Method of Detection Abnormal Features in Ionosphere Critical Frequency Data on the Basis of Wavelet Transformation and Neural Networks Combination

Abstract

The research is focused on the development of automatic detection method of abnormal features, that occur in recorded time series of ionosphere critical frequency fOF2 during periods of high solar or seismic activity. The method is based on joint application of wavelet-transformation and neural networks. On the basis of wavelet transformation algorithms for the detection of features and estimation of their parameters were developed. Detection and analysis of characteristic components of time series are performed on the basis of joint application of wavelet transformation and neural networks. Method's approbation is performed on fOF2 data obtained at the observatory “Paratunka” (Paratunka settlement, Kamchatskiy Kray)

Method for modeling of the components of ionospheric parameter time variations and detection of anomalies in the ionosphere

“…A decrease in the |W Ψ f b,a | coefficient amplitudes depending on scale a is associated with the Lipschitz's uniform and dot smoothness of the Lipschitz function f (Daubechies 1992;Mallat 1999). According to the Zhaffar's theorem (Jaffard 1991;Mallat 1999), when a decreases, the amplitudes of the |W Ψ f b,a | coefficients rapidly decrease to zero where the function f is smooth and has no local features.…”

“…The wavelet basis was chosen among other orthogonal functions and allowed us to perform a numerically stable multiscale wavelet decomposition of the data (Daubechies 1992). To determine the type of orthogonal wavelet, we applied the criterion suggested by Mallat (1999), which allowed the minimization of the number of approximated summands and approximation error. In the dictionary D ¼ ∪ λ∈Λ W λ of orthonormal bases, the basis…”

“…As the latest research (Huang et al 1998;Odintsov et al 2000;Rilling 2003;Huang and Wu 2008;Klionsky et al 2008Klionsky et al , 2009Hamoudi et al 2009;Kato et al 2009;Yu et al 2010;Akyilmaz et al 2011;He et al 2011;Mandrikova et al 2012aMandrikova et al , 2012bMandrikova et al , 2014aGhamry et al 2013;Zaourar et al 2013) shows, the most natural and effective way of representing such data is the construction of non-linear adaptive approximating schemes. As a result, methods of empirical mode decomposition (Huang et al 1998;Rilling 2003;Klionsky et al 2008Klionsky et al , 2009Huang and Wu 2008;Yu et al 2010) and adaptive wavelet decomposition (Hamoudi et al 2009;Kato et al 2009;Akyilmaz et al 2011;He et al 2011;Mandrikova et al 2012aMandrikova et al , 2012bMandrikova et al , 2013aMandrikova et al , 2014aGhamry et al 2013;Zaourar et al 2013) are being intensively developed at present. Given the large variety of orthogonal basis wavelets with compact support and the presence of numerically stable fast algorithms for data transformation, wavelet decomposition provides many possibilities for the analysis of data with a complex structure (Chui 1992;Daubechies 1992;Mallat 1999), including geophysical data (Hamoudi et al 2009;...…”

“…The problems associated with the analysis of ionospheric conditions and detection of anomalies have been addressed by many authors (Bilitza and Reinisch 2007;Liu et al 2008aLiu et al , 2008bNakamura et al 2009;Maruyama et al 2011;Klimenko et al 2012aKlimenko et al , 2012bOyekola and Fagundes 2012;Watthanasangmechai et al 2012;Ezquer et al 2014;Zhao et al 2014). The main approaches include the traditional moving median method (Mikhailov et al 1999;Afraimovich et al 2000Afraimovich et al , 2001Kakinami et al 2010), ionosphere empirical models (Bilitza and Reinisch 2007;Nakamura et al 2009;Klimenko et al 2012b;Oyekola and Fagundes 2012;Watthanasangmechai et al 2012), the application of adaptive algorithms based on neural networks (Martin et al 2005;Nakamura et al 2007Nakamura et al , 2009Mandrikova et al 2012aMandrikova et al , 2012bWang et al 2013;Zhao et al 2014), and the wavelet transform (Hamoudi et al 2009;Kato et al 2009;Mandrikova et al 2012aMandrikova et al , 2012bMandrikova et al , 2013aMandrikova et al , 2014a. At present, the International Reference Ionosphere (IRI) model (Jee et al 2005;Bilitza and Reinisch 2007;Klimenko et al 2012b;Oyekola and Fagundes 2012) is t...…”

“…As a result, methods of empirical mode decomposition (Huang et al 1998;Rilling 2003;Klionsky et al 2008Klionsky et al , 2009Huang and Wu 2008;Yu et al 2010) and adaptive wavelet decomposition (Hamoudi et al 2009;Kato et al 2009;Akyilmaz et al 2011;He et al 2011;Mandrikova et al 2012aMandrikova et al , 2012bMandrikova et al , 2013aMandrikova et al , 2014aGhamry et al 2013;Zaourar et al 2013) are being intensively developed at present. Given the large variety of orthogonal basis wavelets with compact support and the presence of numerically stable fast algorithms for data transformation, wavelet decomposition provides many possibilities for the analysis of data with a complex structure (Chui 1992;Daubechies 1992;Mallat 1999), including geophysical data (Hamoudi et al 2009;Kato et al 2009;Akyilmaz et al 2011;He et al 2011;Mandrikova et al 2012aMandrikova et al , 2012bMandrikova et al , 2013aMandrikova et al , 2014aGhamry et al 2013;Zaourar et al 2013). In this paper, a multiscale wavelet decomposition (MSA) of an ionospheric parameter time series was used.…”