State Reduction Techniques Research Articles

Long-term reliability evaluation of integrated electricity and gas systems considering distributed hydrogen injections

Power-to-gas facilities consume surplus renewable electricity generation to produce alternative gases, such as green hydrogen. They can be injected into, and transported by the gas network for further use, which is a promising way toward a low-carbon energy system. However, injecting alternative gases into the gas systems can adversely affect the gas composition and the lifespan of components (e.g., gas pipelines), and may threaten the reliability of the entire integrated electricity and gas systems (IEGS) in the long term. To address this issue, this paper proposes a long-term reliability evaluation method for IEGS with distributed hydrogen injections. First, new reliability indices are proposed to evaluate both gas adequacy and gas interchangeability under uncertainties. Then, a multi-state reliability model of the pipeline is developed to characterize the corrosion evolution and hydrogen embrittlement in the long term. A contingency management scheme (CMS) is devised to minimize load curtailments and gas interchangeability deviations under component failures. Moreover, several reformulation techniques are tailored to convexify the original two-stage mixed-integer nonlinear CMS optimization problem. An analytical reliability evaluation method embedded with a system state reduction technique is designed to evaluate the long-term reliability of the IEGS more efficiently. Finally, the IEEE 24 bus Reliability Test System and the practical Belgium gas system are used to validate the proposed method. The numerical results show that the injection of alternative gas could jeopardize the reliability of the studied IEGS by 39.73% in the long term. However, we have observed a critical time window (the 8th–9th year), in which if we conduct the inline inspection and maintenance more frequently, the reliability could be improved by up to 53.31%. These results suggest that the injection of alternative gas is beneficial, but should be carefully regulated to maintain the reliability of IEGS.

On Space-Time Block-Encoded 16-APSK in Aeronautical Mobile Telemetry

The two-antenna problem in aeronautical mobile telemetry is created by the reception of two copies of the same RF waveform with different phases and time delays. Alamouti and Alamouti-like space time block codes can solve the two-antenna problem, but the decoder/detector needs to account for the different time delays between the signals received from the two transmit antennas. This paper compares the performance of Alamouti space-time block codes and time-reversed space-time block codes with 16-APSK to solve the two-antenna problem. The maximum likelihood decoder/detector for Alamouti-encoded 16-APSK is a sequence detector operating on a trellis with a large number of states. A practical state-reduction technique is presented that produces a trellis with 256 states and a small loss in bit error rate performance. The decoder/detector for the time-reversed space time block requires only waveform manipulations and pulse shape matched filtering in the case where the two channels are simple delays. The bit error rate performance of the simplified decoder/detector produces no detectable loss in the bit error rate performance.

Towards Scalable Model Checking of Reflective Systems via Labeled Transition Systems

Reflection is a technique that enables a system to inspect or change its structure and/or behavior at runtime. It is a key enabler of many techniques for developing systems that have to function despite rapidly changing requirements and environments. A crucial issue in developing reflective systems is to ensure the correctness of their behaviors, because object-level behaviors are affected by metalevel behaviors. In this paper, we present an extended labeled transition system (LTS), which we call a metalevel LTS (MLTS), that supports data representation of another LTS for use in modeling a reflective tower. We show that two of the existing state reduction techniques for an LTS ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">symmetry reduction</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">divergence-sensitive stutter bisimulation</i> ) are also applicable to an MLTS. Then, we introduce two strategies for implementing an MLTS model in Promela, thereby enabling verification with the SPIN model checker. We also present case studies of applying MLTSs to two reflection applications: self-adaptation of a reconnaissance robot system, and dynamic evolution of an Internet-of-things (IoT) system. The case studies demonstrate the applicability of our approach and its scalability improvement through the state reduction techniques.

Online Optimal State Feedback Control of Linear Systems Over Wireless MIMO Fading Channels

We consider the optimal control of linear systems over wireless MIMO fading channels, where the MIMO wireless fading and random access of the remote controller may cause intermittent controllability or uncontrollability of the closed-loop control system. We formulate the optimal control design over random access MIMO fading channels as an infinite horizon average cost Markov decision process (MDP), and we propose a novel state reduction technique such that the optimality condition is transformed into a time-invariant reduced-state Bellman optimality equation. We provide the closed-form characterizations on the existence and uniqueness of the optimal control solution via analyzing the reduced-state Bellman optimality equation. Specifically, in the case that the closed-loop system is almost surely controllable, we show that the optimal control solution always exists and is unique. In the case that MIMO fading channels and the random access of the remote controller destroy the closed-loop controllability, we propose a novel controllable and uncontrollable positive semidefinite (PSD) cone decomposition induced by the singular value decomposition (SVD) of the MIMO fading channel contaminated control input matrix. Based on the decomposed fine-grained reduced-state Bellman optimality equation, we further propose a closed-form sufficient condition for both the existence and the uniqueness of the optimal control solution. The closed-form sufficient condition reveals the fact that the optimal control action may still exist even if the closed-loop system suffers from intermittent controllability or almost sure uncontrollability.

