Faculty Publications
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Item Anomaly Detection in Electric Powertrain System Software Behaviour(Institute of Electrical and Electronics Engineers Inc., 2023) Vyas, A.; Ghorpade, V.; Kamble, S.; Johnson, P.S.; Kamath, A.; Rawat, K.A software-in-loop (SIL) testing is a method of early testing of control software of a car in virtual environment. A system level testing is carried out on regular basis and it is important to see, if system is behaving as expected or unexpected. For unexpected behaviors, which test engineers not easily notice, modern techniques such as machine learning can give an advantage. This paper presents an application of machine learning algorithms that helps in identifying the abnormal patterns in time series data generated from electric powertrain system testing done in SIL environment for a Mercedes Benz Electric Car. Output of the SIL testing, results in time series data that is a collection of observations that are ordered chronologically and can be used to analyze trends, patterns, and changes over time. Anomaly detection in time series data is a process in machine learning that identifies data points, events, and observations that deviate from a dataset's normal behavior. By monitoring the expected and unexpected behavior of the electric powertrain system, anomaly detection can be a valuable tool for identifying potential issues. This study aims at coming up with an efficient process for anomaly detection in SIL. In order to get this process, various anomaly detection techniques are compared to detect a defined anomaly in time series data. Data pre-processing methods are also discussed before training the model. At the end, we conclude a best-fit method for identified anomaly. With finally identified method, a model was trained and used further in application. © 2023 IEEE.Item Hyers-Ulam stability of linear operators in Frechet spaces(2012) Johnson, P.S.; Balaji, S.Hyers-Ulam stability of a linear operator between Frechet spaces is defined. Necessary and sufficient conditions for the existence of Hyers-Ulam stability of a continuous linear operator from a Frechet space to another Frechet space are given. © 2012 NSP Natural Sciences Publishing Cor.Item On semiclosed subspaces of Hilbert spaces(2012) Johnson, P.S.; Balaji, S.Semiclosed subspaces possess many special features that distinguish them from arbitrary subspaces. Few properties of proper dense semiclosed subspaces of Hilbert spaces are discussed. © 2012 Academic Publications, Ltd.Item Class of bounded operators associated with an atomic system(Tamkang University editor@staff.tku.edu.tw, 2015) Johnson, P.S.; Ramu, G.K-frames, more general than the ordinary frames, have been introduced by Laura G?vru?a in Hilbert spaces to study atomic systems with respect to a bounded linear operator. Using the frame operator, we find a class of bounded linear operators in which a given Bessel sequence is an atomic system for every member in the class.Item Frame operators of K-frames(Springer Nature, 2016) Ramu, G.; Johnson, P.S.A close relation between frames on a separable Hilbert space H and positive invertible bounded operators is known. In this paper, it is shown that for a bounded operator K on H, there is a relationship between K-frames and quotient operators. Results on K-frames have been proved through operator-theoretic results on quotient of bounded operators. © 2016, Sociedad Española de Matemática Aplicada.Item Frames for Operators in Banach Spaces(Springer New York LLC barbara.b.bertram@gsk.com, 2017) Ramu, R.; Johnson, P.S.A family of local atoms in a Banach space has been introduced and it has been generalized to an atomic system for operators in Banach spaces, which has been further led to introduce new frames for operators by Dastourian and Janfada, by making use of semi-inner products. Unlike the traditional way of considering sequences in the dual space, sequences in the original space are considered to study them. Appropriate changes have been made in the definitions of atomic systems and frames for operators to fit them for sequences in the dual space without using semi-inner products so that the new notion for Banach spaces can be thought of as a generalization of Banach frames. With some crucial assumptions, we show that frames for operators in Banach spaces share nice properties of frames for operators in Hilbert spaces. © 2017, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.Item Construction of Mercedes–Benz Frame in R n(Springer, 2017) Parvathalu, B.; Johnson, P.S.In this article, Mercedes–Benz (MB) frame having 3 vectors in R 2 is generalized to the space R n with n+ 1 vectors through a complete concrete method. A necessary and sufficient condition for a normed tight frame to be an MB frame is given and MB frame is explored with the help of diagram vectors. In a new approach, it has been proved that there is no MB frame in R n with more than n+ 1 vectors and there is always an equiangular tight frame for every n? 2 , using MB frame. © 2017, Springer India Pvt. Ltd.Item Product and factorization of hypo-EP operators(De Gruyter peter.golla@degruyter.com, 2018) Johnson, P.S.; Vinoth, A.In this article, we derive some necessary and sufficient conditions for the product of hypo-EP operators to be hypo-EP and we characterize hypo-EP operators through factorizations. © by P. Sam Johnson and A. Vinoth, published by De Gruyter 2018.Item Quotient operators and the open mapping theorem(University of Nis filomat@pmf.ni.ac.rs, 2018) Mahesh Krishna, K.; Johnson, P.S.Quotients of bounded operators on normed spaces have been discussed. Open mapping theorem for quotients of bounded operators and its consequences are given. © 2018, University of Nis. All rights reserved.Item Convergence of operators with closed range(Tusi Mathematical Research Group (TMRG) moslehian@memeber.ams.org, 2019) Johnson, P.S.; Balaji, S.Izumino has discussed a sequence of closed range operators (Tn) that converges to a closed range operator T on a Hilbert space to establish the convergence of Tn† ? T† for Moore-Penrose inverses. In general, if Tn ? T uniformly and each Tn has a closed range, then T need not have a closed range. Some sufficient conditions have been discussed on Tn and T such that T has a closed range whenever each Tn has a closed range. © 2019 Khayyam Journal of Mathematics.