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1

A probabilistic approach for approximation of optical and opto-electronic properties of an opto-semiconductor wafer under consideration of measuring inaccuracy and model uncertainty

Stroka Stefan M., Heumann Christian, Suhrke Fabian, Meindl Kathrin

Opto-Electronics Review

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2023

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Vol. 31, No. 2

art. no. e145863

EN

This paper presents a probabilistic machine learning approach to approximate wavelength values for unmeasured positions on an opto-semiconductor wafer after epitaxy. Insufficient information about optical and opto-electronic properties may lead to undetected specification violations and, consequently, to yield loss or may cause product quality issues. Collection of information is restricted because physical measuring points are expensive and in practice samples are only drawn from 120 specific positions. The purpose of the study is to reduce the risk of uncertainties caused by sampling and measuring inaccuracy and provide reliable approximations. Therefore, a Gaussian process regression is proposed which can determine a point estimation considering measuring inaccuracy and further quantify estimation uncertainty. For evaluation, the proposed method is compared with radial basis function interpolation using wavelength measurement data of 6-inch InGaN wafers. Approximations of these models are evaluated with the root mean square error. Gaussian process regression with radial basis function kernel reaches a root mean square error of 0.814 nm averaged over all wafers. A slight improvement to 0.798 nm could be achieved by using a more complex kernel combination. However, this also leads to a seven times higher computational time. The method further provides probabilistic intervals based on means and dispersions for approximated positions.

2

Discrete uncertainty quantification for offline reinforcement learning

Pérez Torres Jose Luis, Corrochano Jiménez Javier, García Javier, Majadas Rubén, Ibañez-Llano Cristina, Pérez Sergio, Fernández Fernando

Journal of Artificial Intelligence and Soft Computing Research

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2023

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Vol. 13, No. 4

273--287

EN

In many Reinforcement Learning (RL) tasks, the classical online interaction of the learning agent with the environment is impractical, either because such interaction is expensive or dangerous. In these cases, previous gathered data can be used, arising what is typically called Offline RL. However, this type of learning faces a large number of challenges, mostly derived from the fact that exploration/exploitation trade-off is overshadowed. In addition, the historical data is usually biased by the way it was obtained, typically, a sub-optimal controller, producing a distributional shift from historical data and the one required to learn the optimal policy. In this paper, we present a novel approach to deal with the uncertainty risen by the absence or sparse presence of some state-action pairs in the learning data. Our approach is based on shaping the reward perceived from the environment to ensure the task is solved. We present the approach and show that combining it with classic online RL methods make them perform as good as state of the art Offline RL algorithms such as CQL and BCQ. Finally, we show that using our method on top of established offline learning algorithms can improve them.

3

Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

Zhou Shuang, Zhang Jianguo, You Lingfei, Zhang Qingyuan

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 2

231--241

EN

Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.

4

Modelling and control of a failing heart managed by a left ventricular assist device

Son Jeongeun, Du Dongping, Du Yuncheng

Biocybernetics and Biomedical Engineering

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2020

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Vol. 40, no. 1

559--573

EN

Left ventricular assist device (LVAD) recently has been used in advanced heart failure (HF), which supports a failing heart to meet blood circulation demand of the body. However, the pumping power of LVADs is typically set as a constant and cannot be freely adjusted to incorporate blood need from resting or mild exercise such as walking stairs. To promote the adoption of LVADs in clinical use as a long-term treatment option, a feedback controller is needed to regulate automatically the pumping power to support a time-varying blood demand, according to different physical activities. However, the tuning of pumping power induces suction, which will collapse the heart and cause sudden death. It is essential to consider suction when developing control strategy to adjust the pumping power. Further, hemodynamic of a failing heart exhibits variability, due to patient-to-patient heterogeneity and inherent stochastic nature of the heart. Such variability poses challenges for controller design. In this work, we develop a feedback controller to adjust the pumping power of an LVAD without inducing suction, while incorporating variability in hemodynamic. To efficiently quantify variability, the generalized polynomial chaos (gPC) theory is used to design a robust self-tuning controller. The efficiency of our control algorithm is illustrated with three case scenarios, each representing a specific change in physical activity of HF patients.

