Dr Shifali Kalra

2015-2020

In many application areas, experimental analysis are been increasingly replaced by numerical simulations in order to save design and development costs. However, modelling physical systems accurately often result into large order dynamical systems that are computationally heavy to simulate. Thus, approximation becomes important in order to have cost-effective simulation. There are different model order reduction (MOR) techniques that can be used to reduce the order of large dynamical systems. MOR results in a system that is dimensionally reduced and has input-output characteristics almost similar to the large order original system. MOR techniques have been widely used by many researchers across disciplines to successfully reduce large order systems. There are different MOR techniques depending upon the type of system. The two broad categories of MOR techniques for linear systems are based on singular value decomposition (SVD) and on Krylov subspaces. Similarly, there are quite a few MOR techniques that are used for nonlinear systems like proper orthogonal decomposition (POD), trajectory piecewise linear approximation (TPWL) etc. The focus of this thesis is on TPWL and its variants. The TPWL method involves first selection of few linearisation points (LPs) on the system trajectory. The system is then locally linearised at those LPs and reduced using linear MOR technique. The weighted summation of the reduced models is done to obtain the final TPWL approximation. Although TPWL and its variants are very popular among researchers and are widely used as nonlinear order reducing tools, they possess some issues especially with the LP selection that needs attention. Selection of LPs is a crucial step as it decides the effectiveness of the overall approximation. The quality of the approximation does not always depend upon the number of the LPs only but also on the correct placement of LPs on the system trajectory. The conventional approach of deciding the LPs included the uniform division of the system trajectory at a constant preselected distance, often resulting into inadequate sampling. Moreover, the user defined thresholds make the approximation heuristic in nature. The major concern of this thesis focuses on identifying issues related to the conventional LP selection in TPWL and addressing them by proposing new criteria that are capable of judiciously placing LPs on the system trajectory thereby generating better approximations. Later in the thesis, criteria is proposed that not only removes the ambiguity associated with the TPWL method, but also generates better approximations with far less number of sub-models. The proposed schemes have been tested and simulated on few nonlinear circuits including transmission line circuit, RC ladder network and inverter chain circuit.

Publications

Journals

• Shifali Kalra and M. Nabi, "A global maximum error controller based nonlinearity aware TPWL method for reducing nonlinear systems" Cybernetics and Systems, (Taylor & Francis), vol. 51 (4), pp. 370-382, 2020.


• S. Kalra and M. Nabi, "Automated scheme for linearisation points selection in TPWL method applied to non-linear circuits," IET-The Journal of Engineering, vol. 2020, no. 1, pp. 41-49, 1 2020.


• S. Kalra and M. Nabi, "TPWL Simulation of Large Nonlinear Circuits Using Subspace Angle-Based Adaptive Sampling, " IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 3, pp. 575-579, March 2020.

Conferences

• Shifali Kalra, M. Nabi "Effect of reduced model order on accuracy of trajectory piecewise linear approximations for a class of nonlinear circuits", 28th Mediterranean Conference on Control and Automation (MED), 15-18 September 2020, Saint-Raphael, France.


• Shifali Kalra, M. Nabi,"Reduced Order Modelling of Inverter Chain Circuit using Nonlinearity Aware TPWL", 6th International Conference on Control, Decision and Information Technologies (CoDiT 2019), Paris, France, April 23-26,2019.


• Shifali Kalra, M. Nabi,"Reduced Modelling of Transmission Line Circuits using a Novel Nonlinearity Aware TPWL with Adaptive Sampling", 6th International Conference on Control, Decision and Information Technologies (CoDiT 2019), Paris, France, April 23-26,2019.


• Ammu Chathukulam, Shifali Kalra, Debashree Sarkar, M. Nabi ,"Improved TPWL Based Nonlinear MOR For Fast Simulation Of Large Circuits", 32nd European Conference on Modelling and Simulation, Wilhelmshaven, Germany 22-25 May 2018.

Outside the Thesis:


• Shifali Kalra, M. Nabi, "Finite element modelling of pacemaker electrode for time varying excitation", 32nd European Conference on Modelling and Simulation, Wilhelmshaven, Germany 22-25 May 2018.


• Shifali Kalra, M. Nabi, "Implantable Bio-MEMS Applications: A Review", 2nd International Conference on Recent Developments in Control, Automation & Power Engineering (RDCAPE 2017), Noida, UP, India, 26-27 October 2017.


• Shifali Kalra, M. Nabi, "Study of Stent Deformation using Finite Element Method", 11th International Conference on Industrial and Information Systems (ICIIS 2016), Roorkee, Uttarakhand, India, 3-4 December 2016.