불확실성 정량화를 이용한 유기랭킨사이클의 강건한 설계에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 화학생물공학부, 2019. 2. 이원보.운전 조건의 변화에 유연한 대처가 가능하며 열역학 파라미터의 측정 오류에 강건한 유기 랭킨 사이클(ORC)을 설계하는 방법론이 개발되었다. 강건한 유기 랭킨 사이클 설계에 앞서, 액화 천연가스(LNG)로부터 최대로 냉열을 추출하기 위해, 다성분 작동 유체를 사용하여 ORC 을 설계하는 방법론이 제안되었다. 제안된 시스템은 다단계의 형태를 보이는 ORC로, 각 단계의 액화기에서 발생하는 엑서지 손실을 최소로 하기 위하여 이 성분 작동 유체를 사용하였다. 각 단계의 작동 유체로서 최적의 혼합물을 찾기 위하여 혼합물의 질량 분율과 압력을 변화시켜 가며 액화기에서 발생하는 엑서지 손질의 최소화를 진행하였다. 최적 작동 유체 혼합물을 선택한 후에 제안된 ORC의 효율 최적화를 위해 ORC 유닛들의 운전 조건들을 이용한 효율 최적화를 시행하였다. 이에 더해 사용된 열원의 온도 변화에 따른 공정 효율의 민감도 분석을 진행하였다. 이어지는 섹션에서는 운전 중 작동 유체의 조성이 변하는 상황에서도 전력을 최대한으로 생산할 수 있는 ORC 설계 방법론이 개발되었다. 제안된 방법은 ORC의 출력이 평균적으로 최대가 되는 설계를 찾는다. ORC의 안정적인 운전에 악영향을 주는 요소들(열교환기 내의 최소 설계 온도 차 위반과 팽창기 블레이드 표면에 액체방울이 형성)을 억제하기 위해, 이러한 요소들이 발생했을 때 목적 함수가 패널티를 받도록 하였다. 최적화에 필요한 통계학적 모멘트들을 구하는 데에는 두 단계가 필요하다. 우선, 노미날 운전 조건 하에서 ORC 시뮬레이션을 통해 열교환기의 면적을 얻는다. 다음으로 계산된 열교환기 면적을 고정한 상태로 조성을 노미날 값으로부터 변화시켜 다시 시뮬레이션을 진행하고, 이로부터 노미날 운전 조건으로 계산했을 때와는 다른 목적 함수의 값을 얻는다. 조성은 노미날 값을 중심으로 분포되어 있다고 가정하였으며, 이때 조성이 선택될 확률은 모든 범위에서 같다고 가정하였다. ORC 출력의 평균값과 분산값을 적은 수의 샘플들로부터 계산하기 위하여 Polynomial Chaos Expansion(PCE) with sparse grid quadrature가 사용되었다. 최적화를 진행한 결과, 조성의 작은 변화라도 ORC의 안정적인 운전에 심각한 영향을 미칠 수 있다는 사실을 알게 되었으며, 제안된 방법을 통해 조성의 불확실성에도 불구하고 유연한 운전이 가능한 ORC를 설계할 수 있었다. 마지막으로, 조성의 불확실성에 더해 열원의 온도와 열역학 파라미터에도 불확실성이 있는 경우를 위한 최적화 방법이 개발되었다. 이전 섹션에서 조성 변화에 가장 둔감한 것으로 밝혀진 작동 유체를 이용하여, 알려진 임계 온도와 임계 압력에 측정 오차가 있는 경우를 위해 다시 최적화를 진행하였다. 또한, 열원의 온도가 노미날 값에서 벗어나는 경우도 ORC 운전의 유연성을 높이기 위해 고려되었다. 총 9개의 불확실한 열역학 파라미터 혹은 디자인 변수들이 고려되었고, 이는 과도한 계산량을 필요로 하므로 이전 섹션으로 개발된 방법으로는 최적화를 수행하기에 무리가 있었다. 따라서 PCE에 기반한 대체 모델을 이용하여 최적화를 진행하는 방법이 개발되었다. 개발된 대체 모델은 평균과 분산을 분석적으로(analytically) 구할 수 있게 해주기 때문에 최적화에 걸리는 시간을 급격하게 감소시켜 주었다. 대체 모델을 이용하여 최적화를 진행한 결과 열역학 파라미터의 불확실성과 디자인 조건의 불확실성에도 불구하고 평균적으로 높은 전력을 생산할 수 있는 ORC를 설계하게 되었다.A method to design the optimal working fluid mixture of Organic Rankine Cycles (ORC), which is operationally flexible and robust against measurement error in thermodynamic parameters, has been developed. Prior to design robust ORC, an optimal design of ORC for utilizing Liquefied Natural Gas (LNG) as heat sink of which evaporation process is not isothermal is proposed to represent a design procedure to extract as much energy as possible from a multicomponent heat sink without consideration of robustness. The proposed system adopts binary working fluids for each stage to minimize the exergy destroyed in the condensers of each stage of the cycle. The best combination of working fluids was selected through minimization of the amount of destroyed exergy by varying the flow rate, composition, and pressure of the working fluid. After selecting the working fluids, process optimization was performed through a parametric study. In addition, a sensitivity analysis was performed to observe the effect of temperature variation of the heat sources in the range of 25 - 85 ℃ on the net power generation. At the following section, a systematic method to design a robust ORC using LNG and multicomponent working fluid, which yields maximum power output even when the composition of the working fluid varies from the nominal point during operation of ORC has been developed. The proposed method seeks the optimal composition giving both the maximum mean of ORC power output. To suppress the factors that adversely affect the operation of ORC (violation of minimum temperature difference in heat exchanger and formation of liquid droplet in expander), the objective function is penalized when they occur. The procedure to derive the statistical moments consists of two steps. Initially, the required heat exchanger area is obtained by simulation of ORC model with a nominal operating conditions (composition, pump discharge pressure, and expander discharge pressure). At the next step, the simulation is carried out again with the obtained area and the varying composition. The mass fraction of each substance in the working fluid is assumed to follow uniform distribution centered at the nominal point. To obtain the