Universal Generating Function Research Articles

Multi-objective design optimization of hybrid renewable systems using UGF

Purpose – Renewable generation is a main component of most hybrid generation systems. However, randomness on its generation is a characteristic to be considered due to its direct impact on reliability and performance of these systems. For this reason, renewable generation usually is accompanied with other generation elements to improve their general performance. The purpose of this paper is to analyze the power generation system, composed of solar, wind and diesel generation and power outsourcing option from the grid as means of reserve source. A multi-objective optimization for the design of hybrid generation system is proposed, particularly using the cost of energy, two different reliability indexes and the percentage of renewable energy as objectives. Further, the uncertainty of renewable sources and demand is modeled with a new technique that permits to evaluate the reliability quickly. Design/methodology/approach – The multi-state model of the generators and the load is modeled with the Universal Generating Function (UGF) to estimate the reliability indexes for the whole system. Then an evolutionary algorithm NSGA-II (Non-dominated Sorting Genetic Algorithm) is used to solve the multi-objective optimization model. Findings – The use of UGF methodology reduces the computation time, providing effective results. The validation of reliability assessment of hybrid generation systems using the UGF is carried out taking as a benchmark the results obtained with the Monte Carlo simulation. The proposed multi-objective algorithm gives as a result different generators combinations that outline hybrid systems, where some of them could be preferred over others depending on its results for each independent objective. Also it allows us to observe the changes produced on the resulting solutions due to the impact of the power fluctuation of the renewable generators. Originality/value – The main contributions of this paper are: an extended multi state model that includes different types of renewable energies, with emphasis on modeling of solar energy; demonstrate the performance improvement of UGF against SMC regarding the computational time required for this case; test the impact of different multi-states numbers for the representation of the elements; depict through multi-objective optimization, the impact of combining different energies on the cost and reliability of the resultant systems.

Universal generating function based probabilistic production simulation for wind power integrated power systems

According to the demand of sustainable development and low-carbon electricity, it is important to develop clean resources and optimize scheduling generation mix. Firstly, a novel method for probabilistic production simulation for wind power integrated power systems is proposed based on universal generating function (UGF), which completes the production simulation with the chronological wind power and load demand. Secondly, multiple-period multiple-state wind power model and multiple-state thermal unit power model are adopted, and both thermal power and wind power are coordinately scheduled by the comprehensive cost including economic cost and environmental cost. Furthermore, the accommodation and curtailment of wind power is synergistically considered according to the available regulation capability of conventional generators in operation. Finally, the proposed method is verified and compared with conventional convolution method in the improved IEEE-RTS 79 system.

Applying UGF Concept to Enhance the Assessment Capability of FMEA

The purpose of this paper is to propose a modified version of Failure Mode and Effects Analysis (FMEA) to alleviate its drawbacks. FMEA is an important tool in risk evaluation and finding the priority of potential failure modes for corrective actions. In the proposed method, the Universal Generating Function (UGF) approach has been used to improve the assessment capability of the conventional Risk Priority Number (RPN) in ranking. The new method is named as URPN. It generates the most number of unique values in comparison with the previous methods and considers relative importance for the parameters while it is easy to compute. More unique numbers help to avoid from having the same priority level for different failure modes which represent various risk levels. A case study has been employed to demonstrate that the URPN not only can improve the shortcomings but also is able to provide accurate values for risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.

Reliability analysis of excavator rectifier feedback system with multi-state components based on belief universal generating function method

In view of the complexity and uncertainty of system, both the state performances and state probabilities of multi-state components can be expressed by interval numbers. The belief function theory is used to characterize the uncertainty caused by various factors. A modified Markov model is proposed to obtain the state probabilities of components at any given moment and subsequently the mass function is used to represent the precise belief degree of state probabilities. Based on the primary studies of universal generating function (UGF) method, a belief UGF (BUGF) method is utilized to analyze the reliability and the uncertainty of excavator rectifier feedback system. This paper provides an available method to evaluate the reliability of multi-state systems (MSSs) with interval state performances and state probabilities, and also avoid the interval expansion problem.

