Orthogonalized Fourier Polynomials for Signal Approximation and Transfer

In this study, the application of an intelligent digital twin integrated with machine learning for bearing anomaly detection and crack size identification will be observed. The intelligent digital twin has two main sections: signal approximation and intelligent signal estimation. The mathematical vibration bearing signal approximation is integrated with machine learning-based signal approximation to approximate the bearing vibration signal in normal conditions. After that, the combination of the Kalman filter, high-order variable structure technique, and adaptive neural-fuzzy technique is integrated with the proposed signal approximation technique to design an intelligent digital twin. Next, the residual signals will be generated using the proposed intelligent digital twin and the original RAW signals. The machine learning approach will be integrated with the proposed intelligent digital twin for the classification of the bearing anomaly and crack sizes. The Case Western Reserve University bearing dataset is used to test the impact of the proposed scheme. Regarding the experimental results, the average accuracy for the bearing fault pattern recognition and crack size identification will be, respectively, 99.5% and 99.6%.

Download Full-text

New Orthogonal Transforms for Signal and Image Processing

Applied Sciences ◽

10.3390/app11167433 ◽

2021 ◽

Vol 11 (16) ◽

pp. 7433

Author(s):

Andrzej Dziech

Keyword(s):

Symmetric Matrix ◽

Sparse Matrices ◽

Orthogonal Expansion ◽

Orthogonal Matrices ◽

Exponential Form ◽

Orthogonal Transforms ◽

Hadamard Transforms ◽

The Given ◽

Transform Domains ◽

Signal Approximation

In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having an exponential form is also presented. Orthogonal basis functions based on the created matrices can be used for orthogonal expansion leading to signal approximation. An exponential form of orthogonal, sparse matrices with variable parameters is also created. Various versions of orthogonal transforms related to the created full and sparse matrices are proposed. Fast computation of the presented transforms in comparison to fast algorithms of selected orthogonal transforms is discussed. Possible applications for signal approximation and examples of image spectrum in the considered transform domains are presented.

Download Full-text

Dynamics of the Deep Solar Photosphere at Subgranular Scales

Symposium - International Astronomical Union ◽

10.1017/s0074180900239156 ◽

1998 ◽

Vol 185 ◽

pp. 451-452

Author(s):

A. Nesis ◽

R. Hammer ◽

M. Kiefer ◽

H. Schleicher

Keyword(s):

Granular Flow ◽

Approximation Property ◽

High Spatial Resolution ◽

Time Span ◽

Solar Photosphere ◽

Vacuum Tower ◽

Solar Granulation ◽

Wavelet Techniques ◽

The Relationship ◽

Signal Approximation

Extending our previous studies of the dynamics of solar granulation (Nesis et al., 1997) we investigated the relationship between granular flow and the emergence of turbulence in the deep photosphere. Our main goal is to explore if such a relationship exists, and if so, to define it quantitatively. To this end we take advantage of the excellent signal approximation property of wavelets. The material for the present work is a series of spectrograms of high spatial resolution covering a time span of 12 min. They were taken at the center of the solar disk with the German Vacuum Tower Telescope in Izaña (Tenerife, Spain) in 1994, and include several absorption lines of different strengths; for more details see Nesis et al. (1997). The spectrograms were digitized and processed with wavelet techniques and regression analysis, in order to investigate the granular convective flow, the associated turbulence, and their mutual connection.

Download Full-text

Bearing Fault Identification Using Machine Learning and Adaptive Cascade Fault Observer

Applied Sciences ◽

10.3390/app10175827 ◽

2020 ◽

Vol 10 (17) ◽

pp. 5827 ◽

Cited By ~ 1

Author(s):

Farzin Piltan ◽

Jong-Myon Kim

Keyword(s):

Machine Learning ◽

Learning Algorithm ◽

Hybrid Procedure ◽

Second Step ◽

Fault Identification ◽

Support Vector ◽

Bearing Fault ◽

Adaptive Technique ◽

Fuzzy Like ◽

Signal Approximation

In this work, a hybrid procedure for bearing fault identification using a machine learning and adaptive cascade observer is explained. To design an adaptive cascade observer, the normal signal approximation is the first step. Therefore, the fuzzy orthonormal regressive (FOR) technique was developed to approximate the acoustic emission (AE) and vibration (non-stationary and nonlinear) bearing signals in normal conditions. After approximating the normal signal of bearing using the FOR technique, the adaptive cascade observer is modeled in four steps. First, the linear observation technique using a FOR proportional-integral (PI) observer (FOR-PIO) is developed. In the second step, to increase the power of uncertaintie rejection (robustness) of the FOR-PIO, the structure procedure is used serially. Next, the fuzzy like observer is selected to increase the accuracy of FOR structure PI observer (FOR-SPIO). Moreover, the adaptive technique is used to develop the reliability of the cascade (fuzzy-structure PI) observer. Additionally to fault identification, the machine-learning algorithm using a support vector machine (SVM) is recommended. The effectiveness of the adaptive cascade observer with the SVM fault identifier was validated by a vibration and AE datasets. Based on the results, the average vibration and AE fault diagnosis using the adaptive cascade observer with the SVM fault identifier are 97.8% and 97.65%, respectively.

Download Full-text