mean and variance with a small number of simulations, Polynomial Chaos Expansion (PCE) with sparse grid quadrature is employed. It has been shown that small changes in composition can have serious consequences for stable operation of ORC, and the design of working fluid by the proposed method allows flexible ORC operation despite the existence of uncertainty in the composition. Finally, the optimization takes into account uncertainties in thermodynamic parameters and heat source in addition to composition. Using the selected working fluid which was turned out to be the most insensitive from the uncertainty of composition, optimization is carried out again when the critical temperature and pressure of each substance composing the working fluid varies within its measurement uncertainty, which can be found in the literature. Also, the temperature of the heat source varies from the nominal design point to enhance the operational flexibility of ORC. In sum, the design of ORC was performed assuming a total of the nine parameters or design variables with uncertainty, which requires excessive amount of computation with the method suggested in the previous section. Therefore, the optimization using a surrogate model was devised to efficiently find the optimal and robust ORC design. Because the proposed surrogate model is constructed based on PCE, the statistical moments can be derived analytically, which leads to reduce the time for optimization drastically. Comparing the ORC design, which was taken with more uncertainty, to the design obtained in the previous section, the former design showed the highest output even when the parameters and design variables were changing from the nominal point.1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Conventional ORC configuration . . . . . . . . . . . . . . . . . . . . 5 2 Design and optimization of cascade organic Rankine cycle for recovering cryogenic energy from liquefied natural gas using binary working fluid 10 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Description of the proposed cascade organic Rankine cycle . . . . . . 14 2.3 Simulation and optimization of power generation cycle . . . . . . . . 21 2.3.1 LNG cold exergy recovery part . . . . . . . . . . . . . . . . . 25 2.3.2 Recuperation part . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Simulation and optimization results . . . . . . . . . . . . . . . . . . 31 2.4.1 Result for LNG cold exergy recovery part . . . . . . . . . . . 31 2.5 Working fluid selection and process optimization result for recuperation part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 Energy and exergy analyses . . . . . . . . . . . . . . . . . . . . . . . 43 2.7 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3 Robust design of multicomponent working fluid for organic Rankine cycle - consideration on operational uncertainty 52 3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.1.1 Evaluation of the objective function . . . . . . . . . . . . . . 62 3.1.2 Polynomial chaos expansion . . . . . . . . . . . . . . . . . . 66 3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2.1 ORC with LNG heat sink using ternary working fluid . . . . . 71 3.2.2 Precision test for PCE . . . . . . . . . . . . . . . . . . . . . 77 3.2.3 Influence of penalty function . . . . . . . . . . . . . . . . . . 80 3.2.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . 83 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Docto

Efficient uncertainty quantification in aerospace analysis and design

