Stochastic Petri net-based availability analysis of the feeding system in a sugar processing plant

In many engineering applications, it is a formidable task to construct mathematical models that are expected to produce accurate predictions of the behavior of a system of interest. During the construction of such predictive models, errors due to imperfect modeling and uncertainties due to incomplete information about the system and its environment (e.g., input or excitation) always exist and can be accounted for appropriately by using probability logic. To assess the system performance subjected to dynamic excitations, a stochastic system analysis considering all the uncertainties involved has to be performed. In engineering, evaluating the robust failure probability (or its complement, robust reliability) of the system is a very important part of such stochastic system analysis. The word ‘robust’ is used because all uncertainties, including those due to modeling of the system, are taken into account during the system analysis, while the word ‘failure’ is used to refer to unacceptable behavior or unsatisfactory performance of the system output(s). Whenever possible, the system (or subsystem) output (or maybe input as well) should be measured to update models for the system so that a more robust evaluation of the system performance can be obtained. In this thesis, the focus is on stochastic system analysis, model and reliability updating of complex systems, with special attention to complex dynamic systems which can have high-dimensional uncertainties, which are known to be a very challenging problem. Here, full Bayesian model updating approach is adopted to provide a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying system and to its exclusive foundation on the probability axioms. First, model updating of a complex system which can have high-dimensional uncertainties within a stochastic system model class is considered. To solve the challenging computational problems, stochastic simulation methods, which are reliable and robust to problem complexity, are proposed. The Hybrid Monte Carlo method is investigated and it is shown how this method can be used to solve Bayesian model updating problems of complex dynamic systems involving high-dimensional uncertainties. New formulae for Markov Chain convergence assessment are derived. Advanced hybrid Markov Chain Monte Carlo simulation algorithms are also presented in the end. Next, the problem of how to select the most plausible model class from a set of competing candidate model classes for the system and how to obtain robust predictions from these model classes rigorously, based on data, is considered. To tackle this problem, Bayesian model class selection and averaging may be used, which is based on the posterior probability of different candidate classes for a system. However, these require calculation of the evidence of the model class based on the system data, which requires the computation of a multi-dimensional integral involving the product of the likelihood and prior defined by the model class. Methods for solving the computationally challenging problem of evidence calculation are reviewed and new methods using posterior samples are presented. Multiple stochastic model classes can be created even there is only one embedded deterministic model. These model classes can be viewed as a generalization of the stochastic models considered in Kalman filtering to include uncertainties in the parameters characterizing the stochastic models. State-of-the-art algorithms are used to solve the challenging computational problems resulting from these extended model classes. Bayesian model class selection is used to evaluate the posterior probability of an extended model classe and the original one to allow a data-based comparison. The problem of calculating robust system reliability is also addressed. The importance and effectiveness of the proposed method is illustrated with examples for robust reliability updating of structural systems. Another significance of this work is to show the sensitivity of the results of stochastic analysis, especially the robust system reliability, to how the uncertainties are handled, which is often ignored in past studies. A model validation problem is then considered where a series of experiments are conducted that involve collecting data from successively more complex subsystems and these data are to be used to predict the response of a related more complex system. A novel methodology based on Bayesian updating of hierarchical stochastic system model classes using such experimental data is proposed for uncertainty quantification and propagation, model validation, and robust prediction of the response of the target system. Recently-developed stochastic simulation methods are used to solve the computational problems involved. Finally, a novel approach based on stochastic simulation methods is developed using current system data, to update the robust failure probability of a dynamic system which will be subjected to future uncertain dynamic excitations. Another problem of interest is to calculate the robust failure probability of a dynamic system during the time when the system is subjected to dynamic excitation, based on real-time measurements of some output from the system (with or without corresponding input data) and allowing for modeling uncertainties; this generalizes Kalman filtering to uncertain nonlinear dynamic systems. For this purpose, a novel approach is introduced based on stochastic simulation methods to update the reliability of a nonlinear dynamic system, potentially in real time if the calculations can be performed fast enough.

