scholarly journals Research on construction of vehicle driving cycle based on Markov chain and global K-means clustering algorithm

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Yingnan Wu ◽  
Guangzhong Liu
Keyword(s):  
Markov Chain ◽  
Dimension Reduction ◽  
Clustering Algorithm ◽  
Transition Probability ◽  
Time Sequence ◽  
Driving Cycle ◽  
Pollutant Emission ◽  
Specific Work ◽  
Automotive Technology ◽  
The Matrix

Vehicle driving cycle is a time-speed curve used to describe vehicle driving rules. The research and development of vehicle driving cycle not only provide theoretical basis for the test of vehicle fuel’s economy and pollutant emission level, but also guide the design and development of new models in the future. This paper adopts the actual driving data of light vehicles in Fuzhou City, Fujian Province collected by China Automotive Technology Research Center (CATC) through the data collection system, and analyzes and verifies the new data after standardized dimension reduction by combining the global K-means clustering and Markov chain principle. The specific work is divided into the following parts: 1. The global K-means clustering algorithm adopted to cluster the kinematic segment database after standardized dimension reduction; 2. Markov chain is applied to construct the working condition diagram. The basic principle of this method is to regard the short-stroke speed-time sequence as a complete random process, divide the speed intervals by lines, each of which represents a different speed state, and convert the speed into a speed state, so that the speed-time sequence becomes a state-time sequence. Since the next state is only related to the current one, a group of random state sequences can be randomly generated by the program as long as the transition probability between two adjacent states is determined and the matrix of state transition probability is established. 3. The state sequence is converted into a speed sequence, and finally a set of driving cycle conforming to the spatial characteristics of the samples is obtained.

A note on cumulative sums of markovian variables

1965 ◽  
Vol 5 (2) ◽  
pp. 285-287 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Finite Number ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
The Matrix ◽  
Initial Probability Distribution ◽  
Regular Markov Chain ◽  
Image Position ◽  
Cumulative Sums

Consider a positive regular Markov chain X0, X1, X2,… with s(s finite) number of states E1, E2,… E8, and a transition probability matrix P = (pij) where = , and an initial probability distribution given by the vector p0. Let {Zr} be a sequence of random variables such that and consider the sum SN = Z1+Z2+ … ZN. It can easily be shown that (cf. Bartlett [1] p. 37), where λ1(t), λ2(t)…λ1(t) are the latent roots of P(t) ≡ (pijethij) and si(t) and t′i(t) are the column and row vectors corresponding to λi(t), and so constructed as to give t′i(t)Si(t) = 1 and t′i(t), si(o) = si where t′i(t) and si are the corresponding column and row vectors, considering the matrix .

On the matrix occurring in a linear search problem

1991 ◽  
Vol 28 (2) ◽  
pp. 336-346 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Search Problem ◽  
Linear Search ◽  
Natural Position ◽  
The Matrix

In this paper we consider the Markov chain formed by the operation of the move-to-front scheme. We show that the eigenvalues of the transition probability matrix are of the form pi, pi + pj, ···, where pi is the probability of selecting the ith item and N is the number of items; further, that the multiplicity of the eigenvalues of the form Σpi where the summation is over m items is equal to the number of permutations of N – m objects, ordered in some way, such that no object is in its natural position. Finally, we show that the Markov chain is lumpable – many times over.

On the matrix occurring in a linear search problem

1991 ◽  
Vol 28 (02) ◽  
pp. 336-346 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Search Problem ◽  
Linear Search ◽  
Natural Position ◽  
The Matrix

In this paper we consider the Markov chain formed by the operation of the move-to-front scheme. We show that the eigenvalues of the transition probability matrix are of the form pi, pi + pj , ···, where pi is the probability of selecting the ith item and N is the number of items; further, that the multiplicity of the eigenvalues of the form Σpi where the summation is over m items is equal to the number of permutations of N – m objects, ordered in some way, such that no object is in its natural position. Finally, we show that the Markov chain is lumpable – many times over.

scholarly journals THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN

2002 ◽  
Vol 16 (3) ◽  
pp. 351-366 ◽  
Author(s):  
Pauline Coolen-Schrijner ◽  
Erik A. van Doorn
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Deviation Matrix ◽  
The Matrix ◽  
Birth Death

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix Π is the matrix D ≡ ∫0∞(P(t) − Π) dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth–death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.

