A study on infrared thermography processed trough the wavelet transform

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1 A study on infrared thermography processed trough the wavelet transform V. Niola, G. Quaremba, A. Amoresano Department of Mechanical Engineering for Energetics University of Naples Federico II Via Claudio 1, 815, Napoli, ITALY Abstract: - Nowadays, in the industrial field, the predictive maintenance is an important methodology employed for reducing risks of machine stops. Machines are continuously monitored in order to maximize the performance, both in terms of quality and productivity. In this paper it is pointed out a procedure which allows to evaluate in advance which kind of fault can happen on a machinery. The present study, by involving thermal images detected trough infrared camera and the technique of Wavelet Transform, achieves important results in the predictive failure analysis. Key-Words: - IR Analysis, Wavelet Transform, Predictive Maintenance. 1. Introduction In the industrial field, the predictive maintenance is an important methodology and approach employed in order to reduce risks of machine stops. For this reason, for maximizing the performance, both in terms of quality and productivity, tools, machinery and plants are continuously monitored. Nowadays, the study is also steered to their capability of working without any interruption or, at least, without unwanted stops. One can easily understand that this aspect of the research is synergistic to the previous one because the reduction of unproductive time of machines increases the time available for production. The predictive maintenance is based on methods and techniques which are still evolving rapidly, even on a consolidated basis; the approach to the evaluation of economical benefit deriving from its application deserves a particular attention. Many benefits ustify the application of predictive maintenance: 1. reduction of stops due to failure. reduction of repairing times 3. reduction of failures induced by previous failure 4. increasing the lifetime of components 5. limitation of qualitative drift 6. optimization of spare parts.. The Infrared thermography technique The infrared thermography (IT) is based on the detection of electromagnetic waves in the infrared band, invisible to the human eye. The bodies with a temperature over the absolute zero, emit electromagnetic radiation depending on their temperature The measurement of radiation emitted from any kind of material, machinery or mechanical component, performed by using IT, provides the thermal map. The results achieved trough the application of IT encourages for monitoring mechanical systems. In fact, it provides a complete representation of effective working conditions, putting out of sudden failures and allowing better planning of any technical intervention. As said before, the IT is based on the detection of electromagnetic waves in the infrared band, invisible to the human eye. Obects with a temperature above the absolute zero ( K or C ), emit electromagnetic radiation depending on their temperature. The analysis of surface thermal fields allows to detect fractures and / or anomalies that may occur during the working process. In fact, every worn or not properly lubricated mechanism tends to overheat before reaching the fault. A thermographic survey can identify such overheating since its onset and the related thermal assessment should provide many important indications before the fault occurs. ISSN: ISBN:

2 3. An overview on two-dimensional wavelets In our study we used MatLab package and the Toolbox Wavelet ver In particular, the wavelets used in this paper are those proposed by Daubechies [1]. She constructed a series of mather wavelets (indexed by N and denoted by dbn) with each mother in the series having regularity proportional to N []. Each Daubechies' wavelet are compactly supported in the time domain. Typically wavelets are specifically constructed so that some properties are verified [3]. A mother wavelet ψ is a function of zero h-th moment x h ψ ( x) dx =, h N. (1) From this definition, it follows that, if ψ is a wavelet whose all moments are zero, also the function ψ ik is a wavelet, where / ψ ( x) = ψ ( x k). k In fact, we have h / x ψ ( x k) dx = h 1 y + k / ψ ( = dy = / ( + ) h y k ψ ( = ( h+ 1) = dy = h / h h m m ( + 1) k y = h m= m ψ ( dy. () Wavelets, like sinusoidal functions in Fourier analysis, are used for representing signals. In fact, let us consider a wavelet ψ and a function ϕ (father wavelet) such that { }, { }, k Z,,1,,... } = k k ψ (3) is a complete orthonormal system. By Parseval theorem, for every s L ( R), it follows that 1 k k ( t) + d k k ( t) = k s( t) = a ϕ ψ. (4) k The decomposition of a signal s(t) by wavelet is represented by the following detail function coefficients d k 1 τ k = s( τ ) ψ dτ (5) and by the approximating scaling coefficients a k s( τ ) ( τ k) = ψ dτ. (6) Note that d k can be regarded, for any, as a function of k. Consequently, it is constant if the signal s(t) is a smooth function, having considered that a wavelet has zero moments. To show the above mentioned property, it is sufficient to expand the signal in Taylor s series. An example of wavelets is given by Daubechies family {dbn, N = 1,, } [4]. It is supp φ [, N 1] supp ψ [, N 1] and x h ψ ( x) dx =, h =, 1,, N 1. Moreover, there is the following smoothness property: for any N >, the dn wavelets verify φ, ψ HλN,.1936 λ.75, where HλN is the Hölder smoothness class with parameter λ. Now, let us consider two dimensional signals f ( x, which are square-integrable over the real plane: f ( x, L ( R ). A wavelet basis for L ( R) is to take the simple product of onedimensional wavelet Ψ x, =ψ ( x) ψ ( ). (7) ( 1 k1k y 1k1 k ISSN: ISBN:

