• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.1
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• pp.1-6
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• 2004

This paper deals with a balanced model reduction for T-S(Takagi-Sugeno) fuzzy systems with time varying state delay. We define a generalized controllability gramian and a generalized observability gramian for a stable T-S fuzzy delayed systems. We obtain a balanced state space realization using the generalized controllability and observability gramian and obtain a reduced model by truncating states from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability gramian and observability gramian can be computed from solutions of linear matrix inequalities. We demonstrate the efficacy of the suggested method by illustrating a numerical example.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.516-522
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• 2004

In this paper we investigate the properties of a generalized impulse response Gramian. The recursive relationship satisfied by the family of Gramians is established. It is shown that the generalized impulse response Gramian contains information on the characteristic polynomial of a linear time-invariant continuous system. The results are applied to model reduction problem.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.3
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• pp.183-191
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• 2021

Non-intrusive load monitoring is a technology that can be used for predicting and classifying the type of appliances through real-time monitoring of user power consumption, and it has recently got interested as a means of energy-saving. In this paper, we propose a system for classifying appliances from user consumption data by combining GAF(Gramian angular field) technique that can be used for converting one-dimensional data to the two-dimensional matrix with convolutional neural networks. We use REDD(residential energy disaggregation dataset) that is the public appliances power data and confirm the classification accuracy of the GASF(Gramian angular summation field) and GADF(Gramian angular difference field). Simulation results show that both models showed 94% accuracy on appliances with binary-state(on/off) and that GASF showed 93.5% accuracy that is 3% higher than GADF on appliances with multi-state. In later studies, we plan to increase the dataset and optimize the model to improve accuracy and speed.

• International Journal of Control, Automation, and Systems
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• v.2 no.3
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• pp.384-389
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• 2004

Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix$A_r$ of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices $b_r$ and $c_r$ are obtained so that various initial Markov parameters and time-moments of the original system are preserved in the reduced model. In this paper a different approach is presented based on the recursive relationship among the impulse response Gramians.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.571-583
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• 2012

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.6
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• pp.510-520
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• 1988

In this paper, the output error variance due to the differential vcariation of the state-space coefficient [ABCD], which is the coefficient quentization error, is normalized on the variance for cases that infinite wordlength state-space digital filter is realized by the finite one. That is, defining S as the statistical sensitivity and extending controllability gramian, observability gramian, and 2nd order mode analysis method to the state space digital filter, we synthesize the realization structure with the minimum statistical sensitivity and prove the effecency of the minimum statistical sensitivity structure synthesis by the simulation.

• Smart Structures and Systems
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• v.17 no.5
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• pp.773-793
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• 2016

This work presents a methodology to distribute piezoelectric material for structural vibration active control. The objective is to design controlled structures with actuators which maximizes the system controllability. A topology optimization was formulated in order to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material. The objective is the maximization of the smallest eigenvalue of the system controllability Gramian. Analytical sensitivities for the finite element model are derived for the objective functions and constraints. Results and comparisons with previous works are presented for the vibration control of a two-dimensional short beam.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.2
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• pp.144-149
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• 2006

This paper deals with a balanced model reduction for uncertain nonlinear systems via T-S fuzzy approach. We define a generalized controllability/observability gramian and obtain a balanced state space model using generalized gramians which can be obtained from solutions of linear matrix inequalities. We present a balanced model reduction scheme by truncating not only state variables but also uncertain elements. An upper bound of the model reduction error will also be suggested. In order to demonstrate the efficacy of our method, a numerical example will be presented.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.9
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• pp.909-917
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• 1992

This paper proposes the realization of state-space digital filters with minimum output error variance. The algorithm is transforms of controllability and observability gramian in linear time invariant systems by weighted function and can improve performance of the digital filters by reducing the put error variance for state space coeffient variation. A numerical example shows that algorithm structure has much lower output error variance than that of other four structures(canonical, parallel, statistical sensitivity, balanced).

• Smart Structures and Systems
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• v.29 no.1
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• pp.53-62
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• 2022

The deployment of advanced structural health monitoring (SHM) systems in large-scale civil structures collects large amounts of data. Note that these data may contain multiple types of anomalies (e.g., missing, minor, outlier, etc.) caused by harsh environment, sensor faults, transfer omission and other factors. These anomalies seriously affect the evaluation of structural performance. Therefore, the effective analysis and mining of SHM data is an extremely important task. Inspired by the deep learning paradigm, this study develops a novel generative adversarial network (GAN) and convolutional neural network (CNN)-based data anomaly detection approach for SHM. The framework of the proposed approach includes three modules : (a) A three-channel input is established based on fast Fourier transform (FFT) and Gramian angular field (GAF) method; (b) A GANomaly is introduced and trained to extract features from normal samples alone for class-imbalanced problems; (c) Based on the output of GANomaly, a CNN is employed to distinguish the types of anomalies. In addition, a dataset-oriented method (i.e., multistage sampling) is adopted to obtain the optimal sampling ratios between all different samples. The proposed approach is tested with acceleration data from an SHM system of a long-span bridge. The results show that the proposed approach has a higher accuracy in detecting the multi-pattern anomalies of SHM data.