Mechanical Arm Robust Optimization Using Bounded Beta Distribution
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Solution Overview
Problem
Current robust optimization design methods for mechanical arms fail to accurately account for hybrid interval and probabilistic uncertainties, leading to unreliable results due to irrational descriptions of uncertainties and subjective weight factor selections, which affect the loading capacity and working efficiency of mechanical arms.
Innovation Solution
A robust optimization design method for mechanical arms based on hybrid interval and bounded probabilistic uncertainties using a generalized beta distribution to describe probabilistic uncertainties, combined with a genetic algorithm and multi-layered refining Latin hypercube sampling for robustness analysis, to accurately reflect uncertainty distributions and prevent model transformation errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If normal distribution is used to describe probabilistic uncertainty, then the mathematical model is simple, but the description becomes irrational and inconsistent with engineering reality
Solution Approach 1:
The patent changes the distribution parameters from unbounded normal distribution to bounded beta distribution, transforming the uncertainty description to match engineering reality where parameters have finite bounds. This resolves the contradiction by modifying the mathematical parameters to reflect physical constraints.
Solution Approach 2:
Instead of forcing engineering uncertainties into normal distribution, the patent inverts the approach by using beta distribution that naturally accommodates bounded uncertainties, making the mathematics serve the engineering reality rather than vice versa.
2Ease of manufacture
If 6σ robust design criterion with weight factor is used to transform uncertain objective performance function, then the model transformation is achieved, but errors are incurred and results become unreliable
Solution Approach 1:
The patent extracts and eliminates the problematic weight factor and 6σ transformation from the model, directly optimizing the uncertain objective performance function without intermediate transformations that introduce errors and subjectivity.
Solution Approach 2:
The patent removes the 6σ criterion as an intermediary transformation step, allowing direct optimization of the original uncertain function, thereby eliminating the error-introducing mediation process.
3Productivity
If Monte Carlo simulation with conventional sampling method is used for robustness analysis, then the analysis is conducted, but the distribution characteristics of probabilistic uncertainty are not fully reflected
Solution Approach 1:
The patent performs preliminary stratification of the sampling domain based on the beta distribution characteristics before sampling, pre-organizing the sample space to ensure better coverage of high-contribution regions, thereby improving both accuracy and efficiency.
Solution Approach 2:
The patent segments the sampling domain into multiple layers with different sampling densities, concentrating more samples in regions of higher contribution to the robustness metric, thereby efficiently capturing the distribution characteristics without excessive computational cost.
4Ease of operation
If sampling points are uniformly distributed in Monte Carlo simulation, then the sampling is simple, but insufficient samples are provided in high-contribution domains
Solution Approach 1:
The patent pre-stratifies the sampling domain according to the beta distribution characteristics before generating samples, preparing the sampling framework in advance to ensure high-contribution regions receive adequate sample coverage while maintaining operational simplicity.
Solution Approach 2:
The patent applies different sampling densities to different regions of the domain, providing higher sampling density in high-contribution regions and lower density in low-contribution regions, thereby optimizing the distribution of sampling effort across the domain.
Data Source
AI summary
A robust optimization design method for a mechanical arm considering hybrid interval and bounded probabilistic uncertainties is provided. The method includes considering interval and bounded probabilistic uncertainties affecting a performance of a mechanical arm, describing a bounded probabilistic uncertainty by a generalized beta distributed random variable, and establishing a robust optimization design model of the mechanical arm; directly solving the optimization model based on a genetic algorithm, which includes analyzing, by the boundedness of the uncertainties, the robustness of a constraint performance function of an individual in a population, and determining whether the individual is feasible; calculating, a mean and a standard deviation of an objective function of a feasible individual by multi-layered refining Latin hypercube sampling (MRLHS); and ranking, according to a total feasibility robustness index and a distance to negative ideal solution (DNIS), individuals in a current population to obtain a robust optimal design of the mechanical arm.