3 It is easy to show that Ψ s as defined above are indeed wavelets and that they form an orthonormal basis for L ( R ). It can been show that the detail space W is itself made up of three orthogonal subspaces as follows 1 Ψ ( x, = ϕ( x) ψ ( ; Ψ ( x, = ψ ( x) ϕ( ; 3 Ψ ( x, = ψ ( x) ψ (. (8) Mallat [5] notes that the three sets of wavelets correspond to specific spatial orientations, in 1 particular: the wavelet Ψ corresponds to the horizontal direction (H), the wavelet Ψ with the 3 vertical direction (V) and Ψ with the diagonal (D). For more details see [-8]. In the following we show the method developed for the image processing which allows to distinguish the image features and its thermal radiation emitted during the observation of mechanical systems. 5. Materials Four thermographic analyses were performed at different epochs on the same mechanical component (Fig.1). For each thermal recording (roughly two minutes) ten images sequentially sampled were analyzed. The signal processing analysis, performed on the samples, was made by applying the two-dimensional WT. 4. Wavelet Transform and thermography working together As said before, the present study involves thermal images detected by means of infrared camera. The systems showing slow thermal evolution can be defined as apparently stable. The present study concerning criteria for evaluating the system evolution through thermal images, periodically detected. It is one of the most important problem for the prediction of the state of these systems both from a specific and functional point of view. For this reason, in order to analyze the evolutionary state of the system we consider crucial the detection of the smallest detail, with reference to the thermal map, significative for predicting the real situation of the system. In many cases, the thermal gradient determines the density of pixel forming the image. For that reason the study was conducted by specific models, with the aim to resolve reflectance of the observed obect and thermal radiation emitted during its observation. This study illustrates an application of a new method for signal processing based on the decomposition of two-dimensional signal performed by wavelet. It is focused that the integration of the wavelet with the IT technique allows to reveal the dynamical and morphological difference showed by two thermal maps. Fig 1 Thermographic analysis Fig. shows the sequence of the sampled pixel turned out from each image. In other words, the first sequence displays the pixel intensity (i.e., temperature distribution) of the image recorded at epoch T. Similarly, sequences numbered two, three and four represent the pixel intensity of thermal data recorded at subsequent epochs (named as T 1, T, T 3 ) on the same mechanical component. It is clear that the evolution of data, represented in Fig., is almost similar in all four cases. It will be noted that all the sequences show the absolute temperature of the sampled images. In other words, the diagrams show the raw data recovered from a thermographic sensor converted from two-dimensional numerical matrix into onedimensional vector. The observation of the images as well as the evolution of raw data does not provide any information on possible anomalies connected to the monitored obect. Therefore, it is quite ISSN: ISBN:

4 evident that the thermographic analysis, by itself, does not provide sufficient evidence to predict any anomalies related to the mechanical system under control. ampiezza segnale ampiezza segnale ampiezza segnale ampiezza segnale Run17 sc cmb x 1 5 Run5 sc cmb x 1 5 run11 sc cmb segnale x 1 5 run3 sc cmb segnale x 1 5 Fig Sequence of the sampled pixel Fig.3b Comparison of V wavelet coefficients 6. How the WT works The first sequence of data named T provides basic historical information. It is true that starting from this sequence of data it is already possible to obtain interesting information by applying the WT both to thermal maps and to the numerical vectorial sequence. In particular, it is possible to evaluate and to take out the information characterizing the pattern of the signal as well as its morphological features and mean dynamics, with reference to the various epochs. In the diagrams (Fig.3a,b,c) reported below it is illustrated, respectively, the comparison of horizontal (H), vertical (V) and diagonal (D) wavelet coefficients with reference to each epoch. Fig.3a Comparison of H wavelet coefficients Fig.3v Comparison of D wavelet coefficients Information collected from the frames at T shows a stable phenomenon, characterized by a well-defined morpho-dynamical pattern. The diagrams represented in Fig.3 show the steady decay of system under control. In particular, the comparison of thermographic findings, referred to periods T and T 1, no significative decay shows. The results obtained by comparing horizontal, vertical and diagonal wavelet coefficients belonging to maps from T to T 3 show significative differences both qualitative and quantitative. The comparison of thermographic sequences made later (i.e., at T 3 epoch) clearly shows a placement of the thermal signal in a singular position definable as outlier (absolutely not ISSN: ISBN:

