- Email: [email protected]
Detection of Subtle Damage in Structures through Smart Signal Reconstruction
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
Procedia Structural Structural IntegrityIntegrity Procedia1400(2019) (2016)282–289 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
2nd International Conference on Structural Integrity and Exhibition 2018 2nd International Conference on Structural Integrity and Exhibition 2018
Detection of Subtle Damage in Structures through Smart Signal Detection of Subtle Damage in Structures through Smart Signal Reconstruction XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Reconstruction Lakshmia,a,*, A Rama Mohan Raoaa turbine blade of an Thermo-mechanicalK modeling of a high pressure K Lakshmi *, A Rama Mohan Rao CSIR-Structural Engineering Research Taramani,engine Chennai-600113, India. airplane gasCentre, turbine CSIR-Structural Engineering Research Centre, Taramani, Chennai-600113, India. a a
Abstract Abstract
P. Brandãoa, V. Infanteb, A.M. Deusc*
a
Department of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Roviscofeatures Pais, 1, 1049-001 The primary function of structural health monitoring (SHM) Técnico, is the process of extracting theAv.damage from theLisboa, measured Portugal The primary function of structural health monitoring (SHM) is theefficiency process ofofextracting the damage features from the measured raw bdata, recorded using sensors on the structure of interest. The SHM techniques lies in their capability to detect IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, raw recorded on thecharacteristics structure of interest. efficiency of SHMbut techniques liesmanner, in theirincapability to detect earlydata, damage, whichusing alterssensors the dynamic of only The aPortugal few modal responses in a feeble its incipient stage. c damage, which alters the dynamic characteristics of only a few modal responses but in a feeble manner, in its incipient stage. early Isolating these modal responses, hidden in the overall response, damage diagnosis, is aRovisco real challenge to the Lisboa, SHM CeFEMA, Department of Mechanical Engineering, Instituto raw Superior Técnico,for Universidade de Lisboa, Av. Pais, 1, 1049-001 Isolating these modal hiddenaninimproved the overall raw ofresponse, damage diagnosis, (EMD) is a realis challenge to this the paper. SHM Portugal community. In order to responses, handle this issue, version EmpiricalforMode Decomposition employed in community. In order handle this issue, an improved version of Empirical Modecalled Decomposition (EMD) is employed in The this mixed paper. EMD decomposes thetomeasured response signals into mono-component signals, intrinsic mode functions (IMFs). EMD measured response signals criteria into mono-component intrinsic functionsfrom (IMFs). The signal, mixed modesdecomposes in EMD arethe handled using Intermittency in the proposedsignals, EMD. called Once the IMFsmode are extracted the raw Abstract modes in EMD are handled using Intermittency criteria in the proposed EMD. Once the IMFs are extracted from the raw signal, the IMFs (signal components) which possess the valuable information of incipient damage called ‘critical IMFs’, are isolated. To the IMFs (signal components) which possess thecritical valuable information of incipient damagea called ‘critical IMFs’, are isolated. To determine the spatial location of damage, these IMFs are combined to reconstruct new signal with enriched information their operation, modern aircraft engine components are to increasingly demanding operating conditions, determine the spatial location of damage, these IMFs to reconstruct a new signal with enriched onDuring minor/incipient damage. ARMAX model iscritical employed onare thecombined newsubjected signal with enriched damage information. A information normalized especially the high pressureARMAX turbine (HPT) blades. Such conditions cause these parts to undergo different types of A time-dependent on minor/incipient model on the new signal enriched damage information. normalized distance measure ofdamage. ARMAX models, in termsisofemployed subspace angles, is used as a with damage indicator. The numerical and experimental degradation, oneofofARMAX which ismodels, creep. Ainmodel using the finite element method (FEM) was developed, in order toand beexperimental able to predict distance measure terms of subspace angles, is used as a damage indicator. The numerical investigations presented in this paper clearly reflect that the proposed output-only damage diagnostic technique using the smart the creep behaviour ofin HPT blades. Flight data that records (FDR) for a specificdamage aircraft,diagnostic provided technique by a commercial investigations presented thisraw paper clearly reflect the proposed output-only using the aviation smart reconstruction of the measured signal is capable of detecting the three incipient subtleflight damages in the structures. company, were used to obtain thermal and mechanical data for different cycles. In order to create the 3D model reconstruction of the measured raw signal is capable of detecting the incipient subtle damages in the structures. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were © obtained. 2018 TheThe Authors. Published by Elsevier data that wasbygathered was B.V. fed into the FEM model and different simulations were run, first with a simplified 3D © 2019 The Authors. Published Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND rectangular block shape, in order to better establish thelicense model,(https://creativecommons.org/licenses/by-nc-nd/4.0/) and then with the real 3D mesh obtained from the blade scrap. The This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of Peer-review under responsibility ofthe the SICE 2018 overalland expected behaviour in terms of displacement was observed, in particular at trailing edgeorganizers. of the blade. Therefore such a Selection peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. model can be useful in the goal of predicting turbine blade life, given a set of FDR data. Keywords: Structural health monitoring, Damage diagnosis, subtle damage, signal decomposition, time series analysis, Empirical mode Keywords: Structural health monitoring, Damage diagnosis, subtle damage, signal decomposition, time series analysis, Empirical mode decomposition, © 2016 TheARMAX Authors.model. Published by Elsevier B.V. decomposition, ARMAX model.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +91-44-22545721; fax: +91-44-22541508. * E-mail Corresponding Tel.: +91-44-22545721; fax: +91-44-22541508. address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 2018access The Authors. Published B.V. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an © open article under theby CCElsevier BY-NC-ND
This is an and openpeer-review access article under the CC BY-NC-ND licenseunder (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of Peer-review responsibility of the SICE 2018 organizers. Selection and peer-review under * Corresponding author. Tel.: +351responsibility 218419991. of Peer-review under responsibility of the SICE 2018 organizers. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
2452-3216 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 10.1016/j.prostr.2019.05.036
2
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
283
1. Introduction Structural health monitoring (SHM) is one of the potential research areas, during the past two decades, in the civil engineering community. In particular, the damage detection techniques using the output-only responses have become the prime focus of the researchers of SHM. Most of the popularly used vibration-based damage detection methods are modal based and are global in nature, which uses the dynamic properties like natural frequencies and mode shapes (Das et al., 2016). Another class of methods, based on the signal analysis for damage detection is recently becoming equally popular to global methods. Techniques based on time-frequency analysis (Rao and Lakshmi, 2015, Moore et al., 2018), multivariate analysis techniques like PCA (Tibaduiza et al., 2016, Rao et al., 2015) and time series algorithms (Zheng and Mita, 2008; Lakshmi and Rao, 2014, Lakshmi and Rao, 2015) are found to be more powerful and promising for damage detection, especially in the framework of online continuous monitoring. During online monitoring of structures, detecting the minor/incipient damage always becomes the primary and challenging task. While all the above-mentioned techniques have proved to be successful in detecting damage in various structures and scenarios, they fail to detect the minor/incipient damage (i.e. subtle cracks) in the structure. As the minor incipient damage alters only a few modal responses in an insignificant way, the damage features present in those affected modal responses will be hidden in the overall response (i.e., the measured dynamic signature) obtained from the structure. Also, the presence of the effects of environmental variability, which has the capability to alter the dynamic characteristics and signature, mask the existence of the minor incipient damage from diagnosis. In view of this, in this paper, we propose a hybrid approach for detecting subtle damages in the structure by