Bayesian Reliability and Performance Assessment for Multi-State Systems

This paper develops a Bayesian framework to assess the reliability and performance of multi-state systems (MSSs). An MSS consists of multiple multi-state components of which the degradation follows a Markov process. Due to the lack of sufficient data, and only vague knowledge from experts, the transition intensities of multi-state components between any pair of states and the state probabilities cannot be precisely estimated. The proposed Bayesian method can merge prior knowledge from experts' judgments with continuous and discontinuous inspection data to obtain posterior distributions of transition intensities. A simulation method embedded with the universal generating function (UGF) is developed to estimate the posterior state probabilities, the reliability, and the performance of the entire MSS. Two numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Service reliability modeling of distributed computing systems with virus epidemics

Distributed computing (DC) system is widely implemented due to its low setup cost and high computational capability. However, it might be vulnerable to malicious attacks like computer virus due to its network structure. The service reliability, defined as the probability of fulfilling a task before a specified time, is an important metric of the quality of a DC system. This paper attempts to model and compute the service reliability for the DC system under virus epidemics. Firstly, the DC system architecture is modeled by an undirected graph whose nodes (i.e. computers) have a continuous-state model representing its computational capability. Then a set of epidemic differential equations are formulated and solved to obtain the state dynamics of each node under the virus epidemics. A universal generating function (UGF) based approach is proposed to calculate the service reliability of DC system. Numerical results show the effectiveness of the proposed method. The sensitivity analysis on the model parameters, the comparison with centralized computing system and the optimization of defense level parameter are also conducted.

Analyzing comprehensive QoS with security constraints for services composition applications in wireless sensor networks.

Services composition is fundamental to software development in multi-service wireless sensor networks (WSNs). The quality of service (QoS) of services composition applications (SCAs) are confronted with severe challenges due to the open, dynamic, and complex natures of WSNs. Most previous research separated various QoS indices into different fields and studied them individually due to the computational complexity. This approach ignores the mutual influence between these QoS indices, and leads to a non-comprehensive and inaccurate analysis result. The universal generating function (UGF) shows the speediness and precision in QoS analysis. However, only one QoS index at a time can be analyzed by the classic UGF. In order to efficiently analyze the comprehensive QoS of SCAs, this paper proposes an improved UGF technique—vector universal generating function (VUGF)—which considers the relationship between multiple QoS indices, including security, and can simultaneously analyze multiple QoS indices. The numerical examples demonstrate that it can be used for the evaluation of the comprehensive QoS of SCAs subjected to the security constraint in WSNs. Therefore, it can be effectively applied to the optimal design of multi-service WSNs.

A reliability-based design concept for lithium-ion battery pack in electric vehicles

Battery technology is an enabling technology for electric vehicles (EVs), and improving its safety and reliability while reducing its cost will benefit its application to EVs. In this paper, a method on the design and analysis of lithium-ion (Li-ion) battery pack from the reliability perspective is presented. The analysis is based on the degradation of the battery pack, which is related to the cells configuration in the battery pack and the state of health (SoH) of all the Li-ion cells in the pack. Universal Generating Function (UGF) technique is used for reliability analysis. As adding new battery cells to the battery pack in the production process can improve its reliability but it also increases cost, tradeoff between the number of the redundant battery cells, the configuration of the redundant cells and their reliability is investigated in this work.

Reliability Optimization for Multi-State Series-Parallel System Design Using Ant Colony Algorithm

In this paper, an algorithm based ant colony approach (ACA) is designed to find the optimal configuration for redundancy apportionment problem (RAP) of series-parallel multi-state system (MSS). In order to achieve maximum system reliability under cost and performance constraints, the algorithm takes advantage of ACA’s combinatorial optimization, uses heuristic information about reliability to arrange components from available choice. Different from traditional nominal performance and reliability system, universal generating function (UGF) is introduced and used to estimate the multi-state system reliability. Finally the experiment has shown that the presented algorithm can provide optimal and near optimal solutions, and have efficient and convenient calculation performance.

On Reliability Evaluation of Multistate Weighted k-out-of-n System Using Present Value

A new reliability evaluation methodology for multistate weighted k-out-of-n systems is presented in this article. The present value of the cash flow generated by the system components is used as a reliability value. We take a financial view of reliability and consider functioning periods and the time value of money in system reliability analysis. Two approaches, the universal generating function (UGF) and recursive algorithm, are applied to evaluate the reliability of the multistate weighted k-out-of-n system. An illustrative example is calculated based on the proposed system reliability evaluation methodology. It is shown that this evaluation method can also be used to find the value of the maintenance policy. Finally, the UGF and recursive algorithm approaches are compared with each other for large system reliability assessment.

