi.com

Volume 2018

Hindawi Publishing Corporation http://www.hindawi.com Volume 2013Hindawiwww.hindawi.com

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwww.hindawi.com Volume 2018

International Journal of

RotatingMachinery

Hindawiwww.hindawi.com Volume 2018

Modelling &Simulationin EngineeringHindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwww.hindawi.com Volume 2018

Hindawiwww.hindawi.com Volume 2018

Navigation and Observation

International Journal of

Hindawi

www.hindawi.com Volume 2018

Advances in

Multimedia

Submit your manuscripts atwww.hindawi.com