Response surface methodology

Summary

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process. Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. Of late, for formulation optimization, the RSM, using proper design of experiments (DoE), has become extensively used. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques. Basic approach of response surface

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https://en.wikipedia.org/wiki/Response_surface_methodology

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Despite the high number of investments for data-based models in the expansion of Industry 4.0, too little effort has been made to ensure the maintenance of those models. In a data-streaming environment, data-based models are subject to concept drifts. A concept drift is a change in data distribution which will, at some point, decrease the accuracy of the model. To address this problem, various frameworks are presented in the literature, but there is no optimal methodology for implementing them. This paper presents a methodology to implement a problem-oriented complete solution to ensure the maintenance of an industrial data-based model. The final drift-handling solution is composed of a sampling decision system and an update system. The methodology begins with a concept-drift identification phase. Solutions are then pre-selected based on the identified concept drifts. Next, an optimization problem is designed to select the solution that optimizes the costs and respects the constraints. To better link the concept drift characteristics and the drift-handling solutions, a causal concept-drift classification system is proposed. The industrial implementation of such a solution is discussed and several questions are raised. This paper presents an original and detailed methodology that shows encouraging results to address the model-maintenance challenge; however, concept drift identification, and links between concept-drift charac-teristics and drift detection, require further research.

ELSEVIER SCI LTD2022

Discretization Uncertainties of Flow and Fatigue Damage Simulations of a Reversible Francis Pump-Turbine at Off-Design Operation in Turbine Mode

Daniel Biner, Philippe Alexandre Bontemps, Drazen Dujic

In the framework of the XFLEX HYDRO H2020 European Project, a 5 MW reversible Francis pump-turbine prototype, equipped with an industrial full size frequency converter, is investigated to demonstrate enhanced grid regulation capacities of variable speed hydropower units. The targeted high flexibility operation modes imply increased numbers of start and stop cycles, frequent off-design operation and even power reversions. Thereby, the understanding of fatigue mechanisms at off-design conditions and during transitions is crucial to ensure safe long term flexibility operation of hydropower units. The present paper aims to investigate spatial and temporal discretization uncertainties of numerical flow and fatigue damage simulations. For a selected off-design operating point in turbine mode, unsteady CFD simulations and one way coupled FSI simulations are carried out to reveal stress fluctuations and fatigue damage on the Francis pump-turbine runner. First, a classical Grid Convergence Index (GCI) methodology is carried out. Moreover, a design of experiments methodology is applied, comprising a fractional factorial plan, to evaluate the individual effects from the guide vane, runner, and draft tube grid sizes as well as the simulation time step on the flow and fatigue damage results. The guide vane grid size is found to be the most impactful on torque, discharge, and efficiency results. The correlation of the grid sizes with the fatigue damage responses shows less pronounced statistical evidence. Nevertheless, the study reveals expectable numerical error ranges related to discretization uncertainties of runner fatigue damage simulations within practicable grid size and time step ranges.

SPRINGER INTERNATIONAL PUBLISHING AG2022

Mitigation of Lightning-Induced Overvoltages Using Shield Wires: Application of the Response Surface Method

2018