A Limit Theorem for the Solutions of Differential Equations with Random Right-Hand Sides

Stochastic analysis and maintenance planning of the ash handling system in the thermal power plant

A stochastic analysis method of transient responses using harmonic wavelets, part 2: Time-dependent vehicle-bridge systems

Stochastic finite element analysis of a cable-stayed bridge system with varying material properties

This paper discusses the stochastic analysis and performance evaluation of condensate system of a thermal plant. These opportunities will be identified by evaluation of a simulation model to be built for the condensate system. The present system under study consists of six subsystems A, B, C, D, E, and F arranged in series with two feasible states: working and failed. After drawing transition diagram, differential equations are generated and then a probabilistic simulated simulation model using Markov approach has been developed considering some assumptions. Performance matrix for each subsystem is also developed, which provide various availability levels. On the basis of this study, performance of each subsystem of condensate system is evaluated and then maintenance decisions are made for subsystems. Key words: Transition diagram; Markov approach; Performance matrix; Maintenance decisions. DOI: 10.3329/bjsir.v44i4.4587 Bangladesh J. Sci. Ind. Res. 44(4), 387-398, 2009

The identity and behavior of pollinators are among the main factors that determine the reproductive success and mating system of plants; however, few studies have directly evaluated the relationship between pollinators and the breeding system of the plants they pollinate. It is important to document this relationship because the global decline in pollinators may significantly affect the breeding systems of many animal-pollinated plants, particularly specialized systems. Ceiba pentandra is a tropical tree that has chiropterophilic flowers and a variable breeding system throughout its distribution, ranging from fully self-incompatible, to a mixed system with different degrees of selfing. To determine if regional differences in pollinators may result in regional differences in the outcrossing rate of this species, we used systematic observations of pollinator behavior in two tropical life zones and high-resolution genetic analysis of the breeding system of populations from these two regions using microsatellites. We found a predominantly self-incompatible system in regions with high pollinator visitation, while in environments with low pollinator visitation rates, C. pentandra changed to a mixed mating system with high levels of self-pollination.

This paper describes the performance evaluation of pasteurising system of a milk processing plant in terms of its operational availability. For the stochastic modelling and analysis Markov chains has been applied. Particle swarm optimisation (PSO) technique is implemented for optimising the results obtained. The optimum combinations of failure and repair rates for various subsystems can be useful in decision making such as maintenance priorities, spare parts and repairmen, etc. Based on this, a decision support system (DSS) has been developed which indicates the most critical components of the system that need the utmost care while setting maintenance priorities.

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Both logic and stochastic analysis have strong theoretical underpinnings, but they have been traditionally relegated to separate areas of computer science, the former focusing on logic and discrete algorithms, the latter on exact or approximate numerical methods. In the last few years, though, there has been a convergence of research in these two areas, due to the realization that data structures used in one area can benefit the other and that, by merging the goals of the two areas, a more integrated approach to system analysis can be derived. In this paper, we describe some of the beneficial interactions between the two, and some of the research challenges ahead.

Reliability, availability and maintainability (RAM) analysis of a system is helpful in carrying out design modifications, if any, and it is required to achieve minimum failures or to increase mean time between failures (MTBF), and thus it is used to plan maintainability requirements, optimise reliability and maximum equipment availability. To this effect, this paper presents the application of RAM analysis in the process industry. Fuzzy Lambda–Tau methodology is used here to model the system behaviour. Each system components, failure rate and repair time are represented by triangular fuzzy numbers with known spread. The methodology uses Petri nets to model the system instead of fault tree because it allows efficient simultaneous generation of minimal cuts and path sets. Various reliability parameters such as MTBF, expected number of failures (ENOF), reliability, availability, etc. are calculated. The computed results are presented to plant personnel for their performance considerably by adopting and practicing suitable maintenance policies/strategies.