isolating the modal responses which are been affected by the minor damage using a signal decomposition and reconstruction technique. In this paper, an improved version of Empirical Mode Decomposition (EMD) is employed as a preprocessor to identify and isolate the affected modes from the noisy signals. The reconstructed signal using only the isolated modes (affected by damage) is then used in time series analysis. During the process of extracting the minor damage, it becomes mandatory to any technique to handle the effect of environmental variability and measurement noise simultaneously. To handle the uncertainty due to environmental/operational variability, in this work, the time series analysis makes use of the look-up table approach by normalization (Farrar et al., 2001). Scalar ARMAX models(Lakshmi and Rao, 2017) of pristine and the current condition of the structure are utilized to evaluate the distance between them in terms of their subspace angles, which is the damage index to identify the time instant of damage and its spatial location on the structure. With the proposed approach of enhancing the sensitivity of the damage indices by augmenting the EMD to scalar ARMAX model, it is shown robust to locate the subtle damages. Numerical simulation studies have been carried out to test the effectiveness of the proposed algorithm for detecting a small incipient crack in the structure with measurement noise. Experimental studies are also carried out to complement the numerical simulations and also to demonstrate its practical applicability. 2. Empirical mode decomposition Empirical mode decomposition (Huang, 2014) as its name suggests is an empirical method. The aim of this method is to decompose the complicated (non-linear and/or non-stationary) time history response signal into a series of oscillating components obeying some basic properties, called intrinsic mode functions (IMFs). The basic principle in EMD is to decompose a signal y(t) into a set of zero mean mono-components called the IMFs. In each IMF generated, the number of extreme and the number of zero-crossings can differ at most by one. Further, at each point in the generated IMF, the mean value defined by local maxima and the local minima must be zero. Sifting is the name given to the empirical procedure associated with EMD. It works as follows: we first identify the local maxima and minima of the measured time history response y(t) and generate upper and lower envelopes by connecting these points through cubic spline interpolation. We later compute the mean of the upper and lower envelopes and subtract from the time history y(t). The difference between the original time history and the mean value, c1, is called the first IMF if it satisfies the two basic criteria discussed above. We repeat the same sifting process on the new time history obtained after subtracting the C1 component from the original signal y(t), in order to generate the second IMF. This process is repeated to generate rest of the IMFs till the residue becomes a monotonic function or less than specified convergence level. We can reconstruct the original time history y(t) by adding up all the IMFs, nIMF including the residue, rIMF as shown in Eqn. (1).
Lakshmi et al. / Procedia Structural Lakshmi andKRama Mohan Rao/ Structural IntegrityIntegrity Procedia1400(2019) (2018)282–289 000–000
284
y(t)
3
n IMF
Cj(t ) rIMF(t)
(1)
j1
2.1 Empirical Mode Decomposition with intermittency The IMFs generated through the empirical mode decomposition should be complete, adaptive and almost orthogonal decomposition of the original time history signal. However, the sifting process discussed above, cannot produce quality IMFs mainly due to large swings near the ends of the signal. The propagation of these swings inside corrupt the complete signal and it subsequently results in the form of poor IMFS. The large swings near the ends of the signal are basically due to the spline fitting process associated with the sifting. This will be predominant especially when low-frequency components are present in the signal. Apart from this, in the signals with closely spaced frequency components, the modal perturbation phenomena is too prominent to be ignored and it results in the poor sifting. The IMFs thus generated will generally cover more than one modal frequency and can also have some pseudo components. In order to overcome these limitations, several EMD techniques are proposed in the literature and EMD with intermittency criteria is popular among them Initially, EMD with intermittency criteria was proposed by Huang (2005) to locate the intermittent components of the signal. Alternatively, an approach was proposed by Gao et al. (2008) using the Teaser-Kaiser energy operator to locate the intermittent components of the signal. Subsequently, several other researchers have investigated on improving the EMD for generating IMFs. Since our objective is to generate the IMFs and to ensure that each of the IMF generated, represent the individual modal response, we have implemented the EMD with intermittency criteria as given below. Our objective in the present work is to decompose the response signal into IMFs such that each IMF represents one single modal response. In order to accomplish this, we impose an intermittent frequency fi in the sifting process in order to ensure that each of the IMFs generated to represent the modal response contains only one frequency component. We use a bandpass filter during the sifting process to remove all the frequency components which are lower or greater than fi from an IMF. We can obtain the frequency components related to each resonant frequency of the structure using FFT. The frequencies corresponding to the modal components of the structure present in the Fourier spectrum are partitioned into several (say m) subdomains. The centre of each subdomain represent the 0 resonant frequency f k with the upper lower limits of each subdomain (i.e., and fkl (k = 1,2,3,...,m) is defined as (1 0 ± 5%) f k . Accordingly, the resonant frequency band covered in Fourier spectrum will be divided into nm sub-domains as follows:
Ωj
|f |f i f fj1j
1, 2, ....m
(2)
We use band-pass filter by considering the boundaries of each subdomain as the sweep starting and sweep-ending frequency limits, to generate a number of narrowband signals from the original signal. The generated IMFs will have a very good correlation with the original signal as these IMFs contain the frequency components of the original signal. Keeping this in view, we use the correlation strength as a measure to isolate the true IMFs from the other pseudo components. Accordingly, we compute the correlation coefficient, μ i ,( i 1, 2,..., n IMF ) of each of the IMFs with the signal. We normalize the signal and also the IMFs before computing the correlation coefficients, by dividing them with their respective maximum values. This normalization helps in retaining some of the low amplitude real IMFs. In order to differentiate the true IMFs from pseudo IMFs, we use the correlation coefficients with a threshold defined as, J max( μ i ) / k (i=1........n IMF ) , where k is an assumed empirical factor and should be greater than 1.0. We retain the IMFs, if, otherwise, we eliminate by adding to the residue. The main objective here is to guarantee that the selected IMFs include all the resonant modes to be extracted and have no pseudocomponents. In the present work, k is assumed as 10.0. Apart from this, we use the signal extension method employing time series to eliminate the end effects of IMFs generated. As mentioned earlier, the end effects of sifting disturb the EMD process quite significantly. In order to handle these end effects, several distinct approaches are suggested in the literature. We can classify them broadly as
4
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
285
signal extension approaches with or without damping and extrema extension techniques (Shen et al., 2005). However, most of these techniques suggested to handle the end effects associated with periodic or quasi-periodic signals. They are not found to be effective for non-stationary and transient signals. Keeping this in view, in this paper, we use a signal extension technique based on the autoregressive model. 3. Damage detection methodology A proposed damage detection technique combining EMD and time series analysis is an output-only technique capable of detecting damage in the structural system at its earliest stage of incipience. The proposed technique utilizes the acceleration time-history data from the sensors placed on the structure of interest. The process of damage detection is carried out in two phases namely: preliminary phase and testing phase and the step by step procedure is given below: 3.1 Preliminary Phase The measured vibration data, X (i.e. acceleration time-history responses) recorded for time, ‘t’, from all the sensors placed on an undamaged (healthy) structure, is segmented into blocks of data of finite duration, whose elements are denoted by xij(t); i 1,...,ns ; j 1,...,M , where n s is the number of sensors and M is the number of data blocks. Populate a database with these baseline signals. ii. Fit an ARMAX model shown in Eqn. (3) to the subsets of the baseline data for all i and j
i.
