set estimation
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2021 ◽  
pp. 2811-2821
Author(s):  
Yikang He ◽  
Zhenrong Wang ◽  
Zhenhua Wang ◽  
Yi Shen

2021 ◽  
pp. 1-54
Author(s):  
Shogo Iwazaki ◽  
Yu Inatsu ◽  
Ichiro Takeuchi

Abstract In many product development problems, the performance of the product is governed by two types of parameters: design parameters and environmental parameters. While the former is fully controllable, the latter varies depending on the environment in which the product is used. The challenge of such a problem is to find the design parameter that maximizes the probability that the performance of the product will meet the desired requisite level given the variation of the environmental parameter. In this letter, we formulate this practical problem as active learning (AL) problems and propose efficient algorithms with theoretically guaranteed performance. Our basic idea is to use a gaussian process (GP) model as the surrogate model of the product development process and then to formulate our AL problems as Bayesian quadrature optimization problems for probabilistic threshold robustness (PTR) measure. We derive credible intervals for the PTR measure and propose AL algorithms for the optimization and level set estimation of the PTR measure. We clarify the theoretical properties of the proposed algorithms and demonstrate their efficiency in both synthetic and real-world product development problems.


2021 ◽  
Vol 69 (10) ◽  
pp. 836-847
Author(s):  
Felix Wittich ◽  
Andreas Kroll

Abstract In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.


2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Jeong Eun Lee ◽  
Geoff K. Nicholls
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