A two-stage dimension-reduced dynamic reliability evaluation (TD-DRE) method for vibration control structures based...

Area of Science:

• Structural Engineering
• Control Systems
• Reliability Engineering

Background:

• Vibration active control systems often exhibit dynamic uncertainties due to modeling, manufacturing, and environmental factors.
• Accurate structural reliability estimation is crucial for evaluating full-cycle vibratory responses in these systems.

Purpose of the Study:

• To develop a novel two-stage dimension-reduced dynamic reliability evaluation (TD-DRE) method for uncertain linear quadratic regulator (LQR) controlled structures.
• To integrate interval uncertainties and the time-variant reliability (TVR) concept for enhanced reliability assessment.

Main Methods:

• A two-stage approach combining Taylor series expansion for limit state analysis and the interval collocation method.
• Transformation of the time-variant reliability (TVR) problem into a time-invariant reliability (TIR) problem in the second stage.
• Application of the narrow bounds theorem to deduce the TD-DRE index.

Main Results:

• The proposed TD-DRE method demonstrates higher accuracy compared to traditional first-order Taylor expansion.
• The method proves more effective than existing first-passage reliability evaluation techniques.
• Validation through two application examples confirms the effectiveness and accuracy of the TD-DRE approach.

Conclusions:

• The TD-DRE method provides a reliable reference and initial value for structural design under dynamic uncertainties.
• Implementation of TD-DRE can significantly improve the efficiency of LQR controller design in practical engineering applications.