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Robust optimization and uncertainty quantification in the nonlinear mechanics of an elevator brake system

Piotr Wolszczak, Pawel Lonkwic, Americo Cunha, Grzegorz Litak, Szymon Molski

TL;DR

This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.

Abstract

This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to take into account parameters variabilities, a parametric probabilistic approach is employed. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. The uncertainties are propagated by the Monte Carlo method, which provides a detailed statistical characterization of the response. This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.

Robust optimization and uncertainty quantification in the nonlinear mechanics of an elevator brake system

TL;DR

This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.

Abstract

This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to take into account parameters variabilities, a parametric probabilistic approach is employed. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. The uncertainties are propagated by the Monte Carlo method, which provides a detailed statistical characterization of the response. This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.
Paper Structure (15 sections, 39 equations, 14 figures)

This paper contains 15 sections, 39 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Deterministic modeling
  3. Elevator brake system
  4. Mathematical model
  5. Stochastic modeling
  6. Probabilistic framework
  7. Maximum entropy principle
  8. Uncertainty propagation
  9. Optimization framework
  10. Classical optimization
  11. Robust optimization
  12. Results and discussion
  13. Uncertainty quatification
  14. Optimization
  15. Summary and conclusions

Figures (14)

  • Figure 1: Schematic representation of the CHP 2000 safety gear used by a friction crane brake system, which consists of the following parts: 1 - steel body; 2 - brake roller; 3 - thrust plate; 4 - spring package; 5 - braking cam; 6 - lift guide.
  • Figure 2: Illustration of a typical friction crane brake system used by lifting devices, which consists of the following parts: 1 - safety gear cabin; 2 - trigger lever; 3 - safety gears connector; 4 - rope speed limiter.
  • Figure 3: Illustration of the forces (in red) acting on the safety gear steel body and the underlying geometric dimensions (in blue).
  • Figure 4: Illustration of the forces (in red) acting on the wedge and the underlying geometric dimensions (in blue) and
  • Figure 5: Illustration of the forces (in red) acting on the brake roller inside the safety gear and and the underlying geometric dimensions (in blue).
  • ...and 9 more figures