# Adaptive Belief Rule Base Modeling of Complex Industrial Systems Based on Sigmoid Functions

## TL;DR

This paper introduces a new method for modeling complex industrial systems using nonlinear belief rules and improved uncertainty handling.

## Contribution

The novel R-NBRB model uses a smooth S-function and CMA-ES optimization to better handle nonlinear dynamics and reduce decision bias.

## Key findings

- The R-NBRB model achieved a 28.24% reduction in MSE compared to the BRB model in pipeline leak detection.
- The model integrates data, reliability, and expert knowledge using the ER algorithm for uncertainty representation.
- CMA-ES optimization effectively reduces decision bias caused by limited expert knowledge.

## Abstract

In response to the challenges posed by multifactorial nonlinear relationships and uncertainties, and to address the limitations of the existing Belief Rule Base (BRB) in nonlinear fitting, uncertainty representation, and parameter optimization, this paper presents an improved reliable modeling method using a nonlinear belief rule base (R-NBRB). First, the linear inference mechanism is replaced by a smooth nonlinear S-function. This replacement better adapts to nonlinear dynamics in complex industrial systems. Second, attribute reliability is quantified through a reliability assessment method. Data, reliability, and expert knowledge are integrated using the Evidential Reasoning (ER) algorithm. Uncertainty is expressed in the form of belief degrees. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm is applied to optimize the inference parameters. Decision bias caused by insufficient expert knowledge is thereby reduced. Experiments were conducted on a task involving the detection of a petroleum pipeline leak. The mean squared error (MSE) of the R-NBRB model is only 0.2569. This represents a 28.24% reduction compared with the BRB model. The proposed method’s effectiveness and adaptability in complex industrial situations are confirmed.