Sk Satyajit Wattamwar

A Detection Algorithm for Bifurcations in Dynamical Systems Using Reduced Order Models

Abstract Finite element or finite volume discretizations of distributed parameter systems (DPS) typically lead to high order finite dimensional systems. Model approximation is then an important first step towards the construction of optimal controllers. However, model reduction methods hardly take model uncertainties and parameter variations into account. As such, reduced order models are not well equipped when uncertain system parameters vary in time. This is particularly true when system behavior does not depend continuously on the parameters. It is shown in this paper that the performance of reduced order models inferred from Galerkin projections and proper orthogonal decompositions can deteriorate considerable when system parameters vary over bifurcation points. Motivated by these observations, we propose a detection mechanism based on reduced order models and proper orthogonal decompositions that allows to characterize the influence of parameter variations around a bifurcation value. for this, a hybrid model structure is proposed. The ideas are applied on the example of a tubular reactor. In particular, this paper discusses the difficulties in approximating the transition from extinction to ignited state in a tubular reactor.

Identification of Low Order Tensorial Models for Tubular Reactors

Abstract In this paper we propose a novel procedure for obtaining a low order model of a large scale, non-linear process. The method is of generic nature. The efficiency of the proposed approach is illustrated on a benchmark example depicting industrial tubular reactor which are often used in petrochemical industries. The results show good performance of the proposed method. Our approach is based on the combinations of the methods of Proper Orthogonal Decomposition ( POD ), and non-linear System Identification techniques. It is showed here that the modal coefficient corresponding to the spectral decomposition of the system solutions can be viewed as the states of the reduced model. This has paved a way to propose a novel model reduction strategy for large scale systems. In the first step the spectral decomposition of system solutions is used to separate the spatial and temporal patterns (time varying modal coefficients) and in the second step a reduced model structure and its parameters; linear and of non-linear tensorial (multivariable polynomial) type are identified for approximating the temporal patterns obtained by the spectral decomposition. The state space matrices which happens to be the parameters of a black-box to be identified, appears linearly in the identification process. For the same reason, Ordinary Least Square method is used to identify the model parameters. The simplicity and reliability of proposed method gives computationally very efficient linear and non-linear low order models for large scale processes. The novel method also allows the way to compensate the mismatch between real plant and the reduced model outputs.

Identification of Low Order Parameter Varying Models for Large Scale Systems

Abstract In this paper we propose a novel procedure for obtaining reduced dimensional models of large scale multi-phase, non-linear, reactive fluid flow systems with geometric parameter uncertainty (corrosion). Our approach is based on the combinations of methods of Proper Orthogonal Decomposition ( POD ), black box System Identification ( SID ) techniques and nonlinear spline based blending of local black box models to create Reduced Order Linear Parameter Varying ( RO-LPV ) model. The proposed method gives computationally very efficient reduced dimension models for processes with parameter uncertainty. The efficiency of proposed approach is illustrated on a benchmark problem depicting industrial Glass Manufacturing Process ( GMP ) with corrosion of refractory materials as a process parameter uncertainty. The results show good performance of the proposed method.

Identification of low dimensional models for slow geometric parameter variation in an Industrial Glass Manufacturing Process

In this paper we apply the method of Proper Orthogonal Decomposition (POD) to identify a lower dimensional model of a benchmark problem representing an Industrial Glass Manufacturing Process (IGMP). In particular, we identify a reduced model by identifying the mapping from process inputs to POD modal coefficients by a subspace identification method. Reduced models obtained from POD are not well equipped to capture the process behavior under time varying uncertain process parameters. For this reason we propose a novel hybrid detection scheme which approximates the process (benchmark CFD model) exhibiting non-smooth geometric parameter dependence (corrosion and wear) by using lower dimensional models. Given state or output information this detection mechanism detects the process parameter operation regime and suggests a computationally faster lower dimensional model as an approximate for real process.