Bayesian estimate of pre-mixed and diffusive rate of heat release phases in marine diesel engines

Abstract

approach was able to identify the pre-mixed and diffusive combustion phases, for different engine loads. Results were compared with a simple inversion procedure, showing a good agreement. The combustion ignition delay was also calculated, showing its variation with the engine load. Keywords Rate of heat release • Inverse problems • Bayesian technique List of symbols A Area A/F Air/fuel ratio B Piston bore CA Crankshaft angle f Linear or non-linear function of the state variables g Linear or non-linear function representing the observation model h Heat transfer coefficient LHV Lower heating value m Mass n Engine speed in Hz n Vector of noise associated with the observation model P Pressure Q Heat t Time T Temperature v Average gas velocity within the cylinder v Vector of noise associated with the evolution model V Volume w Weights of particles W Covariance matrix x Mass fraction of burned fuel y Vector of state variables z Vector of observation variables Abstract The rate of heat released during the combustion in Diesel engines is important for many reasons, including performance evaluation, pollutant formation, and control. Combustion in Diesel engines can be generally divided into three phases: pre-mixed, diffusive or mixed-controlled, and late combustion. The objective of this paper is to estimate the rate of heat released by the fuel in a marine Diesel engine, in order to identify the pre-mixed and diffusive phases, using the Sampling Importance Resampling (SIR) Bayesian Particle Filter. Experimental pressure data obtained from a piezoelectric sensor, installed in a research marine diesel engine (MAN Innovator 4c), was used to feed the observation model in such Bayesian approach. The evolution model for the pressure was formulated in terms of a set of ordinary differential equations, coming from the First Law of Thermodynamics, together with a random walk model for the unknown state variable. The proposed

Application of Approximate Bayesian Computational for estimate parameter and selection model in dynamic of HIV

“…There are difficulties in obtaining direct measures in several research areas, both for parameters and state variables (BECK and ARNOLD 1977;ORLANDE et al, 2011;KAIPIO and SOMERSALO, 2002;OLIVEIRA et al, 2020;PASQUALETTE et al, 2017). In this scenario, several Bayesian Techniques can be applied to make inferences about the unknown information.…”

Estimativa de parâmetros usando a técnica Monte Carlo via Cadeia de Markov aplicados a modelos epidemiológicos para Covid-19 no estado do Pará

“…A fim de conhecer informações da posteriori é necessário que diversas amostras desta distribuição sejam obtidas de modo a possibilitar a sua caracterização. Para este fim, o método de amostragem de Monte Carlo via Cadeias de Markov (MCMC) tem sido amplamente adotado na literatura (ESTUMANO et al, 2014;PASQUALETTE et al, 2017;OLIVEIRA et al, 2020;NUNES et al, 2021;MOURA et al,2021).…”

Experimental Combustion and Emissions Evaluation of Ternary Mixtures of Diesel-Biodiesel-Ethanol in a CFR-ASTM Engine

“…In this work no correlation -such as that of Wiebe, for instance -was used to estimate the rate of heat release. Details on the technique employed can be found in Pasqualette et al (2017). Bayesian techniques can also incorporate uncertainties in the model and in the measurements.…”

“…An AVL pressure sensor was installed in this engine, giving the indicated work for each blend, as well as their ignition delays and maximum pressure. In the present paper an inverse problem approach (Pasqualette et al, 2017;Hamilton et al, 2014) is also used to evaluate the rate of heat released by the fuel.…”