Certain Probability Of Failure Research Articles

Decentralized stochastic linear-quadratic optimal control with risk constraint and partial observation

This paper addresses a risk-constrained decentralized stochastic linear-quadratic optimal control problem with one remote controller and one local controller, where the risk constraint is posed on the cumulative state weighted variance in order to reduce the oscillation of system trajectory. In this model, local controller can only partially observe the system’s state, and sends the estimate of state to remote controller through an unreliable channel, whereas the channel from remote controller to local controller is perfect; here, the unreliable channel means the Bernoulli channel, that is, when data is transmitted on this channel, there is a certain probability of failure. For the considered constrained optimization problem with Bernoulli channel, we first punish the risk constraint into cost function through Lagrange multiplier method, and the resulting augmented cost function will include a quadratic mean-field term of state. In the sequel, for any but fixed multiplier, explicit solutions to finite-horizon and infinite-horizon mean-field decentralized linear-quadratic problems are derived together with necessary and sufficient condition on the mean-square stability of optimal system. Then, approach to find the optimal Lagrange multiplier is presented based on bisection method. Finally, two numerical examples are given to show the efficiency of the obtained results.

Robust microscale structural superlubricity between graphite and nanostructured surface

Structural superlubricity is a state of nearly zero friction and no wear between two contacted solid surfaces. However, such state has a certain probability of failure due to the edge defects of graphite flake. Here, we achieve robust structural superlubricity state between microscale graphite flakes and nanostructured silicon surfaces under ambient condition. We find that the friction is always less than 1 μN, the differential friction coefficient is on the order of 10−4, without observable wear. This is attributed to the edge warping of graphite flake on the nanostructured surface under concentrated force, which eliminate the edge interaction between the graphite flake and the substrate. This study not only challenges the traditional understanding in tribology and structural superlubricity that rougher surfaces lead to higher friction and lead to wear, thereby reducing roughness requirements, but also demonstrates that a graphite flake with a single crystal surface that does not come into edge contact with the substrate can consistently achieve robust structural superlubricity state with any non-van der Waals material in atmospheric conditions. Additionally, the study provides a general surface modification method that enables the widespread application of structural superlubricity technology in atmospheric environments.

Reliability-Aware Computation Offloading for Delay-Sensitive Applications in MEC-Enabled Aerial Computing

With the advent of light and economical Unmanned Vehicles (UAVs), the Internet of Things (IoT) in air is gaining more popularity. However, IoT in air has its own set of requirements and challenges. It is unwise to upload legacy IoT applications to aerial computing networks. For instance, aerial computing in resource constraint UAVs demands energy-efficient solutions. Fortunately, mobile edge computing (MEC) can assist aerial computing by offloading partial or all applications to edge servers (ESs) in MEC. Nevertheless, ESs are subjected to finite resources, and there is a certain probability of failure, and the application in aerial computing is for high-reliability demands. Given the above issue, we investigate computation offloading for delay-sensitive applications under reliability constraints in MEC-enabled aerial computing network where the delay-sensitive applications are represented as scientific workflow applications. Technically, a two-phase reliability-aware computation offloading approach is proposed. More specifically, in the first stage, a multi-objective reliability-aware energy-efficient computation offloading strategy is proposed for the scientific workflow application. Secondly, an improved lazy shadowing scheme is proposed to enhance reliability, energy efficiency, and load balancing. Extensive experiments have been conducted to show the effectiveness and superiority of our proposed solution under different situations.

Improving the selection methodology rational ways to restore parts when repairing machines

Features of quality assurance of production at machine-building enterprises of repair profile are considered. It is revealed that a large number of methods and means of restoring worn parts are used in the repair of machines − mechanical processing, surfacing and welding, metallization and spraying, electrolytic build-up, plastic deformation, and many others. A critical description of the existing theoretical positions on the choice of the most appropriate ways to restore details is presented. It is revealed that the existing methods are based on the criteria of manufacturability, durability and economy and consider the problem of whether it is appropriate to choose a particular method of restoration for only one part forming a joint. A model has been developed to optimize the cost of repairing parts that form a joint, taking into account both the cost of restoring each part and the cost of processing them. Calculations are made for a certain probability of failure and a given resource according to the criterion of the lowest total costs.

