scholarly journals A Probabilistic Approach to the Asymptotics of the Length of the Longest Alternating Subsequence

10.37236/440 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Christian Houdré ◽  
Ricardo Restrepo
Keyword(s):  
Probabilistic Approach ◽  
Random Permutation ◽  
Probabilistic Methods ◽  
Finite Alphabet ◽  
Restricted Permutations ◽  
Mean Variance

Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in\left[ n\right] $. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}\left( \tau\right) $. Our methodology is robust enough to tackle similar problems for finite alphabet random words or even Markovian sequences in which case our results are mainly original. A sketch of how some cases of pattern restricted permutations can also be tackled with probabilistic methods is finally presented.

A Probabilistic Approach to Fatigue Safety and Integrity of TTRs

2014 ◽  
Author(s):  
Mir Emad Mousavi ◽  
Sanjeev Upadhye ◽  
Vishnu Vijayaraghavan ◽  
Kevin Haverty
Keyword(s):  
Fatigue Damage ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Fatigue Reliability ◽  
Fatigue Design ◽  
Integrity Index ◽  
Biased Estimators ◽  
Integrity Analysis

Probabilistic methods can improve the reliability of fatigue damage evaluation in top tensioned (production) risers because they tend to provide less biased estimators on their safety, which can be used for more reliable decision making concerning their design. Such methods consider the collective impact of uncertainties in the riser system, which is not accurately assessed in conventional fatigue analysis. The large factors of safety that are commonly used in deterministic-based fatigue damage assessment tend to assure the high safety of the design, still they are generic factors that do not take advantage of available data for accurate quantification of system safety. This paper presents a probabilistic method toward fatigue reliability and integrity analysis of TTR systems. By using rules of probability, a simplified method is developed to estimate the probability of failure of the TTR system in its lifetime, considering the uncertainties with the Palmgren-Miner rule, the cyclic loads, and the fatigue strength of the components, and other analysis approximations. The method is then used for a comparative assessment on the fatigue reliability of the TTR components and calculating its fatigue Integrity Index. The method is illustrated in a case study and is used to provide recommendations that could possibly improve the TTR fatigue design by reducing its cost, increasing its safety, and maximizing its integrity.

Choice Numbers of Graphs: a Probabilistic Approach

1992 ◽  
Vol 1 (2) ◽  
pp. 107-114 ◽  
Author(s):  
Noga Alon
Keyword(s):  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Proper Coloring ◽  
Vertex Graph ◽  
Minimum Integer ◽  
Choice Number ◽  
Almost All

The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). By applying probabilistic methods, it is shown that there are two positive constants c1 and c2 such that for all m ≥ 2 and r ≥ 2 the choice number of the complete r-partite graph with m vertices in each vertex class is between c1r log m and c2r log m. This supplies the solutions of two problems of Erdős, Rubin and Taylor, as it implies that the choice number of almost all the graphs on n vertices is o(n) and that there is an n vertex graph G such that the sum of the choice number of G with that of its complement is at most O(n1/2(log n)1/2).

Uncertainties in probabilistic seismic hazard assessment as a function of probability level: A case history for Vancouver, British Columbia

1983 ◽  
Vol 73 (4) ◽  
pp. 1225-1241
Author(s):  
Gail M. Atkinson ◽  
Robin G. Charlwood
Keyword(s):  
British Columbia ◽  
Case History ◽  
Probabilistic Approach ◽  
Seismic Hazard Assessment ◽  
Probabilistic Methods ◽  
Probabilistic Seismic Hazard Assessment ◽  
Probability Level ◽  
Low Probability ◽  
The Stability ◽  
Strong Ground

abstract The stability of probabilistic methods of evaluating expected strong ground motion levels is examined as a function of probability level. A case history for Vancouver, British Columbia, is used to show that when input parameters are screened on the basis of compatibility with low probability calculations, robust (±25 per cent) results are obtained for probabilities in the range of 10−2 to 10−4 per annum. There is no inherent loss of stability with decreasing probability. Probabilistic approaches are not in conflict with deterministic approaches, since deterministic data can be incorporated into the analysis. The usefulness of the probabilistic approach lies in providing a framework for evaluating uncertainties.

Probabilistic Verification of Structures with Respect to Durability

2015 ◽  
Vol 732 ◽  
pp. 313-318
Author(s):  
Jana Marková
Keyword(s):  
Probabilistic Approach ◽  
Theoretical Models ◽  
Probabilistic Methods ◽  
Physical Models ◽  
Background Information ◽  
Probabilistic Verification ◽  
International Standard ◽  
New Procedures

General principles on probabilistic approach to structural verification with respect to durability are provided in the international standard ISO 13823 which is currently being implemented into the system of Czech standards. The operational use of the new procedures in practice would require specification of probabilistic durability criteria, physical models of material deteriorations, and theoretical models of basic variables. It appears that the probabilistic methods of optimisation may provide valuable background information facilitating determination of appropriate criteria for durability.