x(t )
p
q
α x(t i ) β u(t n
i i 1i 1
i
b
i ) δ i ε (t i ) ε (t )
k i 1
(3)
3.2 Testing Phase iii. Obtain new acceleration signal (current data), Y for time ‘t’, from a potentially damaged structure for all the sensors and segment it into finite blocks of data, whose elements are denoted by y ij(t); i 1,....n s ; j 1,..., M ( similar to step i). iv. Fit an ARMAX model to the current data (similar to step 2) y(t )
p
q
α y(t i) β u(t n
i i 1 i 1
v.
i
b
i) δ i ε(t i ) ε(t)
k i 1
(4)
Perform normalization by matching: For each sensor i, every data-block of the current data is matched with a data-block of the signal in the baseline pool using the minimization of the value “Difference” as given below. Difference
p
α k 1
x k
αky
2
(5)
Choose the data segment, q of the baseline data, x(t) whose AR coefficients match closely with the AR coefficients of the current data (i.e. the ‘Difference’ in Eqn. (5) is minimum) and use it for all the subsequent computations vi. Perform empirical mode decomposition on the matched subsets of baseline and current data and obtain the IMFs independently. Choose the ‘critical IMFs ‘with rich damage sensitive features through the correlation coefficients defined in section 2.1. i (t) vii. Add up all the selected critical IMFs and the residue to obtain reconstructed time history responses, y (i = 1,2,3….) corresponding to current data, with damage rich features. The number of modal responses considered for reconstruction can be from one to maximum of m modes. Similarly, reconstruct the reference time history responses, using the modal time history responses chosen in step 6.
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
286
5
viii. Fit ARMAX model to the new reference and current data subsets and evaluate the damage index using the distances of the two ARMAX models in terms of subspace angles. ix. Plot the normalized values of subspace angles based damage index for every sensor, to visualize the spatial location of damage. The sensor nodes which indicate the highest magnitudes of the damage index reveal the location of damage precisely. 4. Validation Studies The numerical example is a simply supported elastic beam with transverse elasto-plastic cracks is used to demonstrate the effectiveness of the proposed EMD augmented ARMAX model. The acceleration time-history responses are simulated by a cracked-beam finite element analysis, where the incipient damage is caused due to the initiation of cracks. Apart from the numerical simulation studies, an experimental verification is also carried out using an RCC beam inflicted with cracks due to static loads. 4.1 Numerical studies The numerical model of a simply supported beam girder, with dimensions of 8000mmx450mmx550mm, and the material properties as shown in Fig. 1, is used to validate the proposed technique. The beam is discretized into 20 elements and is assumed to carry accelerometers on 19 nodes, eliminating the nodes at its supports.
Fig. 1. A Simply supported beam
A stochastic random dynamic loading is simulated for exciting the beam. Newmark’s time marching scheme is used in finite element analysis to compute the 6s long acceleration time history response with a sampling rate of 2000 Hz. The time history data is generated with random loads and normal operational conditions. In order to verify the performance of the proposed technique with respect to the immunity towards measurement noise, the computed time history measurements are corrupted with zero mean white Gaussian noise, by adding a normal random component to the computed noise free acceleration time history response as
x x δ p N noiseσ ( x) m
(6)
where δ p is the percentage level of noise, is the standard normal distribution vector with zero mean and unit standard distribution, σ(x) is the standard deviation of the noise-free measured (computed) time history response. In the present investigations, random noise levels of 5%, are considered. This healthy data generated with 5% measurement noise is segmented into 12 subsets with 1000 samples in each. Similarly, the acceleration data for the current state of the structure, with the simulated damage at element number 15, by introducing cracks of 10mm length, are generated and segmented into subsets. The formulations of the finite element analysis of the cracked beam is used in the present work to obtain the vibration acceleration responses after damage, to form the current data in a way that initially, the structure is healthy and the damage is initiated after few instants of time. To simulate this scenario, the damage is introduced after 4 seconds (i.e. in the 8th current subset data). In order to improve the sensitivity of the technique based on ARMAX models, in the presence of minor damage, in this paper, initially the acceleration time history data (signal) is pre-processed using the EMD with intermittency algorithm, and the IMFs are extracted. The details of the IMFs, of both the dynamic signatures obtained from the healthy structure (baseline) and their fast Fourier spectrum (FFT) plots, are shown in Fig. 2(a) and 2(b) respectively. The FFT plots of the IMFs clearly indicate the efficiency of the improved EMD technique to extract the unimodal IMFs from the noisy acceleration data.
6
Lakshmi and Rama MohanetRao/ Integrity Procedia K Lakshmi al. /Structural Procedia Structural Integrity 00 14 (2018) (2019) 000–000 282–289 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 2 1 0 -1 -2 0.00
(b)
0
100
200
0
100
200
300
400
500
600
700
800
300
400
500
600
700
800
0.3 0.2 0.1 0.0 0.2 0.1 0.0 0.8 0.4 0.0 0.2
Amplitude
Amplitude
(a)
287
0.1 0.0 0.8 0.4 0.0 0.8 0.4 0.0 0.5 0.0 0.1
0.25
0.50
0.75
1.00
Time (s)
1.25
1.50
1.75
0.0 0.6 0.4 0.2 0.0
2.00
Frequency(Hz)
Fig. 2. EMD of the response at node-6 of simply supported beam-Test Case-1: (a) IMFs of healthy data; (b) FFT spectrum of IMFs of healthy data.