Tunnel Ventilation Analysis Using a Probabilistic Approach: Case Study, Fire in Road Tunnels with Longitudinal Ventilation

Tunnels are nowadays key elements in transport networks worldwide. To achieve a safe and efficient operation, a proper integration and design of Mechanical, Electrical and Intelligent Transportation Systems is required. Among these systems, tunnel ventilation is one of the most critical ones from the Fire Life Safety perspective, being smoke control to maintain safe conditions during self-evacuation and rescue operations one of its main objectives. Traditionally tunnel ventilation systems are sized following a deterministic approach. Designers, based on requirements and design criteria from Standards and Recommendations, focus on a limited number of fire scenarios and design parameters to reach a solution considered acceptable from a fire safety perspective. This paper proposes the use of a probabilistic approach to assess, in terms of probability of failure, the capacity of a tunnel ventilation system for fire scenarios. The model applied in the proposed process uses a 1D steady state model based on pressure losses, where critical design variables are considered random (unlike with the deterministic approach) to calculate a failure probability associated to an installed ventilation thrust. A case study example is used to analyse results using both, the traditional deterministic approach and the proposed probabilistic one. Results obtained with the deterministic approach show how, under the same design requirements, tunnels with similar characteristics allow different safety margins for the capacity of the ventilation system. These results are confirmed numerically using the probabilistic approach by evaluating failure probabilities. To avoid this, the paper proposes the use of the probabilistic approach to allow a definition of an equivalent uniform safety margin (to achieve a certain probability of failure) which would be of significant help for designers, administrations and tunnel operators. It is not the aim of the study to define the limit for the probability of failure or to characterise the design variables, but to present a useful tool with which important conclusions about the design criteria can be obtained.

Probabilistic metrology or how some measurement outcomes render ultra-precise estimates

We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision that exceeds the deterministic bounds for the average precision. This establishes a new ultimate bound on the phase estimation precision of particular measurement outcomes (or sequence of outcomes). For probe systems subject to local dephasing, we quantify such precision limit as a function of the probability of failure that can be tolerated. Our results show that the possibility of abstaining can set back the detrimental effects of noise.

AND-Compression of NP-Complete Problems: Streamlined Proof and Minor Observations

Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP is in NP/poly occurs, there is no AND-compression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NP-complete parameterized problems. We present a streamlined proof of Drucker's theorem. An AND-compression is a deterministic polynomial-time algorithm that maps a set of SAT-instances $x_1,\dots,x_t$ to a single SAT-instance of size poly(max $|x_i|$) such that is if and only if all are The in the name stems from the fact that the predicate $y$ is satisfiable can be written as the AND of all predicates $x_i$ is satisfiable. Drucker's result complements the result by Bodlaender et al. (2009) and Fortnow and Santhanam (2010), who proved the analogous statement for OR-compressions, and Drucker's proof not only subsumes that result but also extends it to randomized compression algorithms that are allowed to have a certain probability of failure. Drucker (2012) presented two proofs: The first uses information theory and the minimax theorem from game theory, and the second is an elementary, iterative proof that is not as general. In our proof, we realize the iterative structure as a generalization of the arguments of Ko (1983) for P-selective sets, which use the fact that tournaments have dominating sets of logarithmic size. We generalize this fact to hypergraph tournaments. Our proof achieves the full generality of Drucker's theorem, avoids the minimax theorem, and restricts the use of information theory to a single, intuitive lemma about the average noise sensitivity of compressive maps. To prove this lemma, we use the same information-theoretic inequalities as Drucker.

