On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian...

Area of Science:

• Engineering
• Control Systems
• System Identification

Background:

• Manufacturing process control requires understanding model uncertainty for consistency and quality.
• Deterministic models are insufficient for complex systems, necessitating stochastic approaches to represent disturbances and wear.
• Model uncertainties impact fault diagnosis, safety, and reliability in real-world applications.

Purpose of the Study:

• To develop a maximum likelihood estimation algorithm for uncertainty modeling in linear dynamic systems.
• To incorporate system uncertainties as stochastic error terms within a transfer function framework.
• To enhance process control and fault detection/diagnosis methodologies through accurate dynamic system modeling.

Main Methods:

• Utilized a stochastic embedding approach to represent system uncertainties.
• Modeled the error-model probability density function as a finite Gaussian mixture model.
• Developed an iterative Expectation-Maximization algorithm for estimating the nominal model and error-model parameters from independent experimental data.

Main Results:

• Successfully developed a maximum likelihood estimation algorithm for uncertainty modeling.
• Demonstrated the effectiveness of the stochastic embedding approach in handling system uncertainties.
• Validated the proposed method's benefits through numerical simulations.

Conclusions:

• The proposed method provides a robust way to model uncertainty in linear dynamic systems.
• Accurate uncertainty modeling is crucial for effective process control and fault diagnosis.
• The Expectation-Maximization algorithm offers an efficient approach for parameter and probability density function estimation.