Q2S2: Merging Qualitative Information in Sequential DOE

Sequential Design of Experiments to Maximize Learning from Carbon Capture Pilot Plant Testing

This study describes the use of an analytical model, constructed using sequential design of experiments (DOEs), to optimize and quantify the uncertainty of a Diesel engine operating point. A genetic algorithm (GA) was also used to optimize the design. Three engine parameters were varied around a baseline design to minimize indicated specific fuel consumption (ISFC) without exceeding emissions (NOx and soot) or peak cylinder pressure constraints. An objective merit function was constructed to quantify the strength of designs. The engine parameters were start of injection (SOI), injection duration, and injector included angle. The engine simulation was completed with a sector mesh in the commercial computational fluid dynamics (CFD) software CONVERGE, which predicted the combustion and emissions using a detailed chemistry solver with a reduced mechanism for n-heptane. The analytical model was constructed using the SmartUQ software using DOE responses to construct kernel emulators of the system. Each emulator was used to direct the placement of the next set of DOE points such that they improve the accuracy of the subsequently generated emulator. This refinement was either across the entire design space or a reduced design space that was likely to contain the optimal design point. After sufficient emulator accuracy was achieved, the optimal design point was predicted. A total of 5 sequential DOEs were completed, for a total of 232 simulations. A reduced design region was predicted after the second DOE that reduced the volume of the design space by 96.8%. The final predicted optimum was found to exist in this reduced design region. The sequential DOE optimization was compared to an optimization performed using a GA. The GA was completed using a population of 9 and was run for 71 generations. This study highlighted the strengths of both methods for optimization. The GA (known to be an efficient and effective method) found a better optimum, while the DOE method found a good optimum with fewer total simulations. The DOE method also ran more simulations concurrently, which is an advantage when sufficient computing resources are available. In the second part of the study, the analytical model developed in the first part was used to assess the sensitivity and robustness of the design. A sensitivity analysis of the design space around the predicted optimum showed that injection duration had the strongest effect on predicted results, while the included angle had the weakest. The uncertainty propagation was studied over the reduced design region found with the sequential DoE in the first part. The uncertainty propagation results demonstrated that for the relatively large variations in the input parameters, the expected variation in the ISFC and NOx results were significant. Finally, the predictions from the analytical model were validated against CFD results for sweeps of the input parameters. The predictions of the analytical model were found to agree well with the results from the CFD simulation.

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

마이크로 유전알고리즘은 적은 수의 개체 사용 및 무작위 개체 구성을 통한 돌연변이 기능 대체의 특징을 갖는 진화연산을 수행하여 일반적인 유전알고리즘이 갖는 각 세대당 많은 계산 량이 요구되는 단점을 극복하고자 하였다. 이러한 마이크로 알고리즘은 특히 설계변수가 3~5 개를 갖는 문제에 효율적이라는 것이 많은 연구자들에 의하여 알려졌다. 따라서 본 연구의 목적은 순차적 실험계획법과 마이크로 유전알고리즘을 이용한 최적화 알고리즘을 개발하는 것이며, 이를 수학예제와 구조물 문제에 적용하여 실용성을 확인하고자 한다. 순차적 실험계획법은 저자들의 선행연구에서 제안되었으며, 실험계획법과 반응표면법을 이용하는 근사최적화 기법에 의한 시행착오적인 반복과정을 최소화하고자 하는 방법으로써, 행렬실험과 평균분석을 반복 적용하는 개념이다.

Investigating adaptive sampling strategies for optimal building energy performance using artificial neural networks and kriging surrogate models

The paper considers a sequential Design Of Experiments (DOE) scheme. Our objective is to maximize both information and economic measures over a feasible set of experiments. Optimal DOE strategies are developed by introducing information criteria based on measures adopted from information theory. The evolution of acquired information along various stages of experimentation is analyzed for linear models with a Gaussian noise term. We show that for particular cases, although the amount of information is unbounded, the desired rate of acquiring information decreases with the number of experiments. This observation implies that at a certain point in time it is no longer efficient to continue experimenting. Accordingly, we investigate methods of stochastic dynamic programming under imperfect state information as appropriate means to obtain optimal experimentation policies. We propose cost-to-go functions that model the trade-off between the cost of additional experiments and the benefit of incremental information. We formulate a general stochastic dynamic programming framework for design of experiments and illustrate it by analytic and numerical implementation examples.

