Intelligent Diagnosis and Smart Detection of Crack in a Structure from its Vibration Signatures

In recent years, there has been a growing interest in the development of structural health monitoring for vibrating structures, especially crack detection methodologies and on-line diagnostic techniques. In the current research, methodologies have been developed for damage detection of a cracked cantilever beam using analytical, fuzzy logic, neural network and fuzzy neuro techniques. The presence of a crack in a structural member introduces a local flexibility that affects its dynamic response. For finding out the deviation in the vibrating signatures of the cracked cantilever beam the local stiffness matrices are taken into account. Theoretical analyses have been carried out to calculate the natural frequencies and mode shapes of the cracked cantilever beam using local stiffness matrices. Strain energy release rate has been used for calculating the local stiffness of the beam. The fuzzy inference system has been designed using the first three relative natural frequencies and mode shapes as input parameters. The output from the fuzzy controller is relative crack location and relative crack depth. Several fuzzy rules have been developed using the vibration signatures of the cantilever beam. A Neural Network technique using multi layered back propagation algorithm has been developed for damage assessment using the first three relative natural frequencies and mode shapes as input parameters and relative crack location and relative crack depth as output parameters. Several training patterns are derived for designing the Neural Network. A hybrid fuzzy-neuro intelligent system has been formulated for fault identification. The fuzzy controller is designed with six input parameters and two output parameters. The input parameters to the fuzzy system are relative deviation of first three natural frequencies and first three mode shapes. The output parameters of the fuzzy system are initial relative crack depth and initial relative crack location. The input parameters to the neural controller are relative deviation of first three natural frequencies and first three mode shapes along with the interim outputs of fuzzy controller. The output parameters of the fuzzy-neuro system are final relative crack depth and final relative crack location. A series of fuzzy rules and training patterns are derived for the fuzzy and neural system respectively to predict the final crack location and final crack depth.To diagnose the crack in the vibrating structure multiple adaptive neuro-fuzzy inference system (MANFIS) methodology has been applied. The final outputs of the MANFIS are relative crack depth and relative crack location. Several hundred fuzzy rules and neural network training patterns are derived using natural frequencies, mode shapes, crack depths and crack locations. The proposed research work aims to broaden the development in the area of fault detection of dynamically vibrating structures. This research also addresses the accuracy for detection of crack location and depth with considerably low computational time. The objective of the research is related to design of an intelligent controller for prediction of damage location and severity in a uniform cracked cantilever beam using AI techniques (i.e. Fuzzy, neural, adaptive neuro-fuzzy and Manfis)

Development of Self-Learning Type-2 Fuzzy Systems for System Identification and Control of Autonomous Systems

