scholarly journals OPTIMIZING THE MUTUAL ARRANGEMENT OF PILOT INDICATORS ON AN AIRCRAFT DASHBOARD AND ANALYSIS OF THIS PROCEDURE FROM THE VIEWPOINT OF QUANTUM REPRESENTATIONS

2021 ◽  
pp. 1-10
Author(s):  
L.S. Kuravsky ◽  
I.I. Greshnikov
Keyword(s):  
Transition Probability ◽  
Practical Experience ◽  
Transition Probability Matrix ◽  
Mutual Arrangement ◽  
Similarity Matrix ◽  
Design Decisions ◽  
The Gaze ◽  
Iterative Correction ◽  
Expert Assessments ◽  
The Difference

The purpose of this work is to present the first attempt to provide quantitative analysis and objective justification for designers’ decisions that relate to the arrangement of pilot indicators on an aircraft dashboard with the use of video oculography measurements. To date, such decisions have been made only based on the practical experience accumulated by designers and subjective expert assessments. A new method for optimizing the mutual arrangement of the dashboard indicators is under consideration. This is based on iterative correction of the gaze transition probability matrix between the selected zones of attention, to minimize the difference between the stationary distribution of relative frequencies of gaze that are staying in these zones and the corresponding desirable target eye movements that are given for distribution for qualified pilots. When solving the subsequent multidimensional scaling problem, the gaze transition probability matrix that is obtained is considered to be the similarity matrix, the elements of which quantitatively characterize the proximity between the zones of attention. The main findings of this novel work are as follows: the use of oculography data to justify dashboard design decisions, the optimizing method itself, and its mathematical components, as well as analysis of the optimization in question from the viewpoint of quantum representations, all revealed design mistakes. The results that were obtained can be applied for prototyping variants of aircraft dashboards by rearranging the display areas associated with the corresponding zones of attention.

The Reliability Analysis of Mechanical Leg (2UPS+UP) Based on a Discrete Time Repairable Markov Model

2015 ◽  
Vol 713-715 ◽  
pp. 760-763
Author(s):  
Jia Lei Zhang ◽  
Zhen Lin Jin ◽  
Dong Mei Zhao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Transition Probability ◽  
Continuous Model ◽  
Transition Probability Matrix ◽  
State Equations ◽  
One Step ◽  
The Difference ◽  
Step Transition ◽  
The One

We have analyzed some reliability problems of the 2UPS+UP mechanism using continuous Markov repairable model in our previous work. According to the check and repair of the robot is periodic, the discrete time Markov repairable model should be more appropriate. Firstly we built up the discrete time repairable model and got the one step transition probability matrix. Secondly solved the steady state equations and got the steady state availability of the mechanical leg, by the solution of the difference equations the reliability and the mean time to first failure were obtained. In the end we compared the reliability indexes with the continuous model.

scholarly journals Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Hendrik Baumann ◽  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Transition Probability ◽  
Solution Space ◽  
Transition Probability Matrix ◽  
Discrete State ◽  
Side Condition ◽  
Hitting Probabilities ◽  
All Solutions ◽  
The Difference ◽  
State Difference

In a previous paper, we have shown that forward use of the steady-state difference equations arising from homogeneous discrete-state space Markov chains may be subject to inherent numerical instability. More precisely, we have proven that, under some appropriate assumptions on the transition probability matrix P, the solution space S of the difference equation may be partitioned into two subspaces S=S1⊕S2, where the stationary measure of P is an element of S1, and all solutions in S1 are asymptotically dominated by the solutions corresponding to S2. In this paper, we discuss the analogous problem of computing hitting probabilities of Markov chains, which is affected by the same numerical phenomenon. In addition, we have to fulfill a somewhat complicated side condition which essentially differs from those conditions one is usually confronted with when solving initial and boundary value problems. To extract the desired solution, an efficient and numerically stable generalized-continued-fraction-based algorithm is developed.

scholarly journals An Inverse Transient Nonmetallic Pipeline Leakage Diagnosis Method Based on Markov Quantitative Judgment

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Yongmei Hao ◽  
Yifei Ma ◽  
Juncheng Jiang ◽  
Zhixiang Xing ◽  
Lei Ni ◽  
...  
Keyword(s):  
Objective Function ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Gas Pipeline ◽  
Flow State ◽  
Diagnosis Method ◽  
The Difference ◽  
Leakage Monitoring ◽  
Control Equation ◽  
Leakage Location

Aiming at the problems of early leakage monitoring of urban nonmetallic pipelines and the large positioning error, an inverse transient urban nonmetallic gas pipelines leakage location method based on Markov quantitative judgment was proposed. A Markov flow state transition probability matrix was established based on the flow data under different pressures obtained by experiments to quantitatively determine the pipeline leakage status. On this basis, an inverse transient leakage control equation suitable for urban nonmetallic gas pipeline leakage location was constructed according to the actual. The difference between the pressure and the calculated pressure was sought for the objective function. Finally, the objective function was optimized in conjunction with the sequential quadratic programming (SQP) method to obtain the actual leakage parameters and calculate the size and location of the leakage source. The results show that the inverse transient leakage localization method based on Markov’s quantitative judgment can more accurately determine the leakage status of the pipeline and calculate the early leakage parameters and leakage location of the gas pipeline, which improves the positioning accuracy.

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

2021 ◽  
pp. 107754632198920
Author(s):  
Zeinab Fallah ◽  
Mahdi Baradarannia ◽  
Hamed Kharrati ◽  
Farzad Hashemzadeh
Keyword(s):  
Transition Probabilities ◽  
Sliding Mode ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Linear Matrix ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

2021 ◽  
Author(s):  
Jin Zhu ◽  
Kai Xia ◽  
Geir E Dullerud
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Hidden Markov ◽  
Transition Probability ◽  
Original System ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Weighting Matrix ◽  
Markov Jump Linear Systems

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

Adiabatic Markov Decision Process: Convergence of Value Iteration Algorithm

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Thai Duong ◽  
Duong Nguyen-Huu ◽  
Thinh Nguyen
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Rate Of Change ◽  
Optimal Decision ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Markov Decision ◽  
Value Iteration Algorithm

Markov decision process (MDP) is a well-known framework for devising the optimal decision-making strategies under uncertainty. Typically, the decision maker assumes a stationary environment which is characterized by a time-invariant transition probability matrix. However, in many real-world scenarios, this assumption is not justified, thus the optimal strategy might not provide the expected performance. In this paper, we study the performance of the classic value iteration algorithm for solving an MDP problem under nonstationary environments. Specifically, the nonstationary environment is modeled as a sequence of time-variant transition probability matrices governed by an adiabatic evolution inspired from quantum mechanics. We characterize the performance of the value iteration algorithm subject to the rate of change of the underlying environment. The performance is measured in terms of the convergence rate to the optimal average reward. We show two examples of queuing systems that make use of our analysis framework.

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