scholarly journals Computing reliability for closed-cycle cooling system in thermo-electric power plants by modelling to circular consecutive-2-out-of-n:F system

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 177-184
Author(s):  
Mehmet Gurcan ◽  
Gokhan Gokdere
Keyword(s):  
Power Plants ◽  
State Transition ◽  
Transition Probabilities ◽  
Cooling System ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
The State ◽  
Thermo Electric ◽  
Water Pumps ◽  
Electric Plant

The main motivation of this paper is to compute a reliability for a closed recurring water supply system with n water pumps in a thermo-electric plant by modelling to a repairable circular consecutive-2-out-of-n:F system. In a thermo-electric plant system, let us have n water pumps for pumping the water and steam expelled from a turbine to a cooling tower. These pumps are installed around the system and each pump must be powerful enough to pump water and steam to at least the next two consecutive pumps. If any two or more consecutive pumps in the system are failed, the system is failed. For this system, it is important to determine the reliability. First, we developed mathematical formulations for the state transition probabilities in the system by using the definition of generalized transition probability and the concept of critical component under the assumption that pumps have unequal failure rates. Then, using these formulations we derived the state transition probability matrix of the system. Finally, a special model is given to calculate the system reliability.

Estimation of State Transition Probabilities in Asynchronous Vector Markov Processes

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Waleed A. Farahat ◽  
H. Harry Asada
Keyword(s):  
Population Dynamics ◽  
Markov Processes ◽  
State Transition ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Sampling Schemes ◽  
Markov Chain Sampling ◽  
Bayesian Formulation ◽  
Wide Range

Vector Markov processes (also known as population Markov processes) are an important class of stochastic processes that have been used to model a wide range of technological, biological, and socioeconomic systems. The dynamics of vector Markov processes are fully characterized, in a stochastic sense, by the state transition probability matrix P. In most applications, P has to be estimated based on either incomplete or aggregated process observations. Here, in contrast to established methods for estimation given aggregate data, we develop Bayesian formulations for estimating P from asynchronous aggregate (longitudinal) observations of the population dynamics. Such observations are common, for example, in the study of aggregate biological cell population dynamics via flow cytometry. We derive the Bayesian formulation, and show that computing estimates via exact marginalization are, generally, computationally expensive. Consequently, we rely on Monte Carlo Markov chain sampling approaches to estimate the posterior distributions efficiently. By explicitly integrating problem constraints in these sampling schemes, significant efficiencies are attained. We illustrate the algorithm via simulation examples and show that the Bayesian estimation schemes can attain significant advantages over point estimates schemes such as maximum likelihood.

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.

scholarly journals Grey theory–based BP-NN co-training for dense sequence long-term tendency prediction

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yuling Hong ◽  
Yingjie Yang ◽  
Qishan Zhang
Keyword(s):  
State Transition ◽  
Transition Probability ◽  
Training Model ◽  
Transition Probability Matrix ◽  
Content Type ◽  
Fine Grained ◽  
State Transition Probability ◽  
Dense Sequence ◽  
Popularity Prediction

PurposeThe purpose of this paper is to solve the problems existing in topic popularity prediction in online social networks and advance a fine-grained and long-term prediction model for lack of sufficient data.Design/methodology/approachBased on GM(1,1) and neural networks, a co-training model for topic tendency prediction is proposed in this paper. The interpolation based on GM(1,1) is employed to generate fine-grained prediction values of topic popularity time series and two neural network models are considered to achieve convergence by transmitting training parameters via their loss functions.FindingsThe experiment results indicate that the integrated model can effectively predict dense sequence with higher performance than other algorithms, such as NN and RBF_LSSVM. Furthermore, the Markov chain state transition probability matrix model is used to improve the prediction results.Practical implicationsFine-grained and long-term topic popularity prediction, further improvement could be made by predicting any interpolation in the time interval of popularity data points.Originality/valueThe paper succeeds in constructing a co-training model with GM(1,1) and neural networks. Markov chain state transition probability matrix is deployed for further improvement of popularity tendency prediction.

scholarly journals Stochastic Stability for Time-Delay Markovian Jump Systems with Sector-Bounded Nonlinearities and More General Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Dan Ye ◽  
Quan-Yong Fan ◽  
Xin-Gang Zhao ◽  
Guang-Hong Yang
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Transition Probability Matrix ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Delay Dependent ◽  
Jump Systems

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

scholarly journals On the Convergence Rate of Bonus-Malus Systems

1992 ◽  
Vol 22 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Heikki Bonsdorff
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Convergence Rate ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Limit Probability ◽  
Step Transition

AbstractUnder certain conditions, a Bonus-Malus system can be interpreted as a Markov chain whose n-step transition probabilities converge to a limit probability distribution. In this paper, the rate of the convergence is studied by means of the eigenvalues of the transition probability matrix of the Markov chain.

