[論文レビュー] Polynomial Chaos-based Input Shaper Design under Time-Varying Uncertainty

Johannes Güttler, Karan Baker+3 more|arXiv (Cornell University)|Jan 23, 2026

Probabilistic and Robust Engineering Design被引用数 0

ひとこと要約

The paper develops an intrusive polynomial chaos expansion framework to design input shapers for vibration control under time-varying uncertainty, validating with a spring-mass system and showing improved efficiency over Monte Carlo while achieving similar accuracy.

ABSTRACT

The work presented here investigates the application of polynomial chaos expansion toward input shaper design in order to maintain robustness in dynamical systems subject to uncertainty. Furthermore, this work intends to specifically address time-varying uncertainty by employing intrusive polynomial chaos expansion. The methodology presented is validated through numerical simulation of intrusive polynomial chaos expansion formulation applied to spring mass system experiencing time-varying uncertainty in the spring stiffness. The system also evaluates non-robust and robust input shapers through the framework in order to identify designs that minimize residual energy. Results indicate that vibration mitigation is achieved at a similar accuracy, yet at higher efficiency compared to a Monte Carlo framework.

研究の動機と目的

• Motivate uncertainty quantification for robust input shaping in dynamical systems with time-varying parameters.
• Introduce an intrusive PCE framework to embed time-dependent uncertainty into input shaper design.
• Develop and compare non-robust, robust, and global sensitivity analysis (GSA) time-delay filters (TDF).
• Demonstrate computational advantages of PCE over Monte Carlo in predicting residual vibration energy.

提案手法

• Adopt an intrusive polynomial chaos expansion to represent time-varying uncertainty in the spring-mass system.
• Use Galerkin projections to compute PCE coefficients for the system's acceleration and state.
• Design time-delay filters (TDF) to place zeros at underdamped pole locations for vibration suppression, including non-robust and robust variants.
• Apply a global sensitivity analysis framework to optimize TDF parameters by minimizing objective functionals like expected residual energy and its variance.
• Utilize a two-interval (time-split) PCE with continuity conditions to handle evolving uncertainty.
• Compare PCE results with Monte Carlo simulations to verify convergence and efficiency.

Figure 2 : Functionality of a GSA TDF over time.

実験結果

リサーチクエスチョン

• RQ1 How does time-varying uncertainty in system parameters affect input shaper performance?
• RQ2 Can intrusive PCE maintain accuracy and reduce computational cost for designing robust TDFs under time-dependent uncertainty?
• RQ3 What is the impact of different TDF designs (non-robust, robust, GSA-optimized) on residual vibrational energy and its variance?
• RQ4 How does initializing PCE coefficients at interval boundaries influence continuity and accuracy of the solution?
• RQ5 Do PCE-based designs outperform Monte Carlo in both accuracy and computational efficiency for this setting?

主な発見

• PCE converges to Monte Carlo results for the expected residual energy and its variance with significantly less computational effort.
• A two-interval intrusive PCE with appropriate initialization achieves continuity at the interval boundary and accurate state predictions.
• Global sensitivity analysis-optimized TDFs substantially reduce both the expected residual energy and its variance compared to non-robust and robust baselines.
• GSA-designs reduce Var(V_res) by up to two orders of magnitude relative to non-robust TDFs, and often outperform robust TDF in expected energy.
• PCE construction (with degree P=30) is much faster than 10,000-sample Monte Carlo, by roughly a factor of 12 in the reported setup.
• Results indicate that robust TDFs may outperform GSA-TDF in some parameter regions, but GSA-TDFs generally offer the best overall performance across uncertainty ranges.

Figure 3 : Expected residual energy and its variance for different MC sample sizes.