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Multi-stage temperature compensation method for Lamb wave measurements
Journal of Sound and Vibration ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Multi-stage temperature compensation method for Lamb wave measurements Ziemowit Dworakowski n, Lukasz Ambrozinski, Tadeusz Stepinski AGH University of Science and Technology, Department of Robotics and Mechatronics, Al A. Mickiewicza 30, 30-059 Krakow, Poland
a r t i c l e i n f o
abstract
Article history: Received 24 November 2015 Received in revised form 21 June 2016 Accepted 28 June 2016 Handling Editor: I. Trendafilova
One of the important issues related to the applications of Lamb waves for structural health monitoring is their undesired sensitivity to variation of environmental conditions. Temperature is the main factor that can affect wave propagation and hence significantly reduce performance of a SHM system. Therefore, there is a need for development of robust monitoring methods with low sensitivity to temperature variations. This paper is aimed at verification of efficiency of four methods designed for damage detection using Lamb wave measurements performed in variable environmental conditions. The methods investigated in the comparison are the following: optimal baseline selection approach, the damage index based on a signal alignment with respect to instantaneous phase, and a group measurement approach capable of distinguishing local damage-related changes from temperature-induced global ones. The fourth method relies on fusion all these solutions simultaneously. The methods’ ability to damage detection is compared using a specimen that is subjected to large temperature changes. It is found that although all the methods have their strengths and weaknesses, a cooperation of all solutions allows for significant increase of the damage detection efficiency. & 2016 Elsevier Ltd. All rights reserved.
1. Introduction Applications of Lamb waves (LW) in nondestructive testing and structural health monitoring (SHM) have been increasing in resent decennium despite their complicated physical nature. Their wide application has been caused by their positive features, such as their long-range propagation and high sensitivity to structural changes along propagation path. The former feature enables monitoring of large areas with the use of relatively low amount of sensors. The latter allows for the detection of various types of damage. LW-based monitoring is normally carried out using piezoelectric transducers (PZTs) [1–3]. Waves excited in monitored plate-liked structures are dispersive and multimodal, which renders their interpretation a difficult task. Since reflections from structure boundaries and superposition of different wave modes result in a complicated signal the acquired data contain a large amount of information, mostly irrelevant for the monitoring process. In most cases it is impossible to distinguish incident waves from the damage-related features, therefore, measures of the inspected structure integrity – the predefined damage indices – are calculated based on a comparison of the acquired waveforms. In some cases, the reference waveform can be acquired at a damage condition, prior to the inspection. For instance, a back-propagated time-reversed n
Corresponding author.
http://dx.doi.org/10.1016/j.jsv.2016.06.038 0022-460X/& 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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signal can be compared with the excitation pulse using time-reversal principle [4] or two high-frequency pulses excited at different phases of low-frequency vibrations can be compared, exploring nonlinear behavior of a fatigue crack [5,6]. In most cases, however, the monitoring involves comparison of structure's response to a well-defined, repetitive excitation. In this case an issue of great importance is the sensitivity of LWs to temperature changes. Measurements performed under different temperatures may significantly differ from one another, which may lead to masking of the damage-related information present in the captured signals. Multiple approaches to this problem have been proposed, for instance, the cointegration strategy is based on the assumption, that temperature influence on the signals is stationary while the damage-related input is not. Thus, the cointegrated time series that contain only the environmental influence plus noise are different from those including the damage-related patterns [7]. Another known solution requires the signal to be decomposed into components that relate either to different wave modes or to different reflection sources. It is then possible to distinguish temperature-related signal changes from the damage-related ones because they manifest themselves in different components of the decomposed signal. Such approach can be implemented using, e.g., singular value decomposition [8] or independent component analysis [9]. However, two other approaches to solving this problem appear to be the most common. First of them, recognized under the name of Novelty Detection (ND) relies on acquisition of reference measurements for a healthy structure in a large variety of environmental conditions that are used to define the normal range of structure's behavior. Measurements acquired for the structure in an unknown state are compared with the normal range and classified as either normal or novel. The latter may serve as a premise of damage. An example of ND approach used for GW-based state assessment in variable environmental condition is an optimal baseline selection (OBS) algorithm [10]. The second approach, referred to as signal stretch or signal alignment is based on a single reference only; the acquired signals are modified to remove the temperature influence. An example of such method is an instantaneous phase damage index (DIIP) proposed by Ambrozinski et al. [11]. The former approach requires as many as possible environmental changes to be included in the reference database while the latter one is designed exclusively for the compensation of temperature-related effects and is therefore less efficient in the cases where also other environmental factors occur. Since both methods have different principles of operation, it is expected that their combination might enable obtaining superior performance. This paper is devoted to the verification of this assumption. Its main novelty lies in the combination of three approaches to GW-based monitoring of the structures exposed to variable environmental conditions. We propose combining the OBS and DIIP methods with a third approach that relies on the analysis of damage indications returned by multiple sensor pairs. The main idea of our approach was briefly outlined in [12]; here, it is thoroughly verified in a series of experiments involving monitoring of aluminum plates over an extended time period of 1 month. Remainder of this paper is organized as follows. Section 2 provides theoretical introduction to the subject, including fundamentals of LW propagation in variable temperature as well as a survey on up-to-date diagnostic approaches used in this scope and details concerning the implementation of the three solutions compared in this work. Section 3.1 describes experimental procedures used for verification of the methods efficiency and discusses the obtained results. Finally, Section 4 provides brief summary and conclusions drawn from this work.
2. The methods In the case of damage detection performed under changing environmental conditions, signal processing techniques capable of compensation of these variations are required. These methods can be roughly divided into three groups. To the first group belong the signal-alignment methods that use knowledge of physical phenomena that cause temperature-related changes in the acquired waveforms to modify the signals in order to remove the temperature effect and to build temperature-robust damage index. The second group includes novelty-detection methods that can perform well without full understanding of the interfering phenomena. Instead, it is assumed that the temperature affects signals in a usually similar though unknown fashion. The last category, referred to as group measurement method, utilizes the fact that the temperature changes affect structure globally, while the damage-related effects have local character. The following subsections provide a more profound background to the above-mentioned categories and the methods selected for this work, followed by a description of the proposed data fusion approach. 2.1. The signal-alignment approach The temperature influence on a Lamb-wave based measurements manifests itself in effects that can roughly be divided into two groups; these are related to either temperature dependence of transducers and coupling or to phenomena influencing wave propagation. A significant number of papers were devoted to investigate the effects of LW propagation in the presence of temperature changes or to the influence of temperature on PZTs used for wave emission and acquisition [13–15]. The former effects manifest themselves normally by a change of signal amplitudes. These changes can proceed with time, e.g., in the case of the bonding agent aging or can vanish when the temperature is back to its initial state [16].