The critical IMFs are isolated from the extracted IMFs, using the correlation coefficient presented in the earlier section. All the isolated critical IMFs are added up to reconstruct the new current time series. Similarly, the new baseline time series is reconstructed using the selected critical IMFs. The typical reconstructed signals of sensor node15 (i.e., node closer to crack location) using the critical IMFs of the current and healthy signals based on the presence of damage rich features of the current data are shown in Fig. 3(a). Once the current data subset and the baseline subset are reconstructed using the critical IMFs, distances of ARMAX models in terms of the subspace angles are computed for each of the sensor node signals to locate the damage as shown in Fig. 3(b). The normalized values presented in Fig. 3(b), clearly indicate that the proposed method based on EMD-ARMAX is effective in detecting as well as locating the spatial damage present in the structure in the form of minor crack. Using the count of the current dataset being analyzed, we can arrive at the exact time instant of damage. In this example, the time instant of damage is found to be 4s. 4.2 Experimental verification: The second example to validate the proposed technique to detect minor/incipient damage is the laboratory experimental studies, conducted on a simply supported reinforced cement concrete (RCC) beam. The test structure considered is a simply supported RCC beam with dimensions: 3000mm x165mm x200mm. The bottom longitudinal reinforcement was 2# 16 and the upper was 2# 12 with 25# 6 stirrups. The beam is instrumented with 16 microelectromechanical systems (MEMS) accelerometers, placed equidistantly along the beam to record the acceleration time history data. The beam is excited using a modal shaker of sine peak force capacity of 200N and the tests were carried out in the frequency range of 0-1000Hz, for harmonic and random excitations. The loading frequencies, as well as amplitude, is varied during each set of measurements to simulate operational variability. Initially, acceleration responses of the beam are measured at all the 16 sensor nodes for the undamaged state of the beam. This scenario is named as ‘Healthy’. Each signal is measured for 19 sec and is sampled at 3000 Hz so that the frequencies of the beam can be uncovered, in 0–1500 Hz frequency range.
(a)
0.4
(b)
Reconstructed healthy data Reconstructed current data
0.3
Acceleration (g)
0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4
0.0
0.5
1.0
1.5
2.0
2.5
Subspace angle based damage index
Lakshmi et al. / Procedia Structural Lakshmi andKRama Mohan Rao/ Structural IntegrityIntegrity Procedia1400(2019) (2018)282–289 000–000
288
Time(s)
7
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sensor Number
Fig. 3. Damage diagnosis of simply supported Beam-Test case-1: (a) Reconstructed signals of healthy and current data of Sensor-6; (b) Normalised damage index evaluated using distances of ARMAX models in subspace angles.
The minor damage is inflicted at approximately one-third span from both the supports of the beam (i.e. in element no. 5 and element no.12) by applying the static loads in small increments. The minor cracks appear when the static load applied is nearly 12KN as shown in Fig.4. The experiment with dynamic excitation force is performed to create test data (acceleration response) of the beam with minor damage and is referred to as ‘Damage’. The acceleration data of ‘Healthy’ and ‘Damage’ are used as baseline and current data respectively. The cross-correlated signals of the baseline and the current data are fed to the EMD with intermittency and all the IMFs are extracted. The critical IMFs are selected using the correlation coefficient method and are added up to reconstruct the new signal as shown in Fig. 5(a). Subspace angles are evaluated to calculate the distance between ARMAX models of the reconstructed healthy and current signals. The normalized values of subspace angle based damage indices of ARMAX, shown in Fig. 5(b), clearly reflect the spatial location of damage (at one-third of the beam from both the supports.).
Fig. 4. Scenario of Damage
5.0 Conclusions In the paper, a novel hybrid technique to identify the location of the minor damage like minor cracks is presented. As, the minor damage creates feeble changes in the dynamic characteristics of only a few modes of the structure, the damage features present in those modal responses get hidden in the overall response (i.e., the measured dynamic signature). Additionally, measurement noise and environmental variability also play their role in masking the minor damage features in the overall response of the structure. In view of this, in this paper, an attempt has been made to isolate these damage sensitive modal responses and reconstruct a new signal accordingly using improved EMD with intermittency criteria. The damage enriched signals isolated by EMD are further used for damage diagnosis using the ARMAX time series model, employing a damage index, constructed from the distance measure of any two ARMAX
8
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
289
models, in terms of subspace angles. Numerical simulation studies have been carried out by considering a simply supported beam with minor cracks. Laboratory experimental studies have been carried out by considering an RCC beam to complement the numerical simulations and also demonstrate its practical applicability in the field.
6
Reconstructed healthy data Reconstructed current data
5 4
Acceleration (g)
3 2 1 0 -1 -2 -3 -4 -5 -6
0.0
0.5
1.0
1.5
Time(s)
2.0
2.5
(b)
Subspace angle based damage index
(a)
1.2 1.0 0.8 0.6 0.4 0.2 0.0
1
2
3
4
5
6
7
8
9
10
11
Senso r N um ber
12
13
14
15
16
Fig. 5. Damage diagnosis of RCC beam-Multiple Damage: (a) reconstructed healthy data and current data; (b) normalised damage index evaluated using distances of ARMAX models in subspace angles.
References Das, S., Saha, P., Patro, S. K., 2016. Vibration-based damage detection techniques used for health monitoring of structures: a review. Journal of Civil Structural Health Monitoring 6(3), 477–507. Data normalization- a key for structural health monitoring: Report for 2001, Los Alamos National Laboratory, No. LA-UR-01-4212. Los Alamos National Lab., NM (US), 2001. Gao, Y., Ge, G., Sheng, Z., et al., 2008. Analysis and Solution to the Mode Mixing Phenomenon in EMD, Congress on Image and Signal Processing, Washington, DC, USA, 5, 223-227. Huang, N. E., 2005. Introduction to Hilbert-Huang transform and some recent developments, in “Hilbert-Huang Transform in Engineering”. In: Taylor & Francis, pp. 1-24. Huang, N. E., Shen, S, S., 2014. “Hilbert-Huang Transform and Its Applications”. In World Scientific, 16. Lakshmi, K., Rao, A. R. M., 2014. A robust damage-detection technique with environmental variability combining time-series models with principal components. Nondestructive Testing and Evaluation 29(4), 357–376. Lakshmi, K., Rao, A. R. M., 2015. Damage identification technique based on time series models for LANL and ASCE benchmark structures. Journal of Non-destructive Testing and Condition Monitoring 57(10), 580-588. Lakshmi, K., Rao, A. R. M., Gopalakrishnan,N., 2017. Singular Spectrum Analysis combined with ARMAX model for structural damage detection. Structural Control and Health Monitoring, 24, DOI: 10.1002/stc.1960. Moore, K. J., Kurt, M., Eriten, M., et al., 2018. Wavelet-bounded empirical mode decomposition for measured time series analysis. Mechanical Systems and Signal Processing 99, 14–29. Rao, A. R. M., Lakshmi, K., 2015. Damage diagnostic technique combining POD with time-frequency analysis and dynamic quantum PSO. Meccanica 50(6), 1551–1578. Rao, A. R. M., Lakshmi, K., Krishna Kumar, S., 2015. Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO. Advances in Engineering Software 86 (2015), 85–106. Shen, S. S., Shu, T., Huang, N. E., et al., 2014. HHT Analysis of the Nonlinear and Non-Stationary Annual Cycle of Daily Surface Air Temperature Data, in “Interdisciplinary Mathematical Sciences: Hilbert-Huang Transform and Its Applications”, In: World Scientific, 5, 187–209. Tibaduiza, D. A., Mujica, L. E., Rodellar, J., et al., 2015. Structural damage detection using principal component analysis and damage indices. Journal of Intelligent Material Systems and Structures 27(2), 233–248. Zheng, H., Mita, A., 2008. Damage indicator defined as the distance between ARMA models for structural health monitoring. Structural Control and Health Monitoring 15(7), 992–1005.