Adaptive formal approximations of Markov chains

We explore formal approximation techniques for Markov chains based on state–space reduction that aim at improving the scalability of the analysis, while providing formal bounds on the approximation error. We first present a comprehensive survey of existing state-reduction techniques based on clustering or truncation. Then, we extend existing frameworks for aggregation-based analysis of Markov chains by allowing them to handle chains with an arbitrary structure of the underlying state space – including continuous-time models – and improve upon existing bounds on the approximation error. Finally, we introduce a new hybrid scheme that utilises both aggregation and truncation of the state space and provides the best available approach for approximating continuous-time models. We conclude with a broad and detailed comparative evaluation of existing and new approximation techniques and investigate how different methods handle various Markov models. The results also show that the introduced hybrid scheme significantly outperforms existing approaches and provides a speedup of the analysis up to a factor of 30 with the corresponding approximation error bounded within 0.1%.

Statistical solution of inverse problems using a state reduction

PurposeThe application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.Design/methodology/approachA reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.FindingsFor the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.Practical implicationsThe state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.Originality/valueThe paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

Load service restoration in active distribution network based on stochastic approach

A new stochastic framework is proposed for distribution system restoration (DSR) problem. In this framework, dynamic programming (DP) is used to solve DSR problem for a distribution system that accommodates various technologies of distributed generation units and storage systems. Time and sequence of distribution feeders which should be energised after a blackout are chosen as stages of DP algorithm. In addition, uncertainties associated with the power received from transmission network in the period of system restoration are modelled as some probabilistic scenarios. The complexity of attained optimisation problem is reduced using some state reduction techniques. These techniques enable DP algorithm to reach near-optimal solution as well as computationally efficient calculation procedure. The proposed restoration framework is applied on a real-world test system and the results prove its effectiveness and practicality.

Discussion

Discussion

PCA based state reduction for inverse problems using prior information

PurposeInverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge.Design/methodology/approachIll-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography.FindingsBased on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms.Practical implicationsThe full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm.Originality/valueThe paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.

A randomized point-based value iteration POMDP enhanced with a counting process technique for optimal management of multi-state multi-element systems

Optimal decision-making for systems in the presence of uncertainty poses a significant challenge in many fields of research and for many applications. While Markov Decision Process (MDP) is a capable probabilistic framework to incorporate uncertainties in system behavior, measurement randomness arising from imperfect inspections is disregarded in those models. Additionally, the decision-making problem for multi-state multi-element systems has exponential time complexity with respect to the number of system elements. This paper introduces a new decision-making framework for such systems that incorporates element-level decision variables and their consequences at the system-level of an asset. The framework employs a Partially Observable MDP (POMDP) with a randomized point-based value iteration solution strategy to capture system forecasting uncertainty as well as randomness in inspection measurements. The capability of the framework to handle large-scale optimization problems for element-level decision-making in multi-element systems is considerably enhanced via a counting process state reduction technique that is introduced and integrated into the POMDP model. The application of the proposed framework is demonstrated for long-run decision-making regarding maintenance, rehabilitation, and repair of a bridge system with realistic settings. Based on numerical results, it is concluded that the proposed framework composed of POMDP and the counting process techniques provides an efficient yet accurate approach for the optimal management of multi-state multi-element systems.

Hyper-Minimization for Deterministic Weighted Tree Automata

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the situation in comparison to the unweighted case. In addition, the first hyper-minimization algorithm for deterministic weighted tree automata, weighted over commutative semifields, is provided together with some implementation remarks that enable an efficient implementation. In fact, the same run-time O(m log n) as in the unweighted case is obtained, where m is the size of the deterministic weighted tree automaton and n is its number of states.

High Performance Computing on Fast Lock Delay Locked Loop with Low Power State and Simultanoeus Switching Noise Reduction

Problem statement: In any multimedia processor, controller may consume most of the on- chip memory resources. The memory requirement is directly depends on algorithm shared by different blocks, so leads to failure in the system models. Approach: This study presents the implementation of DLL unit used for memory optimization. Various aspects of the underlying coarse lock detector are explored and modifications are made with software r eference implementation. The whole system is implemented in 0.18 µm CMOS technology, where an input reference clock to an outgoing data clock monitors and true locking is initialized with 50% d uty cycle correction. Results: From the measurement result of DLL operation, the output clo ck jitter is analyzed. Power consumption of DLL including large size output buffer is about few mW. Conclusion: The great challenge in this implementation is communication bandwidth, has brought to process variation and power state reduction techniques. In addition, inefficiency of computing capacity and simultaneous switching noise is reduced in the real time applications.

UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

Computational performance of basic state reduction based dynamic programming algorithms for bi-objective 0–1 knapsack problems

This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking.

A two state reduction based dynamic programming algorithm for the bi-objective 0–1 knapsack problem

In this paper, we present a dynamic programming (DP) algorithm for the multi-objective 0–1 knapsack problem (MKP) by combining two state reduction techniques. One generates a backward reduced-state DP space (BRDS) by discarding some states systematically and the other reduces further the number of states to be calculated in the BRDS using a property governing the objective relations between states. We derive the condition under which the BRDS is effective to the MKP based on the analysis of solution time and memory requirements. To the authors’ knowledge, the BRDS is applied for the first time for developing a DP algorithm. The numerical results obtained with different types of bi-objective instances show that the algorithm can find the Pareto frontier faster than the benchmark algorithm for the large size instances, for three of the four types of instances conducted in the computational experiments. The larger the size of the problem, the larger improvement over the benchmark algorithm. Also, the algorithm is more efficient for the harder types of bi-objective instances as compared with the benchmark algorithm.

Information rates of multidimensional front ends for digital storage channels with data-dependent transition noise

This paper presents a simulation-based method for the computation of the information rates of recently proposed multidimensional front ends for digital storage channels with transition noise. First, we propose an algorithm, based on linear prediction and state reduction techniques, that extends recent work on the information rates of magnetic recording channels affected by colored Gaussian thermal noise, intersymbol interference, and signal-dependent transition noise. Following a previous study on statistical sufficiency, we apply this algorithm to compute the information rates of digital storage systems featuring a multidimensional detection front end. The resulting information rates indicate that significant gains may be achievable by multidimensional signal processing techniques in transition-noise-limited digital storage channels

Fast Graph-Search Algorithms for General-Aviation Flight Trajectory Generation

We consider numerical algorithms for on-board flight trajectory generation and optimization in three dimensional space. Our approach relies on graph search algorithms, which perform a global search over the set of feasible trajectories. We start by formulating a simplified kinematic model that is appropriate for General Aviation aircraft. The cost function to be optimized includes, the cost function to be optimized accounts for position-dependent criteria such as the flight altitude and terrain clearance. Additional “dynamic” components that involve the angular velocities are introduced to account for riding qualities and pilot workload. Using an approximate grid-based discretization scheme, we transform the continuous optimization problem into a search problem over a finite graph, and apply Dijkstra’s shortest-path algorithm to this problem. To reduce the computation time to acceptable levels, we introduce a novel state reduction technique that leads to sub-optimal search. Further speedup is achieved by heuristic search techniques and hierarchical methods. Performance of the proposed algorithms is evaluated for a trajectory optimization problem with terrain following over a 100 × 100 kilometer area. Our experiments demonstrate the potential of these algorithms, when combined, to provide an on-board solution to realistic flight trajectory generation problems. ∗Graduate student, Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel †Department of Aeronautical Engineering, Technion—Israel Institute of Technology, Haifa, Israel ‡Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa, Israel

Distance spectrum analysis of space-time trellis-coded modulations in quasi-static rayleigh-fading channels

In this correspondence, we propose an algorithm for computing the distance spectrum of a space-time trellis code achieving maximal diversity gain in quasi-static fading channels. We further present a state reduction technique for trellis codes that can reduce the complexity of the distance spectrum computation. We provide numerical results supporting the empirical evidence that a truncated union bound obtained from the distance spectrum provides an accurate characterization of the relative performance ordering of different space-time trellis codes and, therefore, it offers a tool for better space-time trellis code design.

Generation of maximally entangled photonic states with a quantum-optical Fredkin gate

When a quantum-optical Fredkin gate is embedded into a Mach-Zehnder interferometer, state reduction techniques permit the generation of maximally entangled states of the radiation field when Fock states are input to the device. These states exactly reach the Heisenberg limit of phase sensitivity. We investigate the consequences of injecting more general states, and particularly coherent states, into the apparatus. Applications to interferometry and photolithography are discussed.

Noncoherent iterative decoding of spectrally efficient coded modulations

In this paper, we consider possible solutions for noncoherent decoding of concatenated codes with spectrally efficient modulations. Two main classes of schemes are considered. A first class is obtained by concatenating parallel coding schemes with differential encoding. A second class considers serially concatenated coding structures and possible schemes derived from turbo trellis coded modulation (T-TCM), which do not employ differential encoding. In the first case, at the receiver side we consider separate detection and decoding, while in the second case we consider joint detection and decoding. The major problem connected with such an iterative decoding procedure is that taking into account an augmented channel memory leads to an intolerable trellis size, and hence to an impractical decoding complexity. Reduced-complexity techniques suited to iterative decoding become fundamental, and we consider a recently proposed state-reduction technique. This way, the performance of a coherent receiver is approached, by keeping the number of receiver states fixed.