DAMAGE DETECTION AND LOCALIZATION IN PIPELINES UNDER NON STATIONARY ENVIRONMENT VARIATION USING SPARSE ESTIMATION OF MONITORING SIGNALS

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1 International Symposium on Structural Health Monitoring and Nondestructive Testing 4-5 October 2018, Saarbruecken, Germany More info about this article: DAMAGE DETECTION AND LOCALIZATION IN PIPELINES UNDER NON STATIONARY ENVIRONMENT VARIATION USING SPARSE ESTIMATION OF MONITORING SIGNALS Mahjoub El Mountassir 1,2*, Slah Yaacoubi 1, Gilles Mourot 2, Didier Maquin 2 1 Institut de Soudure, Plateforme RDI CND, 4 Bvd Henri Becquerel, Yutz 2 CRAN UMR 7039, Université de Lorraine, CNRS, Boulevard des Aiguillettes - BP 70239, Vandœuvre-lès-Nancy * Corresponding Author: m.elmountassir@isgroupe.com ABSTRACT Pipelines are very critical structures, especially those used for transporting oil, gas and other chemical substances. To ensure better working conditions of these structures, they must be monitored on a regular basis. Structural health monitoring (SHM) systems were proposed to tackle this issue. They aim at detecting, localizing and estimating the degree of severity of damage in the structure. The first objective which is damage detection is generally performed by comparing the reference signal obtained from the healthy state and the actual signal. This task of comparison in not easy to achieve because of the signal s complexity. Besides, the healthy state of the structure could vary by changing the environmental and operational conditions (EOCs). In this paper, we develop a method for damage detection based on sparse estimation of the collected signals. The position of the detected damage is obtained by calculating the error of estimation on a sliding window over the damaged signal. This method was tested on signals collected on small scale pipeline placed in laboratory conditions. Results have shown that the created damage was successfully detected and localized. KEYWORDS: Structural Health Monitoring, environmental and operational conditions, sparse estimation, damage detection and localization, pipelines. 1. INTRODUCTION Structural health monitoring (SHM) systems are required to perform periodically (might be real-time) damage assessment of critical structures such as pipelines. Theoretically, to achieve damage detection, the SHM system compares the reference signals acquired from a healthy structure with the measured signal from the current state of the structure [1]. However, before proceeding to this task of comparison, the system should be fed with a database of reference signals (i.e. baseline database). Since the environmental and operational conditions (EOCs) vary with time, the reference state of the structure could also change [2]. Hence, we face a problem of learning in non-stationary environment. If this issue is not taken into consideration, it will lead to false indications of damage. While a small number of false indications are acceptable, frequent false alarms will jeopardize the reliability of the SHM system. Some methods were proposed to compensate the effects of these EOCs namely BSS (Baseline Signal Stretch) and OBS (Optimal Baseline Selection) [3]. However, damage detection with these methods is based on a simple subtraction between the reference signal and current signal which is not reliable. Data-driven method using SVD (Singular Value Decomposition) of the matrix of reference signals was also proposed to address the problem of variation in EOCs [4]. Despite the interesting results showed by this technique, it requires two principal hypotheses. Firstly, it supposes that damage occurs abruptly which is not always true because in real cases, damage may develop progressively during a long period of time. Secondly, EOCs should be constantly changing so a jump cannot be observed in their associated singular vectors. In this paper, we propose a method of damage detection and localization which aims to minimize the influence of the variation of EOCs provided that the database of reference signals contains sufficient variation of these EOCs. The proposed method for damage detection and localization is based on sparse estimation of the current signal by reference signals acquired from a healthy pipeline. The sparse estimation is obtained by solving an optimization problem using the non-negative least squares [5]. This optimization problem consists in finding the minimal number of reference signals that well estimate the current signal. The error of estimation will be then used as index damage. Actually, a signal from a damaged pipeline will be characterized by a high estimation compared to that of a healthy state pipeline. The localization of damage is ensured by