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
Procedia Structural Structural IntegrityIntegrity Procedia1400(2019) (2016)282–289 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
2nd International Conference on Structural Integrity and Exhibition 2018 2nd International Conference on Structural Integrity and Exhibition 2018
Detection of Subtle Damage in Structures through Smart Signal Detection of Subtle Damage in Structures through Smart Signal Reconstruction XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Reconstruction Lakshmia,a,*, A Rama Mohan Raoaa turbine blade of an Thermo-mechanicalK modeling of a high pressure K Lakshmi *, A Rama Mohan Rao CSIR-Structural Engineering Research Taramani,engine Chennai-600113, India. airplane gasCentre, turbine CSIR-Structural Engineering Research Centre, Taramani, Chennai-600113, India. a a
Abstract Abstract
P. Brandãoa, V. Infanteb, A.M. Deusc*
a
Department of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Roviscofeatures Pais, 1, 1049-001 The primary function of structural health monitoring (SHM) Técnico, is the process of extracting theAv.damage from theLisboa, measured Portugal The primary function of structural health monitoring (SHM) is theefficiency process ofofextracting the damage features from the measured raw bdata, recorded using sensors on the structure of interest. The SHM techniques lies in their capability to detect IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, raw recorded on thecharacteristics structure of interest. efficiency of SHMbut techniques liesmanner, in theirincapability to detect earlydata, damage, whichusing alterssensors the dynamic of only The aPortugal few modal responses in a feeble its incipient stage. c damage, which alters the dynamic characteristics of only a few modal responses but in a feeble manner, in its incipient stage. early Isolating these modal responses, hidden in the overall response, damage diagnosis, is aRovisco real challenge to the Lisboa, SHM CeFEMA, Department of Mechanical Engineering, Instituto raw Superior Técnico,for Universidade de Lisboa, Av. Pais, 1, 1049-001 Isolating these modal hiddenaninimproved the overall raw ofresponse, damage diagnosis, (EMD) is a realis challenge to this the paper. SHM Portugal community. In order to responses, handle this issue, version EmpiricalforMode Decomposition employed in community. In order handle this issue, an improved version of Empirical Modecalled Decomposition (EMD) is employed in The this mixed paper. EMD decomposes thetomeasured response signals into mono-component signals, intrinsic mode functions (IMFs). EMD measured response signals criteria into mono-component intrinsic functionsfrom (IMFs). The signal, mixed modesdecomposes in EMD arethe handled using Intermittency in the proposedsignals, EMD. called Once the IMFsmode are extracted the raw Abstract modes in EMD are handled using Intermittency criteria in the proposed EMD. Once the IMFs are extracted from the raw signal, the IMFs (signal components) which possess the valuable information of incipient damage called ‘critical IMFs’, are isolated. To the IMFs (signal components) which possess thecritical valuable information of incipient damagea called ‘critical IMFs’, are isolated. To determine the spatial location of damage, these IMFs are combined to reconstruct new signal with enriched information their operation, modern aircraft engine components are to increasingly demanding operating conditions, determine the spatial location of damage, these IMFs to reconstruct a new signal with enriched onDuring minor/incipient damage. ARMAX model iscritical employed onare thecombined newsubjected signal with enriched damage information. A information normalized especially the high pressureARMAX turbine (HPT) blades. Such conditions cause these parts to undergo different types of A time-dependent on minor/incipient model on the new signal enriched damage information. normalized distance measure ofdamage. ARMAX models, in termsisofemployed subspace angles, is used as a with damage indicator. The numerical and experimental degradation, oneofofARMAX which ismodels, creep. Ainmodel using the finite element method (FEM) was developed, in order toand beexperimental able to predict distance measure terms of subspace angles, is used as a damage indicator. The numerical investigations presented in this paper clearly reflect that the proposed output-only damage diagnostic technique using the smart the creep behaviour ofin HPT blades. Flight data that records (FDR) for a specificdamage aircraft,diagnostic provided technique by a commercial investigations presented thisraw paper clearly reflect the proposed output-only using the aviation smart reconstruction of the measured signal is capable of detecting the three incipient subtleflight damages in the structures. company, were used to obtain thermal and mechanical data for different cycles. In order to create the 3D model reconstruction of the measured raw signal is capable of detecting the incipient subtle damages in the structures. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were © obtained. 2018 TheThe Authors. Published by Elsevier data that wasbygathered was B.V. fed into the FEM model and different simulations were run, first with a simplified 3D © 2019 The Authors. Published Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND rectangular block shape, in order to better establish thelicense model,(https://creativecommons.org/licenses/by-nc-nd/4.0/) and then with the real 3D mesh obtained from the blade scrap. The This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of Peer-review under responsibility ofthe the SICE 2018 overalland expected behaviour in terms of displacement was observed, in particular at trailing edgeorganizers. of the blade. Therefore such a Selection peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. model can be useful in the goal of predicting turbine blade life, given a set of FDR data. Keywords: Structural health monitoring, Damage diagnosis, subtle damage, signal decomposition, time series analysis, Empirical mode Keywords: Structural health monitoring, Damage diagnosis, subtle damage, signal decomposition, time series analysis, Empirical mode decomposition, © 2016 TheARMAX Authors.model. Published by Elsevier B.V. decomposition, ARMAX model.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +91-44-22545721; fax: +91-44-22541508. * E-mail Corresponding Tel.: +91-44-22545721; fax: +91-44-22541508. address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 2018access The Authors. Published B.V. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an © open article under theby CCElsevier BY-NC-ND
This is an and openpeer-review access article under the CC BY-NC-ND licenseunder (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of Peer-review responsibility of the SICE 2018 organizers. Selection and peer-review under * Corresponding author. Tel.: +351responsibility 218419991. of Peer-review under responsibility of the SICE 2018 organizers. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
2452-3216 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 10.1016/j.prostr.2019.05.036
2
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
283
1. Introduction Structural health monitoring (SHM) is one of the potential research areas, during the past two decades, in the civil engineering community. In particular, the damage detection techniques using the output-only responses have become the prime focus of the researchers of SHM. Most of the popularly used vibration-based damage detection methods are modal based and are global in nature, which uses the dynamic properties like natural frequencies and mode shapes (Das et al., 2016). Another class of methods, based on the signal analysis for damage detection is recently becoming equally popular to global methods. Techniques based on time-frequency analysis (Rao and Lakshmi, 2015, Moore et al., 2018), multivariate analysis techniques like PCA (Tibaduiza et al., 2016, Rao et al., 2015) and time series algorithms (Zheng and Mita, 2008; Lakshmi and Rao, 2014, Lakshmi and Rao, 2015) are found to be more powerful and promising for damage detection, especially in the framework of online continuous monitoring. During online monitoring of structures, detecting the minor/incipient damage always becomes the primary and challenging task. While all the above-mentioned techniques have proved to be successful in detecting damage in various structures and scenarios, they fail to detect the minor/incipient damage (i.e. subtle cracks) in the structure. As the minor incipient damage alters only a few modal responses in an insignificant way, the damage features present in those affected modal responses will be hidden in the overall response (i.e., the measured dynamic signature) obtained from the structure. Also, the presence of the effects of environmental variability, which has the capability to alter the dynamic characteristics and signature, mask the existence of the minor incipient damage from diagnosis. In view of this, in this paper, we propose a hybrid approach for detecting subtle damages in the structure by isolating the modal responses which are been affected