Efficient and Robust Compressed Sensing Using Optimized Expander Graphs

Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any n-dimensional vector that is k-sparse can be fully recovered using O(klog n) measurements and only O(klog n) simple recovery iterations. In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond 3/4 and show that, with the same number of measurements, only O(k) recovery iterations are required, which is a significant improvement when n is large. In fact, full recovery can be accomplished by at most 2k very simple iterations. The number of iterations can be reduced arbitrarily close to k, and the recovery algorithm can be implemented very efficiently using a simple priority queue with total recovery time O(nlog(n/k))). We also show that by tolerating a small penal- ty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come up with explicit measurement matrices for this method. We compare our result with other recently developed expander-graph-based methods and argue that it compares favorably both in terms of the number of required measurements and in terms of the time complexity and the simplicity of recovery. Finally, we will show how our analysis extends to give a robust algorithm that finds the position and sign of the k significant elements of an almost k-sparse signal and then, using very simple optimization techniques, finds a k-sparse signal which is close to the best k-term approximation of the original signal

Parametric optimization and heat transfer analysis of a dual loop ORC (organic Rankine cycle) system for CNG engine waste heat recovery

In this study, a dual loop ORC (organic Rankine cycle) system is adopted to recover exhaust energy, waste heat from the coolant system, and intercooler heat rejection of a six-cylinder CNG (compressed natural gas) engine. The thermodynamic, heat transfer, and optimization models for the dual loop ORC system are established. On the basis of the waste heat characteristics of the CNG engine over the whole operating range, a GA (genetic algorithm) is used to solve the Pareto solution for the thermodynamic and heat transfer performances to maximize net power output and minimize heat transfer area. Combined with optimization results, the optimal parameter regions of the dual loop ORC system are determined under various operating conditions. Then, the variation in the heat transfer area with the operating conditions of the CNG engine is analyzed. The results show that the optimal evaporation pressure and superheat degree of the HT (high temperature) cycle are mainly influenced by the operating conditions of the CNG engine. The optimal evaporation pressure and superheat degree of the HT cycle over the whole operating range are within 2.5–2.9 MPa and 0.43–12.35 K, respectively. The optimal condensation temperature of the HT cycle, evaporation and condensation temperatures of the LT (low temperature) cycle, and exhaust temperature at the outlet of evaporator 1 are kept nearly constant under various operating conditions of the CNG engine. The thermal efficiency of the dual loop ORC system is within the range of 8.79%–10.17%. The dual loop ORC system achieves the maximum net power output of 23.62 kW under the engine rated condition. In addition, the operating conditions of the CNG engine and the operating parameters of the dual loop ORC system significantly influence the heat transfer areas for each heat exchanger

Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling

The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.Comment: 40 pages, 4 figure

Multi-objective optimization of a novel reversible High-Temperature Heat Pump-Organic Rankine Cycle (HTHP-ORC) for industrial low-grade waste heat recovery

Nowadays, a high amount of industrial thermal energy is still lost due to the lack of competitive solutions for energy revalorization. Facing this challenge, this paper presents a novel technology, based on a reversible High-Temperature Heat Pump (HTHP) and Organic Rankine Cycle (ORC). The proposed system recovers low-grade waste heat to generate electricity or useful heat in accordance with consumer demand. Compressor and expander semi-empirical models have been considered for the reversible system computational simulation, being HFC-245fa the working fluid selected. The built-in volume ratio and Internal Heat Exchanger (IHX) effectiveness have been optimized to reach the maximum energy efficiency in each operating condition. Although HFC-245fa exhibits energy performance attributes, its high Global Warming Potential (GWP) is an issue for climate change mitigation. Hence, multi-objective optimisation of the environmentally friendly working fluids Butane, Pentane, HFO-1336mzz(Z), R-514A, HCFO-1233zd(E) and HCFO-1224yd(Z) has been carried out. The results show that the system proposed, working with HFC-245fa, achieves a Coefficient of Performance (COP) of 2.44 for condensing temperature of 140 °C, operating in HTHP mode, whereas the ORC mode provides a net electrical efficiency of 8.7% at condensing temperature of 40 °C. Besides, HCFO-1233zd(E) and HCFO-1224yd(Z) are both appropriate alternatives for the HFC-245fa replacement. These working fluids provide a COP improvement of 9.7% and 5.8% and electrical net efficiency improvement of 2.1% and 0.8%, respectively, compared to HFC-245fa. This paper provides a reference study for further designs and developments of reversible HTHP-ORC systems used for industrial low-grade waste heat recovery

Algorithmic and Statistical Perspectives on Large-Scale Data Analysis

In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved worst-case algorithms that are useful for large-scale scientific and Internet data analysis problems. In this chapter, I will describe two recent examples---one having to do with selecting good columns or features from a (DNA Single Nucleotide Polymorphism) data matrix, and the other having to do with selecting good clusters or communities from a data graph (representing a social or information network)---that drew on ideas from both areas and that may serve as a model for exploiting complementary algorithmic and statistical perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors, "Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201

ORCSim: a generalized Organic Rankine cycle simulation tool

An increasing interest in organic Rankine cycle (ORC) technology has led to numerous simulation and optimization studies. In the open-literature different modeling approaches can be found, but general software tools available to the academic/industrial community are limited. A generalized ORC simulation tool, named ORCSim, is proposed in this paper. The framework is developed using object-oriented programming that easily allows improvements and future extensions. Currently two cycle configurations are implemented, i.e. a basic ORC and an ORC with liquid-flooded expansion. The software architecture, the thermo-physical property wrappers, the component library and the solution algorithm are discussed with particular emphasis on the ORC with liquid-flooded expansion. A thorough validation both at component and cycle levels is proposed by considering the aforementioned cycle architectures