2 calculating the estimation error on a moving window over the damaged pipe s signal. This idea is based on the fact that when using a particular mode of propagation of UGW, the effect of damage is local on the signal. In the following, a background section is presented where the method of collecting data namely Ultrasonic Guided Waves (UGW) is explained. Afterthat, in the same section an overview of the sparse estimation of a signal is presented along with some mathematical details. Then, the experimental setup is explained and finally the obtained results are presented and discussed. 2.1 ULTRASONIC GUIDED WAVES (UGW) 2. BACKGROUND UGW are stress waves which propagate through a medium and are guided by the structure s boundary. They can be generated and received using two types of sensors: piezoelectric or magnetostrictive. Also, two configurations of this technique exist: pitch catch and pulse echo. In the former, a sensor can either excite or receive the UGW. In the latter, a sensor can be used for both operations (emission and reception). The UGW can travel in all directions ensuring hence a volumetric coverage and they interact with the structure s discontinuities (this could include damage, welds, structure s ends etc.). At each interaction, the incident field is decomposed into two parts reflected and transmitted. In general, UGW involves some propagation phenomena, and they can be characterized by dispersion, and multi-mode components. Dispersion can be observed when the velocity of the waves is a function of the frequency. 2.2 SPARSE ESTIMATION The sparse estimation will help to determine which of the reference signals will be used to estimate the measured signal. By doing this, if the measured signal comes from a healthy state, it will be estimated by reference signals with very close EOCs. On the contrary, if the current signal is acquired a damaged pipe, then it will be difficult to find the set of reference signals that matches this signal. Basically, a sparse estimation of the measured signal by the matrix of reference signal could be provided by using the lasso regularization method given below [6]: = arg + λ where is the vector of regression coefficients, m and n are the number of reference signals and the number of samples respectively. The lasso method involves the calculation of the l1-norm of the regression coefficients instead of using the Euclidean distance. A solution to this optimization problem can be found. However, the regularization coefficient λ is generally difficult to define. In the case of highly correlated signals, which is an inherent characteristic of ultrasonic guided waves monitoring signals, some studies have demonstrated that instead of using the regularisation coefficient, non-negativity constraint can provide accurate estimation of the measured signals [5,7]. Thus, the optimization problem descried in equation (1) can be simplified as: = arg min subject to The solution of this problem was proposed by Lawson and Hanson [8]. They have developed an algorithm which divides the constraints into passive and active. Passive constraints correspond to positive regression coefficient and active constraints correspond to zero or negative regression coefficients. The algorithm starts with an empty set of passive constraints and at each iteration, it adds a positive regression coefficient to this set until the final set is found. 2

3 Once an estimation of the current signal is obtained. The quadratic estimation error noted by ( ) (where ( ) = will be chosen as damage index. Actually, if the signal is from a damaged structure, its estimation using reference signals will be not accurate. Hence, the error of estimation will be very high compared to that of a signal acquired from healthy structure. To localize the damage, we suggest applying the sparse estimation on a sliding window over the damaged signal. This is motivated by the fact that when dealing with UGW the effect of damage is local on the signal. In other words, at the position of damage, the received signal undergoes significant changes. The detailed implementation of the sliding window algorithm can be found in [9]. By using this technique, two parameters will have an impact on the final result: the moving step and the length of the window. In fact, the moving step is easy to determine, it corresponds to the minimum of point which depends on the sampling frequency of the signal. While the optimal window width depends on the precision of localization. 3.1 METHODOLOGY FOR DATA COLLECTION 3. EXPERIMENTAL SETUP AND PREPROCESSING The specimen considered in this study consists of a tube with 6 m length. It was placed in laboratory conditions where temperature fluctuates between 19 C and 26 C during the monitoring period. Measurements were performed using UGW technique explained in section 2.1. In pipeline structures, three types of propagation modes can coexist: Longitudinal, Torsional and Flexural [10]. In this study, only torsional mode was excited by a particular type of transducer because it is non dispersive. A photo this transducer is illustrated in Figure 1(left). This sensor can generate guided waves at five different frequencies: 14, 18, 24, 30 and 37 khz. For the sake of brevity, only excitation frequency of 14 khz is considered in the present study. Fig.1. (left): Sensor designed for pipeline health monitoring, (right): Example of an ultrasonic guided wave signal excited with torsional mode The specimen has been monitored during a period of almost 3 months. Each week, multiple measurements were scheduled. At each measurement, five signals were acquired in the morning and at the evening in order to capture temperature changes during the day and to investigate its effects on the collected signals. An example of an acquired signal is illustrated in Figure 1 (right). This signal has been acquired using only one sensor (pulse echo configuration). The excitation signal has been removed by the acquisition system (part of the signal around distance of 0 m) and the three echoes with the highest amplitude represent multiple reflections from the end of the pipe. Damage was created in this study by removing material from the inside of the pipeline in six increasing steps in order to simulate corrosion development within the structure. The Figure 2 shows the defect in the last step. 3