by the minor damage using a signal decomposition and reconstruction technique. In this paper, an improved version of Empirical Mode Decomposition (EMD) is employed as a preprocessor to identify and isolate the affected modes from the noisy signals. The reconstructed signal using only the isolated modes (affected by damage) is then used in time series analysis. During the process of extracting the minor damage, it becomes mandatory to any technique to handle the effect of environmental variability and measurement noise simultaneously. To handle the uncertainty due to environmental/operational variability, in this work, the time series analysis makes use of the look-up table approach by normalization (Farrar et al., 2001). Scalar ARMAX models(Lakshmi and Rao, 2017) of pristine and the current condition of the structure are utilized to evaluate the distance between them in terms of their subspace angles, which is the damage index to identify the time instant of damage and its spatial location on the structure. With the proposed approach of enhancing the sensitivity of the damage indices by augmenting the EMD to scalar ARMAX model, it is shown robust to locate the subtle damages. Numerical simulation studies have been carried out to test the effectiveness of the proposed algorithm for detecting a small incipient crack in the structure with measurement noise. Experimental studies are also carried out to complement the numerical simulations and also to demonstrate its practical applicability. 2. Empirical mode decomposition Empirical mode decomposition (Huang, 2014) as its name suggests is an empirical method. The aim of this method is to decompose the complicated (non-linear and/or non-stationary) time history response signal into a series of oscillating components obeying some basic properties, called intrinsic mode functions (IMFs). The basic principle in EMD is to decompose a signal y(t) into a set of zero mean mono-components called the IMFs. In each IMF generated, the number of extreme and the number of zero-crossings can differ at most by one. Further, at each point in the generated IMF, the mean value defined by local maxima and the local minima must be zero. Sifting is the name given to the empirical procedure associated with EMD. It works as follows: we first identify the local maxima and minima of the measured time history response y(t) and generate upper and lower envelopes by connecting these points through cubic spline interpolation. We later compute the mean of the upper and lower envelopes and subtract from the time history y(t). The difference between the original time history and the mean value, c1, is called the first IMF if it satisfies the two basic criteria discussed above. We repeat the same sifting process on the new time history obtained after subtracting the C1 component from the original signal y(t), in order to generate the second IMF. This process is repeated to generate rest of the IMFs till the residue becomes a monotonic function or less than specified convergence level. We can reconstruct the original time history y(t) by adding up all the IMFs, nIMF including the residue, rIMF as shown in Eqn. (1).
Lakshmi et al. / Procedia Structural Lakshmi andKRama Mohan Rao/ Structural IntegrityIntegrity Procedia1400(2019) (2018)282–289 000–000
284
y(t)
3
n IMF
Cj(t ) rIMF(t)
(1)
j1
2.1 Empirical Mode Decomposition with intermittency The IMFs generated through the empirical mode decomposition should be complete, adaptive and almost orthogonal decomposition of the original time history signal. However, the sifting process discussed above, cannot produce quality IMFs mainly due to large swings near the ends of the signal. The propagation of these swings inside corrupt the complete signal and it subsequently results in the form of poor IMFS. The large swings near the ends of the signal are basically due to the spline fitting process associated with the sifting. This will be predominant especially when low-frequency components are present in the signal. Apart from this, in the signals with closely spaced frequency components, the modal perturbation phenomena is too prominent to be ignored and it results in the poor sifting. The IMFs thus generated will generally cover more than one modal frequency and can also have some pseudo components. In order to overcome these limitations, several EMD techniques are proposed in the literature and EMD with intermittency criteria is popular among them Initially, EMD with intermittency criteria was proposed by Huang (2005) to locate the intermittent components of the signal. Alternatively, an approach was proposed by Gao et al. (2008) using the Teaser-Kaiser energy operator to locate the intermittent components of the signal. Subsequently, several other researchers have investigated on improving the EMD for generating IMFs. Since our objective is to generate the IMFs and to ensure that each of the IMF generated, represent the individual modal response, we have implemented the EMD with intermittency criteria as given below. Our objective in the present work is to decompose the response signal into IMFs such that each IMF represents one single modal response. In order to accomplish this, we impose an intermittent frequency fi in the sifting process in order to ensure that each of the IMFs generated to represent the modal response contains only one frequency component. We use a bandpass filter during the sifting process to remove all the frequency components which are lower or greater than fi from an IMF. We can obtain the frequency components related to each resonant frequency of the structure using FFT. The frequencies corresponding to the modal components of the structure present in the Fourier spectrum are partitioned into several (say m) subdomains. The centre of each subdomain represent the 0 resonant frequency f k with the upper lower limits of each subdomain (i.e., and fkl (k = 1,2,3,...,m) is defined as (1 0 ± 5%) f k . Accordingly, the resonant frequency band covered in Fourier spectrum will be divided into nm sub-domains as follows:
Ωj
|f |f i f fj1j
1, 2, ....m
(2)
We use band-pass filter by considering the boundaries of each subdomain as the sweep starting and sweep-ending frequency limits, to generate a number of narrowband signals from the original signal. The generated IMFs will have a very good correlation with the original signal as these IMFs contain the frequency components of the original signal. Keeping this in view, we use the correlation strength as a measure to isolate the true IMFs from the other pseudo components. Accordingly, we compute the correlation coefficient, μ i ,( i 1, 2,..., n IMF ) of each of the IMFs with the signal. We normalize the signal and also the IMFs before computing the correlation coefficients, by dividing them with their respective maximum values. This normalization helps in retaining some of the low amplitude real IMFs. In order to differentiate the true IMFs from pseudo IMFs, we use the correlation coefficients with a threshold defined as, J max( μ i ) / k (i=1........n IMF ) , where k is an assumed empirical factor and should be greater than 1.0. We retain the IMFs, if, otherwise, we eliminate by adding to the residue. The main objective here is to guarantee that the selected IMFs include all the resonant modes to be extracted and have no pseudocomponents. In the present work, k is assumed as 10.0. Apart from this, we use the signal extension method employing time series to eliminate the end effects of IMFs generated. As mentioned earlier, the end effects of sifting disturb the EMD process quite significantly. In order to handle these end effects, several distinct approaches are suggested in the literature. We can classify them broadly as
4
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
285
signal extension approaches with or without damping and extrema extension techniques (Shen et al., 2005). However, most of these techniques suggested to handle the end effects associated with periodic or quasi-periodic signals. They are not found to be effective for non-stationary and transient signals. Keeping this in view, in this paper, we use a signal extension technique based on the autoregressive model. 3. Damage detection methodology A proposed damage detection technique combining EMD and time series analysis is an output-only technique capable of detecting damage in the structural system at its earliest stage of incipience. The proposed technique utilizes the acceleration time-history data from the sensors placed on the structure of interest. The process of damage detection is carried out in two phases namely: preliminary phase and testing phase and the step by step procedure is given below: 3.1 Preliminary Phase The measured vibration data, X (i.e. acceleration time-history responses) recorded for time, ‘t’, from all the sensors placed on an undamaged (healthy) structure, is segmented into blocks of data of finite duration, whose elements are denoted by xij(t); i 1,...,ns ; j 1,...,M , where n s is the number of sensors and M is the number of data blocks. Populate a database with these baseline signals. ii. Fit an ARMAX model shown in Eqn. (3) to the subsets of the baseline data for all i and j
i.