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In the latter, two main effects contributing to the temperature dependence on wave propagation can be distinguished. The first is thermal expansion of the structure, which alters the transducers spacing and affects material density. The second is the temperature dependence of other material parameters, i.e., Young's modulus and Poisson's ratio. Based on these consequences it can be assumed that the temperature effect on Lamb wave signals can be approximated by a stretch of the acquired signal x(t) in time domain: Temp:
xðtÞ ⟶ xðt ξ tÞ;
(1)
where ξ is the stretching constant [17]. Since the temperature affected, stretched signal differs from baseline in phase, many signal similarity measures, e.g. root-mean squared of the signal difference or normalized cross-correlation of the signals, results in high damage indices even for an intact structure [18]. In this case a possible approach is to use local-time coherence difference index (DILTCD) [19]. The method analyzes signals in short time windows and therefore, in contrast to previously mentioned techniques, acts locally. A stretched signal compared to a baseline in a short window will result in a high cross-correlation value, shifted from τ ¼ 0. Other signal-driven methods simply modify the time-axis of the baseline time-traces. Possible approaches to data resampling and the stretching are based on Fourier transform [20] or scale transform [21]. The temperature-resistant Instantaneous Phase damage index (DIIP) proposed by Ambrozinski [11] utilizes the fact that temperature-related changes in signals can be observed as changes in their instantaneous phase. For that feature extraction various tools can be used, including Hilbert [11] or wavelet transforms [22]. Preliminary research, in which DIIP and DILTCD were compared, has shown that the former index has higher potential of compensating the temperature-related effects, therefore, it was used for further investigations. [12] In this work Hilbert transform was used to obtain analytic signals and to extract their instantaneous phase. Using complex representation of the signals, the temperature influence can be easily filtered out by alignment of signal phases using the following equation: y0a ðtÞ ¼ ya ðtÞ ei½arg
xðtÞ arg yðtÞ
;
(2)
0a
where y ðtÞ and y ðtÞ are analytic signals before and after compensation, respectively, while arg xðtÞ and arg yðtÞ denote instantaneous phase of the baseline and the current signal. Aligned signals can further be processed with various damage indices. Since the method does not take into account change of signal amplitude, a correlation of signals is chosen here. Therefore, final Instantaneous Phase index was proposed as: a
R^ xy0 ð0Þ DI IP ¼ 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi; R^ xx ð0ÞR^ y0 y0 ð0Þ
(3)
where xðtÞ and y0 ðtÞ are real parts of the analytic baseline and current state signals with modified phase respectively. Since the index is expected to be insensitive both to phase differences and amplitude changes, only fluctuations of the overall waveform shape caused by damage should result in large DI's values. 2.2. The novelty detection approach In typical SHM problems temperature or operational changes appear periodically. This fact can be exploited by the novelty detection approach [23], which was introduced to SHM by Worden [24] and was later adopted in vast amount of applications [25–27]. The basic concept is based upon the fact that if large amount of reference signals were acquired for undamaged state of an object, and if these signals were acquired under various environmental and operational conditions, they could be used for definition of spectrum of normal changes, that is, those that are not caused by damage. Later, the signals acquired in unknown conditions can be compared with that database. If they differ significantly from the normal ones, they are considered as novel and can be treated as premises of damage. In most cases data that define the normal state is preserved in the form of features – due to large storage space required to save complete time-domain signals. These features are either compared with those calculated from signal representing unknown state with some metric (e.g. Mahalanobis squared distance [28,29]) or used to build model of the normal state, either using probabilistic approach [30] or neural networks [31]. When it is possible to store complete time-domain signals in the database this approach becomes straightforward and the result is based on a direct matching the signal representing unknown state with the most similar baseline from the database. This method was introduced to LW-based damage detection by Michaels under the name of Optimal Baseline Selection (OBS) [10] and was later successfully implemented in several applications [32,20,33]. The OBS method requires acquisition of multiple baseline signals in variable conditions. To ensure efficiency of the method, the signal database should have proper representation for all operational and environmental states possible for given structure. A signal acquired in unknown state of a structure is compared with all signals present in a database. The best match is then treated as a baseline for final structural state assessment. Therefore, the knowledge of the actual temperature during measurement is not required. This can be treated as a benefit – in cases when temperature in distinct points of the inspected structure is different or in the cases when temperature monitoring is difficult to be realized (e.g. when the Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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Fig. 1. Operation principle of the OBS algorithm. Signal registered under unknown environmental conditions is compared with all signals in the database. Minimal DI obtained in such a way is used for diagnose.
Fig. 2. The n-th loop of the OBS database reduction algorithm. All potential signal candidates are compared with those already present in the MR database. The one that yields the highest minimal DI is added to the MR set.
structure is non-uniformly heated by the sun). However, blind reference measurement selection can also be a hindrance, as large amount of signals recorded in unfaulty condition can mask the presence of damage. The operation principle of OBS method is illustrated in Fig. 1. Since storage of multiple signals acquired in variable conditions by a large net of sensors is a costly procedure, both in terms of storage space and calculation time, a simple way of database reduction was implemented here. For all acquired reference measurements the Most Representative (MR) set of signals was chosen by means of the procedure illustrated in Fig. 2; the most diverse signals are added to the representative database until desired number of signals is preserved or diversity measured by a damage index falls below the specified level. This algorithm can also be used for the choice of the proper threshold value – a consecutive passing of the loop, corresponding to adding another signal to the MR set, results in an acquisition of maximum value for all signals in the reference set when compared with the MR set. That value multiplied by a “safety factor” can then be used as a threshold.
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Fig. 3. Illustration of the DI spectrum shapes in different cases of damage or environmental influence. Grey area refers to the values of DIs calculated for all sensor pairs and arranged in ascending order. The GM-median values (blue and violet bars), contrary to the GM-mean values (green bars), are less sensitive to the non-uniform heating and outliers while retaining high efficiency in the severe damage cases. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
2.3. The group measurement approach An efficient SHM system has to encompass the whole monitored structure in order to detect a damage irrespective of its location. Since a damage at an early level of its growth affects structure only locally a system built up of a sparsely located net of sensors should be locally dense at certain hot spots where the damages are likely to occur. Global changes including variations in temperature, operational parameters or humidity alter global properties of structures. This difference can be used to distinguish damage from temperature variations in a local set of sensors. This phenomenon was previously utilized by one of the authors in damage detection based on modal filtration [34,35]. Here, it is introduced for the purpose of LWbased measurements. Let the structure be equipped with a group of sensor pairs that are used for monitoring of its distinct areas. State of the whole structure can be assessed according to Eq. (4), where DIk refers to the kth of all nths DIs listed in the ascending order – so as DI1 would refer to the minimal DI while DIn to the maximal one [12]. A global change would cause most of the signals to differ from their corresponding reference values and the state calculated in such a situation will be assessed as intact (Fig. 3(c)). The same result will be obtained if no damage is present in the structure (Fig. 3(a)). In contrast, local changes affecting only some of the sensor pairs will cause high values of damage index (Fig. 3(b)): Pn 1 DI DIGM ¼ DI n k ¼ 1 k (4) n 1 This way of index calculation is, however, sensitive to several issues. A severe damage detected simultaneously in several sensing paths will cause the mean of all signals to be higher and will therefore diminish the meaning of the highest indication (Fig. 3(e)). Such index will therefore be less effective in the case of severe damage cases. On the other hand, nonuniform external influence (e.g., one side of the structure is heated by the sun) will cause opposite phenomenon – lowering the average value and therefore increasing the value of the DI, although no damage is present in the structure (Fig. 3(d)). To ~ denotes deal with this problems, median of all indications may be used instead of the mean. This leads to Eq. (5), where DI the median of indications obtained for all sensor pairs: ~ DI GM ¼ DI n DI
(5)
