Chaos analysis of acoustic emission signals in spot welding process

Chaos analysis of acoustic emission signals in spot welding process73Chaos analysis of acoustic emission signals in spotwelding process'Luo Zhen, Wang Rui, Shan Ping and Dong An罗震,王蕤,单平,董安**Abstract Based on choos time series and fractal theory, acoustic emission signals 1vere studied in the process of spot welding.According to calculating 8 welding parameters using phase space reconstuction method, the largest Lyapunov exponents wverepositive values and chaos characeristics were frsly discorered from acoustic emission signals in spot selding. In order toevaluate acoustic emission signal, Hausdonf dimension is pul fonoard to analyze and estimate chaos characeristics. Thexperiment and calculation results indicate that the Hausdof" dimension of acoustic emission signal is significanlydistinguishable in the nuggets with diferent welding parameter. This research prorides a new method for measuring theresistance spot rvelding quality.Key words spot welding, acoustic emision signal, chaos analysis0 Introductionvalue is calculated such as dynamic resistancel1-31.Non-contact, truly nondestructive interrogation of spotThis study combines the two methods , and firstly em-welding quality offers both scientifie and technological ad- ploys chaos theory to analyze the time series of acoustic evantages and is an area of rapidly growing interest. Themission signals in spot welding process. According to thenugget is formed by thermal , electric and mechanical cou-phase space reconstruction method, that is, a time evolu-pling, the phase transformation and deformation of thetion of any variable that determines the long evolution ofnugget will emit waves. It is well knowm that materials willhe system includes the information of all variables in therelease deformation energy by the method of elastic waveprocess of the system. A conclusion can be drawnunder deformation and fracture. When the wave is large e-that the chaos characteristic of the system can be analyzednough, it can emit the acoustic sound. In recent decadesby the time series of any variable which can determineof years, the acoustic emission signals research by manylong time evolution of the system'(5-6]. Meanwhile, theexperts in the progress of the welding is mainly focusing on Lyapunov exponents of the acoustic emission signals arethe aspects of arc welding and laser welding. From 1970s,computed in the aluminum spot welding. This exponentsome researches on acoustic emission signals in spot weld-estimates the chaos characteristic of the acoustic emissioning were developed. For example, there was a function re-signals and is very important to evaluate the quality of thelationship between the wave signal and diameter of thespot welding. Owing to the chaos characteristic of the a-nugget. Nowadays there are two kinds of analytical meth.coustie signals, the error will be big if we depict the sig-ods for inspecting the acoustic signals in spot welding, thenals with classical Euclidean geometry and fractal theory isne is waveform method, which waveform has obviousa valid method to analyze the nonlinear characterstic. Forcharacteristics such as amplitude, frequency and the other this reason, fractal dimensions are adopted to estimate theis parameter eigenvalue method, which the signal eigen-acoustic emission signals. The result shows that the fractal中国煤化工* This research was supported by the National High-tech R&D Program.MYHCNMHGural Science Foundation o|Tianjin (06YFJMJC03400, 09]CZDJC24000).# Luo Zhen, Wang Rui, Shan Ping and Dong An, School of Materials Science and Engineering, Tianjin University, Tianjin, 300072.E-mail: lz@ tju. edu. cn (Luo Zhen)74CHINA WELDING Vol. 18 No, 1 March 2009method can detect the tiny changes of the spot weldingquality. Therefore, this research can more accurately re-8x。=|f"(xo +8x0) -f"(x)1 =flect the essential characters of the acoustic emission sig-d"(solan=e"&o(3)nals, and improves the detection precision of the spotdrowelding.where λ is Lyapunov exponent. The magnitude of the Lya-1 Applications of the techniquespunov exponent is a measurement of the sensitivity to ini-In this section, the dynamical behavior of the acous-tial conditions. The system is chaotic and unstable whentic emission signals was studied using techniques fromthe Lyapunov exponent is positive. For an n dimensionalnonlinear dynamical systems['5-8!.map, the largest Lyapunov exponent is preferred to esti-mate whether the system is chaotic or not. This paper a1.1 Phase space reconstruction methoddopts the method introduced by Wolf to calculate the lar-The phase space is reconstructed according to the de-gest Lyapunov exponent of the time series in the spot weld-ay coordinate method proposed by Takens and Pack- ing.ard'9-10). Here, define a discrete time arrayx(i), i=1,2,., n obtained by measurement or simulation, recon-struct the m-dimension state vector X。