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

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.

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.

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.

This work, under the optimal experimental design framework, investigates the sensor placement problem that aims to guide electromagnetic induction (EMI) sensing of multiple objects. We use the linearized model covariance matrix as a measure of estimation error to present a sequential experimental design (SED) technique. The technique recursively minimizes data misfit to update model parameters and maximizes an information gain function for a future survey relative to previous surveys. The fundamental process of the SED seeks to increase weighted sensitivities to targets when placing sensors. The synthetic and field experiments demonstrate that SED can be used to guide the sensing process for an effective interrogation. It also can serve as a theoretic basis to improve empirical survey operation. We further study the sensitivity of the SED to the number of objects within the sensing range. The tests suggest that an appropriately overrepresented model about expected anomalies might be a feasible choice.

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.

Sequential sampling refers to a set of design of experiment (DOE) methods where the next sample point is determined by information from previous experiments. This paper introduces a qualitative and quantitative sequential sampling (Q2S2) technique, in which optimization and user knowledge is used to guide the efficient choice of sample points. This method combines information from multiple fidelity sources including computer simulation models of the product, first principals involved in design, and designer’s qualitative intuitions about the design. Both quantitative and qualitative information from different sources are merged together to arrive at a new sampling strategy. This is accomplished by introducing the concept of a confidence function, C, which is represented as a field that is a function of the decision variables, x, and the performance parameter, f. We compare the sampling plans generated by Q2S2 to previously known sample plans on five test functions using various metrics. In each case, the performance of Q2S2 is highly encouraging.

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.

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

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.

Conducting new experiments for biomass gasifiers is expensive and time consuming. Therefore, it is important to select conditions for new experiments so maximum information is obtained. In this study, sequential Bayesian model-based design of experiments (MBDoE) is used to design new experimental runs for a heat-integrated biomass downdraft gasifier. This MBDoE approach is valuable because it accounts for model structure, prior information about plausible parameter values, and previous experimental data in a relatively simple way. Operating conditions selected for each new run are biomass moisture content, water injection rate, and the desired energy demand from the downstream engine. Three types of MBDoE with different objective functions are considered: A-optimal, V-optimal, and a proposed new type of focused V-optimal design. A-optimal design is used to when the goal is to obtain improved parameter estimates, without specifying how the model will be used. Performing two new A-optimal runs reduced the standard deviations for model parameters by 18.4% on average compared to when only old data are available. The three most-improved parameter estimates are activation energies for char gasification reactions involving carbon dioxide, hydrogen, and steam, respectively. The focused V-optimal methodology results in greater improvements in prediction accuracy for tar concentration and outlet temperature, which are key model responses. Using two designed Vf-optimal runs reduces standard deviations for these variables by 59.4%, on average, compared to when only old data are available. New A-optimal and V-optimal runs lead to corresponding improvements of 30.7% and 50%, respectively.

Glycan structures account for up to 35% of the mass of cardiac sodium ( Nav ) channels. To question whether and how reduced sialylation affects Nav activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4(-/-)) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in INa and AP is difficult without performing in silico studies. However, computer model of Nav channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Nav models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Nav channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Nav channels. Notably, ST3Gal4(-/-) myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.

The fixation of uncemented acetabular components largely depends on the amount of bone ingrowth, which is influenced by the design of the implant surface texture. The objective of this numerical study is to evaluate the effect of these implant texture design factors on bone ingrowth around an acetabular component. The novelty of this study lies in comparative finite element (FE) analysis of 3D microscale models of the implant-bone interface, considering patient-specific mechanical environment, host bone material property and implant-bone relative displacement, in combination with sequential mechanoregulatory algorithm and design of experiment (DOE) based statistical framework. Results indicated that the bone ingrowth process was inhibited due to an increase in interbead spacing from 200 μm to 600 μm and bead diameter from 1000 μm to 1500 μm and a reduction in bead height from 900 μm to 600 μm. Bead height, a main effect, was found to have a predominant influence on bone ingrowth. Among the interaction effects, the combination of bead height and bead diameter was found to have a pronounced influence on bone ingrowth process. A combination of low interbead spacing (P = 200 μm), low bead diameter (D = 1000 μm), and high bead height (H = 900 μm) facilitated peri-acetabular bone ingrowth and an increase in average Young's modulus of newly formed tissue layer. Hence, such a surface texture design seemed to provide improved fixation of the acetabular component.

The tgp package for R is a tool for fully Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes with jumps to the limiting linear model. Special cases also implemented include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian processes. In addition to inference and posterior prediction, the package supports the (sequential) design of experiments under these models paired with several objective criteria. 1-d and 2-d plotting, with higher dimension projection and slice capabilities, and tree drawing functions (requiring maptree and combinat packages), are also provided for visualization of tgp objects.

Multidisciplinary Design Optimization for Car-Body Structure Using Sequential Design of Experiments