Modern Design Of Experiments Research Articles

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

Accelerating Global Sensitivity Analysis via Supervised Machine Learning Tools: Case Studies for Mineral Processing Models

Global sensitivity analysis (GSA) is a fundamental tool for identifying input variables that determine the behavior of the mathematical models under uncertainty. Among the methods proposed to perform GSA, those based on the Sobol method are highlighted because of their versatility and robustness; however, applications using complex models are impractical owing to their significant processing time. This research proposes a methodology to accelerate GSA via surrogate models based on the modern design of experiments and supervised machine learning (SML) tools. Three case studies based on an SAG mill and cell bank are presented to illustrate the applicability of the proposed procedure. The first two consider batch training for SML tools included in the Python and R programming languages, and the third considers online sequential (OS) training for an extreme learning machine (ELM). The results reveal significant computational gains from the methodology proposed. In addition, GSA enables the quantification of the impact of critical input variables on metallurgical process performance, such as ore hardness, ore size, and superficial air velocity, which has only been reported in the literature from an experimental standpoint. Finally, GSA-OS-ELM opens the door to estimating online sensitivity indices for the equipment used in mineral processing.

Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures

Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation.

Picking up good vibrations: Exploration of the intensified vibratory mill via a modern design of experiments

The aim of this work was to strengthen the understanding of the intensified vibratory mill by unravelling the milling process in terms of the particle size reduction and heat generation via a modern design of experiments approach. Hence, the influence of five process parameters (acceleration, breaks during milling, bead size, milling time and bead-suspension ratio) was investigated via an I-optimal design. Particle size was measured via laser diffraction and the temperature of the sample after milling was computed. To advance our understanding, a mechanistic model for the set-up of wet-stirred media milling processes was applied on the observed milling trends. A generic approach for the optimisation of the milling process was retrieved and included the optimisation of the bead size and intermittent pausing for effective cooling. To finetune the remaining process parameters, the present work provides contour plots and strong predictive models. With these models, the particle size and the temperature after milling of suspensions manufactured with the intensified vibratory mill could be forecasted for the first time.

Comparison of meta-modeling methodologies through the statistical-empirical prediction modeling of hydrodynamic bodies

A methodology for directly establishing the forces and moments on a maneuvering body based on the instantaneous state of the vehicle is demonstrated. Both classical and modern Design of Experiments were used to develop experimental design regions consisting of different combinations of inflow conditions. Data was generated using computational fluid dynamic simulations which were performed on DARPA SUBOFF and the Virginia Tech ellipsoid model at the parameters prescribed by the designed experiments. Nonlinear polynomial regression modeling and artificial neural network modeling were used to develop prediction models for the normal and side force coefficients of both geometries with functional dependence on the inflow conditions. The prediction models were compared to published experimental data which showed excellent agreement within the experimental design region. The classical and modern approaches were also compared to each other and various strengths and applicability were illustrated. Nonlinear polynomial regression modeling and classical Design of Experiments proved to be very insightful by elucidating which inflow parameters and inflow parameter interactions were significant to the prediction model. Artificial neural network modeling coupled with modern Design of Experiments was shown to be more accurate, however, gave no insight to the underlying physical flow phenomena.

Efficient high-throughput biological process characterization: Definitive screening design with the ambr250 bioreactor system.

The burgeoning pipeline for new biologic drugs has increased the need for high-throughput process characterization to efficiently use process development resources. Breakthroughs in highly automated and parallelized upstream process development have led to technologies such as the 250-mL automated mini bioreactor (ambr250™) system. Furthermore, developments in modern design of experiments (DoE) have promoted the use of definitive screening design (DSD) as an efficient method to combine factor screening and characterization. Here we utilize the 24-bioreactor ambr250™ system with 10-factor DSD to demonstrate a systematic experimental workflow to efficiently characterize an Escherichia coli (E. coli) fermentation process for recombinant protein production. The generated process model is further validated by laboratory-scale experiments and shows how the strategy is useful for quality by design (QbD) approaches to control strategies for late-stage characterization.

Improving Quality of Wind Tunnel Test Data Through the MDOE

Researching on the improvement of the wind tunnel data quality through Modern Design Of Experiments (MDOE) was carried out. A body with fin model was tested in wind tunnel through the MDOE and traditional OFAT (One Factor at A Time) methods. The uncertainties of data from these two different methods were analyzed, and mechanism of defense against systematic error of Randomization and Repetition in the MDOE method was studied. The defense abilities against the time various systematic errors in wind tunnel tests of the MDOE and the OFAT method were compared, and the mean to improve test data quality using repetition principle in the MDOE was studied with the increasing of cost. Main conclusions: The MDOE method can test and eliminate the time various systematic errors during the wind tunnel tests, while the OFAT test data were polluted by the time various systematic errors; The independent variable changes sequently in the OFAT tests, so the test data are not statistically independent. It is the reason of the disability of the defense against the time various systematic errors in OFAT tests. Randomization can transform the systematic errors into random errors in MDOE tests, which can be eliminated. Repetition in MDOE tests can improve the quality of test data since the average variance in the predicted response can be reduced by adding sample points, and amount of the measured data are still less than the amount in OFAT tests.

A Case Study of Application of Modern Design of Experiment Methods in High Speed Wind Tunnel Test

For the development trend of advanced aircraft wind tunnel tests which require shorter cycle time and lower cost, a new wind tunnel testing process called Modern Design of Experiments (MDOE) is under development at NASA Langley Research Center. This paper presents a case study of application of Modern Design of Experiment methods in high speed wind tunnel tests based on the aerodynamic data of certain type of aircrafts. The full process including experiment design, execution, analysis of variance, and block design is described. Comparisons between MDOE predictions and OFAT measurements were made in the present study. The results show that the MDOE methods have well predictive capability to meet specific test objectives with less data volume, less cost and less time compared to the conventional OFAT methods, which means the MDOE approach established and used in this study is feasible enough to meet specific aerodynamic wind tunnel testing objectives in place of conventional OFAT methods.