If the number of sensor pairs used for monitoring is large or an additional knowledge of situation allows it, more advanced features may be implemented based on expected damage signatures. Here, a simple outlier removal procedure is proposed – one extreme value registered in sensor network can be excluded from the calculations so the highest damage detected in the sensor network would not influence the result. This modification renders the algorithm to be more reliable, since an outlier (which might have been caused by, e.g., an impact or a sensor fault) would not cause the system to raise false alarm. Such a benefit is usually possible at a cost of lower probability of early damage detection. In the case of LWPlease cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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based measurements, however, it can be employed without affecting the algorithm sensitivity. In standard pitch-catch arrangement of transducers each sensing path is duplicated, because both sensors are used sequentially as actuators and receivers. Theoretically speaking, response obtained in both arrangements should be similar. As a result, it leads to the robust version of Eq. (5), where DIn is replaced with DIn 1 (a second-maximum DI): ~ DI GMR ¼ DI n 1 DI;
(6)
which will be referred to as GMR in the sequel. In this approach the outliers that occur because of a single external influence (an impact or electronic fault) can be filtered out and they will not influence the resulting measurement (see Eq. (6)). A graphical illustration of this concept is illustrated in Fig. 3(f). 2.4. Fusion of solutions Since the operation principles of the methods presented above are different, their fusion may yield an improved result. Due to their diversity and since they are employed at different stages of signal processing, the drawbacks of each method should be compensated by the advantages of the others. To achieve this goal we propose the following strategy for the combined state assessment evaluation: 1. In all cases when similarity between signals is calculated, use the temperature-resistant DI (here: DIIP) as a metric. 2. For each pair of sensors build the MR dataset for the OBS algorithm using data acquired in the initial stage of monitoring. Use it to obtain damage indication for each sensor pair independently. 3. Merge these indications according to the GMR approach (i.e., group measurement with outlier removal and median setting) to obtain a single indication for the whole structure under investigation. The strengths and weaknesses of all methods considered in this work are summarized in Table 1; the results that are expected to be obtained by their fusion are also included in the most right column of the table. The OBS method can work in a variable environmental and operational conditions, provided that any external change (including non-uniform heating, loading, change of humidity, etc.) is included in the reference database. Therefore it requires a long set-up phase in order to acquire large set of baselines under different conditions. The method can only mark new measurements as known or unknown being therefore sensitive to outliers not related to damage. In contrast, the DIIP method needs one baseline only but it can be insensitive to the presence of some faults – wave diffraction caused by a damage can be observed in the form of signal delay and therefore can be filtered out during the signal alignment. Moreover, it can compensate for the temperature-related effects only and is incapable of handling outliers or other environmental changes. The GM is not prone to these effects, but instead it requires several sensors and is less sensitive to small damage, as values of the DIs become lowered due to the median subtraction. Fusion of all these solutions has two limitations: firstly, due to the presence of the OBS component a large amount of baselines have to be acquired. Secondly, it needs at least four sensors to operate. The first issue is less severe in comparison to the OBS method. Database can be smaller because three means of temperature compensation are applied, instead of just one in the simple OBS Table 1 Advantages and disadvantages of the methods considered in this work. Feature
OBS
DIIP
GM
Fusion of solutions
Can filter out influence of multiple environmental conditions Does not require long set-up phase Can work under non-uniform external influence Sensitive to multiple types of damage Can filter out outliers Sensitive to small damage Can work with a pair of sensors only
Table 2 Experimental setup. Transducers
PZT Steminc SMD07
Data acquisition unit Sampling frequency Excitation frequency Excitation signal Mode of operation
EC Electronics PAQ 16000D 2.5 MHz 100 kHz 8 periods of sine wave modulated by Hanning window Pitch-catch, all transducers used sequentially as actuators
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algorithm. The latter issue is not troublesome, as it is a normal practice to perform monitoring with groups of sensors distributed over entire structure instead of using a pair of sensors only. Therefore, fusion of solutions inherits two limitations, which are minor from the practical point of view. It allows, however, for suppression of several other drawbacks of its components. Firstly, it surpasses both the OBS and DIIP methods (operating alone) due to the ability of distinguishing single outliers from permanent changes: an outlier visible in one sensing path might be denoted as a damage by the first two methods, but will be ignored by the final GMR step due to the choice of second-maximum damage indication. Moreover, the OBS component allows for filtering any environmental change, which is not limited by using the DIIP as metric. Including such temperature-resistant metric allows, however, for the compensation of non-uniform temperature changes, which might be hard to compensate by the OBS alone due to difficulties in the MR dataset calculation. Finally, the sensitivity of a tandem consisting of the OBS and DIIP methods motivates application of the GMR approach even in the presence of small damage – which might have been challenging otherwise.
3. Experimental evaluation The experimental evaluation of the proposed solutions consists of the experiments performed in a similar setup for three different aluminum specimens. In each case 8 piezoelectric transducers were mounted to the plate in the configuration given in Table 2. Since each transducer was sequentially used as a transmitter while the others acted as receivers, 56 signals were acquired for each monitoring step. For each specimen, the experiment was divided into two phases, baseline acquisition and monitoring. In addition to the natural daily temperature variations the samples were also subjected to heating with a set of halogen lamps.
Fig. 4. Image (a) and drawing (b) of one of the aluminum samples used in the experiments. Damage locations for all evaluated cases are marked in red and color intensity refers to the time of damage introduction – darker areas were damaged later. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Table 3 Experimental data acquired for temperature-compensation algorithms. OBS amount refers to the amount of signals acquired to form the OBS database. Experiment
Amount of baselines
OBS amount
Total amount
Acquisition period (days)
Temperature
#0 #1 #2
640 280 479
400 150 300
691 305 1456
29 16 35
Unknown Registered Registered
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Fig. 5. Monitoring results for the experiment #1 obtained for all diagnostic approaches (a)–(e) for temperature variations shown in (f). Red line represents extent of damage present in the specimen. Horizontal lines represent from bottom the 3σ, low and high thresholds, respectively. Period of signal acquisition for the OBS algorithm is marked in blue. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
The sensor layout and the dimensions of the specimens along with an image of the third specimen are provided in Fig. 4. The temperature of specimens was acquired by means of a temperature sensor, which was attached to the plate. One of the samples was treated in a preliminary experiment without temperature monitoring. Damages in the form of notches (two specimens) and a hole (one specimen) were introduced to the specimens. Both the size of the notches and the diameter of the hole were gradually increased throughout the experiment. The aim of the first series of measurements (without temperature measurement) was to preliminary test the experiment concept and instrumentation used. Since it appeared that the obtained results were interesting due to the presence of outliers it was also included in this section. 3.1. Signal processing The data acquired in the experiments were fed to the temperature-compensation algorithms. Additionally, a simple DINSE feature calculated as normalized squared error (NSE) between two signals was used for comparison. The feature was calculated according to the Eq. (7), where x(t) and y(t) denote the baseline and the signal, while t1 and t2 denote the time interval in which the feature calculation is performed: R t2 2 t ½yðtÞ xðtÞ (7) DI NSE ¼ 1 1 R t2 2 t 1 xðtÞ Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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The data were divided into three experimental cases, each containing a large number of baseline signals and the data acquired for gradually introduced damage. The amount of data acquired in each experiment is provided in Table 3. Since the GM method is designed to return damage value for the whole structure at once, evaluation of all methods was performed in a similar fashion – where the GM measurement was not used the structure state was calculated as a maximum indication for a given measurement. Thresholds were defined for all methods using the procedure described in Section 2.3 – the threshold was set equal to the highest value of DI obtained on the set used for the OBS calculation multiplied by, respectively, 1 (Low threshold) and 2 (High threshold). Additionally, the third threshold was calculated as a sum of the indications’ median plus their triple standard deviation (denoted as 3σ threshold).
