Sensors Fault Detection and Diagnosis Based On Morphology-wavelet Algorithm

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1 Sensors Falt Detection and Diagnosis Based On Morpholog-wavelet Algorithm GoLian Ho Department of Atomation North China Electric Power Universit Beijing,China Yi Zhang Department of Atomation North China Electric Power Universit Beijing,China JianHa Zhang Department of Atomation North China Electric Power Universit Beijing,China Abstract This paper proposed a novel method to falt detection and diagnosis of sensors sing trend analsis of inpt and otpt signals related to the sensor itself. Firstl, generalized morphological filter with mlti-strctre elements is designed to filter the random noise and implse noise in sensor s inpt and otpt signals. And secondl, to effectivel extract the incipient falt and abrptl falt characteristic, a wavelet transform was sed to decompose and analze the filtered signals in this paper. Throgh the Mlti Resoltion Analsis (MRA), the falt can be located accratel. There tpical sensor falts sch as fix, gain, bias, drift falts were stdied. The simlation reslts show that this algorithm is capable of locating accratel. Kewords falt detection and diagnosis, Morphologwavelet, sensor, Mlti Resoltion Analsis (MRA) I. INTRODUCTION Process spervision and control rel fndamentall on the process measre information obtained b sensors. Conseqentl, a sensor s falt ma be lead to the measrements corrpted or the whole control sstem ineffective. For this reason, falt detection and diagnosis of sensors have received particlar attention. The methods of model-based and model-freed abot sensor falt detection and diagnosis were stdied in these ears. In reference [], the Kalman filter was designed to the diagnosis of incipient sensor falts. However, the nknown inpts sch as sstem distrbances and noises were not considered in this paper. A new descriptor estimator was constrcted via the Linear Matrix Ineqalit (LMI) to decople both the inpt and otpt distrbances completel and simltaneosl estimate the descriptor sstem state. Then the new estimator was applied to the sensor falt diagnosis []. However, the diagnosis scheme was relaed on the model. In the large-scale sstems, modelbased methods are inefficientl when the process model is not available or not eas to obtain. Recentl, the knowledge-based approaches in sensor s detecting and diagnosing also have been pblished in [3]. In reference [4], the mltisensor information fsion techniqe based on Dempster-Shafer theor is applied to the sensors falt detection and diagnosis. Bt there are some drawbacks. If the nmber of sensor is larger, the method can be indeed heav to compting. In reference [5], to address the problems associated with detecting and identifing falts that occr in the sensor of dnamical sstems with discrete-valed inpt and otpt signals. At present, wavelet analsis, which processes signals with both time and freqenc domain localizations, is powerfl tool for processing transient signals to handle the problems of model-restricted. Wavelet transform was introdced in to the sensor of abrpt diagnosis [6]. The major drawbacks of wavelet analsis approaches mentioned above is that it is nsitable for extracting abrpt falt information. Bt de to the limited nmber of scales, a single wavelet amplitde map has not enogh scales to describe all details of the signal. To make p for the deficienc of wavelet transform in the application of abrpt diagnosis, mlti-wavelet packets transform was introdced into abrpt sensor falt diagnosis[7]. This method has been proved to be qite effective in the detection of sensor abrpt falt. However, when the sensor signal was changed slowl (incipient falts), the method is not accratel. Becase wavelet transform reqires the se of a window of adeqate length and a high freqenc to ensre that the all details of falt component is extracted b the wavelet transform. Bt the signal is difficlt to be separated from interference noise when the freqenc is too mch high. To make sre wavelet transform relativel extract fll-valed information, some new techniqes are adopted to remove random noise (white noise and implse noise). Mathematical Morpholog (MM) is developed from set theor and integral geometr, and is concerned with the shape of a signal waveform in the complete time domain rather than the freqenc domain. MM has been widel applied in the areas of image processing [8], pattern recognition; signal processing [9] for their robstness in preserving the shape while sppressing the noise. MM can be developed as an efficient nonlinear filter. Using morphological filters, the radical shape of the distrbed can be recognized, even if the original is mixed with strong noise (white noise and implse noise). In addition, MM has the featre of eas calclation and implementation. Therefore, it is desired to seek for a sstematic wa to deal with how to exactl detect and diagnose the falt when the fllvaled information was drowned b the noise. In this paper, the method of morpholog-wavelet to deals with the detection and /08 /$ IEEE RAM 008

