Nonlinear dynamic numerical analysis and prediction of complex system based on bivariate cycling time stochastic differential equation

Remote sensing image analysis and prediction based on improved Pix2Pix model for water environment protection of smart cities

“…The prediction models based on sensor numerical data are mainly divided into two categories: mathematical-statistical methods and artificial intelligence methods. Mathematical statistical models are more generalizable than mechanistic models but do not apply to systems with significant nonlinearity ( Wang et al, 2020b ; Wang et al, 2019a ); artificial intelligence models include both traditional machine learning and deep learning methods. Traditional machine learning has shown strong self-learning and self-adaptive capabilities when dealing with nonlinear problems such as water environment pollution ( Feki-Sahnoun et al, 2020 ; Juan Wu et al, 2020 ; Yajima & Derot, 2018 ), and is suitable for complex nonlinear systems ( Wang et al, 2019b ), but still requires manual feature setting and is not suitable for learning large amounts of data ( Kashyap et al, 2022 ; Wang et al, 2019b ; Ying, 2022 ); while deep learning is a type of representation learning, it is capable of learning a higher level of abstract representation of data and automatically extracting deep features from the data ( LeCun, Bengio & Hinton, 2015 ), and the model capability grows exponentially with increasing depth ( Dong, Wang & Abbas, 2021 ).…”

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

“…Therefore, time-series modeling and forecasting methodology have attracted significant attention in the communities of knowledge engineering, data-based science, and artificial intelligence community, etc. [4][5][6][7] During the past few decades, to model nonlinearity of stochastic time-series accurately, tremendous types of prognostic methods/models/algorithms/techniques are reported, for example, some prognostic methods that focus on single-channel data such as autoregressive integrated moving average (ARIMA), 8,9 long-range dependence, 10,11 fractional Brownian motion, 12,13 particle filter (PF), 14,15 stochastic differential equation, 16 but they ignore the mutual information (e.g., shaft centerline orbit) and spatial statistical properties (e.g., autocorrelation coefficient) between each channel and have obvious insufficiency in dealing with hyperdimension signals. Fortunately, instead of treating each dimensional data individually, issues aforementioned can be alleviated via some prognostic methods that focus on multichannel data, for example, neural networks (NNs), 17,18 multilayer perceptron networks, 19 deep neural networks, 20,21 have been reported currently.…”