Fig. 6. The results averaged for the three threshold settings, obtained for the investigated methods: the DI based on normalized square error (DINSE), the DI based on instantaneous phase alignment (DIIP), the optimal baseline selection (OBS) and the group measurement (GM), and their combinations calculated for all three investigated experimental cases. The bars at left hand side of each plot refer to the percentage of false positives while the right side bars show the percentage of false negatives. Superiority of the fusion of all solutions (DI IP þ GM þ OBS) is well pronounced for each experiment.
Fig. 7. The results averaged for the three experiments, obtained for the investigated methods: the DI based on normalized square error (DINSE), the DI based on instantaneous phase alignment (DIIP), the optimal baseline selection (OBS) and the group measurement (GM). Each plot refers to different threshold setting (for threshold description refer to Section 3.2). The bars at left hand side of each plot refer to the percentage of false positives while the right side bars show the percentage of false negatives. The superiority of the fusion of all solutions ðDI IP þ GM þ OBSÞ does not depend on the threshold choice. However, higher thresholds render better overall results.
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3.2. Results Detailed output of all methods in experiment #1 is presented in Fig. 5. State of the structure was calculated using all methods individually and also by fusion of all solutions. For the sake of clarity signals were scaled to 0–1 range, i.e., the result returned for each method was divided by the maximum indication for the experiment. The methods are expected to return 1 for damage presence and 0 for lack of damage. The specimen state was assigned to the notch size – the maximum size corresponds to ”1” while lower value of state refers to proportionally lower severity of damage. The data range used for forming the OBS database is marked with a blue rectangle. The threshold lines are also marked in the plots. It is worth noting that the temperature range registered during set-up of the methods (i.e., the MR dataset calculation for OBS algorithm) did not cover all temperature variations in the monitoring phase, which is seen in Fig. 5(f), where peak value of the temperature during measurements used for calculation of the OBS MR set was lower than the maximum obtained during the experiment. The accumulated results of the structural state assessment obtained for the experiments #0–#2 are presented in Figs. 6 and 7. In Fig. 6 the numbers of errors obtained by each of the methods in all experiments are depicted. The results obtained using all the three threshold values are averaged for each experiment. On the contrary, Fig. 7 shows the results obtained for three threshold settings – this time averaged for the three experiments investigated. In both settings, the fusion method that incorporates DIIP, GM and OBS approaches results in lowest amount of errors for both the intact state (false positives) and the damaged state (lack of damage detection). Consequently, the fusion of methods appears to be superior regardless of threshold setting or particular damage case. The following paragraphs contain detailed discussion of each method tested in scope of this work. 3.2.1. No compensation (DINSE) As it was anticipated, the DINSE method revealed high sensitivity to temperature. Temperature variations present during the method's set-up phase caused the thresholds to be high in all three experiments, thus reducing the method's sensitivity and limiting its damage detection capabilities. Although in Fig. 5(a) the method actually detected damage, it was true only for the maximum size of the notch. Furthermore, also the second cycle of the increasing temperature in the experiment #1 was denoted as damage. Overall performance presented in Figs. 6 and 7 was the weakest. 3.2.2. Instantaneous phase alignment (DIIP) The DIIP method achieved slightly better performance than the DINSE and appeared to be less sensitive to temperature changes. However, in the experiment #0 its performance was significantly limited due to a large amount of outliers, while in experiment #2 it showed very weak damage detection capabilities due to the type of damage introduced to the specimen. Since in this experiment a small hole was introduced as a damage, its main influence on the signals took the form of signal diffraction on a hole, which resulted in signal translation and was filtered out by the instantaneous phase alignment. 3.2.3. Group measurement ðDI NSE þ GMÞ Since the GM approach takes into account the state detected by each sensor pair it is impossible to employ it without any other damage-sensitive metric. However, in order to test its capabilities as a single method for temperature compensation the authors decided to use it with the simple DINSE metric which is merely a comparison between two signals with no temperature-resistant effect. The performance of the group measurement approach resulted in lower numbers of errors than these obtained by the DIIP and DINSE, but significantly higher than the results of the OBS algorithm. The most important observation, however, is that this method allows to compensate outliers in the data. This can be seen both in Fig. 5(d), where small peaks in the second part of experiment were filtered out by the algorithm, and by the results of experiment #0 shown in Fig. 6. The most difficult challenge in the analysis of these data was a large number of outliers present both in the initial and the latter phase of the experiment caused mainly by malfunctions of the data acquisition unit. All of them were successfully filtered out by the algorithm, which allowed for proper threshold choice and, consequently, zero error. 3.2.4. Optimal baseline selection ðDINSE þ OBSÞ Similarly to the GM algorithm, the OBS requires a metric for the assessment signal difference, thus it is impossible to use it alone. In this case it was employed with the simple DINSE metric so all temperature-compensation potential could be assigned to the OBS component only. The method achieved very good performance. In both Figs. 6 and 7 it performs significantly better than any other method tested alone. Its main limitation was revealed by the experiment #0, where a large amount of outliers exceeded thresholds set up by the OBS method. Similar case can be seen in Fig. 5(c) – although temperature compensation appears to be brilliant and the damage is well pronounced, the thresholds are exceeded by a few of outliers caused by instantaneous events during the monitoring, which resulted in few false positive detections. Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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3.2.5. Fusion of methods ðDI IP þ GM þ OBSÞ The results of the fusion approach were outstanding in each experimental case and for each threshold. That is because of the synergy of all three solutions. Compensation of the temperature was possible mainly due to the OBS algorithm. The cases in which the temperature exceeded range present during composition of the MR dataset were filtered out due to the temperature-resistant DIIP component. Finally, outliers present in the experiments #0 and #1 (visible in Fig. 5(a)) were successfully filtered due to the GM component. It is seen in Fig. 5(e) that fusion method allowed not only for the lack of false positives and clearly detected damage (threshold exceeded instantly after damage introduction), but also highest damage indication with respect to threshold values.
4. Summary and conclusions Four algorithms for guided-wave-based damage detection in variable ambient conditions were considered in the paper: firstly, the OBS – optimal baseline selection based on acquisition of multiple reference signals. Secondly, the DIIP – instantaneous phase damage index employing signal alignment to compensate for temperature-related signal stretch. Thirdly, the GM – group measurement capable of distinguishing the environmental changes from damage by the assessment whether the change is local or global, and, finally, the solution that fuses together all the above-mentioned approaches. All methods were tested using data from the three long-term experiments performed under variable environmental conditions. Detailed analysis of the results revealed that the GM algorithm is more universal when compared to the OBS and other solutions since it allows not only for the recognition of the temperature-related input but also other changes that do not fit expected damage signature, such as patterns that are non-local or short-term. The GM versatility, however, comes at the cost of low efficiency – in the case of filtering of temperature influence the specialized methods score higher results. What is more, a global change that occurs simultaneously with a local damage-related signal alterations may mask their input and thus cause a false-negative indication. It was shown that high simultaneous versatility and efficiency of the assessment can be obtained using the proposed fusion of the three base approaches. The fusion of solutions that incorporated the OBS method for the reference database management, the signal-alignment approach (e.g., the DIIP) for signal comparison and the GM method for managing different indications, clearly outperformed the rest of the methods used alone. Such results were consistent over all the experimental cases and all threshold settings.
Acknowledgments The second author would like to acknowledge support from Foundation for Polish Science (FNP) through stipend for young researchers “START”.