2 diagnosis of sensors was proposed. Firstl, generalized morphological filter with mlti-strctre elements is designed to filter the white noise and implse noise in sensor s inpt and otpt signals. And secondl, to effectivel extract the drifting incipient falt and abrptl falt characteristic, a wavelet transform was sed to decompose and analze the filtered signals in this paper. Throgh the Mlti Resoltion Analzing (MRA), the falt can be located accratel. The efficienc and relativit of the morpholog-wavelet algorithm are verified b sper-heated steam temperatre sensor of power plant. II. THEORY OF MORPHOLOGICAL FILTER AND WAVELET TRANSFORM A Morphological Filter The Mathematical Morpholog (MM) is nonlinear signal transformation concerned with the shape of a waveform in time domain rather than freqenc. The morphological filtering techniqe is to process signals b a fnction, known generall as Strctring Element (SE) or the strctring fnction in order to captre signals, keep detail and redce noises. In MM, dilation and erosion are two basic operations. Using the mbra of a fnction, the binar MM operators can be extended to -dimension (-D) and n-dimension (n-d) signals. Here we onl present the -D transformation. Definition Let f ( n) and g( n) denote two real-valed fnctions defined on the two discrete F,, N G =,, M, domain = { } and { } respectivel. It is frther assmed that M < N. f ( n ) is an inpt signal and g( n ) is a strctring element. Then the for basic morphological operations are defined b: Erosion: ( fθ g)( n) = min { f ( n+ m) gm } p=,, M { } Dilation: ( f g)( n) = max f ( n m) + g( m) p=,, M Opening operator: ( f g)( n) = ( fθg g)( n) () () (3) Closing operator: ( f g)( n) = ( f gθ g)( n) (4) Where Θ is the smbol of erosion. is the smbol of dilation. is the smbol of opening. is the smbol of closing. Opening and closing are two operators commonl sed in morphological filter and the smooth a signal in different was. Opening can be thoght of as moving the strctring element beneath the graph of the signal and removing positive implse that do not match the shape of the strctring element. Closing can be thoght of as moving the strctring element above the graph the signal and filtering negative implse that the strctring element does not fit into. In morphological filtering, the reslts of the operations depend on not onl the form of morphological transformation bt also the size and shape of the strctring element. Usall, a flat strctring element which the vales are all zero is sed if there is no a priori knowledge abot the profile of the signal. In (3) and (4), opening and closing filters defined b Maragos se the same strctring element. In order to effective remove all positive and negative implsive noise and sppress additive white noise in signals, the generalized opening and closing filter with different sized strctring elements are proposed as follows. In order to improve existing methods, this paper constrcts a kind of parallel composite filter with different SE. This kind of filter also keeps more sefl information. Flat line fnction can be chosen as the shape of SE in this paper. First level: g ( n ) = { 0,0,0,0,0,0,0} (5) Second level: g ( n ) = { 0,0,0,0} (6) Sppose that there is an inpt signal f ( n) and SE aggregation { g, g }. The strctres of new morphological filters are: oc [ f ( n) ] MAX ( OCg, OCg) co [ f ( n) ] MIN ( COg, COg) Where, OCg = ( f g )(,) i i gi n i= CO = ( f g g )( n) ( i=,) ψ = (7) ψ = (8) gi i i Ths ( n ) = ( + ) ψ ψ (9) oc co Then the otpt signal of morphological filter is the average vale of both otpts, this reslt cold be mch approach the practical signal. B Wavelet Transform Wavelet transform has powerfl abilit in signal processing. Since wavelet transformation can localize sensor signal characteristics both in time and freqenc domain. The std of sensor falt detection and diagnosis is based on the singlarit of continos wavelet transformation. Firstl, according to the wavelet transformation of inpt and otpt signals, extract the sefl information to locate the singlarit of inpt and otpt signals. Secondl, throgh compare the maximm which is mtated b inpt and otpt signals, get the ride of the maximm which is mtated b inpt signals. Then the other maximm are the falts of sensor. The wavelet transform of a continos signal f ( t) is defined as t b WTf ( ab, ) = f () t ψ dt (0) a a Where WTf ( ab, ) is the wavelet transform of coefficient. ψ () t is the mother wavelet, a is the time scaling factor and b is the time shifting factor.