x(t )
p
q
α x(t i ) β u(t n
i i 1i 1
i
b
i ) δ i ε (t i ) ε (t )
k i 1
(3)
3.2 Testing Phase iii. Obtain new acceleration signal (current data), Y for time ‘t’, from a potentially damaged structure for all the sensors and segment it into finite blocks of data, whose elements are denoted by y ij(t); i 1,....n s ; j 1,..., M ( similar to step i). iv. Fit an ARMAX model to the current data (similar to step 2) y(t )
p
q
α y(t i) β u(t n
i i 1 i 1
v.
i
b
i) δ i ε(t i ) ε(t)
k i 1
(4)
Perform normalization by matching: For each sensor i, every data-block of the current data is matched with a data-block of the signal in the baseline pool using the minimization of the value “Difference” as given below. Difference
p
α k 1
x k
αky
2
(5)
Choose the data segment, q of the baseline data, x(t) whose AR coefficients match closely with the AR coefficients of the current data (i.e. the ‘Difference’ in Eqn. (5) is minimum) and use it for all the subsequent computations vi. Perform empirical mode decomposition on the matched subsets of baseline and current data and obtain the IMFs independently. Choose the ‘critical IMFs ‘with rich damage sensitive features through the correlation coefficients defined in section 2.1. i (t) vii. Add up all the selected critical IMFs and the residue to obtain reconstructed time history responses, y (i = 1,2,3….) corresponding to current data, with damage rich features. The number of modal responses considered for reconstruction can be from one to maximum of m modes. Similarly, reconstruct the reference time history responses, using the modal time history responses chosen in step 6.
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
286
5
viii. Fit ARMAX model to the new reference and current data subsets and evaluate the damage index using the distances of the two ARMAX models in terms of subspace angles. ix. Plot the normalized values of subspace angles based damage index for every sensor, to visualize the spatial location of damage. The sensor nodes which indicate the highest magnitudes of the damage index reveal the location of damage precisely. 4. Validation Studies The numerical example is a simply supported elastic beam with transverse elasto-plastic cracks is used to demonstrate the effectiveness of the proposed EMD augmented ARMAX model. The acceleration time-history responses are simulated by a cracked-beam finite element analysis, where the incipient damage is caused due to the initiation of cracks. Apart from the numerical simulation studies, an experimental verification is also carried out using an RCC beam inflicted with cracks due to static loads. 4.1 Numerical studies The numerical model of a simply supported beam girder, with dimensions of 8000mmx450mmx550mm, and the material properties as shown in Fig. 1, is used to validate the proposed technique. The beam is discretized into 20 elements and is assumed to carry accelerometers on 19 nodes, eliminating the nodes at its supports.
Fig. 1. A Simply supported beam
A stochastic random dynamic loading is simulated for exciting the beam. Newmark’s time marching scheme is used in finite element analysis to compute the 6s long acceleration time history response with a sampling rate of 2000 Hz. The time history data is generated with random loads and normal operational conditions. In order to verify the performance of the proposed technique with respect to the immunity towards measurement noise, the computed time history measurements are corrupted with zero mean white Gaussian noise, by adding a normal random component to the computed noise free acceleration time history response as
x x δ p N noiseσ ( x) m
(6)
where δ p is the percentage level of noise, is the standard normal distribution vector with zero mean and unit standard distribution, σ(x) is the standard deviation of the noise-free measured (computed) time history response. In the present investigations, random noise levels of 5%, are considered. This healthy data generated with 5% measurement noise is segmented into 12 subsets with 1000 samples in each. Similarly, the acceleration data for the current state of the structure, with the simulated damage at element number 15, by introducing cracks of 10mm length, are generated and segmented into subsets. The formulations of the finite element analysis of the cracked beam is used in the present work to obtain the vibration acceleration responses after damage, to form the current data in a way that initially, the structure is healthy and the damage is initiated after few instants of time. To simulate this scenario, the damage is introduced after 4 seconds (i.e. in the 8th current subset data). In order to improve the sensitivity of the technique based on ARMAX models, in the presence of minor damage, in this paper, initially the acceleration time history data (signal) is pre-processed using the EMD with intermittency algorithm, and the IMFs are extracted. The details of the IMFs, of both the dynamic signatures obtained from the healthy structure (baseline) and their fast Fourier spectrum (FFT) plots, are shown in Fig. 2(a) and 2(b) respectively. The FFT plots of the IMFs clearly indicate the efficiency of the improved EMD technique to extract the unimodal IMFs from the noisy acceleration data.
6
Lakshmi and Rama MohanetRao/ Integrity Procedia K Lakshmi al. /Structural Procedia Structural Integrity 00 14 (2018) (2019) 000–000 282–289 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 0.1 0.0 -0.1 2 1 0 -1 -2 0.00
(b)
0
100
200
0
100
200
300
400
500
600
700
800
300
400
500
600
700
800
0.3 0.2 0.1 0.0 0.2 0.1 0.0 0.8 0.4 0.0 0.2
Amplitude
Amplitude
(a)
287
0.1 0.0 0.8 0.4 0.0 0.8 0.4 0.0 0.5 0.0 0.1
0.25
0.50
0.75
1.00
Time (s)
1.25
1.50
1.75
0.0 0.6 0.4 0.2 0.0
2.00
Frequency(Hz)
Fig. 2. EMD of the response at node-6 of simply supported beam-Test Case-1: (a) IMFs of healthy data; (b) FFT spectrum of IMFs of healthy data.
The critical IMFs are isolated from the extracted IMFs, using the correlation coefficient presented in the earlier section. All the isolated critical IMFs are added up to reconstruct the new current time series. Similarly, the new baseline time series is reconstructed using the selected critical IMFs. The typical reconstructed signals of sensor node15 (i.e., node closer to crack location) using the critical IMFs of the current and healthy signals based on the presence of damage rich features of the current data are shown in Fig. 3(a). Once the current data subset and the baseline subset are reconstructed using the critical IMFs, distances of ARMAX models in terms of the subspace angles are computed for each of the sensor node signals to locate the damage as shown in Fig. 3(b). The normalized values presented in Fig. 3(b), clearly indicate that the proposed method based on EMD-ARMAX is effective in detecting as well as locating the spatial damage present in the structure in the form of minor crack. Using the count of the current dataset being analyzed, we can arrive at the exact time instant of damage. In this example, the time instant of damage is found to be 4s. 4.2 Experimental verification: The second example to validate the proposed technique to detect minor/incipient damage is the laboratory experimental studies, conducted on a simply supported reinforced cement concrete (RCC) beam. The test structure considered is a simply supported RCC beam with dimensions: 3000mm x165mm x200mm. The bottom longitudinal reinforcement was 2# 16 and the upper was 2# 12 with 25# 6 stirrups. The beam is instrumented with 16 microelectromechanical systems (MEMS) accelerometers, placed equidistantly along the beam to record the acceleration time history data. The beam is excited using a modal shaker of sine peak force capacity of 200N and the tests were carried out in the frequency range of 0-1000Hz, for harmonic and random excitations. The loading frequencies, as well as amplitude, is varied during each set of measurements to simulate operational variability. Initially, acceleration responses of the beam are measured at all the 16 sensor nodes for the undamaged state of the beam. This scenario is named as ‘Healthy’. Each signal is measured for 19 sec and is sampled at 3000 Hz so that the frequencies of the beam can be uncovered, in 0–1500 Hz frequency range.