Hybrid fuzzy interface model of sports rehabilitation activities

2021 ◽  
pp. 1-10
Author(s):  
Wu Shoujiang
Keyword(s):  
Evaluation System ◽  
Clustering Algorithm ◽  
Mixed Model ◽  
Expectation Maximization Algorithm ◽  
Rehabilitation Training ◽  
Development Platform ◽  
Longitudinal Tracking ◽  
Database Structure ◽  
The Matrix ◽  
Matrix Normal

At present, the relevant test data and training indicators of athletes during rehabilitation training lack screening and analysis, so it is impossible to establish a long-term longitudinal tracking research system and evaluation system. In order to improve the practical effect of sports rehabilitation activities, this paper successively introduces the matrix normal mixed model and the fuzzy clustering algorithm based on the K-L information entropy regularization and the matrix normal mixed model. Moreover, this paper uses the expectation maximization algorithm to estimate the parameters of the model, discusses the framework, key technologies and core services of the development platform, and conducts certain research on the related technologies of the three-tier architecture. At the same time, according to the actual needs of sports rehabilitation training, this paper designs the functions required for exercise detection and prescription formulation. In addition, this paper analyzes and designs the database structure involved in each subsystem. Finally, this paper designs experiments to verify the performance of the model constructed in this paper. The research results show that the performance of the model constructed in this paper meets the expectations of model construction, so it can be applied to practice.

scholarly journals Infinitely divisible random transition probabilities with application to dependent Markov chains

1984 ◽  
Vol 25 (4) ◽  
pp. 463-472
Author(s):  
Peter L. Chesson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
White Noise ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Rates ◽  
Infinitely Divisible ◽  
Random Transition ◽  
Transition Probability Matrices ◽  
Probability Matrices

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

The WLTC vs NEDC: A Case Study on the Impacts of Driving Cycle on Engine Performance and Fuel Consumption

2021 ◽  
Vol 18 (3) ◽  
pp. 9071-9081
Author(s):  
Jakub Lasocki
Keyword(s):  
Fuel Consumption ◽  
Combustion Engine ◽  
Engine Performance ◽  
Driving Cycle ◽  
Performance Characteristics ◽  
Pollutant Emission ◽  
Strong Impact ◽  
Light Duty ◽  
Light Duty Vehicles

The World-wide harmonised Light-duty Test Cycle (WLTC) was developed internationally for the determination of pollutant emission and fuel consumption from combustion engines of light-duty vehicles. It replaced the New European Driving Cycle (NEDC) used in the European Union (EU) for type-approval testing purposes. This paper presents an extensive comparison of the WLTC and NEDC. The main specifications of both driving cycles are provided, and their advantages and limitations are analysed. The WLTC, compared to the NEDC, is more dynamic, covers a broader spectrum of engine working states and is more realistic in simulating typical real-world driving conditions. The expected impact of the WLTC on vehicle engine performance characteristics is discussed. It is further illustrated by a case study on two light-duty vehicles tested in the WLTC and NEDC. Findings from the investigation demonstrated that the driving cycle has a strong impact on the performance characteristics of the vehicle combustion engine. For the vehicles tested, the average engine speed, engine torque and fuel flow rate measured over the WLTC are higher than those measured over the NEDC. The opposite trend is observed in terms of fuel economy (expressed in l/100 km); the first vehicle achieved a 9% reduction, while the second – a 3% increase when switching from NEDC to WLTC. Several factors potentially contributing to this discrepancy have been pointed out. The implementation of the WLTC in the EU will force vehicle manufacturers to optimise engine control strategy according to the operating range of the new driving cycle.

Adaptive calibration of Diesel engine injection for minimising fuel consumption with constrained NOx emissions in actual driving missions

2020 ◽  
pp. 146808742091880
Author(s):  
José Manuel Luján ◽  
Benjamín Pla ◽  
Pau Bares ◽  
Varun Pandey
Keyword(s):  
Diesel Engine ◽  
Fuel Consumption ◽  
Time Window ◽  
Transition Probability ◽  
Estimation Method ◽  
Engine Performance ◽  
Driving Cycle ◽  
Vehicle Speed ◽  
Adaptive Calibration ◽  
Emission Limits

This article proposes a method for fuel minimisation of a Diesel engine with constrained [Formula: see text] emission in actual driving mission. Specifically, the methodology involves three developments: The first is a driving cycle prediction tool which is based on the space-variant transition probability matrix obtained from an actual vehicle speed dataset. Then, a vehicle and an engine model is developed to predict the engine performance depending on the calibration for the estimated driving cycle. Finally, a controller is proposed which adapts the start-of-injection calibration map to fulfil the [Formula: see text] emission constraint while minimising the fuel consumption. The calibration is adapted during a predefined time window based on the predicted engine performance on the estimated cycle and the difference between the actual and the constraint on engine [Formula: see text] emissions. The method assessment was done experimentally in the engine test set-up. The engine performace using the method is compared with the state-of-the-art static calibration method for different [Formula: see text] emission limits on real driving cycles. The online implementation of the method shows that the fuel consumption can be reduced by 3%–4% while staying within the emission limits, indicating that the estimation method is able to capture the main driving cycle characterstics.

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