3 C Mlti-Resoltion Analsis The concept of mlti-resoltion is described as follows: sqare integrable fnction f ( t) L ( R) can be regarded as the limit case of certain gradal approach, ever approximation is the reslt of the smoothness of low-pass smooth fnction ϕ ( t) towards f ( t ), the smooth fnction ϕ ( t) is also expanding and contracting gradall while approaching b degrees, that is, the analzed fnction f ( t ) is approached gradall b sing different resoltion. Here is a realization of signal Mlti-resoltion decomposition. As the orthogonal WT above is adopted, mlti-resoltion analsis can be applied to decompose random signal f t L R (sqare integrable fnction) as follows []: () = ϕ () + ψ () f t c t d t mk, mk, k Z m= k Z j () Where c f ( t), ( t) = ϕ (), d = f t ψ t (3) The decomposing coefficient c is called discrete smooth approach signal, and ( t) ϕ is called scale fnction; the decomposing d is called discrete detail signal, which reflects the detail difference between two smooth approaches of an ψ t is called wavelet fnction. adjacent scale, and In order to frther apprehend mlti-resoltion analsis, here takes a decomposition of a 3 scales for example, the wavelet decomposing tree is shown in Fig.. f ( n) a ( k ) d ( k) a ( k ) d ( k) a3 ( k ) d ( k) 3 Fig. The block diagram of 3 scales mlti-resoltion decomposing tree. III. MORPHOLOGY-WAVELET ALGORITHM FOR FAULT DETECTION Wavelet transform has been applied in varios areas benefiting from its otstanding abilit of detecting singlar signal and the great filtering abilit, while morphological filter is a new non-linear tool for digital signal processing; both of them have their speriorities. Wavelet algorithm is sperior to the morphological filter in aspect of the filtering effectiveness on white noises, bt it is less effective on sppressing the implsive noises. This paper presents a novel tpe of integrated filter named morpholog-wavelet algorithm. Firstl, generalized morphological filter with mlti-strctre elements is designed to filter the white noise and implse noise in sensor s inpt and otpt signals. Then, the mlti-resoltion wavelet transform applied to extract the drifting incipient falt and abrptl falt characteristic. And, wavelet transform can also advance to filter abilit, especiall deal with white noise. Consider linear sstems: s = Gss + Gss + Es (4) Where ( s ) is otpt signal; ( s ) is inpt signal; G( s ) is sstem transfer fnction. G( s) reflect the change of sstem parameters; E( s ) is random noise. Morpholog-wavelet algorithm for falt detection and diagnosis of this sstem is presented in 4 steps. The framework of the morpholog-wavelet algorithm is shown in Fig.. Step: The generalized morphological filter with mltistrctre elements is emploed to filter the white noise and t. The implse noise in sensor s inpt ( t ) and otpt filter s otpts are ( t ) and ( t ) respectivel. () t = [( t () gi gi ) + ( t () gi gi )] ( i=,) (5) () t = [( t () gi gi ) + ( t () gi gi )] ( i=,) (6) Step: The wavelet transform is applied to analze the t. Throgh the mlti-resoltion filter s otpts t and analsis, sefl information is extracted to locate the singlarit of inpt and otpt signals. According to the, W st,, the maximm transformation reslts W ( st ) and of inpt and otpt signals can be calclated. Step3: (, ), W st = t ψ t (7) (, ), W st = t ψ t (8) Throgh comparing the maximms mtated, W st,, maximm mtated respectivel b W ( st) and b W (, ) st will be eliminated. Then the other maximm is the falt of sensor. The algorithm is shown as fellow:

4 Where: () (, ) (, ) r t = W st kw st (9) Λ (, ) (, ) W ( st, ) W stw st Λ k = (0) Step4: Set the soft threshold to remove the distrbances of the detection reslts. The soft threshold is calclated as follows [3]: N r ( n ) N Strength factor: n= σ = () Soft threshold: Th= σ ln( N) () Where the signal r() t is sampled as discrete signal rn. N is the sampled nmber. Then the detection reslt was transformed as below: ' R ( n) r( n), 0, <= Th = r n r n > Th (3) Fig. The framework of the morpholog-wavelet algorithm IV. SIMULATION OF SENSOR FAULTS The possible falts of a sensor ma be classified as abrpt falts and incipient falts. This paper focses on fix, gain, bias falts (abrpt falt) and drift falt (incipient falt) of sensors. The proposed algorithm is simlated in the sper-heated stream temperatre sensor. The measrement range of the temperatre sensor is from 400 to 600. And the main steam temperatre is varied from 535 to 545. Several falts of the temperatre sensors are simlated in this paper, sch as fix, bias, gain and drift falts. The simlation signals go with heav noises in this paper. Fig.3. Diagnosis process of morpholog-wavelet algorithm. Assme that fix falt of the sper-heated stream temperatre sensor signal occrred at the moment of 00s. Under this condition, the original signals and the de-noised signals of the inpt and fix falt otpt are shown respectivel in Fig.3 and Fig.3, in which the de-noised signals are handled with the morphological filter. Fig.3 shows the components of the signal at different nodes (d, d, d3) of the

5 scale throgh the wavelet. It shows the diagnosis reslts of the different scales based on morpholog-wavelet algorithm. In the same sensor condition, the bias falt of sensor otpt signal occrred at the moment of 50s. Fig.4 illstrated the original inpt and the bias falt signals of the temperatre sensor. Trogh the morphological filter, the magnitde of the bias falt in the sensor is shown in Fig.4. Fig.4 shows the three resoltion analsis (d, d, d3) of the wavelet transform. In the same sensor condition, when the sensor gain falt takes place at 50s. The original inpt and the gain falt signals of the temperatre sensor are shown in Fig.5. Trogh the morphological filter, the magnitde of the gain falt in the sensor is shown in Fig.5. Fig.5 shows the three resoltion analsis (d, d, d3) of the wavelet transform. The simlation reslts as above have shown that the morphologwavelet algorithm is capable of accratel extracting the abrpt featres of sensor falt signals. The transient falt was also presented as below. Fig 4. Diagnosis process of morpholog-wavelet algorithm. Fig 5. Diagnosis process of morpholog-wavelet algorithm.