4 Location of damage Zoom Fig.2. Defect created inside the pipe (1 euro coin is presented to have an idea about the size of damage) At the end of the monitoring period, a total of 236 signals were collected where 207 ones have served as baseline and 29 signals were acquired from the damage state. 3.2 TEMPERATURE EFFECT AND DAMAGE EFFECT The analysis of the collected signals in the time domain shows that the reference signals underwent drastic changes in both amplitude and phase. Since temperature is the only environmental factor that varied during the measurements, the observed changes in the collected signals are due to the variation of this factor. This can be clearly noticed in Figure 3 (left) which illustrates a zoom over a part of two reference signals acquired at different temperatures. Figure 3 (right) illustrates an example of a damaged pipe s signal and a reference one. Note that, to clearly see the differences between the two signals, a zoom was displayed at the position of damage. This figure shows that the effect of damage is drift in the amplitude with a significant change in the phase. These results seem to be very similar to those observed in the case of temperature variation. In this case, the use of classical statistic descriptors to detect the presence of damage, as used by Rizzo et al [11] will be inefficient. Fig.3. Zoom over two signals (right: baseline signal and damaged signal, Left: tow baseline signals) 4

5 4. DAMAGE DETECTION AND LOCALIZATION To detect the damage, the sparse estimation was applied on the collected signals. One hundred and forty signals were used as a database of reference signals and the others served for the test of the method. This database includes baseline signals with different and/or same temperature variation. Each new signal ( ) is estimated by sparse parameters calculated by solving the constrained minimization problem described in equation 2. Figure 4(left) shows the quadratic error of estimation for all signals of test. The result presented in this figure shows that the damaged pipe s signals can be clearly separated from the healthy pipe s signals. Hence, all steps of damage were successfully detected. Besides, a large gap can be observed between the damaged pipe s signals and healthy pipe s signals ensuring hence good damage sensitivity. As the damage was successfully detected, its position must be determined in order to trigger the maintenance procedure. This will help to prevent the growth of damage. Figure 4 (right) shows the position of the created defect using the proposed method for damage localization. It corresponds to the maximum of the quadratic estimation error J( ). The sliding window was set at forty samples. This window was moved with one sample per step. At each step, we calculate the J( ) of estimation error as in the case of damage detection. At the end, we obtain a value of J( ) at each moving window of the original signal. To know the position of damage, the samples should be converted into distances. But first, they have to be converted into time by considering the sampling frequency of the data acquisition system. After that, since the sensor excite single non dispersive mode, distances can be obtained by knowing the wave velocity in the pipe. Damaged pipe s signals Healthy pipe s signals Position of damage Fig.4. Results of damage detection (left) and localization (right) 5. CONCLUSIONS In this paper, it was shown that the variation of EOCs represents a real challenge when implementing a SHM system because it impacts severely the collected signals. To overcome this issue, sparse estimation of the measured signals was applied. Results have shown that all steps of damage were successfully detected with a large gap between the damaged pipe s signals and healthy pipe s signals. This reveals that the proposed method for damage detection presents good damage sensitivity. Once the damage was detected, its localisation was ensured by applying the sparse estimation on a sliding window over the damage signal. As a perspective of this work, an online implementation of the proposed method could be considered. Also, this method has to be validated on operational pipeline which serves with different EOCs. 5

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