using the delay co-1.3 Definition and computing Hausdorff dimensionordinate method.The fractal dimension of a function may be interpretedas a measure of the quantity of space that the graph occu-pies between m and m + 1 dimensional spaces. FractalsX。=x(n),x(n+ T),x(n +27)"",can be seen as space filing“objects". For the curve de-x(n+ (m-1)T)(1)scribed above, it is the space that flls or occupies, be-tween a 1-dimension line and a 2-dimension plane.where T is called time delay and m is embedding dimen-With the improving of the application of fractal theo-sion.ry, the definitions of fractal dimension include informationT and m are two important parameters in the phasedimension, box counting dimension, and correlation di-space reconstruction. Values of T, m are obtained by themension and so on. Especially in the subler and more 8C-mutual iformation method" and Cao' s ethod(2), re-curate, the Hausdorff dimension is widely implemented.spectively.1.3. 1 Hausdorff dimension1.2 Largest Lyapunov exponentsThe Hausdorf dimension of a set in a metric spaceBased on the reconstructed phase space, the spatio-may be expressed as:temporal behavior of the time series is analyzed. The Lya-punov exponent is an important parameter for describingD.=lim-In[ N(e)l(4)the non-linear system behavior and shows the rate of expo-lnεnential divergence from initial perturbed conditions.Consider a 1-dimensional mapwhere N(e) is the number of open balls of a radius 8 nee-ded to cover the set.%+ =f(x.)(2)1.3.中国煤化工MHCNMHGfractal dimension areAssume the diference of the initial value x is 8&xo.programmed in Labview software. The flow chart of the a-The n time iteration value is:coustic signal is as follows',seeFig.1..Chaos analysis of acoustic emission signals in spot welding process75四CeveEor- Chaert习回回回的5Eoxlmoabor目5园| evefore CGraDDBOOFBaaensiop0.000)POAOF旺G)日ndez回与团区Gp2eng0000)-回回日=D0BDDE000Fig. 1 LabVIEW sample program2 Experimental studyby PC computer with sample rate 400 kHz.2. l MaterialsThe material in the present work was 5A02 commer-3 Results and discussioncial aluminum aloys sheets. The etched specimens of the3.1 ldentification of chaos state with Lyapunov ex-spot weld, 50 mm x350 mm x0.8 mm, were used duringponentthe complete investigation.Whether the time series data is stochastic ，chaoequantification is a main problem in analytical acoustic e2.2 Spot welding machinemission signal. The solving method that matches with theDC spot welding machine incorporating MAYACHItime series signal can be chosen properly. If the acousticMM-326B Inverter Welding Power Source was used foremission signal is stochastic, it will be unecessary to ana-welding the specimens involved in the present work.lyze the characteristic of chaos atractor, even to recon-struct the basic dynamic systems. The research purpose is '2.3 Data acquisition systemto judge whether there is chaos characteristic in the acous-The data acquisition system has been developed totic emission signal, establish a signal testing system usingsample the acoustic signal from spot welding process andchaos theory and also tries to have more comprehensiveMP201 electret condenser microphone measures the acous-understanding of the spot welding quality.tic signal. The open circuit sensitivity is 43.7 mV/Pa andThe research object is the acoustic time series signalthe frequency response curve is from 20 Hz to 16 kHz within the aluminum spot welding. The Lyapunov exponent2dB deviation. The computer system is based on a stand-will中国煤化工space reconstruction ofard IBM compatible PC M with data acquisition card thiHC N M H Gaos cacteristic of the(DAQ-2010, the sampling rate is 2 MHz and A/D solu-acoustic emission signal. In the experiment, the sampletion is 14 bits. ). The acoustic emission signal is recordeddata on the state of non-fusion, from 22% nugget area to76CHINA WELDING Vol. 18 No. 1 March 200991% nugget area and over-heat are chosen to compute theumented by China patent ZL03130440. 0). From Fig.2,largest Lyapunov exponent from 0. 