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Multi-stage temperature compensation method for Lamb wave measurements Ziemowit Dworakowski n, Lukasz Ambrozinski, Tadeusz Stepinski AGH University of Science and Technology, Department of Robotics and Mechatronics, Al A. Mickiewicza 30, 30-059 Krakow, Poland
a r t i c l e i n f o
abstract
Article history: Received 24 November 2015 Received in revised form 21 June 2016 Accepted 28 June 2016 Handling Editor: I. Trendafilova
One of the important issues related to the applications of Lamb waves for structural health monitoring is their undesired sensitivity to variation of environmental conditions. Temperature is the main factor that can affect wave propagation and hence significantly reduce performance of a SHM system. Therefore, there is a need for development of robust monitoring methods with low sensitivity to temperature variations. This paper is aimed at verification of efficiency of four methods designed for damage detection using Lamb wave measurements performed in variable environmental conditions. The methods investigated in the comparison are the following: optimal baseline selection approach, the damage index based on a signal alignment with respect to instantaneous phase, and a group measurement approach capable of distinguishing local damage-related changes from temperature-induced global ones. The fourth method relies on fusion all these solutions simultaneously. The methods’ ability to damage detection is compared using a specimen that is subjected to large temperature changes. It is found that although all the methods have their strengths and weaknesses, a cooperation of all solutions allows for significant increase of the damage detection efficiency. & 2016 Elsevier Ltd. All rights reserved.
1. Introduction Applications of Lamb waves (LW) in nondestructive testing and structural health monitoring (SHM) have been increasing in resent decennium despite their complicated physical nature. Their wide application has been caused by their positive features, such as their long-range propagation and high sensitivity to structural changes along propagation path. The former feature enables monitoring of large areas with the use of relatively low amount of sensors. The latter allows for the detection of various types of damage. LW-based monitoring is normally carried out using piezoelectric transducers (PZTs) [1–3]. Waves excited in monitored plate-liked structures are dispersive and multimodal, which renders their interpretation a difficult task. Since reflections from structure boundaries and superposition of different wave modes result in a complicated signal the acquired data contain a large amount of information, mostly irrelevant for the monitoring process. In most cases it is impossible to distinguish incident waves from the damage-related features, therefore, measures of the inspected structure integrity – the predefined damage indices – are calculated based on a comparison of the acquired waveforms. In some cases, the reference waveform can be acquired at a damage condition, prior to the inspection. For instance, a back-propagated time-reversed n
Corresponding author.
http://dx.doi.org/10.1016/j.jsv.2016.06.038 0022-460X/& 2016 Elsevier Ltd. All rights reserved.
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signal can be compared with the excitation pulse using time-reversal principle [4] or two high-frequency pulses excited at different phases of low-frequency vibrations can be compared, exploring nonlinear behavior of a fatigue crack [5,6]. In most cases, however, the monitoring involves comparison of structure's response to a well-defined, repetitive excitation. In this case an issue of great importance is the sensitivity of LWs to temperature changes. Measurements performed under different temperatures may significantly differ from one another, which may lead to masking of the damage-related information present in the captured signals. Multiple approaches to this problem have been proposed, for instance, the cointegration strategy is based on the assumption, that temperature influence on the signals is stationary while the damage-related input is not. Thus, the cointegrated time series that contain only the environmental influence plus noise are different from those including the damage-related patterns [7]. Another known solution requires the signal to be decomposed into components that relate either to different wave modes or to different reflection sources. It is then possible to distinguish temperature-related signal changes from the damage-related ones because they manifest themselves in different components of the decomposed signal. Such approach can be implemented using, e.g., singular value decomposition [8] or independent component analysis [9]. However, two other approaches to solving this problem appear to be the most common. First of them, recognized under the name of Novelty Detection (ND) relies on acquisition of reference measurements for a healthy structure in a large variety of environmental conditions that are used to define the normal range of structure's behavior. Measurements acquired for the structure in an unknown state are compared with the normal range and classified as either normal or novel. The latter may serve as a premise of damage. An example of ND approach used for GW-based state assessment in variable environmental condition is an optimal baseline selection (OBS) algorithm [10]. The second approach, referred to as signal stretch or signal alignment is based on a single reference only; the acquired signals are modified to remove the temperature influence. An example of such method is an instantaneous phase damage index (DIIP) proposed by Ambrozinski et al. [11]. The former approach requires as many as possible environmental changes to be included in the reference database while the latter one is designed exclusively for the compensation of temperature-related effects and is therefore less efficient in the cases where also other environmental factors occur. Since both methods have different principles of operation, it is expected that their combination might enable obtaining superior performance. This paper is devoted to the verification of this assumption. Its main novelty lies in the combination of three approaches to GW-based monitoring of the structures exposed to variable environmental conditions. We propose combining the OBS and DIIP methods with a third approach that relies on the analysis of damage indications returned by multiple sensor pairs. The main idea of our approach was briefly outlined in [12]; here, it is thoroughly verified in a series of experiments involving monitoring of aluminum plates over an extended time period of 1 month. Remainder of this paper is organized as follows. Section 2 provides theoretical introduction to the subject, including fundamentals of LW propagation in variable temperature as well as a survey on up-to-date diagnostic approaches used in this scope and details concerning the implementation of the three solutions compared in this work. Section 3.1 describes experimental procedures used for verification of the methods efficiency and discusses the obtained results. Finally, Section 4 provides brief summary and conclusions drawn from this work.
2. The methods In the case of damage detection performed under changing environmental conditions, signal processing techniques capable of compensation of these variations are required. These methods can be roughly divided into three groups. To the first group belong the signal-alignment methods that use knowledge of physical phenomena that cause temperature-related changes in the acquired waveforms to modify the signals in order to remove the temperature effect and to build temperature-robust damage index. The second group includes novelty-detection methods that can perform well without full understanding of the interfering phenomena. Instead, it is assumed that the temperature affects signals in a usually similar though unknown fashion. The last category, referred to as group measurement method, utilizes the fact that the temperature changes affect structure globally, while the damage-related effects have local character. The following subsections provide a more profound background to the above-mentioned categories and the methods selected for this work, followed by a description of the proposed data fusion approach. 2.1. The signal-alignment approach The temperature influence on a Lamb-wave based measurements manifests itself in effects that can roughly be divided into two groups; these are related to either temperature dependence of transducers and coupling or to phenomena influencing wave propagation. A significant number of papers were devoted to investigate the effects of LW propagation in the presence of temperature changes or to the influence of temperature on PZTs used for wave emission and acquisition [13–15]. The former effects manifest themselves normally by a change of signal amplitudes. These changes can proceed with time, e.g., in the case of the bonding agent aging or can vanish when the temperature is back to its initial state [16].
