The Stability Criterion and Stability Analysis of Three-Phase Grid-Connected Rectifier System Based on Gerschgorin Circle Theorem

Xie, Lingling; Huang, Jiajia; Tan, Enkun; He, Fangzheng; Liu, Zhi-Pei

doi:10.3390/electronics11203270

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…This approach not only simplifies the understanding of a matrix’s spectral properties but also requires fewer computational operations compared to other eigenvalue estimation methods ( Varga, 2010 ). As a result, the GC theorem has found extensive applications across various fields, such as stability analysis of nonlinear systems ( Ortega Bejarano et al, 2018 ), power grids ( Xie et al, 2022 ), and graph sampling ( Wang et al, 2020 ), demonstrating its versatility and effectiveness. Furthermore, subsequent advancements have refined the theorem, enhancing the precision of the eigenvalue inclusions and bringing them closer to the actual eigenvalues of a matrix.…”

Section: Introductionmentioning

confidence: 99%

Gershgorin circle theorem-based feature extraction for biomedical signal analysis

Patel,

Smith,

Yildirim

2024

Front. Neuroinform.

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Recently, graph theory has become a promising tool for biomedical signal analysis, wherein the signals are transformed into a graph network and represented as either adjacency or Laplacian matrices. However, as the size of the time series increases, the dimensions of transformed matrices also expand, leading to a significant rise in computational demand for analysis. Therefore, there is a critical need for efficient feature extraction methods demanding low computational time. This paper introduces a new feature extraction technique based on the Gershgorin Circle theorem applied to biomedical signals, termed Gershgorin Circle Feature Extraction (GCFE). The study makes use of two publicly available datasets: one including synthetic neural recordings, and the other consisting of EEG seizure data. In addition, the efficacy of GCFE is compared with two distinct visibility graphs and tested against seven other feature extraction methods. In the GCFE method, the features are extracted from a special modified weighted Laplacian matrix from the visibility graphs. This method was applied to classify three different types of neural spikes from one dataset, and to distinguish between seizure and non-seizure events in another. The application of GCFE resulted in superior performance when compared to seven other algorithms, achieving a positive average accuracy difference of 2.67% across all experimental datasets. This indicates that GCFE consistently outperformed the other methods in terms of accuracy. Furthermore, the GCFE method was more computationally-efficient than the other feature extraction techniques. The GCFE method can also be employed in real-time biomedical signal classification where the visibility graphs are utilized such as EKG signal classification.

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Section: Introductionmentioning

confidence: 99%

Gershgorin circle theorem-based feature extraction for biomedical signal analysis

Patel,

Smith,

Yildirim

2024

Front. Neuroinform.

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“…The GC theorem estimates an eigenvalue inclusion of a given square matrix. The GC theorem has been used in several diverse applications, such as stability analysis of nonlinear systems [15], graph sampling in Graph theory [16], and evaluating the stability of power grids [17]. Over time, several extensions of the GC theorem have provided a better close estimation of eigenvalue inclusion of matrices [18,19].…”

Section: Introductionmentioning

confidence: 99%

Overcoming Dimensionality Constraints: A Gershgorin Circle Theorem-Based Feature Extraction for Weighted Laplacian Matrices in Computer Vision Applications

Patel,

Yildirim

2024

J. Imaging

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In graph theory, the weighted Laplacian matrix is the most utilized technique to interpret the local and global properties of a complex graph structure within computer vision applications. However, with increasing graph nodes, the Laplacian matrix’s dimensionality also increases accordingly. Therefore, there is always the “curse of dimensionality”; In response to this challenge, this paper introduces a new approach to reducing the dimensionality of the weighted Laplacian matrix by utilizing the Gershgorin circle theorem by transforming the weighted Laplacian matrix into a strictly diagonal domain and then estimating rough eigenvalue inclusion of a matrix. The estimated inclusions are represented as reduced features, termed GC features; The proposed Gershgorin circle feature extraction (GCFE) method was evaluated using three publicly accessible computer vision datasets, varying image patch sizes, and three different graph types. The GCFE method was compared with eight distinct studies. The GCFE demonstrated a notable positive Z-score compared to other feature extraction methods such as I-PCA, kernel PCA, and spectral embedding. Specifically, it achieved an average Z-score of 6.953 with the 2D grid graph type and 4.473 with the pairwise graph type, particularly on the E_Balanced dataset. Furthermore, it was observed that while the accuracy of most major feature extraction methods declined with smaller image patch sizes, the GCFE maintained consistent accuracy across all tested image patch sizes. When the GCFE method was applied to the E_MNSIT dataset using the K-NN graph type, the GCFE method confirmed its consistent accuracy performance, evidenced by a low standard deviation (SD) of 0.305. This performance was notably lower compared to other methods like Isomap, which had an SD of 1.665, and LLE, which had an SD of 1.325; The GCFE outperformed most feature extraction methods in terms of classification accuracy and computational efficiency. The GCFE method also requires fewer training parameters for deep-learning models than the traditional weighted Laplacian method, establishing its potential for more effective and efficient feature extraction in computer vision tasks.

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“…These analysis techniques rely on the basic principles. These principles and techniques can be applied to different types of circuits used in a diverse range of applications [23]. In addition to these fundamental techniques, there are a number of theorems which are available for circuit analysis.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of an RL Circuit Transient Response under Inductor Failure Conditions

et al. 2022

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We apply probability theory for the analysis of the exponentially decaying transient response of a resistor inductor electric circuit with partially known value of the inductance due to its failure. The inductance is known to be within a continuous interval, and the exact value is unknown, which may happen as a result of inductor faults due to a variety of factors—for example, when the circuit is deployed in an unusually harsh environment. We consider the inductance as a continuous uniform random variable for our analysis, and the transient voltage is treated as a derived random variable which is a function of the inductance random variable. Using this approach, a probability model of the transient voltage at the output terminals of the circuit is derived in terms of its cumulative distribution function and the probability density function. In our work, we further elaborate that the probability model of any other circuit parameter can also be obtained in a similar manner, or it can be derived from the transient voltage probability model. This is demonstrated by getting the model of a branch current from the probability distribution of the transient voltage. Usage of the probability model is demonstrated with the help of examples. The probability of the transient voltage falling in a certain interval at a given instant of time is evaluated. Similarly, the probability values of the branch current in different intervals are determined and analyzed. The derived probability model is checked for its validity and correctness as well. The model is found to be useful for probabilistic analysis of the circuit.

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The Stability Criterion and Stability Analysis of Three-Phase Grid-Connected Rectifier System Based on Gerschgorin Circle Theorem

Cited by 6 publications

References 23 publications

Gershgorin circle theorem-based feature extraction for biomedical signal analysis

Gershgorin circle theorem-based feature extraction for biomedical signal analysis

Overcoming Dimensionality Constraints: A Gershgorin Circle Theorem-Based Feature Extraction for Weighted Laplacian Matrices in Computer Vision Applications

Probabilistic Analysis of an RL Circuit Transient Response under Inductor Failure Conditions

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