Probabilistic Robust Design Research Articles

A novel logistic regression-embedded 0–1 mixed-integer probabilistic robust design model to obtain optimum sustainable factor settings

Quality by design (QbD) focuses on satisfying the needs of products or processes when aiming for variance reduction. On the other side, sustainability is associated with carrying on to conduct so over time. The research gap is also addressed in sustainability and QbD in this paper. Next, robust design (RD) is a suitable approach to QbD to reduce the process or product variation regarding quantitative and qualitative design factors. For a number of situations, a binomial random response variable is considered to decrease the variability of the production process. Thus, this paper is four-fold. First of all, a modified distance-based criterion is developed to generate the design matrix when dealing with quantitative and qualitative design factors. Second, a logistic regression technique is presented for modeling responses when the random response variable is binomial. Third, a new logistic regression-based 0–1 mixed-integer probabilistic RD model is proposed to find optimum sustainable design factors. Fourth, an Industry 4.0 associated case study is performed in order to design sustainable process development, and the comparison and verification studies are also presented to show the effectiveness of the proposed probabilistic model. Further, managerial insights are provided based on the sustainable development goals (SDGs).

Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Probabilistic robust design of control systems for high-fidelity cyber–physical testing

Cyber–physicalempirical methods consist in partitioning a dynamical system under study into a set of physical and numerical substructures that interact in real-time through a control system. In this paper, we define and investigate the fidelity of such methods, that is their capacity to generate systems whose outputs remain close to those of the original system under study. In practice, fidelity is jeopardized by uncertain and heterogeneous artefacts originating from the control system, such as actuator dynamics, time delays and measurement noise. We present a computationally efficient method, based on surrogate modelling and active learning techniques, to (1) verify that a cyber–physical empirical setup achieves probabilistic robust fidelity, and (2) to derive fidelity bounds, which translate to absolute requirements to the control system. For verification purposes, the method is first applied to the study of a simple mechanical system. Its efficiency is then demonstrated on a more complex problem, namely the active truncation of slender marine structures, in which the substructures’ dynamics cannot be described by an analytic solution.

Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented using a Bayesian inference framework. The objective of the study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modeling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest are derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system.

Probabilistic robust design for covariance minimization of nonlinear system

A linear or second-order model is usually used to approximate a practical nonlinear system in probabilistic robust designs. This approximation often makes these designs less effective when the system has strong nonlinearity as well as large uncontrollable variation. In this paper, a novel probabilistic design approach is proposed to design a nonlinear system to be robust under circumstance of large random variation. First, a variable sensitivity approach is employed to place the nonlinear influence under the sensitivity matrix of the covariance model. On this basis, a robust design approach is proposed to minimize the influence of random variation in relation to the performance covariance. Since this proposed approach considers both nonlinear influence and probabilistic distribution in a large uncertain region, it can effectively ensure robustness of nonlinear systems even if large random variation exists.

Minimizing Cost of Multiple Response Systems by Probabilistic Robust Design

In the design of products and processes, a methodology that helps adjust the means and tolerances of the design variables to both improve conformance and lower costs is a valuable tool. In this paper, the cost of a product at the manufacturing stage is the sum of the production cost, which includes known costs for tolerances, inspection, and so forth, plus any cost for scrapping or reworking products that do not conform to specifications. We call this added cost the so-called loss-of-quality cost and evaluate it as the probability of nonconformance (of the responses) times established scrap or rework costs. Accurate probability estimates are obtained using full distributions, limit-state functions, and first-order reliability methods (FORM). Probabilities are adjusted through probabilistic robust design. The production costs and the loss-of-quality cost are competing costs and thus their sum provides a single objective function in terms of the means and tolerances of the design variables. The need to satisfy the equations in both the product model and the workings of FORM introduce nonlinear equality constraints. The minimum of the objective function, hence the minimum cost, is obtained by solving a nonlinear, constrained, optimization problem. The design of a mechanism for controlling a grating diffraction spectroscope serves as a case study using the presented method. A minimum cost, the probability of conformance, and the respective parameter settings are found for both complete and zero inspection strategies.

Probabilistic robust design with linear quadratic regulators

In this paper, we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators (LQR). We consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism. The approach followed here is a blend of randomization techniques for the uncertainty together with convex optimization for the controller parameters. In particular, we propose an iterative algorithm for designing a controller which is based upon subgradient iterations. At each step of the sequence, we first generate a random sample and then we perform a subgradient step for a convex constraint defined by the LQR problem. The main result of the paper is to prove that this iterative algorithm provides a controller which quadratically stabilizes the uncertain system with probability one in a finite number of steps. In addition, at a fixed step, we compute a lower bound of the probability that a quadratically stabilizing controller is found.