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In the latter, two main effects contributing to the temperature dependence on wave propagation can be distinguished. The first is thermal expansion of the structure, which alters the transducers spacing and affects material density. The second is the temperature dependence of other material parameters, i.e., Young's modulus and Poisson's ratio. Based on these consequences it can be assumed that the temperature effect on Lamb wave signals can be approximated by a stretch of the acquired signal x(t) in time domain: Temp:
xðtÞ ⟶ xðt ξ tÞ;
(1)
where ξ is the stretching constant [17]. Since the temperature affected, stretched signal differs from baseline in phase, many signal similarity measures, e.g. root-mean squared of the signal difference or normalized cross-correlation of the signals, results in high damage indices even for an intact structure [18]. In this case a possible approach is to use local-time coherence difference index (DILTCD) [19]. The method analyzes signals in short time windows and therefore, in contrast to previously mentioned techniques, acts locally. A stretched signal compared to a baseline in a short window will result in a high cross-correlation value, shifted from τ ¼ 0. Other signal-driven methods simply modify the time-axis of the baseline time-traces. Possible approaches to data resampling and the stretching are based on Fourier transform [20] or scale transform [21]. The temperature-resistant Instantaneous Phase damage index (DIIP) proposed by Ambrozinski [11] utilizes the fact that temperature-related changes in signals can be observed as changes in their instantaneous phase. For that feature extraction various tools can be used, including Hilbert [11] or wavelet transforms [22]. Preliminary research, in which DIIP and DILTCD were compared, has shown that the former index has higher potential of compensating the temperature-related effects, therefore, it was used for further investigations. [12] In this work Hilbert transform was used to obtain analytic signals and to extract their instantaneous phase. Using complex representation of the signals, the temperature influence can be easily filtered out by alignment of signal phases using the following equation: y0a ðtÞ ¼ ya ðtÞ ei½arg
xðtÞ arg yðtÞ
;
(2)
0a
where y ðtÞ and y ðtÞ are analytic signals before and after compensation, respectively, while arg xðtÞ and arg yðtÞ denote instantaneous phase of the baseline and the current signal. Aligned signals can further be processed with various damage indices. Since the method does not take into account change of signal amplitude, a correlation of signals is chosen here. Therefore, final Instantaneous Phase index was proposed as: a
R^ xy0 ð0Þ DI IP ¼ 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi; R^ xx ð0ÞR^ y0 y0 ð0Þ
(3)
where xðtÞ and y0 ðtÞ are real parts of the analytic baseline and current state signals with modified phase respectively. Since the index is expected to be insensitive both to phase differences and amplitude changes, only fluctuations of the overall waveform shape caused by damage should result in large DI's values. 2.2. The novelty detection approach In typical SHM problems temperature or operational changes appear periodically. This fact can be exploited by the novelty detection approach [23], which was introduced to SHM by Worden [24] and was later adopted in vast amount of applications [25–27]. The basic concept is based upon the fact that if large amount of reference signals were acquired for undamaged state of an object, and if these signals were acquired under various environmental and operational conditions, they could be used for definition of spectrum of normal changes, that is, those that are not caused by damage. Later, the signals acquired in unknown conditions can be compared with that database. If they differ significantly from the normal ones, they are considered as novel and can be treated as premises of damage. In most cases data that define the normal state is preserved in the form of features – due to large storage space required to save complete time-domain signals. These features are either compared with those calculated from signal representing unknown state with some metric (e.g. Mahalanobis squared distance [28,29]) or used to build model of the normal state, either using probabilistic approach [30] or neural networks [31]. When it is possible to store complete time-domain signals in the database this approach becomes straightforward and the result is based on a direct matching the signal representing unknown state with the most similar baseline from the database. This method was introduced to LW-based damage detection by Michaels under the name of Optimal Baseline Selection (OBS) [10] and was later successfully implemented in several applications [32,20,33]. The OBS method requires acquisition of multiple baseline signals in variable conditions. To ensure efficiency of the method, the signal database should have proper representation for all operational and environmental states possible for given structure. A signal acquired in unknown state of a structure is compared with all signals present in a database. The best match is then treated as a baseline for final structural state assessment. Therefore, the knowledge of the actual temperature during measurement is not required. This can be treated as a benefit – in cases when temperature in distinct points of the inspected structure is different or in the cases when temperature monitoring is difficult to be realized (e.g. when the Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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Fig. 1. Operation principle of the OBS algorithm. Signal registered under unknown environmental conditions is compared with all signals in the database. Minimal DI obtained in such a way is used for diagnose.
Fig. 2. The n-th loop of the OBS database reduction algorithm. All potential signal candidates are compared with those already present in the MR database. The one that yields the highest minimal DI is added to the MR set.
structure is non-uniformly heated by the sun). However, blind reference measurement selection can also be a hindrance, as large amount of signals recorded in unfaulty condition can mask the presence of damage. The operation principle of OBS method is illustrated in Fig. 1. Since storage of multiple signals acquired in variable conditions by a large net of sensors is a costly procedure, both in terms of storage space and calculation time, a simple way of database reduction was implemented here. For all acquired reference measurements the Most Representative (MR) set of signals was chosen by means of the procedure illustrated in Fig. 2; the most diverse signals are added to the representative database until desired number of signals is preserved or diversity measured by a damage index falls below the specified level. This algorithm can also be used for the choice of the proper threshold value – a consecutive passing of the loop, corresponding to adding another signal to the MR set, results in an acquisition of maximum value for all signals in the reference set when compared with the MR set. That value multiplied by a “safety factor” can then be used as a threshold.
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Fig. 3. Illustration of the DI spectrum shapes in different cases of damage or environmental influence. Grey area refers to the values of DIs calculated for all sensor pairs and arranged in ascending order. The GM-median values (blue and violet bars), contrary to the GM-mean values (green bars), are less sensitive to the non-uniform heating and outliers while retaining high efficiency in the severe damage cases. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
2.3. The group measurement approach An efficient SHM system has to encompass the whole monitored structure in order to detect a damage irrespective of its location. Since a damage at an early level of its growth affects structure only locally a system built up of a sparsely located net of sensors should be locally dense at certain hot spots where the damages are likely to occur. Global changes including variations in temperature, operational parameters or humidity alter global properties of structures. This difference can be used to distinguish damage from temperature variations in a local set of sensors. This phenomenon was previously utilized by one of the authors in damage detection based on modal filtration [34,35]. Here, it is introduced for the purpose of LWbased measurements. Let the structure be equipped with a group of sensor pairs that are used for monitoring of its distinct areas. State of the whole structure can be assessed according to Eq. (4), where DIk refers to the kth of all nths DIs listed in the ascending order – so as DI1 would refer to the minimal DI while DIn to the maximal one [12]. A global change would cause most of the signals to differ from their corresponding reference values and the state calculated in such a situation will be assessed as intact (Fig. 3(c)). The same result will be obtained if no damage is present in the structure (Fig. 3(a)). In contrast, local changes affecting only some of the sensor pairs will cause high values of damage index (Fig. 3(b)): Pn 1 DI DIGM ¼ DI n k ¼ 1 k (4) n 1 This way of index calculation is, however, sensitive to several issues. A severe damage detected simultaneously in several sensing paths will cause the mean of all signals to be higher and will therefore diminish the meaning of the highest indication (Fig. 3(e)). Such index will therefore be less effective in the case of severe damage cases. On the other hand, nonuniform external influence (e.g., one side of the structure is heated by the sun) will cause opposite phenomenon – lowering the average value and therefore increasing the value of the DI, although no damage is present in the structure (Fig. 3(d)). To ~ denotes deal with this problems, median of all indications may be used instead of the mean. This leads to Eq. (5), where DI the median of indications obtained for all sensor pairs: ~ DI GM ¼ DI n DI
(5)