5 deducible from the observation of thermographic sequence, shown in Fig.. This results suggest a preventive maintenance to be performed on the mechanical system under control. Now, in order to illustrate the capability of wavelet to capture the smallest details, in the picture below are reported identical thermal maps. The Fig. 4, referred to the thermal map at T, was converted into gray levels and magnified as in Fig.5. The difference between the right and the left one was one pixel only. In fact, one pixel was manually modified in order to show how sensitive the WT is. Fig. 6 Standard view of the thermal map and position of manually modified pixel The point circled in Fig.6 was highlighted in white and was pointed out by wavelet analysis. In fact it does not exhibit a significative variance in terms of colour and chromatism if compared to neighbored points. A signal processing performed by means of standard analysis or through FFT does not highlight any change or beginning of decay. Fig. 4 Standard thermal map Fig. 5 Blow-up of the thermal map at T Matching Reference T #T grey lev. Table 1 H V D T #T mod Table 1 shows the results achieved by comparing the matrix (i.e., horizontal, vertical and diagonal) obtained by wavelet decomposition of the images of Fig.5. Note that the first row shows the correlation values of each matrix compared between two frames randomly sampled from the same sequence, recorded at time T. The second row shows the correlation values of each matrix of the left map with the modified map on the right. Qualitative and quantitative differences are quite evident. The correlation of grey level matrix are clearly the same. Finally, the Fig.7 compares the initial thermal pattern of the mechanical component, i.e., when the monitoring test started at T, with the situation at T 3, i.e., before the mechanical ISSN: ISBN:

6 collapse, due to fatigue, of a rotating mechanical obect happens. It is evident the dynamical and morphological difference showed by two thermographic patterns. compressing the images captured in order to create a wide database in which we can storage the templates of the main anomalies. To summarize, there are five main answers to the question Why wavelets? : Signal processing Image analysis Denoising Fast algorithms Data compression. Wavelet transforms can model irregular data patterns such as sharp changes, better than the Fourier transforms and standard statistical procedures and provide a multi-resolution approximation. Fig. 7 Comparison of thermal pattern T #T 3 7. Conclusions This study illustrates an application of a new method for signal processing based on the decomposition of two-dimensional signal performed by wavelet. It was focused that the integration of the wavelet with the infrared thermography technique allows to reveal the dynamical and morphological difference showed by two thermographic patterns. This study illustrates an application of a new method for signal processing based on the decomposition of two-dimensional signal performed by wavelet. It was focused that the integration of the wavelet with the infrared thermography technique allows to reveal the dynamical and morphological difference showed by two thermographic patterns. The contribution of wavelet signal processing is also important for the noise reduction. In fact one of the most important application of discrete wavelet transform (DWT), today, is the optimization of the estimation of the noise level. The methodology exposed in this paper, should concur to perform the diagnose of some anomalies useful for a reliable maintenance [9-1]. The DWT is able to perform such an assessment. At the same time, wavelets have proven extremely useful for solving problems of data compression. If we consider that an other important step, will be the diagnosis of anomalies inducted by wear, it is clear the importance of 8. References [1] Daubechies, I., Ten lectures on Wavelets, SIAM, Philadelphia, Pennsylvania, 199. [] Strang, G., Nguyen, T., Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, [3] Meyer, Y., Wavelets: Algorithms and Applications, SIAM, Philadelphia, [4] Härdle, W., Kerkyacharian, G, Picard, D. and Tsybakov, A., Wavelets Approximation and Statistical Applications, Springer, Berlin, [5] Mallat, S.G., A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11: , [6] Ogden,,R.,T., Essential Wavelets for Statistical Applications and Data Analysis. Birkhäuser, Boston, [7] Antoniadis, A., Oppenheim, G., Lecture notes in Statistics - Wavelets and Statistics, Springer, [8] Kaiser, G., A Friendly Guide to Wavelets, Birkhäuser, [9] Niola, V., Oliviero, R., Quaremba, G., A method for classifying turbulence simulated in a lubricating oil flow. Proceedings of 4 AIMETA, International Tribology Conference, September 14-17, Rome, Italy. [1] Niola, V., Quaremba, G., A Method for 3-D Reconstruction Based on Photometric Stereo Techniques. Proceedings of International Conference on Advanced Optical Diagnostics in Fluids, Solids and Combustion. Tokyo Dec. 4-6, 4. ISSN: ISBN: