Review of Techniques for Fault Diagnosis in Damaged Structure and Engineering System

Abstract

Focus has been made to give an overview of various methodologies used in fault diagnosis and condition monitoring. A crack in vibrating structures can lead to premature failure if it is not detected in time. Researchers have been working on the dynamics of cracked structures for decades to be able to monitor a structure and diagnose fault at the earliest possible stage. An effort has been made in the current paper to understand different techniques and methodologies for fault diagnosis and condition monitoring of damaged structures subjected to varied dynamic loading. The methods used are classical, wavelet transform, and finite element methods, artificial intelligence methods, and numerical and experimental methods. Using classical methods, engineers are able to predict faults. But using artificial intelligence techniques, it is observed that the forecasting time for fault diagnosis improves a lot in comparison to other methodologies.

1. Introduction

Engineering structures fail in their long working lives from initiation and subsequent growth of faults to catastrophic levels. A lot of research throughout the world has focused on the methodologies to delay, arrest, or stop the initiation of faults. In the current research, such methodologies, both traditional and nontraditional, are reviewed.

The relationship between the physical damage to a structure and changes in the dynamic characteristic has been studied by Richardson [1]. In his survey he has focused on modal analysis, modal testing method, and relation between the extent of damage and changes in the modes of vibration. Duringa review process of structural health monitoring, Rytter[2] has classified the damage detection technique as four levels. The level 1 determines the presence of damage in structures. The level 2 determines the geometric location of the damage. The level 3 quantifies the extent of damage and level 4 predicates the life of the structure. The local flexibility that affects the vibration signatures has been suggested by Dimarogonas [3] in his review paper. The crack opening and closing happen in time that depends upon the vibration and rotation amplitude. He has suggested that the local stiffness matrix at the cracked section of a shaft leads to a coupled system and for uncracked shaft, the system is decoupled. Doebling et al. [4] have reviewed different techniques of detection, location, and characterization of structural damage. Their analyses include changes in modal frequency, changes in mode shapes, and changes in flexibility coefficients. The technique to be used for a particular structure for damage detection depends upon the type of structure.

Alsabbagh et al. [5] proposed a simplified formula for the stress correction factor in terms of the crack depth to the beam height ratio. They used the proposed formula to examine the lateral vibration of an Euler-Bernoulli beam with a single edge open crack and compared the mode shapes for the cracked and uncracked beam to identify the crack parameters. Richardson [6] have devised a unique technique for identifying the modal properties of elastic structures in testing laboratories. This technique includes the digital processing and Fast Fourier Transform (FFT) from which transfer function data is obtained and is converted to modal properties by a least square error estimator. In their research the analytical and experimental results are in good agreement.

Zimmerman [7] has analyzed the effect of measurement of noise on the damage detection performance of the minimum rank Perturbation theory. He has developed the closed form solution for the sensitivity of the minimum rank Perturbation theory damage vectors and calculated stiffness perturbations with respect to the errors in the mode shapes or frequency response functions. The structural damage has been detected and identified by Yang et al. [8] by studying the changes in the characteristic signal of the damaged structures. These characteristic signals are obtained from the random vibrational response utilizing the signal processing technique. This damage detection technique obtained from dynamic response measurement has been validated with theoretical and experimental tests. Nahvi and Jabbari [9] developed a technique for identification of crack in cantilever beam using analytical, finite element method based on measured natural frequencies and mode shapes of the beam structure. The crack location and crack size have been determined by Shen and Taylor [10] utilizing the dynamic measurement. This technique is based on the minimization of either the “mean-square” or “max” of the difference between the measured value of the vibration signature (natural frequency and mode shapes) and corresponding predications obtained from computational model. This technique is in good agreement with experimental results. The damaged location, detection and its severity have been investigated by Cawley and Adams [11] by measuring the structural natural frequencies at the single point of the structure. This method has been adopted for any structure utilizing Finite Element Analysis. This is good agreement between the actual damage and predicated damage. Taha and Lucero [12] introduced a method to improve pattern recognition and damage detection by supplementing intelligent health monitoring with fuzzy inference system. The Bayesian methodology is used to demarcate the levels of damage for developing the fuzzy system and is examined to provide damage identification using data obtained from finite element analysis for a prestressed concrete bridge. Artificial neural network (ANN) based methodology has been used by Hoffman and Van Der Merwe [13] and later byMahamad et al. [14]to predict accurate remaining useful life (RUL) for a bearing system. The ANN model was designed using measurements of hazard rates of root mean square and kurtosis from its present and previous state. Kong and Chen [15] proposed a fault diagnosis methodology using wavelet transform fuzzy logic and neural network technique to identify the faults. Liu et al. [16] took the help of genetic algorithm (GA) for optimal sensor placement on a spatial lattice structure. They took the modal strain energy (MSE) and modal assurance criterion (MAC) as the fitness function. A computational simulation of 12-bay plain truss model was used as modified GA, and the data was compared against the existing GA results using the binary coding method. Better results were found through the modified GA. Sanz et al. [17] presented a new technique for health monitoring of rotating machinery by integrating the capabilities of wavelet transform and auto associative neural network for analyzing the vibration signature. The proposed technique's effectiveness was evaluated using numerical and experimental vibration data and the developed technique demonstrated accurate results. Curry and Collins [18] proposed a closed loop system with the help of sensors to formulate a fault detection and isolation methodology based on fixed threshold. Heyder et al. [19] used 3D corner singularity method and stress intensity factor concept to investigate the influence of corner singularity on 3D fatigue crack propagation.

In the current paper different approaches have been analyzed and discussed systematically to accumulate the possible methodologies and systems followed for fault diagnosis and condition monitoring of various dynamic structures. The methodologies followed are described in the next section.

2. Review of Various Methodologies for Fault Diagnosis

In the present review of methodologies used for fault diagnosis of vibrating cracked structures and condition monitoring of machineries and structural systems, it is observed that the proposed techniques may be broadly divided intothe following categories:

classical method,

wavelet transform and finite element method (FEM),

artificial intelligence (AI) techniques,

numerical and experimental techniques.

2.1. Classical Techniques for Fault Detection

In the current section, spatial variation of the transferred response, modal response methods, energy-based method, analytical methods and algorithms based on vibration, and so forth, have been cited and used for determination of crack location and its size in dynamically vibrating damaged structures.

Müller et al. [20] used the theory of Lyapunov exponents in their model-based method for crack detection in dynamic systems. Owolabi et al. [21] carried out experimental investigations of crack location and crack intensity for fixed beams and simply supported beams and measured the changes in the first three natural frequencies and the corresponding amplitudes to forecast the crack location and intensity. Chinchalkar [22]developed a generalized numerical method for fault finding with wide variations in crack depth using finite element approach using different boundary conditions. This approach is based on the measurement of first three natural frequencies of the cracked beam. Dado and Abuzeid [23] analyzed the vibration behavior of a cracked beam structure carrying end mass coupled with transverse and axial vibrations. The coupling effect was found out to be weak for the first two modes under moderate crack depth condition as compared to high crack depth ratio. Loutridis et al. [24] used instantaneous frequency and empirical mode decomposition for crack detection in a beam. Coupled with their experimental results, they concluded that the variation of the instantaneous frequencies increases with increase in crack depth and this variation was used to estimate crack size.

Song et al. [25] describe an exact solution methodology based on Laplace transform to analyze the bending free vibration of a cantilever-laminated composite beam having surface cracks. They used Hamilton's variation principle in conjunction with Timoshenko beam model to develop a damage detection technique. Law and Lu [26] proposed a time domain method for crack identification in structural member by modeling the open crack using Dirac delta function and evaluated the dynamic response based on modal superposition. They validated the proposed identification algorithm by comparing the results from impact hammer tests on a beam with a single crack. Douka and Hadjileontiadis [27] studied the nonlinear dynamic behavior of a cantilever beam having breathing crack both theoretically and experimentally. They analysed both the simulated and experimental response data by applying empirical mode decomposition and Hilbert transform method. Benfratello et al. [28] used the skewness coefficient of the rotational degrees of freedom for identification of crack in a damaged structure. Zheng and Kessissoglou [29] analysed the natural frequencies and mode shapes of a cracked and uncracked beam by developing an overall additional flexibility matrix and shape function.

Behzad et al. [30] devised a continuous model for flexural vibration of beams with horizontal and vertical edge crack perpendicular to neutral plane of the beam. They took the crack displacement as the product of time function and exponential space function, and the results obtained are in good agreement with the results from FEA. Prasad et al. [31]investigatedthe effect of location of crack from free end to fixed end in a vibrating cantilever beam. They compared and analyzed crack growth rate at different frequencies using the experimental setup as presented in Figure 1. Rezaee and Hassannejad [32, 33]used both perturbation method and energy balance for analysis of vibration of a simply supported beam with breathing crack. It was found that for a given crack location on the beam structure (Figure 2) with the increase in the relative crack depth (α) the stiffness of the beam decreases with time. The considered equivalent stiffness of the cracked beam is given by (1):

\begin{matrix} k (t) = k_{o} + \frac{1}{2} (k_{c} - k_{o}) [1 + \cos (ω t)], \end{matrix}

(1)

where ω is the fundamental frequency, k_c is the equivalent stiffness of the intact beam, and k_o is the equivalent stiffness of the cracked beam when the crack is fully open.

Figure 1:

Block diagram of forced vibration experimental setup.

Figure 2:

(a) Simply supported beam with a crack and (b) equivalent SDOF model.

2.2. Wavelet and Finite Element Methods for Fault Detection

Wavelet and finite element analyses have also been used, apart from the classical methods, for fault detection in cracked structures. Some of the research papers from this domain are described in this section.

Srinivasarao et al. [34] presented a method for crack identification in a cracked cantilever beam by analyzing the vibration signatures using continuous wavelet transform technique. The effectiveness of the method was validated by analytical and experimental methods. Quek et al. [35] investigated and presented the sensitivity of wavelet technique in the detection of cracks in beam structures considering the effects of different crack characteristics, boundary conditions, and wavelet functions. Loutridis et al. [36] presented a method based on wavelet analysis using the sudden changes in the spatial variations of the dynamic response of cracked structures, and the same has been validated analytically and experimentally. Gentile and Messina [37] proposed a technique based on continuous wavelet transform for detecting the location of open crack in damaged beams by minimizing the measurement data and baseline information of the structure. Kim and Stubbs [38] devised a nondestructive method for finding out the crack size and its location using the changes in natural frequency of vibration due to the presence of crack. In their method, they developed an algorithm for crack detection by formulating the crack size model and crack location model using changes in modal energy with the change in natural frequency. They used the natural frequencies on the modal characteristics to detect the crack location and estimation of its size through the crack detection method shown in Figure 3. Saavedra and Cuitio [39] presented a theoretical and experimental vibration analysis of a multibeam structure containing transverse crack. They derived a new cracked finite element stiffness matrix to analyse the vibration behavior of crack systems with different boundary conditions. Qian et al. [40] developed a finite element model for crack detection in a damaged beam using stress intensity factors. This proposed method is also applicable to complex structures with crack. Andreaus et al. [41] investigated the features of nonlinear response of a cracked beam using two-dimensional finite element model (FEM). They considered the behavior of the breathing crack as a frictionless contact problem. They compared the linear dynamic response with the nonlinear dynamic response of the cantilever beam and presented a nonlinear technique for crack identification. Viola et al. [42] developed a finite element model for a cracked Timoshenko beam for crack identification based on the changes in the dynamic behavior of the structure. They derived the stiffness matrix and consistent mass matrix for developing the crack identification technique. Chondros and Labeas [43] studied the torsional vibration behavior of a circumferentially cracked cylindrical shaft using analytical and numerical finite element analysis. They used HU-WASHIZU-BARR variational formulation to develop the analytical method for the cracked shaft.

Figure 3:

Nondestructive crack detection scheme.

Ariaei et al. [44] presented an analytical approach for determining the dynamic response of the undamped Euler-Bernoulli beams with breathing crack and subjected to the moving mass using discrete element technique and finite element method. They observed that the presence of cracks alters the beam response patterns. Potirniche et al. [45] developed a two-dimensional finite element method to study the influence of local flexibility on the dynamic response of a structure. Narkis [46] detected the crack by using inverse technique, that is, through the measurement of frequency of first two natural frequencies of a simply supported uniform beam.

2.3. Fault Diagnosis Using AI Technique

Various types of algorithms based on AI techniques for fault diagnosis have been analyzed and presented in the current section. The methods are broadly divided into four categories as follows:

fuzzy inference technique,

neural network technique,

genetic algorithm (GA) technique,

hybrid technique.

2.3.1. Fuzzy Logic Technique Used for Fault Detection

Different types of Fuzzy inference techniques used for crack and fault identification are depicted in the current section.

Chandrashekhar and Ganguli [47] showed that the geometric and measurement uncertainty cause considerable problem in the damage assessment. They used Monte Carlo simulation to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. The results obtained from the simulation are used for developing and testing the fuzzy logic system. In this paper they addressed the uncertainty associated with the fuzzy logic system for structural damage detection. Kim et al. [48] presented a computer-based crack diagnosis system for concrete structures using Fuzzy set theory. They used the crack symptoms and characteristics to build the rooms for the proposed fuzzy inference system. When they applied the developed methodology to diagnose the crack the proposed system provided results similar to those obtained by experts system. Saravanan et al. [49] proposed a technique based on the vibration signals acquired from the operating machines to effectively diagnose the conditions of inaccessible moving components inside the machine. The proposed technique was designed using fuzzy classifier and decision tree to generate the rules automatically from the feature set. The developed fuzzy classifier was tested with representative data and the results were encouraging. Boutros and Liang [50] developed four condition monitoring indicators for detection of transient and gradual abnormalities using fuzzy logic approach. They successfully tested and validated the fuzzy-based technique in two different applications.

Wu [51]proposed a novelfuzzy robust wavelet support vector classifier (FRWSVC) based on a wavelet function and he developed an adaptive Gaussian particle swarm optimization (AGPSO) algorithm to seek the optimal unknown parameter of the FRWSVC. The results obtained from experimentation were compared with that of the hybrid diagnosis model and were found to be closer. Sugumaran and Ramachandran [52] presented the use of decision tree of a fuzzy classifier for selecting best few features that will discriminate the fault condition of the bearing from given trained samples. The vibration signal from a piezoelectric transducer is captured for different types of fault condition of bearing and is used to build the fuzzy rules. The results drawn from the fuzzy classifier when compared with results from the experimental analysis were found to be in close proximity. Miguel and Blázquez [53] developed a decision-making module-based on fuzzy logic for model based fault diagnosis applications. A fault detection and isolation system based on the input and output parameters were successfully applied in laboratory equipments to reduce the uncertainties for the output parameter.

2.3.2. Neural Network Technique Used for Fault Detection

In this section Neural Network techniques are applied to locate damage in structural members are described.

The Artificial Neural Networks (ANNs) have been used as promising technique in the domain of inverse problem. Mehrjoo et al. [54]presented a fault detection inverse algorithm to estimate the damage intensities of joints in truss bridge structure using back propagation neural network method. Just-Agosto et al. [55] applied neural network method with a combination of vibration and thermal damage detection signatures to develop a damage defection tool. They applied the developed technique on sandwich composite for the purpose of crack detection. Saravanan et al. [56] dealt with the robustness of an artificial neural network, wave let and, proximal support vector machine based on fault diagnostic methodology for a gear box. Oberholster and Heyns [57]presented a methodology for online structure health monitoring of axially flow for blades with the use of neural network. The developed neural network was trained with the extracted vibration features from the experimental test structures. They used frequency response function and finite element models for designing the neural-network-based technique. According to them the proposed technique can handle the online damage classification using sensor for the test structures. Wu and Chan [58] described a condition monitoring and fault identification techniques for rotating machineries using wavelet transform and neural network method. The sound emission from the gear set was used along with continuous wavelet transform technique and feature selection of energy spectrum to design the neural-network-based fault diagnostic tool. The experimental results from their methodology pointed out that the sound emission from the system can be used for effective fault diagnosis for condition monitoring.

Wu and Liu [59] investigated a fault diagnosis technique for internal combustion engine using discrete wavelet transform (DWT) and neural network. The DWT technique was combined with feature selection of energy spectrum for the development of the purposed fault detection algorithm. The experiment results obtained from the proposed system indicated that the sound emission signal can be effectively used for fault diagnosis of engines under different operating conditions.

2.3.3. Genetic Algorithm for Fault Detection

Researchers and scientists have used methods based on Genetic Algorithm for fault diagnosis in engineering systems. Some of the GA-based methods are presented in the current section.

Xiang et al. [60] used rotating Rayleigh-Euler and Rayleigh-Timoshenko beam elements of B-spline wavelet on the interval (BSWI) to discretise slender shaft and stiffness disc, respectively. They used wavelet-based model to find out frequencies. The first three frequencies, were used in crack detection process, and subsequently genetic algorithm was used to measure crack location and crack depth. He et al. [61] studied the crack detection in a rotating machine shaft by using finite element method to optimize the problem and subsequently used genetic algorithm to search the solution. Their proposed method was found to solve a wide range of inverse identification problem. Zhang et al. [62] used genetic programming (GP) to find faults in rotating machinery. They compared the solution through GP with other techniques like artificial neural network (ANN) and support vector machines (SVMs). They found that GP demonstrates performance equal or better compared to ANN and SVMs. Zhang and Randall [63] studied the fault in rolling element bearing by the combination of genetic algorithm (GA) and fast kurtogram. For the initial analysis of the vibration signals of the bearing they used fast kurtogram and subsequently for final optimization they used GA. The results of their combined applications of GA and kurtogram gave better results over other optimal resonance demodulation techniques.

Baghmisheh et al. [64] used genetic algorithm (GA) to monitor the changes in natural frequencies of a cantilever beam having crack. They used an analytical model to formulate the crack beam structure and numerical methods to obtain the natural frequencies. The depths and crack locations were solved by using binary and continuous genetic algorithms (BGA, CGA). Perera et al. [65] used genetic algorithm for solving multiobjective optimization to detect damage. They compared GA optimization based on aggregating functions with pareto optimality. Friswell et al. [66] combined genetic algorithm (GA) and eigen sensitivity method for determination of location of damage in structures. GA was used by them to optimize the discrete damage location variables.

2.3.4. Hybridized Method for Fault Detection

In the process of development of methods for crack diagnosis, the different Artificial Intelligent techniques, such as, fuzzy inference, neural network, and genetic algorithm have been hybridized. The hybrid techniques used for identification of crack are discussed in this section.

(1) Neurofuzzy Technique for Fault Detection

The various types of technique based on Neurofuzzy methodologies for damage identification have been briefly analyzed in this section.

Quteishat and Lim [67] proposed a modified fuzzy min-max (FMM) network for improved performance when large hyper boxes are formed in the network. This methodology was used to facilitate the extraction of rule set from FMM to justify the predictions. The results from the developed FMM were authenticated with the sensor measurements collected from a power generation plant for fault diagnosis. Topçu et al. [68] studied the optimum uses of pozzolans as supplementary cementing material for blended cement production. They developed a system based on artificial neural network and fuzzy logic for predicting the strength parameters for different types of cement mortars. Tran et al. [69] presented a fault diagnosis technique based on adaptive neurofuzzy inference system in combination with classification and regression tree. The ANFIS controller has been trained with the results obtained from the least square algorithm. They observed that the developed ANFIS model has the potential for fault diagnosis of induction motors. Fang et al. [70] explored performance of a structural damage defection technique based on frequency response and neural network. In this paper they investigated a tunable steepest discount algorithm using heuristics approach for improving the converging speed. From the analysis of the result of the proposed method for a cantilever beam they have concluded that the neural network technique can estimate the damage condition with high accuracy. Beena and Ganguli [71] proposed a new approach for fault detection in structural system based on the fuzzy logic technique. They used continuum mechanics and finite element method to measure the vibration parameters because of structure damage. The developed technique worked quite well for structural damage even in the presence of noise. They also used neural network based on hebbian learning to develop the damage detection system based on fuzzy cognitive map. Kuo [72] presented a symbiotic-evolution-based fuzzy neural diagnostic system for fault detection of a propeller shaft used in the marine propulsion system. The system auto generates its own optimal fuzzy neural architecture for fault diagnosis. They stated that the results from the hybrid fuzzy neural system have been found to be closer with the real conditions than the other traditional methods. Ye et al. [73]developed a new online diagnostic algorithm to find out the mechanical fault of electrical machine using wavelet packet decomposition method and adaptive neuro fuzzy inference system. According to them the new integrated fault diagnostic system significantly reduces the seal complexity and computational time of the system. They validated results from the diagnostic technique for a 3-phase induction motor drive system. Kuo and Chang [74] proposed a fault detection system using data acquisition, feature extraction, and pattern recognition for detecting faults of blades by applying multiple vibration sensors. The feature extraction algorithm was developed based on back propagation artificial neural network. The fuzzy logic technique was employed to speed up the training speed. According to him the results from the system are very close to the results obtained from the experimental analysis. Zio and Gola [75] presented a fault diagnostic problem using neurofuzzy approach. They used this approach for the purpose of high rate of correct classification and to obtain an easily interpretable classification model. The efficiency of the approach was verified by applying to a motor-bearing system, and the results obtained were quite encouraging. Wang et al. [76]presented the comparison of the performance for two fault diagnosis systems, recurrent neural networks and neurofuzzy systems, using two benchmark data sets. As described by them, the neurofuzzy prognostic system was found to be more reliable for machine health condition monitoring than the neural network fault diagnostic system.

Zhang et al. [77] proposed a bearing fault detection technique based on multiscale entropy and adaptive neurofuzzy inference system (ANFIS) to measure the nonlinearity existing in a bearing system. They conducted experiments on electrical motor bearing with three different fault categories, and the results obtained from the experimentation were used to design and train the ANFIS system for fault diagnosis.

(2) Genetic Algorithm-Fuzzy Inference Technique Used for Fault Detection

Pawar and Ganguli [78] devised a structural health monitoring methodology using genetic fuzzy system for online damage detection. They used displacement and force-based measurement deviations between damage and undamaged condition for building the rules and data pool for the fuzzy and genetic system, respectively. The developed methodology was applied for composite rotor blades and the results were encouraging. Yuan and Chu [79] proposed an artificial immunization algorithm (AIA) to optimize the parameters obtained from support vector machines (SVMs) generally used as machine-learning tool for fault diagnosis. They used the proposed fault diagnosis model for a turbo pump rotor and found that the SVM optimized by AIA gave higher accuracy than the normal SVM.

(3) Genetic Algorithm-Neural Network Technique for Fault Detection

Firpi and Vachtsevanos [80] used genetically programmed artificial feature (GPAF) for fault detection of a rotating machine part. They extracted artificial features using GPAF algorithm while taking vibration data as a source of information. Samanta [81] compared the performance of gear fault detection using artificial neural network (ANN) and support vector machines (SVMs) and found that the classification accuracy of SVMs is better than ANN without genetic algorithm (GA) optimization while with GA optimization performance of both classifiers is comparable. Jack and Nandi [82] used support vector machines (SVMs) and artificial neural network (ANN) with genetic algorithm (GA) optimization technique to detect faults in rotating machinery. They compared the performance of this classification and improved the overall performance by using GA-based features selection process.

(4) Genetic Algorithm-Fuzzy Inference-Neural Network Technique for Fault Detection

Saridakis et al. [83] studied the dynamic behavior of a shaft with two transverse cracks considered to the along arbitrary angular positions at some distance from the clamped end. They developed a fuzzy-logic-based crack diagnosis model by using the effect of bending vibrations of the cracked shaft. Genetic algorithm and neural network were used for the developed technique to reduce the computational time without any significant loss in accuracy. Kolodziejczyk et al. [84] investigated the potential of various artificial intelligence techniques to predict the damage parameters mainly arising due to wearing out of the contact surfaces. The proposed technique was designed using fuzzy logic, neural network, and genetic algorithm. The results from the developed methodology were closer to the experimental data. They also optimized the proposed crack diagnose model to reach high robustness.

2.4. Numerical and Experimental Techniques

In this section, various numerical and experimental techniques used as fault diagnostic tools in damaged structures are briefly explained.

Cao and Qiao [85] developed a novel Laplacian scheme to form an improved damage identification algorithm. They measured the modal curvature to develop the diagnostic method. The results from the proposed Laplacian scheme were validated with experimental results. Fagerholtet al. [86] described an investigation on the fracture behavior of a cast aluminium alloy. They used classical flow theory for modeling the fracture and also have used digital image correlation (DIC) to obtain information of the displacement and strain field in the specimen. Karaagac et al. [87] worked numerically and with experiments to study the effect of crack ratios and positions on the natural frequencies and buckling loads of a slender cantilever Euler beam with a single edge crack using the local flexibility concept. Rucka and Wilde [88] established a method to localize damage in a beam structure using static deflection technique. They have used wavelet transform for crack identification. In their experimental setup an optical method which allowed simultaneous measurements of static deflection lines to estimate the locations of crack and their severities was used. Benfratello et al. [89] presented both numerical and experimental investigations in order to assess the capability of non-Gaussianity measures to detect the crack locations and crack magnitudes. In their experimental setup a shaking table, amplifier model and accelerometer with amplifiers are being used for measurement of bending frequency for the vertical cantilever beam subjected to horizontal shaking with noise. Karthikeyan and Tiwari [90] carried out an experimental investigation to establish an identification procedure for flaws in beam structure. In their experimental setup they used a circular beam as specimen and measured the dynamic response using a multichannel data acquisition system to validate the results from their proposed methods. Rus and Gallego [91] presented a work based on hyper singular shape sensitivity boundary integral equation for solution of the inverse problem for crack estimation. The accuracy, convergence, and sensitivity for the proposed method have been verified against simulated/experimental results. Stoisser and Audebert [92] presented theoretical, numerical, and experimental approach for crack detection in rotating machineries used in power plants. The experimental technique used in their analysis observes the bending and torsion resonance frequency shifts introduced by the presence of crack in the shaft.

3. Discussions

Discussions made from the analysis of different methodologies applied for fault diagnosis since last two decades are depicted in the current section.

Modal response methods have been successfully used to estimate the crack location and its severity present in damaged structure. Various methods, such as, Hilbert transform method, Lyapunov exponent's theory, and Hamilton's variation principle and can be used to measure the natural frequencies and mode shape of the structural members, which are subsequently used for identification of faults in cracked members. Algorithms based on vibration analysis can be effectively used for identification of crack, and the authentication of the methods has been made comparing the results from experimental investigation. From the review of the literature it is evident that the presence of cracks have a noticeable effect on the dynamic behavior of the member. Acoustic emission technique have been used to monitor the changes in modal parameters for fault identification. The nonlinearity produced due to presence of cracks is measured and analyzed using Dirac delta function, empirical mode decomposition transform method, frequency response function, and so forth. In the process of development of crack identification algorithm the beams are assumed as Timoshenko and Euler Bernoulli's beam, and numerical methods are employed to calculate the modal response, subsequently used for designing of fault detection methodology for damage structures.