The main purpose of this study is to apply a computationally efficient uncertainty quantification approach, Non-Intrusive Polynomial Chaos (NIPC) based stochastic expansions, to robust aerospace analysis and design under mixed (aleatory and epistemic) uncertainties and demonstrate this technique on model problems and robust aerodynamic optimization. The proposed optimization approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes the stochastic measures which are minimized simultaneously to ensure the robustness of the final design to both aleatory and epistemic uncertainties. For model problems with mixed uncertainties, Quadrature-Based and Point-Collocation NIPC methods were used to create the response surfaces used in the optimization process. For the robust airfoil optimization under aleatory (Mach number) and epistemic (turbulence model) uncertainties, a combined Point-Collocation NIPC approach was utilized to create the response surfaces used as the surrogates in the optimization process. Two stochastic optimization formulations were studied: optimization under pure aleatory uncertainty and optimization under mixed uncertainty. As shown in this work for various problems, the NIPC method is computationally more efficient than Monte Carlo methods for moderate number of uncertain variables and can give highly accurate estimation of various metrics used in robust design optimization under mixed uncertainties. This study also introduces a new adaptive sampling approach to refine the Point-Collocation NIPC method for further improvement of the computational efficiency. Two numerical problems demonstrated that the adaptive approach can produce the same accuracy level of the response surface obtained with oversampling ratio of 2 using less function evaluations. --Abstract, page iii

Iterative learning control of crystallisation systems

Under the increasing pressure of issues like reducing the time to market, managing lower production costs, and improving the flexibility of operation, batch process industries thrive towards the production of high value added commodity, i.e. specialty chemicals, pharmaceuticals, agricultural, and biotechnology enabled products. For better design, consistent operation and improved control of batch chemical processes one cannot ignore the sensing and computational blessings provided by modern sensors, computers, algorithms, and software. In addition, there is a growing demand for modelling and control tools based on process operating data. This study is focused on developing process operation data-based iterative learning control (ILC) strategies for batch processes, more specifically for batch crystallisation systems. In order to proceed, the research took a step backward to explore the existing control strategies, fundamentals, mechanisms, and various process analytical technology (PAT) tools used in batch crystallisation control. From the basics of the background study, an operating data-driven ILC approach was developed to improve the product quality from batch-to-batch. The concept of ILC is to exploit the repetitive nature of batch processes to automate recipe updating using process knowledge obtained from previous runs. The methodology stated here was based on the linear time varying (LTV) perturbation model in an ILC framework to provide a convergent batch-to-batch improvement of the process performance indicator. In an attempt to create uniqueness in the research, a novel hierarchical ILC (HILC) scheme was proposed for the systematic design of the supersaturation control (SSC) of a seeded batch cooling crystalliser. This model free control approach is implemented in a hierarchical structure by assigning data-driven supersaturation controller on the upper level and a simple temperature controller in the lower level. In order to familiarise with other data based control of crystallisation processes, the study rehearsed the existing direct nucleation control (DNC) approach. However, this part was more committed to perform a detailed strategic investigation of different possible structures of DNC and to compare the results with that of a first principle model based optimisation for the very first time. The DNC results in fact outperformed the model based optimisation approach and established an ultimate guideline to select the preferable DNC structure. Batch chemical processes are distributed as well as nonlinear in nature which need to be operated over a wide range of operating conditions and often near the boundary of the admissible