Boosted Enhanced Quantile Regression Neural Networks with Spatiotemporal Permutation Entropy for Complex System Prognostics

Abstract

This paper presents a novel framework for pattern prediction and system prognostics centered on Spatiotemporal Permutation Entropy analysis integrated with Boosted Enhanced Quantile Regression Neural Networks (BEQRNNs). We address the challenge of understanding complex dynamical patterns in multidimensional systems through an approach that combines entropy-based complexity measures with advanced neural architectures. The system leverages dual computational stages: first implementing spatiotemporal entropy extraction optimized for multiscale temporal and spatial data streams, followed by an integrated BEQRNN layer that enables probabilistic pattern prediction with uncertainty quantification. This architecture achieves 81.17% accuracy in spatiotemporal pattern classification with prediction horizons up to 200 time steps and maintains robust performance across diverse regimes. Field testing across chaotic attractors, reaction-diffusion systems, and industrial datasets shows a 79% increase in critical transition detection accuracy and 81.22% improvement in long-term prediction reliability. The framework's effectiveness in processing complex, multimodal entropy features demonstrates significant potential for real-time prognostic applications.

Figures (2)

• Figure 1: Dynamic sensor profile analysis displaying normal spatiotemporal wave propagation patterns as baseline reference for the B-EQRNN prediction framework. The 3D surface visualisation shows typical waveform data across spatial coordinates (X and Y) with amplitude variations representing standard sensor operating conditions. The uniform blue colour gradient indicates normal amplitude intensity ranges without anomalous patterns, demonstrating stable wave propagation characteristics. This baseline normal wave profile serves as a reference for comparison with the 155-hour ahead anomaly predictions, enabling the spatiotemporal permutation entropy analysis to effectively distinguish between normal operational states and predicted sensor degradation patterns in complex electronic sensor environments.
• Figure 2: Dynamic sensor profile analysis showing spatiotemporal wave propagation patterns predicted 155 hours ahead using B-EQRNN framework. The 3D surface visualisation displays anomalous waveform data across spatial coordinates (X and Y) with amplitude variations indicating predicted sensor abnormalities. The colour gradient from blue to yellow represents increasing amplitude intensity of the predicted wave anomalies, with peak regions (yellow/red) indicating critical sensor states requiring immediate attention. The spatiotemporal permutation entropy analysis enables accurate prediction of wave propagation characteristics and anomaly formation 155 hours in advance, demonstrating the framework's capability for long-term sensor degradation forecasting in complex electronic sensor environments.