If the number of sensor pairs used for monitoring is large or an additional knowledge of situation allows it, more advanced features may be implemented based on expected damage signatures. Here, a simple outlier removal procedure is proposed – one extreme value registered in sensor network can be excluded from the calculations so the highest damage detected in the sensor network would not influence the result. This modification renders the algorithm to be more reliable, since an outlier (which might have been caused by, e.g., an impact or a sensor fault) would not cause the system to raise false alarm. Such a benefit is usually possible at a cost of lower probability of early damage detection. In the case of LWPlease cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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based measurements, however, it can be employed without affecting the algorithm sensitivity. In standard pitch-catch arrangement of transducers each sensing path is duplicated, because both sensors are used sequentially as actuators and receivers. Theoretically speaking, response obtained in both arrangements should be similar. As a result, it leads to the robust version of Eq. (5), where DIn is replaced with DIn 1 (a second-maximum DI): ~ DI GMR ¼ DI n 1 DI;
(6)
which will be referred to as GMR in the sequel. In this approach the outliers that occur because of a single external influence (an impact or electronic fault) can be filtered out and they will not influence the resulting measurement (see Eq. (6)). A graphical illustration of this concept is illustrated in Fig. 3(f). 2.4. Fusion of solutions Since the operation principles of the methods presented above are different, their fusion may yield an improved result. Due to their diversity and since they are employed at different stages of signal processing, the drawbacks of each method should be compensated by the advantages of the others. To achieve this goal we propose the following strategy for the combined state assessment evaluation: 1. In all cases when similarity between signals is calculated, use the temperature-resistant DI (here: DIIP) as a metric. 2. For each pair of sensors build the MR dataset for the OBS algorithm using data acquired in the initial stage of monitoring. Use it to obtain damage indication for each sensor pair independently. 3. Merge these indications according to the GMR approach (i.e., group measurement with outlier removal and median setting) to obtain a single indication for the whole structure under investigation. The strengths and weaknesses of all methods considered in this work are summarized in Table 1; the results that are expected to be obtained by their fusion are also included in the most right column of the table. The OBS method can work in a variable environmental and operational conditions, provided that any external change (including non-uniform heating, loading, change of humidity, etc.) is included in the reference database. Therefore it requires a long set-up phase in order to acquire large set of baselines under different conditions. The method can only mark new measurements as known or unknown being therefore sensitive to outliers not related to damage. In contrast, the DIIP method needs one baseline only but it can be insensitive to the presence of some faults – wave diffraction caused by a damage can be observed in the form of signal delay and therefore can be filtered out during the signal alignment. Moreover, it can compensate for the temperature-related effects only and is incapable of handling outliers or other environmental changes. The GM is not prone to these effects, but instead it requires several sensors and is less sensitive to small damage, as values of the DIs become lowered due to the median subtraction. Fusion of all these solutions has two limitations: firstly, due to the presence of the OBS component a large amount of baselines have to be acquired. Secondly, it needs at least four sensors to operate. The first issue is less severe in comparison to the OBS method. Database can be smaller because three means of temperature compensation are applied, instead of just one in the simple OBS Table 1 Advantages and disadvantages of the methods considered in this work. Feature
OBS
DIIP
GM
Fusion of solutions
Can filter out influence of multiple environmental conditions Does not require long set-up phase Can work under non-uniform external influence Sensitive to multiple types of damage Can filter out outliers Sensitive to small damage Can work with a pair of sensors only
Table 2 Experimental setup. Transducers
PZT Steminc SMD07
Data acquisition unit Sampling frequency Excitation frequency Excitation signal Mode of operation
EC Electronics PAQ 16000D 2.5 MHz 100 kHz 8 periods of sine wave modulated by Hanning window Pitch-catch, all transducers used sequentially as actuators
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algorithm. The latter issue is not troublesome, as it is a normal practice to perform monitoring with groups of sensors distributed over entire structure instead of using a pair of sensors only. Therefore, fusion of solutions inherits two limitations, which are minor from the practical point of view. It allows, however, for suppression of several other drawbacks of its components. Firstly, it surpasses both the OBS and DIIP methods (operating alone) due to the ability of distinguishing single outliers from permanent changes: an outlier visible in one sensing path might be denoted as a damage by the first two methods, but will be ignored by the final GMR step due to the choice of second-maximum damage indication. Moreover, the OBS component allows for filtering any environmental change, which is not limited by using the DIIP as metric. Including such temperature-resistant metric allows, however, for the compensation of non-uniform temperature changes, which might be hard to compensate by the OBS alone due to difficulties in the MR dataset calculation. Finally, the sensitivity of a tandem consisting of the OBS and DIIP methods motivates application of the GMR approach even in the presence of small damage – which might have been challenging otherwise.
3. Experimental evaluation The experimental evaluation of the proposed solutions consists of the experiments performed in a similar setup for three different aluminum specimens. In each case 8 piezoelectric transducers were mounted to the plate in the configuration given in Table 2. Since each transducer was sequentially used as a transmitter while the others acted as receivers, 56 signals were acquired for each monitoring step. For each specimen, the experiment was divided into two phases, baseline acquisition and monitoring. In addition to the natural daily temperature variations the samples were also subjected to heating with a set of halogen lamps.
Fig. 4. Image (a) and drawing (b) of one of the aluminum samples used in the experiments. Damage locations for all evaluated cases are marked in red and color intensity refers to the time of damage introduction – darker areas were damaged later. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Table 3 Experimental data acquired for temperature-compensation algorithms. OBS amount refers to the amount of signals acquired to form the OBS database. Experiment
Amount of baselines
OBS amount
Total amount
Acquisition period (days)
Temperature
#0 #1 #2
640 280 479
400 150 300
691 305 1456
29 16 35
Unknown Registered Registered
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Fig. 5. Monitoring results for the experiment #1 obtained for all diagnostic approaches (a)–(e) for temperature variations shown in (f). Red line represents extent of damage present in the specimen. Horizontal lines represent from bottom the 3σ, low and high thresholds, respectively. Period of signal acquisition for the OBS algorithm is marked in blue. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
The sensor layout and the dimensions of the specimens along with an image of the third specimen are provided in Fig. 4. The temperature of specimens was acquired by means of a temperature sensor, which was attached to the plate. One of the samples was treated in a preliminary experiment without temperature monitoring. Damages in the form of notches (two specimens) and a hole (one specimen) were introduced to the specimens. Both the size of the notches and the diameter of the hole were gradually increased throughout the experiment. The aim of the first series of measurements (without temperature measurement) was to preliminary test the experiment concept and instrumentation used. Since it appeared that the obtained results were interesting due to the presence of outliers it was also included in this section. 3.1. Signal processing The data acquired in the experiments were fed to the temperature-compensation algorithms. Additionally, a simple DINSE feature calculated as normalized squared error (NSE) between two signals was used for comparison. The feature was calculated according to the Eq. (7), where x(t) and y(t) denote the baseline and the signal, while t1 and t2 denote the time interval in which the feature calculation is performed: R t2 2 t ½yðtÞ xðtÞ (7) DI NSE ¼ 1 1 R t2 2 t 1 xðtÞ Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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The data were divided into three experimental cases, each containing a large number of baseline signals and the data acquired for gradually introduced damage. The amount of data acquired in each experiment is provided in Table 3. Since the GM method is designed to return damage value for the whole structure at once, evaluation of all methods was performed in a similar fashion – where the GM measurement was not used the structure state was calculated as a maximum indication for a given measurement. Thresholds were defined for all methods using the procedure described in Section 2.3 – the threshold was set equal to the highest value of DI obtained on the set used for the OBS calculation multiplied by, respectively, 1 (Low threshold) and 2 (High threshold). Additionally, the third threshold was calculated as a sum of the indications’ median plus their triple standard deviation (denoted as 3σ threshold).