6 According to the morpholog-wavelet algorithm, the detection and diagnosis of drift falt of the sensors were stdied. Assme that the drift falt of sper-heated stream temperatre sensor signal occrred at the moment of 00s. Under this condition, the inpt and fix falt otpt original signals and the de-noised signals which handled with the morphological filter are shown in Fig.6 the wavelet. It shows the diagnosis reslts of the morphologwavelet algorithm. V. CONCLUSIONS A novel model-free method applied to the detection of abrpt and incipient sensor falts has been presented. The morphological filter is good at dealing with the implse noise while the wavelet transform is good at sppressing white noise. The integrated morpholog-wavelet algorithm incorporates the advantages of both morpholog and wavelet transform, so it has the excellent capabilit of restraining white noise and implse noise. It can also appl to efficientl extracting the incipient falt and abrpt falt characteristic, and the falt can be located accratel. The simlation reslts confirmed that the algorithm have effectivel sed in sensors falt detection. The frther std of the morpholog-wavelet algorithm will be extended into falt diagnosis of control sstem. REFERENCES Fig 6. Diagnosis process of morpholog-wavelet algorithm. and Fig.6, respectivel. Fig.6 shows the components of the signal at different nodes (d, d, d3) of the scale throgh [] M.Jaakmar, B.Das.Bijan, Diagnosis of Incipient Sensor Falts in a Flight Control Actation Sstem, SICE-ICASE International Joint Conference 006 Oct. 8-, in Bexco, Bsan, Korea, 006, pp [] Zhiwei Gao, Daniel W. C. Ho, State/Noise Estimator for Descriptor Sstems With Application to Sensor Falt Diagnosis, IEEE transactions on signal processing, vol.54,pp [3] J. Zhang, B.S. Wang et al., Falt Diagnosis of Sensor Network Using Information Fsion Defined on Different Reference Sets, Radar, 006.CIE 06. International Conference on Oct. 006,pp.-5. [4] J. Lnze, J. Schröder, Sensor and Actator Falt Diagnosis of Sstems with Discrete Inpts and Otpts, IEEE Transactions on sstems. Man and Cbernetics-Part B: Cbernetics, vol. 34, 004, pp [5] M. Y. Yang, S. X. Wang, M. Y. Chen, Research on the arithmetic of non-nit voltage protection for EHV transmission line based on wavelet analsis, 005 IEEE/PES Transmission and Distribtion Conference & Exhibition: Asia and Pacific Dalian, China,005,pp.- 5. [6] A. Sreshbab, J.A. Farrell, Wavelet-based sstem identification for nonlinear control, IEEE Trans. Atomatic Control, vol.44, pp [7] S. S. Goh, Q. Jiang and T. Xia, Constrction of biorthogonal mltiwavelets sing the lifting scheme, preprint. [8] M. H. Sedaaghi, Q. H. W, Real-time implementation of gre-scale morphological operators, Insf. Elect. Eng. Electron. Len., vol.33, pp [9] T. Chen and Q. H. W, A psedo tap-hat mathematical morphological approach to edge detection in dark regions, Parrem Recognil., vol.35, pp [0] Li-an Chen, Peiming Zhang, Detection and Protection of Short Circit Falt Based on Morpholog-wavelet, 005 IEEE/PES Transmission and Distribtion Conference & Exhibition: Asia and Pacific Dalian, China 005,pp.-5. [] J. Zhen, D.Y. Shi, Q. Li and Q.H. W, Noise redction and confidence level analsis in MMG-based Transient falt location, 005 IEEE/PES Transmission and Distribtion Conference & Exhibition: Asia and Pacific Dalian, China,005,pp.-5. [] S.A. Mallat. Theor of mlti-resoltion signal decomposition: the wavelet transform, IEEE Trans.on PAMI, 989,(7): [3] D.L.Donoho, De-noising b Soft-thresholding, IEEE Trans on I nformation Theor, vol.4,pp.63~67.