Optimal service distribution in WSN service system subject to data security constraints.

Services composition technology provides a flexible approach to building Wireless Sensor Network (WSN) Service Applications (WSA) in a service oriented tasking system for WSN. Maintaining the data security of WSA is one of the most important goals in sensor network research. In this paper, we consider a WSN service oriented tasking system in which the WSN Services Broker (WSB), as the resource management center, can map the service request from user into a set of atom-services (AS) and send them to some independent sensor nodes (SN) for parallel execution. The distribution of ASs among these SNs affects the data security as well as the reliability and performance of WSA because these SNs can be of different and independent specifications. By the optimal service partition into the ASs and their distribution among SNs, the WSB can provide the maximum possible service reliability and/or expected performance subject to data security constraints. This paper proposes an algorithm of optimal service partition and distribution based on the universal generating function (UGF) and the genetic algorithm (GA) approach. The experimental analysis is presented to demonstrate the feasibility of the suggested algorithm.

Availability modeling and optimization of dynamic multi-state series–parallel systems with random reconfiguration

Most studies on multi-state series–parallel systems focus on the static type of system architecture. However, it is insufficient to model many complex industrial systems having several operation phases and each requires a subset of the subsystems combined together to perform certain tasks. To bridge this gap, this study takes into account this type of dynamic behavior in the multi-state series–parallel system and proposes an analytical approach to calculate the system availability and the operation cost. In this approach, Markov process is used to model the dynamics of system phase changing and component state changing, Markov reward model is used to calculate the operation cost associated with the dynamics, and universal generating function (UGF) is used to build system availability function from the system phase model and the component models. Based upon these models, an optimization problem is formulated to minimize the total system cost with the constraint that system availability is greater than a desired level. The genetic algorithm is then applied to solve the optimization problem. The proposed modeling and solution procedures are illustrated on a system design problem modified from a real-world maritime oil transportation system.

Random Fuzzy Extension of the Universal Generating Function Approach for the Reliability Assessment of Multi-State Systems Under Aleatory and Epistemic Uncertainties

Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties. First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle. Finally, an efficient algorithm is designed to extract probability boxes ( p-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system availability and reliability estimation. The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.

Financial view and profitability evaluation on multi-state weighted k-out-of-n:F system reliability

A financial view is proposed for reliability evaluation of multi-state weighted k-out-of-n:F systems. Failure cost as the cost which is imposed on the components by failures is used to denote the importance weight of each component. The deterioration process of components over time is modelled by Markov chain. System failure behaviour is formulated by Universal Generating Function (UGF). Furthermore, the present value of system failure is calculated by considering time value of money. As a result, the system reliability is demonstrated as cost which is more sensible for managers. A numerical example is presented to illustrate the proposed approach. After that, a way is suggested to transform the system cost present value into system reliability value. MATLAB programming is developed to make a sensitivity analysis on example results. Therefore, the impact of maintenance activities is investigated to show how they can reduce system cost through improving the system reliability.

Probabilistic production simulation of a power system with wind power penetration based on improved UGF techniques

Universal Generating Function (UGF) techniques have been applied to Multi-State System (MSS) reliability analysis, such as long term reserve expansion of power systems with high wind power penetration. However, using simple steady-state distribution models for wind power and large generating units in reliability assessment can yield pessimistic appraisals. To more accurately assess the power system reliability, UGF techniques are extended to dynamic probabilistic simulation analysis on two aspects of modelling improvement. Firstly, a principal component analysis (PCA) combined with a hierarchal clustering algorithm is used to achieve the salient and time-varying patterns of wind power, then a sequential UGF equivalent model of wind power output is established by an apportioning method. Secondly, other than the traditional two-state models, the conventional generator UGF equivalent model is established as a four discrete-state continuous-time Markov model by Lz-transform. In the construction process of such a UGF model, the state values are transformed into the integral multiples of one common factor by choosing proper common factors, thus effectively restraining the exponential growth of its state number and alleviating the explosion thereof. The method is suitable for reliability assessment with dynamic probabilistic distributed random variables. In addition, by acquiring the clustering information of wind power, the system reliability indices, such as fuel cost and CO2 emissions through different seasons and on different workdays, are calculated. Finally, the effectiveness of the method is verified by a modified IEEE-RTS 79 system integrated with several wind farms of historical hourly wind power data of Zhangbei wind farm in North China.