Fig. 6. The results averaged for the three threshold settings, obtained for the investigated methods: the DI based on normalized square error (DINSE), the DI based on instantaneous phase alignment (DIIP), the optimal baseline selection (OBS) and the group measurement (GM), and their combinations calculated for all three investigated experimental cases. The bars at left hand side of each plot refer to the percentage of false positives while the right side bars show the percentage of false negatives. Superiority of the fusion of all solutions (DI IP þ GM þ OBS) is well pronounced for each experiment.
Fig. 7. The results averaged for the three experiments, obtained for the investigated methods: the DI based on normalized square error (DINSE), the DI based on instantaneous phase alignment (DIIP), the optimal baseline selection (OBS) and the group measurement (GM). Each plot refers to different threshold setting (for threshold description refer to Section 3.2). The bars at left hand side of each plot refer to the percentage of false positives while the right side bars show the percentage of false negatives. The superiority of the fusion of all solutions ðDI IP þ GM þ OBSÞ does not depend on the threshold choice. However, higher thresholds render better overall results.
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3.2. Results Detailed output of all methods in experiment #1 is presented in Fig. 5. State of the structure was calculated using all methods individually and also by fusion of all solutions. For the sake of clarity signals were scaled to 0–1 range, i.e., the result returned for each method was divided by the maximum indication for the experiment. The methods are expected to return 1 for damage presence and 0 for lack of damage. The specimen state was assigned to the notch size – the maximum size corresponds to ”1” while lower value of state refers to proportionally lower severity of damage. The data range used for forming the OBS database is marked with a blue rectangle. The threshold lines are also marked in the plots. It is worth noting that the temperature range registered during set-up of the methods (i.e., the MR dataset calculation for OBS algorithm) did not cover all temperature variations in the monitoring phase, which is seen in Fig. 5(f), where peak value of the temperature during measurements used for calculation of the OBS MR set was lower than the maximum obtained during the experiment. The accumulated results of the structural state assessment obtained for the experiments #0–#2 are presented in Figs. 6 and 7. In Fig. 6 the numbers of errors obtained by each of the methods in all experiments are depicted. The results obtained using all the three threshold values are averaged for each experiment. On the contrary, Fig. 7 shows the results obtained for three threshold settings – this time averaged for the three experiments investigated. In both settings, the fusion method that incorporates DIIP, GM and OBS approaches results in lowest amount of errors for both the intact state (false positives) and the damaged state (lack of damage detection). Consequently, the fusion of methods appears to be superior regardless of threshold setting or particular damage case. The following paragraphs contain detailed discussion of each method tested in scope of this work. 3.2.1. No compensation (DINSE) As it was anticipated, the DINSE method revealed high sensitivity to temperature. Temperature variations present during the method's set-up phase caused the thresholds to be high in all three experiments, thus reducing the method's sensitivity and limiting its damage detection capabilities. Although in Fig. 5(a) the method actually detected damage, it was true only for the maximum size of the notch. Furthermore, also the second cycle of the increasing temperature in the experiment #1 was denoted as damage. Overall performance presented in Figs. 6 and 7 was the weakest. 3.2.2. Instantaneous phase alignment (DIIP) The DIIP method achieved slightly better performance than the DINSE and appeared to be less sensitive to temperature changes. However, in the experiment #0 its performance was significantly limited due to a large amount of outliers, while in experiment #2 it showed very weak damage detection capabilities due to the type of damage introduced to the specimen. Since in this experiment a small hole was introduced as a damage, its main influence on the signals took the form of signal diffraction on a hole, which resulted in signal translation and was filtered out by the instantaneous phase alignment. 3.2.3. Group measurement ðDI NSE þ GMÞ Since the GM approach takes into account the state detected by each sensor pair it is impossible to employ it without any other damage-sensitive metric. However, in order to test its capabilities as a single method for temperature compensation the authors decided to use it with the simple DINSE metric which is merely a comparison between two signals with no temperature-resistant effect. The performance of the group measurement approach resulted in lower numbers of errors than these obtained by the DIIP and DINSE, but significantly higher than the results of the OBS algorithm. The most important observation, however, is that this method allows to compensate outliers in the data. This can be seen both in Fig. 5(d), where small peaks in the second part of experiment were filtered out by the algorithm, and by the results of experiment #0 shown in Fig. 6. The most difficult challenge in the analysis of these data was a large number of outliers present both in the initial and the latter phase of the experiment caused mainly by malfunctions of the data acquisition unit. All of them were successfully filtered out by the algorithm, which allowed for proper threshold choice and, consequently, zero error. 3.2.4. Optimal baseline selection ðDINSE þ OBSÞ Similarly to the GM algorithm, the OBS requires a metric for the assessment signal difference, thus it is impossible to use it alone. In this case it was employed with the simple DINSE metric so all temperature-compensation potential could be assigned to the OBS component only. The method achieved very good performance. In both Figs. 6 and 7 it performs significantly better than any other method tested alone. Its main limitation was revealed by the experiment #0, where a large amount of outliers exceeded thresholds set up by the OBS method. Similar case can be seen in Fig. 5(c) – although temperature compensation appears to be brilliant and the damage is well pronounced, the thresholds are exceeded by a few of outliers caused by instantaneous events during the monitoring, which resulted in few false positive detections. Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i
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3.2.5. Fusion of methods ðDI IP þ GM þ OBSÞ The results of the fusion approach were outstanding in each experimental case and for each threshold. That is because of the synergy of all three solutions. Compensation of the temperature was possible mainly due to the OBS algorithm. The cases in which the temperature exceeded range present during composition of the MR dataset were filtered out due to the temperature-resistant DIIP component. Finally, outliers present in the experiments #0 and #1 (visible in Fig. 5(a)) were successfully filtered due to the GM component. It is seen in Fig. 5(e) that fusion method allowed not only for the lack of false positives and clearly detected damage (threshold exceeded instantly after damage introduction), but also highest damage indication with respect to threshold values.
4. Summary and conclusions Four algorithms for guided-wave-based damage detection in variable ambient conditions were considered in the paper: firstly, the OBS – optimal baseline selection based on acquisition of multiple reference signals. Secondly, the DIIP – instantaneous phase damage index employing signal alignment to compensate for temperature-related signal stretch. Thirdly, the GM – group measurement capable of distinguishing the environmental changes from damage by the assessment whether the change is local or global, and, finally, the solution that fuses together all the above-mentioned approaches. All methods were tested using data from the three long-term experiments performed under variable environmental conditions. Detailed analysis of the results revealed that the GM algorithm is more universal when compared to the OBS and other solutions since it allows not only for the recognition of the temperature-related input but also other changes that do not fit expected damage signature, such as patterns that are non-local or short-term. The GM versatility, however, comes at the cost of low efficiency – in the case of filtering of temperature influence the specialized methods score higher results. What is more, a global change that occurs simultaneously with a local damage-related signal alterations may mask their input and thus cause a false-negative indication. It was shown that high simultaneous versatility and efficiency of the assessment can be obtained using the proposed fusion of the three base approaches. The fusion of solutions that incorporated the OBS method for the reference database management, the signal-alignment approach (e.g., the DIIP) for signal comparison and the GM method for managing different indications, clearly outperformed the rest of the methods used alone. Such results were consistent over all the experimental cases and all threshold settings.
Acknowledgments The second author would like to acknowledge support from Foundation for Polish Science (FNP) through stipend for young researchers “START”.
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Please cite this article as: Z. Dworakowski, et al., Multi-stage temperature compensation method for Lamb wave measurements, Journal of Sound and Vibration (2016), http://dx.doi.org/10.1016/j.jsv.2016.06.038i