Interval and Fuzzy Computing in Neural Network for System Identification Problems

Increase of population and growing of societal and commercial activities with limited land available in a modern city leads to construction up of tall/high-rise buildings. As such, it is important to investigate about the health of the structure after the occurrence of manmade or natural disasters such as earthquakes etc. A direct mathematical expression for parametric study or system identification of these structures is not always possible. Actually System Identification (SI) problems are inverse vibration problems consisting of coupled linear or non-linear differential equations that depend upon the physics of the system. It is also not always possible to get the solutions for these problems by classical methods. Few researchers have used different methods to solve the above mentioned problems. But difficulties are faced very often while finding solution to these problems because inverse problem generally gives non-unique parameter estimates. To overcome these difficulties alternate soft computing techniques such as Artificial Neural Networks (ANNs) are being used by various researchers to handle the above SI problems. It is worth mentioning that traditional neural network methods have inherent advantage because it can model the experimental data (input and output) where good mathematical model is not available. Moreover, inverse problems have been solved by other researchers for deterministic cases only. But while performing experiments it is always not possible to get the data exactly in crisp form. There may be some errors that are due to involvement of human or experiment. Accordingly, those data may actually be in uncertain form and corresponding methodologies need to be developed. It is an important issue about dealing with variables, parameters or data with uncertain value. There are three classes of uncertain models, which are probabilistic, fuzzy and interval. Recently, fuzzy theory and interval analysis are becoming powerful tools for many applications in recent decades. It is known that interval and fuzzy computations are themselves very complex to handle. Having these in mind one has to develop efficient computational models and algorithms very carefully to handle these uncertain problems. As said above, in general we may not obtain the corresponding input and output values (experimental) exactly or in crisp form but we may have only uncertain information of the data. Hence, investigations are needed to handle the SI problems where data is available in uncertain form. Identification methods with crisp (exact) data are known and traditional neural network methods have already been used by various researchers. But when the data are in uncertain form then traditional ANN may not be applied. Accordingly, new ANN models need to be developed which may solve the targeted uncertain SI problems. Hence present investigation targets to develop powerful methods of neural network based on interval and fuzzy theory for the analysis and simulation with respect to the uncertain system identification problems. In this thesis, these uncertain data are assumed as interval and fuzzy numbers. Accordingly, identification methodologies are developed for multistorey shear buildings by proposing new models of Interval Neural Network (INN) and Fuzzy Neural Network (FNN) models which can handle interval and fuzzified data respectively. It may however be noted that the developed methodology not only be important for the mentioned problems but those may very well be used in other application problems too. Few SI problems have been solved in the present thesis using INN and FNN model which are briefly described below. From initial design parameters (namely stiffness and mass in terms of interval and fuzzy) corresponding design frequencies may be obtained for a given structural problem viz. for a multistorey shear structure. The uncertain (interval/fuzzy) frequencies may then be used to estimate the present structural parameter values by the proposed INN and FNN. Next, the identification has been done using vibration response of the structure subject to ambient vibration with interval/fuzzy initial conditions. Forced vibration with horizontal displacement in interval/fuzzified form has also been used to investigate the identification problem. Moreover this study involves SI problems of structures (viz. shear buildings) with respect to earthquake data in order to know the health of a structure. It is well known that earthquake data are both positive and negative. The Interval Neural Network and Fuzzy Neural Network model may not handle the data with negative sign due to the complexity in interval and fuzzy computation. As regards, a novel transformation method have been developed to compute response of a structural system by training the model for Indian earthquakes at Chamoli and Uttarkashi using uncertain (interval/fuzzified) ground motion data. The simulation may give an idea about the safety of the structural system in case of future earthquakes. Further a single layer interval and fuzzy neural network based strategy has been proposed for simultaneous identification of the mass, stiffness and damping of uncertain multi-storey shear buildings using series/cluster of neural networks. It is known that training in MNN and also in INN and FNN are time consuming because these models depend upon the number of nodes in the hidden layer and convergence of the weights during training. As such, single layer Functional Link Neural Network (FLNN) with multi-input and multi-output model has also been proposed to solve the system identification problems for the first time. It is worth mentioning that, single input single output FLNN had been proposed by previous authors. In FLNN, the hidden layer is replaced by a functional expansion block for enhancement of the input patterns using orthogonal polynomials such as Chebyshev, Legendre and Hermite, etc. The computations become more efficient than the traditional or classical multi-layer neural network due to the absence of hidden layer. FLNN has also been used for structural response prediction of multistorey shear buildings subject to earthquake ground motion. It is seen that FLNN can very well predict the structural response of different floors of multi-storey shear building subject to earthquake data. Comparison of results among Multi layer Neural Network (MNN), Chebyshev Neural Network (ChNN), Legendre Neural Network (LeNN), Hermite Neural Network (HNN) and desired are considered and it is found that Functional Link Neural Network models are more effective and takes less computation time than MNN. In order to show the reliability, efficacy and powerfulness of INN, FNN and FLNN models variety of problems have been solved here. Finally FLNN is also extended to interval based FLNN which is again proposed for the first time to the best of our knowledge. This model is implemented to estimate the uncertain stiffness parameters of a multi-storey shear building. The parameters are identified here using uncertain response of the structure subject to ambient and forced vibration with interval initial condition and horizontal displacement also in interval form