Modelling and control of dynamic systems are faced by multiple technical challenges, mainly due to the nature of uncertain complex, nonlinear, and time-varying systems. Traditional modelling techniques require a complete understanding of system dynamics and obtaining comprehensive mathematical models is not always achievable due to limited knowledge of the systems as well as the presence of multiple uncertainties in the environment. As universal approximators, fuzzy logic systems (FLSs), neural networks (NNs) and neuro-fuzzy systems have proved to be successful computational tools for representing the behaviour of complex dynamical systems. Moreover, FLSs, NNs and learning-based techniques have been gaining popularity for controlling complex, ill-defined, nonlinear, and time-varying systems in the face of uncertainties. However, fuzzy rules derived by experts can be too ad-hoc, and the performance is less than optimum. In other words, generating fuzzy rules and membership functions in fuzzy systems is a potential challenge especially for systems with many variables. Moreover, under the umbrella of FLSs, although type-1 fuzzy logic control systems (T1-FLCs) have been applied to control various complex nonlinear systems, they have limited capability to handle uncertainties. Aiming to accommodate uncertainties, type-2 fuzzy logic control systems (T2-FLCs) were established. This thesis aims to address the shortcomings of existing fuzzy techniques by utilisation of type-2 FLCs with novel adaptive capabilities. The first contribution of this thesis is a novel online system identification technique by means of a recursive interval type-2 Takagi-Sugeno fuzzy C-means clustering technique (IT2-TS-FC) to accommodate the footprint-of-uncertainties (FoUs). This development is meant to specifically address the shortcomings of type-1 fuzzy systems in capturing the footprint-of-uncertainties such as mechanical wear, rotor damage, battery drain and sensor and actuator faults. Unlike previous type-2 TS fuzzy models, the proposed method constructs two fuzzifiers (upper and lower) and two regression coefficients in the consequent part to handle uncertainties. The weighted least square method is employed to compute the regression coefficients. The proposed method is validated using two benchmarks, namely, real flight test data of a quadcopter drone and Mackey-Glass time series data. The algorithm has the capability to model uncertainties (e.g., noisy dataset). The second contribution of this thesis is the development of a novel self-adaptive interval type-2 fuzzy controller named the SAF2C for controlling multi-input multi-output (MIMO) nonlinear systems. The adaptation law is derived using sliding mode control (SMC) theory to reduce the computation time so that the learning process can be expedited by 80% compared to separate single-input single-output (SISO) controllers. The system employs the `Enhanced Iterative Algorithm with Stop Condition' (EIASC) type-reduction method, which is more computationally efficient than the `Karnik-Mendel' type-reduction algorithm. The stability of the SAF2C is proven using the Lyapunov technique. To ensure the applicability of the proposed control scheme, SAF2C is implemented to control several dynamical systems, including a simulated MIMO hexacopter unmanned aerial vehicle (UAV) in the face of external disturbance and parameter variations. The ability of SAF2C to filter the measurement noise is demonstrated, where significant improvement is obtained using the proposed controller in the face of measurement noise. Also, the proposed closed-loop control system is applied to control other benchmark dynamic systems (e.g., a simulated autonomous underwater vehicle and inverted pendulum on a cart system) demonstrating high accuracy and robustness to variations in system parameters and external disturbance. Another contribution of this thesis is a novel stand-alone enhanced self-adaptive interval type-2 fuzzy controller named the ESAF2C algorithm, whose type-2 fuzzy parameters are tuned online using the SMC theory. This way, we expect to design a computationally efficient adaptive Type-2 fuzzy system, suitable for real-time applications by introducing the EIASC type-reducer. The proposed technique is applied on a quadcopter UAV (QUAV), where extensive simulations and real-time flight tests for a hovering QUAV under wind disturbances are also conducted to validate the efficacy of the ESAF2C. Specifically, the control performance is investigated in the face of external wind gust disturbances, generated using an industrial fan. Stability analysis of the ESAF2C control system is investigated using the Lyapunov theory. Yet another contribution of this thesis is the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). T2-EFCS has two phases, namely, the structure learning and the parameters learning. The structure of T2-EFCS does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one rule. The rules are then added and pruned in an online fashion to achieve the desired set-point. The proposed technique is applied to control an unmanned ground vehicle (UGV) in the presence of multiple external disturbances demonstrating the robustness of the proposed control systems. The proposed approach turns out to be computationally efficient as the system employs fewer fuzzy parameters while maintaining superior control performance

Development of finite memory neural fuzzy networks for lag-free improved time series forecasting