(a)
0.4
(b)
Reconstructed healthy data Reconstructed current data
0.3
Acceleration (g)
0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4
0.0
0.5
1.0
1.5
2.0
2.5
Subspace angle based damage index
Lakshmi et al. / Procedia Structural Lakshmi andKRama Mohan Rao/ Structural IntegrityIntegrity Procedia1400(2019) (2018)282–289 000–000
288
Time(s)
7
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Sensor Number
Fig. 3. Damage diagnosis of simply supported Beam-Test case-1: (a) Reconstructed signals of healthy and current data of Sensor-6; (b) Normalised damage index evaluated using distances of ARMAX models in subspace angles.
The minor damage is inflicted at approximately one-third span from both the supports of the beam (i.e. in element no. 5 and element no.12) by applying the static loads in small increments. The minor cracks appear when the static load applied is nearly 12KN as shown in Fig.4. The experiment with dynamic excitation force is performed to create test data (acceleration response) of the beam with minor damage and is referred to as ‘Damage’. The acceleration data of ‘Healthy’ and ‘Damage’ are used as baseline and current data respectively. The cross-correlated signals of the baseline and the current data are fed to the EMD with intermittency and all the IMFs are extracted. The critical IMFs are selected using the correlation coefficient method and are added up to reconstruct the new signal as shown in Fig. 5(a). Subspace angles are evaluated to calculate the distance between ARMAX models of the reconstructed healthy and current signals. The normalized values of subspace angle based damage indices of ARMAX, shown in Fig. 5(b), clearly reflect the spatial location of damage (at one-third of the beam from both the supports.).
Fig. 4. Scenario of Damage
5.0 Conclusions In the paper, a novel hybrid technique to identify the location of the minor damage like minor cracks is presented. As, the minor damage creates feeble changes in the dynamic characteristics of only a few modes of the structure, the damage features present in those modal responses get hidden in the overall response (i.e., the measured dynamic signature). Additionally, measurement noise and environmental variability also play their role in masking the minor damage features in the overall response of the structure. In view of this, in this paper, an attempt has been made to isolate these damage sensitive modal responses and reconstruct a new signal accordingly using improved EMD with intermittency criteria. The damage enriched signals isolated by EMD are further used for damage diagnosis using the ARMAX time series model, employing a damage index, constructed from the distance measure of any two ARMAX
8
K Lakshmi et al. / Procedia Structural Integrity 14 (2019) 282–289 Lakshmi and Rama Mohan Rao/ Structural Integrity Procedia 00 (2018) 000–000
289
models, in terms of subspace angles. Numerical simulation studies have been carried out by considering a simply supported beam with minor cracks. Laboratory experimental studies have been carried out by considering an RCC beam to complement the numerical simulations and also demonstrate its practical applicability in the field.
6
Reconstructed healthy data Reconstructed current data
5 4
Acceleration (g)
3 2 1 0 -1 -2 -3 -4 -5 -6
0.0
0.5
1.0
1.5
Time(s)
2.0
2.5
(b)
Subspace angle based damage index
(a)
1.2 1.0 0.8 0.6 0.4 0.2 0.0
1
2
3
4
5
6
7
8
9
10
11
Senso r N um ber
12
13
14
15
16
Fig. 5. Damage diagnosis of RCC beam-Multiple Damage: (a) reconstructed healthy data and current data; (b) normalised damage index evaluated using distances of ARMAX models in subspace angles.
References Das, S., Saha, P., Patro, S. K., 2016. Vibration-based damage detection techniques used for health monitoring of structures: a review. Journal of Civil Structural Health Monitoring 6(3), 477–507. Data normalization- a key for structural health monitoring: Report for 2001, Los Alamos National Laboratory, No. LA-UR-01-4212. Los Alamos National Lab., NM (US), 2001. Gao, Y., Ge, G., Sheng, Z., et al., 2008. Analysis and Solution to the Mode Mixing Phenomenon in EMD, Congress on Image and Signal Processing, Washington, DC, USA, 5, 223-227. Huang, N. E., 2005. Introduction to Hilbert-Huang transform and some recent developments, in “Hilbert-Huang Transform in Engineering”. In: Taylor & Francis, pp. 1-24. Huang, N. E., Shen, S, S., 2014. “Hilbert-Huang Transform and Its Applications”. In World Scientific, 16. Lakshmi, K., Rao, A. R. M., 2014. A robust damage-detection technique with environmental variability combining time-series models with principal components. Nondestructive Testing and Evaluation 29(4), 357–376. Lakshmi, K., Rao, A. R. M., 2015. Damage identification technique based on time series models for LANL and ASCE benchmark structures. Journal of Non-destructive Testing and Condition Monitoring 57(10), 580-588. Lakshmi, K., Rao, A. R. M., Gopalakrishnan,N., 2017. Singular Spectrum Analysis combined with ARMAX model for structural damage detection. Structural Control and Health Monitoring, 24, DOI: 10.1002/stc.1960. Moore, K. J., Kurt, M., Eriten, M., et al., 2018. Wavelet-bounded empirical mode decomposition for measured time series analysis. Mechanical Systems and Signal Processing 99, 14–29. Rao, A. R. M., Lakshmi, K., 2015. Damage diagnostic technique combining POD with time-frequency analysis and dynamic quantum PSO. Meccanica 50(6), 1551–1578. Rao, A. R. M., Lakshmi, K., Krishna Kumar, S., 2015. Detection of delamination in laminated composites with limited measurements combining PCA and dynamic QPSO. Advances in Engineering Software 86 (2015), 85–106. Shen, S. S., Shu, T., Huang, N. E., et al., 2014. HHT Analysis of the Nonlinear and Non-Stationary Annual Cycle of Daily Surface Air Temperature Data, in “Interdisciplinary Mathematical Sciences: Hilbert-Huang Transform and Its Applications”, In: World Scientific, 5, 187–209. Tibaduiza, D. A., Mujica, L. E., Rodellar, J., et al., 2015. Structural damage detection using principal component analysis and damage indices. Journal of Intelligent Material Systems and Structures 27(2), 233–248. Zheng, H., Mita, A., 2008. Damage indicator defined as the distance between ARMA models for structural health monitoring. Structural Control and Health Monitoring 15(7), 992–1005.