Wavelet-based technique can be used effectively for the damage detection in structural system considering the effects of different crack characteristics and boundary conditions. The nonlinear dynamic response of cracked and uncracked beam structures can be/are used to formulate finite element model for damage identification. The torsional vibration behavior of circumferentially cracked cylindrical shaft has been used for development of a crack detection tool with help of FEA. The results from the finite-element-based crack detection model are found to be in close proximity with the results obtained from experimental investigation.

Various structural health monitoring and machine condition monitoring (vibration analyses, bending and torsion resonance frequency shifts, use of pressure gauges to measure the changes in natural frequencies, etc.) are proposed for real time scenario. Artificial intelligent technique can be suitably used for crack diagnosis in various types of structures and engineering systems. The fuzzy logic approach has been used to design crack diagnosis tool using the dynamic response of the damaged members. The vibration signal captured from faulty beams system has been used to develop fuzzy based system to forecast the fault present in the bearings. Artificial neural network (ANN) has been used as a robust technique with the help of discrete wavelet transform, finite element analysis for fault diagnosis in different types of engineering systems. The ANN model has been designed using measured vibration parameters obtained from analytical and numerical analysis. Genetic algorithm (BGA, CGA) can be used to measure crack location and crack depth in rotating machine shaft, bearing and mechanical systems with the help of wavelet transform and finite element method. Different types of hybrid techniques such as neurofuzzy, GA fuzzy, GA neural, and GA fuzzy neural have been proved to be promising techniques for development of health diagnostic tool in mechanical and electrical machines.

4. Conclusions

In the current investigation, various methodologies based on the dynamic response and stiffness of the structures have been reviewed for fault diagnosis, and the application of the proposed techniques has been described. From the analysis of the methodologies for fault detection/crack detection of dynamically vibrating machine elements/structures it is found that besides the classical, wavelet, finite element methods, various types of algorithms developed using artificial intelligence techniques such as fuzzy logic, artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS), genetic algorithm (GA), GA fuzzy, GA neural, GA neural fuzzy are effectively used for estimation of crack locations and their severity during the analysis of the vibration signatures. The following conclusions can be drawn by analyzing the various techniques used for condition monitoring of the damaged structures.

In the development of crack detection technique using classical approach, the stiffness, energy functions and vibration parameters play a major role for quantifying the crack parameters. The classical techniques are designed using theoretical methods, such as, Lyapunov exponent's theory, Laplace transform, Hamilton's variation principle, and Dirac delta function.

Wavelet analysis and finite element analysis have been employed to derive the vibration indices (e.g., natural frequencies and mode shapes) of the structure which are subsequently used for identification of damages in cracked structures.

The fuzzy logic approach has been used to develop fuzzy controller using the vibration signals acquired from the operating machines/structures. Researchers have used different types of fuzzy membership functions, such as, Gaussian and Triangular to design the fuzzy inference system for diagnosis of faults.

In some cases, scientists have adopted ANN to design online fault diagnostic tool with the help of wavelet and finite element analysis for identification of crack in damaged structure.

Adaptive neurofuzzy inference system (ANFIS), neurofuzzy technique are used by many authors for fault diagnosis of induction motors, propeller shaft of marine propulsion system, and motor drive system.

Genetic algorithm has also been successfully applied for development of inverse diagnostic tool. The computational time for fault diagnoses using genetic-algorithm-based techniques is found to be in term of milliseconds.

Scientists have proposed hybrid techniques, such as, GA fuzzy, GA neural, GA fuzzy neural network for structural health monitoring by estimating the crack parameters.

From the analysis of the reviews of the research papers cited in Section 2.4. It has been found that experimental techniques, such as, optical method, vibration analyzer, shifting of frequency in relation to pressure change, and static deflection method have been used successfully by the scientists to locate the crack in different kinds of engineering structures or components.

The classical and finite element method can be used as direct method for getting the vibration signatures (e.g., natural frequencies and mode shapes) where as the artificial intelligence methods can be used as an inverse technique for condition monitoring of vibrating systems. In future the scope of hybrid AI techniques can be studied for analyzing the behavior of dynamic structures.

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