Time series modelling/ forecasting is one of the most popular areas of research in the machine learning and data science community. It has widespread applications across various domains from different sectors such as energy demand prediction, weather forecasting, wind speed forecasting, stock price prediction, Exchange rate prediction, pandemic growth forecasting etc. to name a few and the list goes on. This ever-growing field of study has seen some significant improvements over the past few decades since its inception starting from the classical statistical methods such as Auto-Regressive Moving Average (ARMA). The recent advents in artificial neural network based deep learning algorithms have propelled this research to a new high. However, with ever increasing amount of data every hour of each day, there are always more challenges and improvements to be made in this field. This thesis addresses a few of the major challenges associated with time series modelling which are well known to the community. I also look at some of the problems which are relatively under-explored. One of the major known challenges of time series modelling is capturing the inherent temporal characteristics of the data. Most time series data are non-stationary in nature i.e. their statistical properties change over time. To model such data, it is of utmost importance to trace the underlying dynamics i.e. the temporal behavior. Another, big problem of time series modelling is to handle the uncertainty. Realworld time series data are often riddled with noise and volatility. Hence it is crucial to address the issue of uncertainty associated with such real-world data. Online learning from a time series data can also pose a novel issue as it requires the model to learn in a single epoch without any repetition. In the first two chapters, this thesis proposes two novel neuro-fuzzy systems to address these three challenges. A Spatio-Temporal Fuzzy Inference System (or SPATFIS) with memory type neurons is proposed first which retains all past information to capture the system dynamics. It utilizes a new self-adaptive learning mechanism to add, eliminate and unify its fuzzy rules which helps it to attain a parsimonious structure. At the same time, the linguistic nature of the fuzzy inference system makes it well capable of handling the uncertainty. SPATFIS also adopts a projection-based algorithm to update its parameters in a sequential manner thereby it is capable of online time series forecasting. However, when the system dynamics changes rapidly then memory neurons fail to adapt to the quickly changing dynamics (as they retain the effect of all past instances, thereby its output takes longer to get adjusted to a sudden shock). Therefore, it is very important to ensure that the temporal output is finite in nature and it is not depending on all pasts. The Neuro-Fuzzy Inference System with Dynamic Neurons (NFIS-DN) addresses the aforementioned problem. The proposed Dynamic Neuron (DN) is designed in such way, that its temporal output considers only the effect of finite past instances, enabling the system with finite memory. The benefits of dynamic neurons (DNs) become more apparent in areas where there is a sudden change in the system dynamics as commonly seen in non-linear dynamic system identification problems. However, there is one drawback to the implementation of DN. All the samples need to be present to perform an empirical test to choose the number of past instances required for the model (i.e. temporal order or temporality: N), thereby making this process offline in nature. Hence in case of an online learning scenario, this method of choosing N will not hold. Hence, a novel Bayesian method of online temporality analysis is proposed to estimate how many past instances a model requires for an improved time series forecasting; this results in finite memory. Temporality change or drift can be a common occurrence in online time series, hence a drift detection mechanism is also developed. The entire mechanism is termed as Learning Elastic Memory Online or LEMON. This method is agnostic of the underlying network or learning mechanism and can be utilized in any time series model. A neuro-fuzzy adaptation of LEMON is also developed by the name of Bayesian Neuro-Fuzzy Inference System (BaNFIS) to handle the problem of online temporality estimation and uncertainty handling simultaneously. NFIS-DN, LEMON, and BaNFIS, all three of these models utilize only finite past information (hence finite memory) within their respective neural fuzzy frameworks to provide superior prediction performance. Apart from the aforementioned challenges, there is one more challenge i.e. ‘Lag in predicted sequence’ which is often overlooked in the time series literature as it does not contribute to a high mean squared prediction error. Most neural network and neuro-fuzzy based time series models in literature (including proposed SPATFIS, NFIS-DN, LEMON and BaNFIS), trained with historical data alone can often lead to a lagged time series where the predicted sequence is always trailing the original sequence. This leads to poor forecast in terms of movement prediction. In the final chapter of this thesis a novel trend driven Dual Network Solution (DNS) is proposed. Trend, defined as the inherent pattern of the data, is extracted here and utilized next to perform lag-free forecasting. DNS exhibits a substantially improved performance compared to more complex and resource-intensive state-ofthe-art algorithms in large scale time series problems. Apart from the traditional Mean Squared Error (MSE), a new Movement Prediction Metric or MPM (for detection of lag in time series) is also developed as a new complementary performance metric to evaluate the efficacy of DNS better. The performance of each of these proposed methods is evaluated meticulously on several benchmark data sets as well as real-world problems with a main focus on energy demand prediction and wind speed forecasting along with financial indicator prediction. The superior performance of the proposed methods further indicates their applicability across domains, especially in the energy sector. These methods could be instrumental for producing better renewable energy, reducing energy wastage, better planning and grid management etc. for a sustainable earth. Overall, this thesis tackles several problems of time series forecasting, starting with the challenging tasks of capturing system dynamics, online learning and handling uncertainty of real-world data. It also addresses some under-explored issues of this domain including estimation of temporal order and the problem of lag. Future research in this domain, can benefit from this thesis and improve upon the presented methods to address other fundamental challenges of time series modellingDoctor of Philosoph