Robust Randomized Neural Networks for Antenna Application

Abstract

Randomized neural networks (RandNNs) are a class of single-hidden layer feedforward networks (SLFNs). Compared with classic SLFNs, the weights connecting the input and hidden layers in the RandNN model are randomly assigned and fixed during training. As a result, only the weights between the hidden and output layers are trainable. This structure preserves the strong approximation capabilities of traditional SLFNs while offering increased simplicity, higher computational efficiency, and avoidance of local minima. Inspired by the RandNN framework, models such as the random vector functional link (RVFL) network and the extreme learning machine (ELM) have been derived for various classification and regression tasks.

However, the performance of RandNN-based models can deteriorate under non-ideal practical conditions. These faulty conditions include weight noise, node faults, outliers, and output errors—particularly prevalent in antenna fabrication. To address these challenges, this thesis proposes a suite of robust RandNN models specifically designed to mitigate the impact of such imperfections and enhance reliability in real-world applications, with a particular focus on antenna design.

Chapter 1 provides an overview of the background and theoretical foundation of RandNNs, including their derivation and key variations. A comprehensive review of the classical RandNN model and several state-of-the-art robust RandNN algorithms is presented. In particular, the maximum correntropy criterion is introduced as a technique for improving robustness against outliers. This criterion is integrated into all three robust algorithms proposed in this thesis.

Chapter 2 introduces a novel objective function designed to simultaneously address weight noise and outliers in the RandNN methods. Based on this formulation, a robust noise-aware RandNN (NARNN) model is developed. The proposed model demonstrates strong resilience and effectiveness under various levels of weight noise and outlier conditions. Furthermore, it is shown that the NARNN framework can be extended to ensemble deep RVFL networks.

Chapter 3 introduces a robust fault-aware ELM (RFAELM) algorithm that extends beyond outliers and weight noise to also address hidden-node faults in hardware implementations. Unlike NARNN, which focuses on weight noise and outliers, RFAELM incorporates the fault status of hidden neurons, leading to a more complex error formulation. Despite this added complexity, the convergence of both the objective function and the weight sequence is established. By jointly addressing three types of imperfections, RFAELM significantly enhances network resilience under practical and challenging faulty conditions.

Chapter 4 extends the robust RandNN framework to dielectric resonator antenna (DRA) design for dimension determination, where fabrication errors and outliers in the dataset are considered. Traditionally, DRA dimensions are determined using the dielectric waveguide model (DWM), which requires iterative solutions of transcendental equations. However, the accuracy of DWM heavily depends on the initial guess. A poor initialization in DWM can lead to significant deviations from the true solution, resulting in outliers. Given the presence of such outliers in DWM outputs and inevitable fabrication errors in practical antenna design, a robust predictive model is necessary. A novel model, termed robust output-error aware ELM (ROAELM), is proposed. This model integrates output error tolerance and outlier resistance into its objective function, enabling it to account for fabrication variances and outliers during prediction. A DRA is designed using ROAELM, and stable results in both simulation and experiments validate the robustness and effectiveness of ROAELM under practical imperfections.

In summary, this thesis presents three novel robust RandNN algorithms tailored to address different types of faulty conditions. The theoretical convergence of these algorithms is rigorously proven. Comparative simulations further demonstrate that the proposed models outperform existing methods across a range of imperfect scenarios. The demonstrated robustness and reliability highlight the practical potential of these algorithms in real-world defective environments, especially in the application of antenna design.

Date of Award	11 Sept 2025
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Kwok Wa LEUNG (Supervisor)