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This research explores the intricate-coupling relationship between typhoons and the ionosphere by the high-frequency surface wave radar's (HFSWR) over-the-horizon capabilities. This letter describes the gravity wave features in travelling ionospheric disturbances (TIDs) and ionospheric drift information. Further discussion is raised on the chaotic properties of gravity wave features using the Lyapunov exponents and chaotic attractors, particularly as they are influenced by typhoon. To predict these gravity wave features more accurately, a new model is developed by synergizing phase space reconstruction theory and statistical learning theory, a chaotic prediction model for gravity wave features constructed on a third-order Volterra filter. The experimental findings confirm that the gravity waves features detected via HFSWR present the hyperchaotic behaviour. More importantly, the innovative gravity wave prediction model based on chaotic attractor can capture the dynamics of the original chaotic system. Notably, the model's prediction accuracy has been improved by 98.6% after the introduction of phase space reconstruction modelling. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the optimal control problem governed by linear parabolic equation with box constraints on control variables. We employ the Fenchel duality scheme to derive an unconstrained dual problem. Compared with the primal problem, the objective functional of the dual problem includes a projection onto the box constraints. We prove the existence and uniqueness of solutions to the dual problem and derive the first‐order optimality conditions. Furthermore, we investigate the saddle point property between the solutions of the primal problem and the solutions of the dual problem. To solve the dual problem, we design two implementable methods: the conjugate gradient method and the semi‐smooth Newton method. The solutions of the primal problem can be easily obtained through the solutions of the dual problem. We demonstrate the effectiveness and accuracy of the proposed methods by solving three example problems. [ABSTRACT FROM AUTHOR]

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

Ship detection has been an area of focus for high-frequency surface wave radar (HFSWR). The detection and identification of ship formation have proven significant in early warning, while studies on the formation identification are limited due to the complex background and low resolution of HFSWR. In this paper, we first establish a spatial distribution model of ship formation in HFSWR. Then, we propose a cascade identification algorithm of ship formation in the clutter edge. The proposed algorithm includes a preprocessing stage and a two-stage formation identification stage. The Faster R-CNN is introduced in the preprocessing stage to locate the clutter regions. In the first stage, we propose an extremum detector based on connected regions to extract suspicious regions. The suspicious regions contain ship formations, single-ship targets, and false targets. In the second stage, we design a network connected by a convolutional neural network (CNN) and an extreme learning machine (ELM) to identify two densely distributed ship formations from inhomogeneous clutter and single-ship targets. The experimental results based on the factual HFSWR background demonstrate that the proposed cascade identification algorithm is superior to the extremum detector combined with the classical CNN algorithm for ship formation identification. Meanwhile, the proposed algorithm performs well in weak formation and deformed formation identification. [ABSTRACT FROM AUTHOR]

This paper proposes a method for the intelligent detection of high-frequency surface wave radar (HFSWR) targets. This method cascades the adaptive constant false alarm (CFAR) detector variability index (VI) with the convolutional neural network (CNN) to form a cascade detector (VI)CFAR-CNN. First, the (VI)CFAR algorithm is used for the first-level detection of the range–Doppler (RD) spectrum; based on this result, the two-dimensional window slice data are extracted using the window with the position of the target on the RD spectrum as the center, and input into the CNN model to carry out further target and clutter identification. When the detection rate of the detector reaches a certain level and cannot be further improved due to the convergence of the CNN model, this paper uses a dual-detection maps fusion method to compensate for the loss of detection performance. First, the optimized parameters are used to perform the weighted fusion of the dual-detection maps, and then, the connected components in the fused detection map are further processed to achieve an independent (VI)CFAR to compensate for the (VI)CFAR-CNN detection results. Due to the difficulty in obtaining HFSWR data that include comprehensive and accurate target truth values, this paper adopts a method of embedding targets into the measured background to construct the RD spectrum dataset for HFSWR. At the same time, the proposed method is compared with various other methods to demonstrate its superiority. Additionally, a small amount of automatic identification system (AIS) and radar correlation data are used to verify the effectiveness and feasibility of this method on completely measured HFSWR data. [ABSTRACT FROM AUTHOR]

Investigating the dynamic evolution process of the ocean and ionosphere in sudden sea conditions poses a challenging problem. To address this objective, this study utilizes actual data from high-frequency surface wave radar (HFSWR) to analyze, validate, summarize, and characterize the echo properties of the ocean and ionosphere during the severe Typhoon Muifa. By employing the short-time Fourier transform (STFT) method, the HFSWR ocean and ionosphere echoes stimulated by typhoon-induced gravity waves are observed, and the joint gravity wave features of the ocean and ionosphere echoes at different time scales are extracted. Additionally, the phase-space reconstruction method is employed to characterize the dynamical evolution of the joint gravity wave features in higher-dimensional space. Furthermore, the chaotic dynamics behavior of the joint gravity wave features is analyzed using the largest Lyapunov exponents. By combining the gravity wave features with chaotic dynamics, this study introduces a method to characterize the joint gravity wave features. The extraction of joint gravity wave features in HFSWR echoes stimulated by typhoons, along with the construction of a chaotic characterization scheme for the gravity wave features, provides an innovative approach and a solid technical foundation for studying the ocean and ionosphere using HFSWR under sudden sea conditions. [ABSTRACT FROM AUTHOR]