Transition probabilities between synoptic weather types as a fingerprint for climate model evaluation

2021 ◽  
Author(s):  
Juan Antonio Fernandez-Granja ◽  
Ana Casanueva ◽  
Joaquín Bedia ◽  
Jesús Fernández
Keyword(s):  
Atmospheric Circulation ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Weather Types ◽  
Observational Uncertainty ◽  
Leibler Divergence ◽  
Synoptic Conditions ◽  
Large Scale Atmospheric Circulation

<p>Global Climate Models (GCMs) generally exhibit significant biases in the representation of large-scale atmospheric circulation. Even after bias adjustment, these errors remain and are inherited to some extent by the derived downscaling products, impairing the credibility of future regional projections. </p><p>We perform a process-based evaluation of state-of-the-art GCMs from CMIP5 and CMIP6, with a focus on the simulation of the synoptic climatological patterns having a most prominent effect on the European climate. To this aim, we use the Lamb Weather Type Classification (LWT, Lamb, 1972). We undertake a comprehensive assessment based on several evaluation measures, such as Kullback-Leibler divergence (KL), Relative Bias and Transition Probability Matrix Score (TPMS), used to assess the ability of the GCMs in reproducing not only the frequencies of the different Lamb Weather Types (LWTs), but also the daily probabilities of transitions among them. We show that the novel TPMS score poses a stringent test on the GCM performance, allowing for a convenient model ranking based on each model’s transition probability matrix fingerprint. Deficiencies in the transition probabilities from one LWT to another might explain the misrepresentation of the synoptic conditions and their frequencies by the GCMs. Four different reanalysis products of varying characteristics are considered as pseudo-observational reference in order to assess observational uncertainty. </p><p>Our results unveil an overall improvement of salient atmospheric circulation features of CMIP6 with respect to CMIP5, demonstrating the ability of the new models to better capture key synoptic conditions. The improvement is consistent across observational references, although it is uneven across models and large frequency biases still remain for the dominant LWTs in many cases. In particular, some CMIP6 models attain similar or even worse results than their CMIP5 counterparts. In light of the large differences found across models, we advocate for a careful selection of driving GCMs in downscaling experiments with a special focus on large-scale atmospheric circulation aspects.</p><p> </p>

scholarly journals Stochastic LU factorizations, Darboux transformations and urn models

2018 ◽  
Vol 55 (3) ◽  
pp. 862-886 ◽  
Author(s):  
F. Alberto Grünbaum ◽  
Manuel D. de la Iglesia
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Free Parameter ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Urn Models ◽  
Triangular Matrices ◽  
New Family ◽  
Step Transition

Abstract We consider upper‒lower (UL) (and lower‒upper (LU)) factorizations of the one-step transition probability matrix of a random walk with the state space of nonnegative integers, with the condition that both upper and lower triangular matrices in the factorization are also stochastic matrices. We provide conditions on the free parameter of the UL factorization in terms of certain continued fractions such that this stochastic factorization is possible. By inverting the order of the factors (also known as a Darboux transformation) we obtain a new family of random walks where it is possible to state the spectral measures in terms of a Geronimus transformation. We repeat this for the LU factorization but without a free parameter. Finally, we apply our results in two examples; the random walk with constant transition probabilities, and the random walk generated by the Jacobi orthogonal polynomials. In both situations we obtain urn models associated with all the random walks in question.

Some explicit results for correlated random walks

1989 ◽  
Vol 26 (4) ◽  
pp. 757-766 ◽  
Author(s):  
Ram Lal ◽  
U. Narayan Bhat
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Equilibrium Distribution ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Correlated Random Walks ◽  
Finite State ◽  
Direction Of Movement ◽  
Step Transition

In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).

The square root law in the embedding detection problem for Markov chains with unknown matrix of transition probabilities

2019 ◽  
Vol 29 (1) ◽  
pp. 59-68
Author(s):  
Artem V. Volgin
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Classical Model ◽  
Transition Probability Matrix ◽  
Square Root ◽  
Detection Problem ◽  
Asymptotic Growth

Abstract We consider the classical model of embeddings in a simple binary Markov chain with unknown transition probability matrix. We obtain conditions on the asymptotic growth of lengths of the original and embedded sequences sufficient for the consistency of the proposed statistical embedding detection test.

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