144 to 0. 208，see .the correlation coffcient is 0. 93 between Lyapunov expo-Table 1( method of evaluating the nugget area is well doc-nent and nugget area.Table 1 Acoustic emission signals Lyapunov exponents and fractal dimensions of aluminum spot welding in different nugget areaNuggetSpot welding parameterEmbeddingTimeLargestHausdoflNo.StateareaI/kAF/kNl/ms ,dimensiondelay Lyapunov exponentdimension DNon-fusion17.54.5500. 144Chaos1.3122%18.54.2110.1491.4244%19.2100.1581.4762%20.13.5i00. 1621.6774%20.60.1731.6988%180.1791.7391%21.53.00.1921.74Over-heat22.5210. 2081.822.0get. So some interal energy is released to the surround-1.ings as acoustic wave. The acoustic wave also includeschaos characteristic produced by initial tiny differences atcontact resistance, working character of spot welding ma-0.chine, welding parameter etc. These different initial stateswill make changing nugget emit pseudorandom signal in0 0.20.4 0.6 0.8 1.0 1.2some degree. Through analyzing this signal , more informna-Nugget areation will be achieved. The calculated results show that all(a) Correlation coffcent is 0.98the Lyapunov exponents of acoustic data are positive on the0.25different nugget area. A conclusion can be drawn that the0.20acoustic emission signal is chaotic. So author should adopt0.15chaos theory to research the signal such as phase space re-0.10construction, statistical character of strange attractor etc.0.05In the theory of chaos time series，largest Lyapunov expo-nent means high complexity system and the relatively big).4 0.6 0.81.0 1.2embedding dimensions indicate that there are complex in-formation in the acoustic emission signal. From the com-(b) Correlation coffcient is 0.93puted results of the acoustic signals, the Lyapunov expo-nent is from0 to 1. It indicates that the data of the acous-Fig.2 Correlation analysis diagramtic emission signals include weak periodicity and can beAccording to the theory of forming nugget, the acous-ore中国煤化工tic signal acquisition by the microphone is mainly relatedYHCNMHGto the nugget energy and surrounding medium vibration.3.2 Character extraction of acoustic signalsThe signal includes certain changes such as changing nug-In the aluminum spot welding, the acoustic emissionChaos analysis of acoustic emission signals in spot welding process77signals are related to the materials and the changing nug-(2) A method is put forward to qualify the chaotic aget. From Fig.2, the correlation coefficient is 0. 98 be-coustic emission signals using fractal dimension. Thetween Hausdoff dimension and nugget area, 0. 93 betweenHausdorff dimension of the acoustic emission signal can in-Lyapunov exponent and nugget area. The microphone candicate the tiny changing nugget. It can supply a new meth-receive the continuous signal that has a close relationshipod of quality measuring in the spot welding.with the nugget area. So, there are difterent fractal dimen-(3) Because Lyapunov exponent method is new tech-sions corresponding to different nugget states.nique and just started to investigate chaos characteristic ofForm Table 1, the Hausdorff dimension is differentacoustice emission signals in spot welding process, the a-under various nugget areas. The fractal dimension of D, isplications of the techniques have many problems to be1.31 in non-fusion state, D2, D3, D, D, D。and D, issolved and the computing method can be improved in some1.42,1. 47,1.67,1.69,1. 73,1. 74 respectively fromdegree. Thereby it is necessary to lucubrate the method22% nugget area to 91 % nugget area, and Dg is 1.82 infrom the theory to the computing method.over-heat nugget. The value sequence of them is Dg > D, .>D。>Ds >D, >D, > D2 > D. The fractal dimensionsReferencesindicate the complexity degree of the acoustic emission sig-[1] Hao M, Osman K A, Boomer D R, et al. Developments innals in spot welding.characterization of resistance spot welding of aluminum. Weld-In over-heat state, the energy of foming nugget is soing Joumal, 1996, 75(1):5-8.2] Luo z. Study on method of monitoring and control in thehigh that some melted metal overflows with splashing.process for aluminum alloys resistance spot welding, Tianjin:Some aluminum is taken away and the nugget shape be-Tanjin University, 2003. (in Chinese)comes small. These cases will enhance the nonlinear state[ 3] Kuugjumtzis D. State epace reconstruction parameters in theand the complexity of the curve. 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