5

Numerical modeling of uncertainty in acoustic propagation via generalized Polynomial Chaos

Dammak Khalil, Koubaa Sana, Elhami Abdelkhalak, Walha Lassaad, Haddar Mohamed

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 1

3--15

EN

This work aims at increasing the performance prediction for acoustic propagation systems that will operate in the presence of the inevitable parameters uncertainty. In the present contribution, the finite element method is applied to solve an acoustic problem described by the Helmholz equation when the geometric and material properties present uncertainty. The influence of the uncertainty of physical parameters on the pressure field is discussed. The results using the polynomial chaos expansion method are compared with Monte Carlo simulations. It is show that uncertainty levels in the input data could result in large variability in the calculated pressure field in the domain.

6

A new assessment method of mechanism reliability based on chance measure under fuzzy and random uncertainties

Zhang L., Zhang J., Zhai H., Zhou S.

Eksploatacja i Niezawodność

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2018

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Vol. 20, no. 2

219--228

EN

The traditional reliability analysis methods based on probability theory and fuzzy set theory have been widely used in engineering practice. However, these methods are unable directly measure the uncertainty of mechanism reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to address this problem, a new quantification method for the mechanism reliability based on chance theory is presented to simultaneously satisfy the duality of randomness and the subadditivity of fuzziness in the reliability problem. Considering the fact that systems usually have multilevel performance and the components have multimode failures, this paper proposes a chance theory based multi-state performance reliability model. In the proposed method, the chance measure is adopted instead of probability and possibility measures to quantify the mechanism reliability for the subjective probability or fuzzy variables. The hybrid variables are utilized to represent the random and fuzzy parameters, based on which solutions are derived to analyze the chance theory based mechanism reliability with chance distributions. Since the input parameters of the model contain fuzziness and randomness simultaneously, an algorithm based on chance measure is designed. The experimental results on the case application demonstrate the validity of the proposed method.

PL

Tradycyjne metody analizy niezawodności oparte na teorii prawdopodobieństwa i teorii zbiorów rozmytych znajdują szerokie zastosowanie w praktyce inżynierskiej. Jednak metod tych nie można stosować do bezpośredniego pomiaru niepewności niezawodności przy niepewnych zmiennych, tj. subiektywnych zmiennych losowych i rozmytych. Aby zaradzić temu problemowi, przedstawiono nową metodę kwantyfikacji niezawodności opartą na teorii szansy, która jednocześnie spełnia aksjomaty dwoistości losowości oraz subaddytywności związanej z rozmytością w problemach niezawodności. Biorąc pod uwagę fakt, że systemy zazwyczaj charakteryzują się wielopoziomową strukturą, a uszkodzenia elementów składowych mają charakter wieloprzyczynowy, w niniejszym artykule zaproponowano model niezawodności eksploatacji systemu wielostanowego oparty na teorii szansy. W proponowanej metodzie, zamiast miar prawdopodobieństwa i możliwości, do kwantyfikacji niezawodności, w przypadku gdy dane są subiektywne zmienne losowe lub zmienne rozmyte, przyjęto miarę szansy wystąpienia zdarzenia. Do reprezentacji parametrów losowych i rozmytych wykorzystano zmienne hybrydowe, które stanowią podstawę dla wyprowadzenia rozwiązań w celu analizy niezawodności mechanizmu opartej na teorii szansy z rozkładem szans. Ponieważ parametry wejściowe modelu noszą jednocześnie znamiona rozmytości i losowości, opracowano algorytm oparty na mierze szansy. Wyniki eksperymentalne otrzymane na podstawie studium przypadku dowodzą poprawności proponowanej metody.

7

Regression Points in Non-Intrusive Polynomial Chaos Expansion Method and D-Optimal Design

Szepietowska K., Magnain B., Lubowiecka I., Florentin E.