Surrogate models are widely used to predict response function of any system and in quantifying uncertainty associated with the response function. It is required to have response quantities at some preselected sample points to construct a surrogate model which can be processed in two way. Either the surrogate model is constructed using one shot experimental design techniques, or, the sample points can be generated in a sequential manner so that optimum sample points for a specific problem can be obtained. This paper addresses a comprehensive comparisons between these two types of sampling techniques for the construction of more accurate surrogate models. Two most popular one shot sampling strategies: Latin hypercube sampling and Sobol sequence, and four different type sequential experimental designs (SED) namely, Monte Carlo intersite projected (MCIP), Monte Carlo intersite projected threshold (MCIPT), optimizer projected (OP) and LOLA-Voronoi (LV) method are taken for the present study. Two most widely used surrogate models, namely polynomial chaos expansion and Kriging are used to check the applicability of the experimental design techniques. Three different types of numerical problems are solved using the two above-mentioned surrogate models considering all the experimental design techniques independently. Further, all the results are compared with the standard Monte Carlo simulation (MCS). Overall study depicts that SED performs well in predicting the response functions more accurately with an acceptable number of sample points even for high-dimensional problems which maintains the balance between accuracy and efficiency. More specifically, MCIPT and LV method based Kriging outperforms other combinations.

Microbial bioprospecting in contaminated environments is a promising strategy for identifying biosurfactant-producing bacteria; however, translating environmentally adapted strains into predictable cultivation processes remains challenging. In this study, a microbial consortium subjected to long-term evolutionary laboratory adaptation in oily sludge was investigated to evaluate strain-specific phenotypic responses related to biosurfactant production. Phylogenetic analysis based on 16S rDNA sequencing identified three taxonomically distant isolates: Faucicola sp. strain BS5C, Pseudomonas sp. strain BS16B, and Enterobacter sp. BS14MR. Biosurfactant production was evaluated using a sequential Design of Experiments (DOE) approach, including fractional factorial and central composite rotatable designs, with the emulsification index (E24) used as a semi-quantitative response variable. Initial screening revealed a statistically significant negative effect (p < 0.10) of high dextrose concentrations for all isolates. Strain-specific differences in model adequacy were observed, with a statistically adequate quadratic model obtained for Pseudomonas sp. BS16B (R2 = 0.8658, p = 0.0225), whereas the other isolates showed significant lack of fit (p < 0.05). ATR-FTIR analysis revealed spectral profiles consistent with lipopeptide-like compounds. Overall, these results indicate that isolates derived from the same long-term adapted system may differ substantially in process predictability, suggesting that productivity-based screening alone may be insufficient for selecting robust strains.

Surrogate-based optimization (SBO) is a powerful approach for global optimization of high-dimensional expensive black-box functions, commonly consisting of four modules: design of experiment, function evaluation, surrogate construction, and infill sampling criterion. This work develops a robust and efficient SBO framework for aerodynamic shape optimization using discontinuous Galerkin methods as the computational fluid dynamics evaluation. Innovatively, the prior adjoint gradient information of the baseline shape is used to improve the performance of the sampling plan in the preliminary design of the experiment stage and further improve the robustness and efficiency of the construction of surrogate(s). Specifically, the initial sample points along the direction of objective rise have a high probability of being transformed into feasible points in a subspace of objective descending. Numerical experiments verified that the proposed gradient-improved sampling plan is capable of stably exploring the design space of objective descending and constraint satisfaction even with limited sample points, which leads to a stable improvement of the resultant aerodynamic performance of the final optimized shape.

ABSTRACTAn acceptance sampling plan (ASP) is a commonly used tool in quality assurance that allows business partners to make decisions about lot disposition. To enhance the efficiency and applicability of inspection, various ASPs have been constructed to meet different circumstances in practical applications. One of these ASPs is the skip‐lot sampling plan (SkSP), which reduces inspection time and cost for a series of product lots from a supplier with excellent quality records. Based on the structure of the SkSP, we propose an improved variables SkSP that uses a repetitive group sampling (RGS) plan based on the most commonly used capability index Cpk as the reference plan, designated as Cpk‐based SkSP‐RGS. This plan is optimized using a model that ensures the operating characteristic function meets a two‐point condition and minimizes the average sample number (ASN). Additionally, two main performance measures of sampling plans, ASN and discriminatory power, are investigated. The results reveal the superiority of the proposed plan over conventional Cpk‐based sampling plans. Lastly, a case study from the liquid crystal module industry is demonstrated using the proposed plan to show its applicability and practicality.

