The power of dynamic causality in observer-based design for soft sensor applications

This paper introduces a novel framework for optimizing observer-based soft sensors through dynamic causality analysis. Traditional approaches to sensor selection often rely on linearized observability indices or statistical correlations that fail to capture the temporal evolution of complex systems. We address this gap by leveraging liquid-time constant (LTC) networks, continuous-time neural architectures with input-dependent time constants, to systematically identify and prune sensor inputs with minimal causal influence on state estimation. Our methodology implements an iterative workflow: training an LTC observer on candidate inputs, quantifying each input's causal impact through controlled perturbation analysis, removing inputs with negligible effect, and retraining until performance degradation occurs. We demonstrate this approach on three mechanistic testbeds representing distinct physical domains: a harmonically forced spring-mass-damper system, a nonlinear continuous stirred-tank reactor, and a predator-prey model following the structure of the Lotka-Volterra model, but with seasonal forcing and added complexity. Results show that our causality-guided pruning consistently identifies minimal sensor sets that align with underlying physics while improving prediction accuracy. The framework automatically distinguishes essential physical measurements from noise and determines when derived interaction terms provide complementary versus redundant information. Beyond computational efficiency, this approach enhances interpretability by grounding sensor selection decisions in dynamic causal relationships rather than static correlations, offering significant benefits for soft sensing applications across process engineering, ecological monitoring, and agricultural domains.