Machine Dynamics Research

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2017

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Vol. 41, No. 2

5--16

EN

The paper addresses selected issues of uncertainty quantification in the modelling of a system containing surgical mesh used in ventral hernia repair. Uncertainties in the models occur due to variability of abdominal wall properties among others. In order to include them, a nonintrusive regression-based polynomial chaos expansion method is employed. Its accuracy depends on the choice of regression points. In the study, a relation between error of mean, standard deviation, 95th percentile and location of regression points is investigated in the models of implants with a single random variable. This approach is compared with a classic choice of points based on the D-optimality criterion.

8

Materials modelling in industrial bulk metal forming processes and process chains

Hirt G., Bambach M., Lohmar J., Guvenc O., Henke T., Schwich G.

Computer Methods in Materials Science

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2015

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Vol. 15, No.1

5--12

EN

Bulk metal forming processes range from processes with a single deformation step such as certain closed-die forging operations to processes with many subsequent stages such as hot rolling, ring rolling or open die forging. Modelling of these manufacturing processes requires both precise process models as well as adequate material models. Microstructure evolution by recrystallization is decisive in all of these processes since the microstructure determines the flow stress and hence the forming forces but it also influences the product properties. In this context, the propagation of variations in the processing conditions and in the material behavior are of special importance and methods for the quantification of uncertainties and their effect on model predictions are required. Such questions can be approached using models of different complexity on various scales as shown in the following examples: In closed die forging of a gear wheel from 25MoCr4 alloy the complex geometry requires a Finite Element process model which in this case is combined with a JMAK type material model. In plate rolling a simplified process model can be applied successfully. Based on the slab theory, which is enhanced for spatial resolution of shear strain using a meta model derived by FEM, this model can simulate even longer roll pass schedules within seconds and offers the possibility to combine it with numerical optimization techniques. Recrystallization of a high-manganese steel in interpass times between hot rolling passes is an example where models with spatial resolution (CP-FEM and phase field) are combined on the micro-scale to predict the recrystallization kinetics based on physically meaningful variables such as grain boundary mobility. In ring rolling the process model must include the closed-loop control system of the rolling machine to achieve a realistic prediction of the process kinematics. Feedback control loops for up to eight kinematic degrees of freedom (velocities and positions of all radial, axial and guiding rolls) have been defined using virtual sensors integrated in the simulation. Offline coupling with microstructure simulation is used to predict the final grain size and determine under which conditions static recrystallization occurs during the rolling sequence.

9

Probabilistic multiscale analysis of inelastic localized failure in solid mechanics

Ibrahimbegovic A., Matthies H. G.

Computer Assisted Methods in Engineering and Science

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2012

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Vol. 19, no. 3

277-304

EN

In this work, we discuss the role of probability in providing the most appropriate multiscale based uncertainty quantification for the inelastic nonlinear response of heterogeneous materials undergoing localized failure. Two alternative approaches are discussed: i) the uncertainty quantification in terms of constructing the localized failure models with random field as parameters of failure criterion, ii) the uncertainty quantification in terms of the corresponding Bayesian updates of the corresponding evolution equation. The detailed developments are presented for the model problem of cement-based composites, with a two-phase meso-scale representation of material microstructure, where the uncertainty stems from the random geometric arrangement of each phase. Several main ingredients of the proposed approaches are discussed in detail, including microstructure approximation with a structured mesh, random field KLE representation, and Bayesian update construction. We show that the first approach is more suitable for the general case where the loading program is not known and the best one could do is to quantify the randomness of the general failure criteria, whereas the second approach is more suitable for the case where the loading program is prescribed and one can quantify the corresponding deviations. More importantly, we also show that models of this kind can provide a more realistic prediction of localized failure phenomena including the probability based interpretation of the size effect, with failure states placed anywhere in-between the two classical bounds defined by continuum damage mechanics and linear fracture mechanics.