Digital Human Forward Kinematic and Dynamic Reliabilities

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Jared Gragg ◽  
James Yang
Keyword(s):  
Inverse Kinematics ◽  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Probabilistic Design ◽  
Digital Human Modeling ◽  
End Effector ◽  
Dynamic Reliability ◽  
Human Modeling ◽  
Forward Kinematic ◽  
Digital Human

Probabilistic methods have been applied to many problems in various fields of study. There are many distinct applications of probabilistic design in the biomechanics field, in particular. Traditionally, deterministic methods have been applied in digital human modeling (DHM). Transforming the deterministic approach of digital human modeling into a probabilistic approach is natural since there is inherent uncertainty and variability associated with DHM problems. Typically, deterministic studies in this field ignore this uncertainty or try to limit the uncertainty by employing optimization procedures. Often, inverse kinematics or dynamics techniques are introduced to point the system to the desired solution, or “best solution.” Due to the variability in the inputs, a deterministic study may not be enough to account for the uncertainty in the system. Probabilistic design techniques allow the designer to predict the likelihood of an outcome while also accounting for uncertainty, in contrast to deterministic studies. The purpose of this study is to incorporate probabilistic approaches to a deterministic DHM problem that has already been studied, analyzing human forward kinematics and dynamics. The problem is transformed into a probabilistic approach where the human forward kinematic and dynamic reliabilities are determined. The forward kinematic reliability refers to the probability that the human end-effector position (and/or orientation) falls within a specified distance from the desired position (and/or orientation) in an inverse kinematics problem. The forward dynamic reliability refers to the probability that the human end-effector position (and/or velocity) falls within a specified distance from the desired position (and/or velocity) along a specified trajectory in the workspace. The dynamic equations of motion are derived by the Lagrangian backward recursive dynamics formulation.

scholarly journals Deep Learning of Adaptive Control Systems Based on a Logical-probabilistic Approach

2021 ◽  
Vol 38 ◽  
pp. 65-83
Author(s):  
A. V. Demin ◽  
Keyword(s):  
Adaptive Control ◽  
Control Systems ◽  
Adaptive Learning ◽  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Control Problems ◽  
Adaptive Control Systems ◽  
Control Scheme ◽  
Theory Of Functional Systems ◽  
Selection Of

The problem of automatic selection of subgoals is currently one of the most relevant in adaptive control problems, in particular, in Reinforcement Learning. This paper proposes a logical-probabilistic approach to the construction of adaptive learning control systems capable of detecting deep implicit subgoals. The approach uses the ideas of the neurophysiological Theory of functional systems to organize the control scheme, and logical-probabilistic methods of machine learning to train the rules of the system and identify subgoals. The efficiency of the proposed approach is demonstrated by an example of solving a three-stage foraging problem containing two nested implicit subgoals

scholarly journals Analyzing the Long-Term Service Life of MEP Using the Probabilistic Approach in Residential Buildings

2018 ◽  
Vol 10 (10) ◽  
pp. 3803 ◽  
Author(s):  
Sanghyo Lee ◽  
Yonghan Ahn
Keyword(s):  
Decision Making ◽  
Service Life ◽  
Residential Buildings ◽  
Probabilistic Approach ◽  
Life Time ◽  
Probabilistic Methods ◽  
The Cost ◽  
Maintenance Plan ◽  
Term Maintenance

Establishing an effective long-term maintenance plan is essential to ensure the sustainability of a building. Among the various components of a building, the mechanical, electrical, and plumbing (MEP) components are complexly affected by various parameters, such as quality and user pattern, with respect to the service life. Besides, these components are replaced at different points in time, which becomes one of the main risks when establishing a maintenance plan for the building. Therefore, it is very important to consider the uncertainty in calculating the service lives of MEP components in a systematic and reasonable way. This study aims to systemize the MEP components of residential buildings and analyze their service life patterns using a probabilistic approach for long-term maintenance planning. The analysis was performed on 54,318 maintenance cases from 1998 to 2017 at 65 twenty-five-year-old rental apartment buildings in South Korea. Before performing the analysis, a service life matrix was established by classifying the MEP components into 12 types and setting the service life time at 6–25 years. Then, the service life distribution was derived for each MEP component. The probabilistic approach can provide information for rational maintenance decision-making regarding each MEP component as well as basic service life settings. Since the performance of the MEP components deteriorates due to various reasons, de facto uncertainty exists in the service life of each component; thus, the probabilistic approach can serve as an important decision-making method. If probabilistic methods are developed by acquiring the cost data in addition to the frequency of maintenance activity used in this study, a more effective long-term maintenance plan can be established.