The present paper is a comparative analysis of a two-unit autoclave system in a manufacturing plant. Most of the studies have been done by considering standby units to remain as good as new ones in this mode, but practically they may be corrupted by any environmental issues. This fact makes us concerned about the standby unit. Two stochastic models were developed based on such concern. Model 1 is constructed based on basically two possibilities; firstly, the standby unit is inspected after a fixed amount of time to check its feasibility. Secondly, either it will be repaired or replaced. Replacement is instant. Model 2 is constructed based on the same assumptions but replacement is not instant, it takes some random amount of time to be replaced. Stochastic analysis uses Markov processes to investigate how these dynamic factors interact and impact system profitability, availability, and dependability. By studying various scenarios about repair prices, replacement costs, inspection frequency, and fluctuating demand patterns, this research provides vital insights into the most effective approaches for handling redundant units and preserving system functionality. The results guide managing complex decision-making processes for safeguarding and maximizing system functionality, which has practical ramifications for sectors and systems that depend on redundancy to guarantee continuity and reliability.

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth-death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman-Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga-Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strate- gies to enhance the performance of the urea synthesis system of the fertilizer plant.

This chapter addresses the need for efficient numerical stochastic techniques in the analysis and design optimization of dynamic systems. Most stochastic analysis techniques result in a heavy computational burden, the cost of which is amplified if embedded into a design optimization framework. This work seeks to alleviate the computational costs of analyzing dynamic systems by reduced order modeling techniques. The key to utilizing reduced order models for stochastic analysis and optimization lies in making them adaptable to design changes and variations in random parameters. This chapter presents an extended reduced order modeling method approximating the response of a dynamic system in the space of design and random parameters. The extended reduced order modeling technique is embedded into a stochastic analysis and design optimization framework. The accuracy and computational efficiency of extended reduced order models are verified with the stochastic analysis and design optimization of a linear structural dynamic system. Stochastic analyses are performed using Monte Carlo simulation, the first-order reliability method, and polynomial chaos expansion. The utility of the extended reduced order modeling method for design optimization purposes is illustrated by solving deterministic and reliability-based design optimization problems. Comparing the stochastic analyses and design optimization results using full and reduced order models show that the overall computational costs can be significantly diminished by the extended reduced order modeling method presented.

In this paper, the operation of the raw water pumping system for a water treatment plant is redesigned to sequence pump operation and improve energy efficiency. Using field data for the pump system’s flow, power, and head pressure, the parameters for the new pump operation sequence are set. By defining the system operation to use the more efficient pumps to satisfy base load conditions, the system inefficiency is diminished. Secondly, field data analysis revealed a persistent overlapping of pump operation, where multiple pumps would operate at one moment only to cause an unnecessary increase in head pressure as required flow had already been achieved. The system analysis uses the total system flowrate as its control parameter. In the new system operation, the most efficient pump is loaded to its best efficiency point (BEP) then the remainder flowrate is given to the following pumps based on their efficiency. With an absence of pump curves, a variable speed drive (VSD) speed versus motor power relation can be made to predict, with a polynomial data fit, the motor power at calculated VSD speeds. With system operation sequenced by efficient motors and keeping head pressure near constant, a decrease in energy usage of 29.6% is demonstrated over the duration of the field data. The proposed system operation is shown to operate remainder flow rate pumps at partial loads below their minimum design flowrate, due to the need to keep total flowrate parameter constant. By highlighting these operation points below the minimum design flow rate, the flow rate must be increased to that minimum for the pump, thus proposed operation is simulated with a slightly increased average flow rate. The pump system is comprised of 4 centrifugal raw water pumps, one 200 HP and three 150 HP, with an average annual flowrate of 9,200 GPM. The raw water pumping system moves raw water from the federally managed water source to the treatment plant. The proposed system operation would be performed by a motor controller capable of managing at least four pumps at different sites as one pump is separated from the other three pumps. The specifications defined by the analysis in this study would be parameters for the controller programming along with the predicted performance after controller implementation. Analytical characteristics of such controllers are discussed along with their effect on the total pumping system. Finally, the economic impact and carbon emissions reduction of the proposed operational design are discussed.