region. As the linear lumped model predictive controllers (MPCs) often subject to severe performance limitations, there is a growing demand of simple data driven nonlinear control strategy to control batch crystallisers that will consider the spatio-temporal aspects. In this study, an operating data-driven polynomial chaos expansion (PCE) based nonlinear surrogate modelling and optimisation strategy was presented for batch crystallisation processes. Model validation and optimisation results confirmed this approach as a promise to nonlinear control. The evaluations of the proposed data based methodologies were carried out by simulation case studies, laboratory experiments and industrial pilot plant experiments. For all the simulation case studies a detailed mathematical models covering reaction kinetics and heat mass balances were developed for a batch cooling crystallisation system of Paracetamol in water. Based on these models, rigorous simulation programs were developed in MATLAB®, which was then treated as the real batch cooling crystallisation system. The laboratory experimental works were carried out using a lab scale system of Paracetamol and iso-Propyl alcohol (IPA). All the experimental works including the qualitative and quantitative monitoring of the crystallisation experiments and products demonstrated an inclusive application of various in situ process analytical technology (PAT) tools, such as focused beam reflectance measurement (FBRM), UV/Vis spectroscopy and particle vision measurement (PVM) as well. The industrial pilot scale study was carried out in GlaxoSmithKline Bangladesh Limited, Bangladesh, and the system of experiments was Paracetamol and other powdered excipients used to make paracetamol tablets. The methodologies presented in this thesis provide a comprehensive framework for data-based dynamic optimisation and control of crystallisation processes. All the simulation and experimental evaluations of the proposed approaches emphasised the potential of the data-driven techniques to provide considerable advances in the current state-of-the-art in crystallisation control

Sensitivity study of dynamic systems using polynomial chaos

International audienceGlobal sensitivity has mainly been analyzed in static models, though most physical systems can be described by differential equations. Very few approaches have been proposed for the sensitivity of dynamic models and the only ones are local. Nevertheless, it would be of great interest to consider the entire uncertainty range of parameters since they can vary within large intervals depending on their meaning. Other advantage of global analysis is that the sensitivity indices of a given parameter are evaluated while all the other parameters can be varied. In this way, the relative variability of each parameter is taken into account, revealing any possible interactions. This paper presents the global sensitivity analysis for dynamic models with an original approach based on the polynomial chaos (PC) expansion of the output. The evaluation of the PC expansion of the output is less expensive compared to direct simulations. Moreover, at each time instant, the coefficients of the PC decomposition convey the parameter sensitivity and then a sensitivity function can be obtained. The PC coefficients are determined using non-intrusive methods. The proposed approach is illustrated with some well-known dynamic systems

Vehicle parameter sensitivity with polynomial chaos