An extension of Universal Generating Function in Multi-State Systems Considering Epistemic Uncertainties

Many practical methods and different approaches have been proposed to assess Multi-State Systems (MSS) reliability measures. The universal generating function (UGF) method, introduced in 1986, is known to be a very efficient way of evaluating the availability of different types of MSSs. In this paper, we propose an extension of the UGF method considering epistemic uncertainties. This extended method allows one to model ill-known probabilities and transition rates, or to model both aleatory and epistemic uncertainty in a single model. It is based on the use of belief functions which are general models of uncertainty. We also compare this extension with UGF methods based on interval arithmetic operations performed on probabilistic bounds.

Maintenance optimisation of a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals

This paper presents a maintenance optimisation method for a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals. The objective function considered in the paper is the average revenue per unit time calculated based on the semi-regenerative theory and the universal generating function (UGF). A new algorithm using the stochastic ordering is also developed in this paper to reduce the search space of maintenance strategies and to enhance the efficiency of optimisation algorithms. A numerical simulation is presented in the study to evaluate the efficiency of the proposed maintenance strategy and optimisation algorithms. The simulation result reveals that maintenance strategies with opportunistic maintenance and state-dependent inspection intervals are more cost-effective when the influence of economic dependence and inspection cost is significant. The study further demonstrates that the optimisation algorithm proposed in this paper has higher computational efficiency than the commonly employed heuristic algorithms.

A multi-state model for the reliability assessment of a distributed generation system via universal generating function

The current and future developments of electric power systems are pushing the boundaries of reliability assessment to consider distribution networks with renewable generators. Given the stochastic features of these elements, most modeling approaches rely on Monte Carlo simulation. The computational costs associated to the simulation approach force to treating mostly small-sized systems, i.e. with a limited number of lumped components of a given renewable technology (e.g. wind or solar, etc.) whose behavior is described by a binary state, working or failed. In this paper, we propose an analytical multi-state modeling approach for the reliability assessment of distributed generation (DG). The approach allows looking to a number of diverse energy generation technologies distributed on the system. Multiple states are used to describe the randomness in the generation units, due to the stochastic nature of the generation sources and of the mechanical degradation/failure behavior of the generation systems. The universal generating function (UGF) technique is used for the individual component multi-state modeling. A multiplication-type composition operator is introduced to combine the UGFs for the mechanical degradation and renewable generation source states into the UGF of the renewable generator power output. The overall multi-state DG system UGF is then constructed and classical reliability indices (e.g. loss of load expectation (LOLE), expected energy not supplied (EENS)) are computed from the DG system generation and load UGFs. An application of the model is shown on a DG system adapted from the IEEE 34 nodes distribution test feeder.

Joint importance measures for multistate reliability systems

Importance and joint importance measures in reliability engineering are used to identify the weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Existing joint reliability importance measure of a multistate system with n components provides the joint reliability importance of k (k ≤ n) components. This paper introduces, for two multistate components, joint performance achievement worth, joint performance reduction worth, joint performance Fussell–Vesely measure and joint performance Birnubaum importance measure, using reliability, availability and risk as output performance measures (OPMs) of the multistate system. With reference to a predefined threshold of component performance, the component’s reachable states are restricted to those corresponding to performances either larger or not larger than the threshold level. A steady state performance level distribution with restriction to the component’s states is used to obtain the introduced measures. Use of universal generating function (UGF) for the evaluation of proposed joint importance measures is given. An illustrative example is provided.

Multi-state Reliability Modeling and Analysis of Reconfigurable Manufacturing Systems

To solve the problem that there is combination problem when multi-state system reliability model is formulated by traditional methods,the multi-state reliability model of Reconfigurable manufacturing system(RMS) is built based on the stochastic process and the universal generating function(UGF) technique.In order to get all the steady-state probability,the Markov process model of reconfigurable machine tool(RMT) with the characteristic of non-adjacent state transition is established.Through defining the buffer states and analysing the influence of buffer states on the machine availability,both the buffer availability and the actual steady-state probability are obtained.According to the characteristics of RMS and RMT,UGF technique is perfected,and by which generating functions of machine level and system level are expressed followed by the establishment of multi-state reliability model of repairable RMS for multi-parts family.Furthermore,the performance indexes of RMS are also discussed.A parallel-serial hybrid machining system with four stages for double-parts family composed of cylinder heads is taken as an example to verify the effectiveness of the model and the validity of the analysis method.