This paper discusses a new sequential adaptive design of experiments (DoE) approach for global Kriging metamodeling applications. The sequential implementation is established by using the current metamodel, formulated based on the existing experiments, to guide the selection of the optimal new experiment(s). The score function, defining the DoE objective, combines two components: (1) the metamodel prediction variability, expressed through the predictive variance, and (2) the metamodel bias, approximated through the leave-one-out cross validation (LOOCV) error. The latter is used as a weighting factor to extend traditional DoE approaches that focus solely on the metamodel prediction variability. Two such approaches are considered here, adopting either the integrated mean squared error or the maximum mean squared error as the basic component of the score function. The incorporation of bias information as weighting within these well-established approaches facilitates a direct extension of their respective computational workflows, making the proposed implementation attractive from computational perspective. An efficient optimization scheme for identification of the next experiment, as well as the balancing of exploration and exploitation between the two components of the score function, are also discussed. The incorporation of LOOCV weightings is shown to be highly beneficial in a total of six analytical and engineering examples. Furthermore, these examples demonstrate that for DoE approaches which use LOOCV information as weights, it is preferable to update the predictive variance to explicitly consider the impact of the new experiment, rather than relying strictly on the current metamodel variance.

On the costs of parameter uncertainties. Effects of parameter uncertainties during optimization and design of experiments

Aim/purpose – This work aims to assess stochastic properties of finite population mean estimators under Pathak’s fixed-cost sequential sampling scheme by deriving their co- variance and proposing its estimator. This scheme enables strict control over survey- -related monetary expenditures when individual data acquisition costs differ and survey budget excesses are unacceptable. It facilitates economically efficient use of available resources. Our work is aimed at extending its applicability. Design/methodology/approach – This paper’s main theoretical result concerning the covariance of Pathak mean value estimators and the unbiasedness of its proposed estima- tor was derived analytically. A short simulation study supports this. Findings – The proposed estimator for the covariance between Pathak’s estimators of population averages is unbiased under the sequential fixed-cost sampling scheme, which prevents survey budget excesses when the per-unit costs of acquiring information are known in advance but not homogeneous. Research implications/limitations – Our findings facilitate accuracy assessment for complex estimators of population parameters that utilize auxiliary information under restricted-budget sequential sampling and, in particular, for ratio, product, and regression estimators. They are potentially applicable to any quantities of interest that could be expressed in terms of averages, including, among others, unemployment rates, poverty measures, inflation indices, and GDP indicators. Their application is justified if the per- unit costs of acquiring information vary. Originality/value/contribution – Our results allowed us to assess various economic variables’ distribution characteristics while controlling for randomly varying survey costs. This facilitates planning and managing sample surveys in an economically effi- cient way. Keywords: Pathak’s estimator, sequential sampling, fixed-cost sampling, sum-quota sampling. JEL Classification C15, C83.

The dimensionality and complexity of typical multidisciplinary systems hinders the use of formal optimization techniques in application to this class of problems. The use of approximations to represent the system design metrics and constraints has become vital for achieving good performance in many multidisciplinary design optimization (MDO) algorithms. This paper reports recent research efforts on the use of variable fidelity response surface approximations (RSA) to drive the convergence of MDO problems using a trust region model management algorithm. The present study focuses on a comparative study of different response sampling strategies based on design of experiment (DOE) approaches within the disciplines to generate the zero order data to build the RSAs. Two MDO test problems that have complex coupling between disciplines are used to benchmark the performance of each sampling strategy. The results show that these types of variable fidelity RSAs can be effectively managed by the trust region model management strategy to drive convergence of MDO problems. It is observed that the efficiency of the optimization algorithm depends on the sampling strategy used. A comparison of the DOE approaches with those obtained using a optimization based sampling strategy (i.e. concurrent subspace optimization --- CSSO) shows the DOE methodologies to be competitive with the CSSO based sampling methodology in some cases. However, the CSSO based sampling strategy was found to be, in general, more efficient in driving the optimization.