Related Experiment Video
Updated: Jan 10, 2026
09:04
A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
Published on: June 1, 2022
3.6K
Adaptive Belief Rule Base Modeling of Complex Industrial Systems Based on Sigmoid Functions
Haolan Huang1, Shucheng Feng1, Jingying Li1
1The School of Computer Science and Information Engineering, Harbin Normal University, Harbin 150025, China.
Entropy (Basel, Switzerland)
|November 26, 2025
Summary
This study introduces a reliable nonlinear belief rule base (R-NBRB) model to improve nonlinear fitting and uncertainty representation in complex systems. The R-NBRB model significantly reduces errors in industrial applications like petroleum leak detection.
Area of Science:
- Engineering
- Computer Science
- Artificial Intelligence
Background:
- Existing Belief Rule Base (BRB) models struggle with nonlinear dynamics, uncertainty representation, and parameter optimization in complex industrial systems.
- Multifactorial nonlinear relationships and inherent uncertainties pose significant challenges for traditional modeling approaches.
Purpose of the Study:
- To develop an improved and reliable nonlinear belief rule base (R-NBRB) modeling method.
- To enhance nonlinear fitting, uncertainty representation, and parameter optimization capabilities.
- To address limitations of existing BRB models in handling complex industrial system dynamics.
Main Methods:
- Replaced the linear inference mechanism with a smooth nonlinear S-function for better adaptation to nonlinear dynamics.
- Quantified attribute reliability using a reliability assessment method and integrated data, reliability, and expert knowledge via the Evidential Reasoning (ER) algorithm.
- Applied the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm for inference parameter optimization to reduce decision bias.
Main Results:
- The R-NBRB model demonstrated effectiveness in complex industrial scenarios, as validated by petroleum pipeline leak detection.
- Achieved a mean squared error (MSE) of 0.2569, representing a 28.24% reduction compared to the standard BRB model.
- Successfully integrated data, reliability, and expert knowledge, expressing uncertainty through belief degrees.
Conclusions:
- The proposed R-NBRB method offers superior performance and adaptability for modeling complex industrial systems with nonlinear relationships and uncertainties.
- The integration of nonlinear functions, reliability assessment, ER algorithm, and CMA-ES optimization provides a robust framework for reliable modeling.
- The method effectively reduces decision bias and improves accuracy, showcasing its practical applicability in critical industrial monitoring tasks.
Related Concept Videos
01:26Classification of Systems-I
543
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
543
01:16SFG Algebra
299
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
299
01:26Feedback control systems
676
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
676
01:20Mason's Rule
993
Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...
993
01:27State Space Representation
504
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
504
01:21Mechanistic Models: Overview of Compartment Models
339
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
339