[ES] Es de gran interés analizar la sensibilidad de los parámetros de modelos matemáticos que describen sistemas físicos, y merece una atención particular estudiar esta sensibilidad en modelos con incertidumbre en el valor de sus parámetros. La llamada sensibilidad global considera todo el intervalo de incertidumbre de los parámetros al considerarlos variables aleatorias. Este trabajo presenta el análisis de sensibilidad global en frecuencia del modelo matemático paramétrico de la dinámica lateral de un modelo de automóvil, con un enfoque basado en la expansión de la respuesta del modelo con polinomios de caos. Esta técnica permite representar fácilmente el sistema como un modelo estocástico, donde los parámetros pasan a ser variables aleatorias que varían de acuerdo a su incertidumbre. El modelo estocástico debe ser una aproximación muy cercana del modelo original.[EN] It is interesting to analyze the parameter sensitivity of mathematical models that describe physical systems, and it deserves particular attention the sensitivity study of models with uncertainty in the parameter values. Global sensitivity takes into account the entire range of parameter uncertainty because it considers the parameters as random variables. This paper presents the global sensitivity analysis in frequency of a parametric mathematical model of lateral dynamics of a vehicle model, with an approach based on the polynomial chaos expansion of the model response. This technique allows to easily represent the system as a stochastic model, where the parameters become random variables that vary according to their uncertainty. The stochastic model should be a very close approximation of the original model.Haro, E.; Acebedo, M.; Velázquez, R. (2015). Sensibilidad paramétrica de un automóvil con polinomios de caos. Revista Iberoamericana de Automática e Informática industrial. 12(3):253-259. https://doi.org/10.1016/j.riai.2015.04.001OJS253259123Crestaux, T., Le Maıˆtre, O., & Martinez, J.-M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering & System Safety, 94(7), 1161-1172. doi:10.1016/j.ress.2008.10.008Cukier, R. ., Levine, H. ., & Shuler, K. . (1978). Nonlinear sensitivity analysis of multiparameter model systems. Journal of Computational Physics, 26(1), 1-42. doi:10.1016/0021-9991(78)90097-9Field, R., 2002. Numerical methods to estimate the coefficients of the polynomial chaos expansion. En: 15th ASCE Engineering Mechanics Conference.Ghanem, R., & Red-Horse, J. (1999). Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach. Physica D: Nonlinear Phenomena, 133(1-4), 137-144. doi:10.1016/s0167-2789(99)00102-5Sandoval, E. H. (2008). Estimación de los parámetros físicos de un automóvil. Revista Iberoamericana de Automática e Informática Industrial RIAI, 5(4), 28-35. doi:10.1016/s1697-7912(08)70174-2Haro Sandoval, E., Anstett-Collin, F., & Basset, M. (2012). Sensitivity study of dynamic systems using polynomial chaos. Reliability Engineering & System Safety, 104, 15-26. doi:10.1016/j.ress.2012.04.001Homma, T., & Saltelli, A. (1996). Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering & System Safety, 52(1), 1-17. doi:10.1016/0951-8320(96)00002-6Jacques, J., Lavergne, C., & Devictor, N. (2006). Sensitivity analysis in presence of model uncertainty and correlated inputs. Reliability Engineering & System Safety, 91(10-11), 1126-1134. doi:10.1016/j.ress.2005.11.047Mara, T. A., & Tarantola, S. (2008). Application of global sensitivity analysis of model output to building thermal simulations. Building Simulation, 1(4), 290-302. doi:10.1007/s12273-008-8129-5McKay, M. D., Morrison, J. D., & Upton, S. C. (1999). Evaluating prediction uncertainty in simulation models. Computer Physics Communications, 117(1-2), 44-51. doi:10.1016/s0010-4655(98)00155-6Saltelli, A., Tarantola, S., & Chan, K. P.-S. (1999). A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output. Technometrics, 41(1), 39-56. doi:10.1080/00401706.1999.10485594Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93(7), 964-979. doi:10.1016/j.ress.2007.04.002Turyani, T., Rabitz, H., 2000. Local methods in sensitivity analysis. A. Saltelli, K. Chan, E. M. Scott, John Wiley and Sons, Chichester.Wiener, N. (1938). The Homogeneous Chaos. American Journal of Mathematics, 60(4), 897. doi:10.2307/2371268Witteveen, J., Bijl, H., 2006. Modeling arbitrary uncertainties using Gram-Schmidt polynomial chaos. En: 44th AIAA Aerospace Sciences Meeting and Exhibit.Xiu, D., & Karniadakis, G. E. (2003). Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics, 187(1), 137-167. doi:10.1016/s0021-9991(03)00092-