An Assessment of Non-Intrusive Probabilistic Methods for Turbomachinery Problems

2010 ◽  
Author(s):  
Sriram Shankaran ◽  
Brian Barr ◽  
Ramakrishna Mallina ◽  
Ravikanth Avancha ◽  
Alex Stein
Keyword(s):  
Monte Carlo ◽  
Performance Measures ◽  
Performance Metrics ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Optimal Choice ◽  
Probabilistic Methods ◽  
Probabilistic Algorithms ◽  
Optimal Basis ◽  
The Impact

The ability to quantify the impact of uncertainty on performance is an important facet of engineering design. Computational Fluid Dynamics (CFD) studies during the design cycle typically utilize estimates of boundary conditions, geometry and model constants, all of which have uncertainty that could lead to variations in the estimated performance of the design. Traditionally, engineering environments have relied on Monte-Carlo (MC) simulations to obtain probabilistic estimates. But MC methods have poor convergence rate leading to prohibitive computational requirements when used in conjunction with medium to high fidelity computational tools. In this study, we will use an alternate probabilistic approach. We assume that the uncertainties in our computational system can be modeled as random variables with known/prescribed distributions, use CFD solvers to estimate the performance measures and then use a psuedo-spectral probabilistic collocation technique to determine regression/interpolation fits. The psuedo-spectral discrete expansion uses the orthogonal polynomials from the Askey-Wiener basis and finds the coefficients of the expansion [1]. We will restrict our attention to problems with one random variable and hence can without ambiguity choose the Gauss quadratures as the optimal choice to obtain statistical data (mean, variance, moments etc.) of the performance measures. The computational frame-work will be first validated against Monte-Carlo simulations to assess convergence of pdfs. It will then be used to assess the variability in compressor blade efficiency and turbine vane loss due to uncertainty in inflow conditions. The results will be used to answer the following questions. Do we need new probabilistic algorithms to quantify the impact of uncertainty? What is the optimal basis for standard performance metrics in turbomachinery? What are the computational and accuracy requirements of this probabilistic approach? Are there alternate (more efficient) techniques? We believe that the answers to the above questions will provide a quantitative basis to assess the usefulness of non-intrusive (and possibly intrusive) probabilistic methods to analyze variability in engineering designs.

scholarly journals Reliability Assessment of Existing Structures

2008 ◽  
Vol 4 (1) ◽  
pp. 149-164
Author(s):  
Marková Jana
Keyword(s):  
Probabilistic Approach ◽  
Reliability Assessment ◽  
Probabilistic Methods ◽  
International Standard ◽  
Existing Structures

Reliability Assessment of Existing Structures The international standard ISO 13822 provides procedures for the reliability assessment of existing structures including the application of probabilistic methods. Probabilistic approach facilitates to decide about new exploitation of existing structures. Application of probabilistic methods for the reliability assessment of existing structures is shown on the example of deteriorated balcony beams.

Pipeline corrosion risk analysis – an assessment of deterministic and probabilistic methods

2005 ◽  
Vol 52 (1) ◽  
pp. 3-10 ◽  
Author(s):  
K. Lawson
Keyword(s):  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Probabilistic Assessment ◽  
Time Interval ◽  
Deterministic Approach ◽  
Worst Case ◽  
Content Type ◽  
Corrosion Risk ◽  
Pipeline Corrosion ◽  
Failure Probabilities

PurposeThis paper compares and contrasts two approaches to the treatment of pipeline corrosion “risk” – the probabilistic approach and the more traditional, deterministic approach. The paper aims to discuss the merits and potential pitfalls of each approach.Design/methodology/approachProvides an outline of each approach. The probabilistic approach to the assessment of pipeline corrosion risks deals with many of the uncertainties that are common to the data employed and those with regard to the predictive models that are used also. Rather than considering each input parameter as an average value the approach considers the inputs as a series of probability density functions, the collective use during the assessment of risk yields a risk profile that is quantified on the basis of uncertain data. This approach differs from the traditional deterministic assessment in that the output yields a curve that shows how the “risk” of failure increases with time. The pipeline operator simply chooses the level of risk that is acceptable and then devises a strategy to deal with those risks. The traditional (deterministic) approach merely segments the output risks as either “high”, “medium” or “low”; a strategy for managing is devised based on the selection of an appropriate time interval to allow a reasonable prospect of detecting deterioration before the pipeline corrosion allowance is exceeded, or no longer complies with code. Applies both approaches to the case of a 16.1 km long, 14 in. main export line in the North Sea.FindingsThe deterministic assessment yielded a worst‐case failure probability of “medium” with a corresponding consequence of “high”; classifications that are clearly subjective. The probabilistic assessments quantified pipeline failure probabilities, although it is important to note that more effort was required when performing such an assessment. Using target probabilities for “high” and “normal” consequence pipeline segments, indications were that between 8.5 and 13 years was the time period for which the target (predicted) failure probabilities would be reached, again depending on how effective corrosion mitigation activities are in practice. Basing pipeline inspections in particular on the outputs from the deterministic assessment would therefore be conservative in this instance; but this may not necessarily always be so. That the probabilistic assessment indicates that inspections justifiably may be extended beyond that suggested by the deterministic assessment is a clear benefit, in that it affords the opportunity to defer expenditure on pipeline inspections to a later date, but it may be the case that the converse may be required. It may be argued therefore, that probabilistic assessment provides a superior basis for driving pipeline corrosion management activities given that the approach deals with the uncertainties in the basic input data.Originality/valueA probabilistic assessment approach that effectively mirrors pipeline operations, provides a superior basis upon which to manage risk and would therefore likely maximize both safety and business performance.

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