Analyzing process flexibility: A distribution-free approach with partial expectations

We develop a distribution-free model to evaluate the performance of process flexibility structures when only the mean and partial expectation of the demand are known. We characterize the worst-case demand distribution under general concave objective functions, and apply it to derive tight lower bounds for the performance of chaining structures under the balanced systems (systems with the same number of plants and products). We also derive a simple lower bound for chaining-like structures under unbalanced systems with different plant capacities. Keywords: Process flexibility; Distributionally-robust analysis; Chaining; Production system desig

Combinatorics

Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing abstracts of the presentations and a summary of the problem session

Expander Graphs and Coding Theory

Expander graphs are highly connected sparse graphs which lie at the interface of many different fields of study. For example, they play important roles in prime sieves, cryptography, compressive sensing, metric embedding, and coding theory to name a few. This thesis focuses on the connections between sparse graphs and coding theory. It is a major challenge to explicitly construct sparse graphs with good expansion properties, for example Ramanujan graphs. Nevertheless, explicit constructions do exist, and in this thesis, we survey many of these constructions up to this point including a new construction which slightly improves on an earlier edge expansion bound. The edge expansion of a graph is crucial in applications, and it is well-known that computing the edge expansion of an arbitrary graph is NP-hard. We present a simple algo-rithm for approximating the edge expansion of a graph using linear programming techniques. While Andersen and Lang (2008) proved similar results, our analysis attacks the problem from a different vantage point and was discovered independently. The main contribution in the thesis is a new result in fast decoding for expander codes. Current algorithms in the literature can decode a constant fraction of errors in linear time but require that the underlying graphs have vertex expansion at least 1/2. We present a fast decoding algorithm that can decode a constant fraction of errors in linear time given any vertex expansion (even if it is much smaller than 1/2) by using a stronger local code, and the fraction of errors corrected almost doubles that of Viderman (2013)

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

On the design of sparse but efficient structures in operations

It is widely believed that a little flexibility added at the right place can reap significant benefits for operations. Unfortunately, despite the extensive literature on this topic, we are not aware of any general methodology that can be used to guide managers in designing sparse (i.e., slightly flexible) and yet efficient operations. We address this issue using a distributionally robust approach to model the performance of a stochastic system under different process structures. We use the dual prices obtained from a related conic program to guide managers in the design process. This leads to a general solution methodology for the construction of efficient sparse structures for several classes of operational problems. Our approach can be used to design simple yet efficient structures for workforce deployment and for any level of sparsity requirement, to respond to deviations and disruptions in the operational environment. Furthermore, in the case of the classical process flexibility problem, our methodology can recover the k-chain structures that are known to be extremely efficient for this type of problem when the system is balanced and symmetric. We can also obtain the analog of 2-chain for nonsymmetrical system using this methodology. This paper was accepted by Yinyu Ye, optimization. </jats:p

The existence of designs via iterative absorption: hypergraph FF-designs for arbitrary FF

We solve the existence problem for $F$-designs for arbitrary $r$-uniform hypergraphs~$F$. This implies that given any $r$-uniform hypergraph~$F$, the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any sufficiently large complete $r$-uniform hypergraph into edge-disjoint copies of~$F$, which answers a question asked e.g.~by Keevash. The graph case $r=2$ was proved by Wilson in 1975 and forms one of the cornerstones of design theory. The case when~$F$ is complete corresponds to the existence of block designs, a problem going back to the 19th century, which was recently settled by Keevash. In particular, our argument provides a new proof of the existence of block designs, based on iterative absorption (which employs purely probabilistic and combinatorial methods). Our main result concerns decompositions of hypergraphs whose clique distribution fulfills certain regularity constraints. Our argument allows us to employ a `regularity boosting' process which frequently enables us to satisfy these constraints even if the clique distribution of the original hypergraph does not satisfy them. This enables us to go significantly beyond the setting of quasirandom hypergraphs considered by Keevash. In particular, we obtain a resilience version and a decomposition result for hypergraphs of large minimum degree.Comment: This version combines the two manuscripts `The existence of designs via iterative absorption' (arXiv:1611.06827v1) and the subsequent `Hypergraph F-designs for arbitrary F' (arXiv:1706.01800) into a single paper, which will appear in the Memoirs of the AM

Applications of Coding Theory to Massive Multiple Access and Big Data Problems

The broad theme of this dissertation is design of schemes that admit iterative algorithms with low computational complexity to some new problems arising in massive multiple access and big data. Although bipartite Tanner graphs and low-complexity iterative algorithms such as peeling and message passing decoders are very popular in the channel coding literature they are not as widely used in the respective areas of study and this dissertation serves as an important step in that direction to bridge that gap. The contributions of this dissertation can be categorized into the following three parts. In the first part of this dissertation, a timely and interesting multiple access problem for a massive number of uncoordinated devices is considered wherein the base station is interested only in recovering the list of messages without regard to the identity of the respective sources. A coding scheme with polynomial encoding and decoding complexities is proposed for this problem, the two main features of which are (i) design of a close-to-optimal coding scheme for the T-user Gaussian multiple access channel and (ii) successive interference cancellation decoder. The proposed coding scheme not only improves on the performance of the previously best known coding scheme by ≈ 13 dB but is only ≈ 6 dB away from the random Gaussian coding information rate. In the second part construction-D lattices are constructed where the underlying linear codes are nested binary spatially-coupled low-density parity-check codes (SCLDPC) codes with uniform left and right degrees. It is shown that the proposed lattices achieve the Poltyrev limit under multistage belief propagation decoding. Leveraging this result lattice codes constructed from these lattices are applied to the three user symmetric interference channel. For channel gains within 0.39 dB from the very strong interference regime, the proposed lattice coding scheme with the iterative belief propagation decoder, for target error rates of ≈ 10^-5, is only 2:6 dB away the Shannon limit. The third part focuses on support recovery in compressed sensing and the nonadaptive group testing (GT) problems. Prior to this work, sensing schemes based on left-regular sparse bipartite graphs and iterative recovery algorithms based on peeling decoder were proposed for the above problems. These schemes require O(K logN) and Ω(K logK logN) measurements respectively to recover the sparse signal with high probability (w.h.p), where N, K denote the dimension and sparsity of the signal respectively (K (double backward arrow) N). Also the number of measurements required to recover at least (1 - €) fraction of defective items w.h.p (approximate GT) is shown to be cv€_K logN/K. In this dissertation, instead of the left-regular bipartite graphs, left-and- right regular bipartite graph based sensing schemes are analyzed. It is shown that this design strategy enables to achieve superior and sharper results. For the support recovery problem, the number of measurements is reduced to the optimal lower bound of Ω (K log N/K). Similarly for the approximate GT, proposed scheme only requires c€_K log N/ K measurements. For the probabilistic GT, proposed scheme requires (K logK log vN/ K) measurements which is only log K factor away from the best known lower bound of Ω (K log N/ K). Apart from the asymptotic regime, the proposed schemes also demonstrate significant improvement in the required number of measurements for finite values of K, N