Evaluation of Bearing Capacity of Strip Footing Using Random Layers Concept

Abstract The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

Cutting plane versus compact formulations for uncertain (integer) linear programs

Robustness is about reducing the feasible set of a given nominal optimization problem by cutting “risky” solutions away. To this end, the most popular approach in the literature is to extend the nominal model with a polynomial number of additional variables and constraints, so as to obtain its robust counterpart. Robustness can also be enforced by adding a possibly exponential family of cutting planes, which typically leads to an exponential formulation where cuts have to be generated at run time. Both approaches have pros and cons, and it is not clear which is the best one when approaching a specific problem. In this paper we computationally compare the two options on some prototype problems with different characteristics. We first address robust optimization a la Bertsimas and Sim for linear programs, and show through computational experiments that a considerable speedup (up to 2 orders of magnitude) can be achieved by exploiting a dynamic cut generation scheme. For integer linear problems, instead, the compact formulation exhibits a typically better performance. We then move to a probabilistic setting and introduce the uncertain set covering problem where each column has a certain probability of disappearing, and each row has to be covered with high probability. A related uncertain graph connectivity problem is also investigated, where edges have a certain probability of failure. For both problems, compact ILP models and cutting plane solution schemes are presented and compared through extensive computational tests. The outcome is that a compact ILP formulation (if available) can be preferable because it allows for a better use of the rich arsenal of preprocessing/cut generation tools available in modern ILP solvers. For the cases where such a compact ILP formulation is not available, as in the uncertain connectivity problem, we propose a restart solution strategy and computationally show its practical effectiveness.

Decoding for iterative Reed-Solomon coding schemes

For high density data storage systems channel errors may appear in the form of bursts. This error correlation can significantly degrade the bit error rate on the subsequent stages of data processing. To correct error bursts the interleaved Read-Solomon (RS) codes are used. Usually, after the deinterleaving, the received words are decoded one by one by the same error correction algorithm. In this paper, a novel approach for the decoding of interleaved codes is proposed. It is based on a notion of covering error locators that locate error positions in two or more adjacent words. To compute the covering error locator polynomial, a modification of the Berlekamp-Massey algorithm is proposed. It is shown that with a certain probability of failure the proposed algorithm can correct more errors than the designed error correction ability. The algorithm may also be useful in a more general case of interleaved coding schemes with both rows and columns encoded by RS code.

Probabilistic assessment of the stability of rock slopes

The performance functions for several, two dimensional failure modes are presented. Most of the parameters of the performance function have to be considered as statistically dispersive. Therefore, prior to a reliability analysis, the statistics of the parameters are discussed. Subsequently, probabilistic sensitivity studies, using the First Order Second Moment Approach, are carried out. Furthermore, design factors are derived, which provide a certain probability of failure. This study may help to minimize both the risk of failure and the costs of reinforcing rock slopes.

A Simple Method for Reliability Evaluation of a Communication System

Very few techniques exist for reliability evaluation of communication systems where links as well as nodes have certain probability of failure. This correspondence describes a technique by which the reliability expression for such a system can be conveniently derived. It is also shown that using the concept of this correspondence, it is possible to extend all the existing reliability-evaluation algorithms to communication systems with little effort.

The Relevance of Intra-Cellular Damage to Effects in the Complex Organism

As the three previous papers in this Symposium have shown (Ord and Stocken 1968; Evans 1968; Court-Brown 1968) the exploration of radiation effects within the cell has its own intrinsic fascination quite apart from its relevance to an understanding of the phenomena which may be observed after irradiation of the complex organism, vertebrate or invertebrate. Whitmore (cf. Whitmore Gulyas and Botond 1965) has been one of the pioneer workers on a previously unsuspected phenomenon, the quantitatively substantial recovery of the ability to divide which occurs within the first hour or two after exposure to low LET radiation. In cultures of mammalian cells in vitro this kind of recovery was shown to have nothing to do with cell division, to occur at all stages of the cell cycle, and to be little, if at all, affected by a reduction in temperature which would be expected a priori to modify profoundly the rate of chemical reactions. Whitmore's technique for synchronising asynchronously dividing cell cultures by the selective suicide of DNA synthesising cells following the incorporation of radioactively labelled DNA precursors with high specific activity has a wide application (Whitmore and Gulyas 1966). Workers from his laboratory have proposed an interesting approach to the real meaning of “ability to divide” and “recovery” based on the idea that there is a certain probability of failure at each cell division and that this probability may be permanently increased by exposure to radiation (Till, McCulloch and Siminovitch 1964). Thus radiation damage may be expressed by failure of cell division not only at the first or second divisions after exposure but also at any subsequent division in the distant future.