Data-driven methods for complex electromagnetic analysis

Abstract

In modern research, scientists from diverse disciplines have obtained abundant data sets due to advanced experimental and simulation techniques. Data-driven methods have attracted a lot of attentions, which is expected to discover applicable value from the data. As a complement to conventional numerical and empirical approaches, these data-driven schemes have been considered as a new practical solution to real-world problems. These motivated us to explore the state-of-art data-driven methods to advance complex electromagnetic analysis methodologies in this dissertation.

Firstly, a novel data-driven characterization method is proposed to analyze the electromagnetic (EM) radiations from both linear and nonlinear circuits. It employs the dynamic mode decomposition (DMD) to simultaneously extract the temporal patterns and their corresponding dynamic modes. The temporal patterns show high order harmonics generated by the circuit's nonlinearity. These spatial-temporal coherent patterns provide the physical meaning of the radiation and the fast prediction of future states in circuits and EM systems.

Secondly, we propose a modified DMD approach to analyze the orbital angular momentum (OAM) modes. The accurate topological charges and high-resolution amplitude patterns of both single OAM mode and composite OAM modes can be obtained simultaneously. Then, to address OAM beam divergence and misalignment challenges, we develop a novel hybrid algorithm based on the differential evolution (DE) and the modified DMD method to extract characteristics of vortex beams with a partial receiving aperture~(PRA) at arbitrary locations. Besides, we propose a novel partial arc sampling receiving~(PASR) scheme based on the augmented dynamic mode decomposition~(ADMD) for the OAM demultiplexing in the wireless communication system. Also, to sort superposed OAM modes in a boisterous environment, we develop an antinoise dynamic mode decomposition (AN-DMD) approach, which has high accuracy and stability in noisy conditions with the whole aperture receiving (WAR) and PAR.

Thirdly, we propose a novel data-driven method based on the DMD to detect, reconstruct, and locate the Kelvin wake on the two-dimensional dynamic sea surface. The sea's dynamic characteristics, including the oscillation frequency and decay/growth rate of ship wakes and the time-varying sea surface, can be obtained through the proposed method. Meanwhile, the spatial features of ship wakes can be derived by dynamic modes as well. The proposed method can distinguish the dynamic characteristics between the Kelvin wake and sea background. Then the corresponding modes of the Kelvin wake can be successfully identified. Besides, a data-driven method based on the Koopman mode decomposition (KMD) is proposed for modelling spatial-temporal correlated complex sea clutter. The method decomposes the coherent sea clutter dynamic behaviour in terms of Koopman modes and corresponding temporal patterns. These spatiotemporal patterns are used to construct the sea clutter state over time according to the approximate solution.

Finally, we propose a novel data-driven approach for deriving the governing partial differential equations based on the spatial-temporal samples of current and voltage in the transmission line system. The proposed method is based on the ridge regression algorithm to determine the active spatial differential terms from the candidate library that includes nonlinear functions, in which the time and spatial derivatives are estimated by using polynomial interpolation.

The above proposed data-driven methods are demonstrated by corresponding examples. The accuracy, efficiency, and robustness of these methods are clearly observed.