An intelligent parameter varying (IPV) approach for non-linear system identification of base excited structures

Health monitoring and damage detection strategies for base-excited structures typically rely on accurate models of the system dynamics. Restoring forces in these structures can exhibit highly non-linear characteristics, thus accurate non-linear system identification is critical. Parametric system identification approaches are commonly used, but require a priori knowledge of restoring force characteristics. Non-parametric approaches do not require this a priori information, but they typically lack direct associations between the model and the system dynamics, providing limited utility for health monitoring and damage detection. In this paper a novel system identification approach, the intelligent parameter varying (IPV) method, is used to identify constitutive non-linearities in structures subject to seismic excitations. IPV overcomes the limitations of traditional parametric and non-parametric approaches, while preserving the unique benefits of each. It uses embedded radial basis function networks to estimate the constitutive characteristics of inelastic and hysteretic restoring forces in a multi-degree-of-freedom structure. Simulation results are compared to those of a traditional parametric approach, the prediction error method. These results demonstrate the effectiveness of IPV in identifying highly non-linear restoring forces, without a priori information, while preserving a direct association with the structural dynamics

Damage classification and estimation in experimental structures using time series analysis and pattern recognition

Peer reviewedPreprin

Structural health monitoring and damage detection using an intelligent parameter varying (IPV) technique

Most structural health monitoring and damage detection strategies utilize dynamic response information to identify the existence, location, and magnitude of damage. Traditional model-based techniques seek to identify parametric changes in a linear dynamic model, while non-model-based techniques focus on changes in the temporal and frequency characteristics of the system response. Because restoring forces in base-excited structures can exhibit highly non-linear characteristics, non-linear model-based approaches may be better suited for reliable health monitoring and damage detection. This paper presents the application of a novel intelligent parameter varying (IPV) modeling and system identification technique, developed by the authors, to detect damage in base-excited structures. This IPV technique overcomes specific limitations of traditional model-based and non-model-based approaches, as demonstrated through comparative simulations with wavelet analysis methods. These simulations confirm the effectiveness of the IPV technique, and show that performance is not compromised by the introduction of realistic structural non-linearities and ground excitation characteristics

Artificial neural network based numerical solution of ordinary differential equations

In this investigation we introduced the method for solving Ordinary Differential Equations (ODEs) using artificial neural network. The feed forward neural network of the unsupervised type has been used to get the approximation of the given ODEs up to the required accuracy without direct use of the optimization techniques. The problem is formulated in such a manner that it satisfies the initial/boundary conditions by its construction. The trail solution of the ODE is the sum of two terms. The first term satisfies the initial or boundary conditions, while the second one is the feed forward neural output produced by n number of inputs and h number of hidden sigmoid units. The error gradient has been reduced by applying general learning method to get the desired output.The results have been verified for different problems and the convergence of Artificial Neural Network (ANN) output has been checked for arbitrary points. It may be noted that the interpolation is also possible through this process. The advantage of neuron processor is that the output can be produced to any arbitrary accuracy, while the targets or exact results are unknown or hard to find out