Universal Generating Function Research Articles

Reliability modeling and optimization of a two-dimensional system considering performance sharing mechanism

Photovoltaic (PV) power generation systems are increasingly installed on the factory rooftop. The installed PV power generation system exits a two-dimensional structure since the factories are usually designed to be square or rectangular. Motivated by real industry practice, this research proposes a two-dimensional performance sharing reliability model for the factory rooftop PV power generation system, where a common bus exists in each row and across all rows. The component availability is affected by both internal failure and external impacts. The system reliability is the probability that each component can meet its own demand and each row can meet its required demand after performance sharing. To mitigate external impacts, the factory rooftop PV power generation system employs both overarching protection and individual protection measures. We extend the universal generating function (UGF) technique to propose a reliability evaluation algorithm and use the genetic algorithm (GA) to determine optimal protection resource allocation to improve system reliability. Further, the proposed two-dimensional performance sharing reliability model is extended to consider multiple phased-mission. Numerical studies indicate that both expanding common bus capacity and optimizing the protection allocation strategy are effective ways to improve the factory rooftop PV power generation system reliability.

Reliability analysis for complex electromechanical multi-state systems utilizing universal generating function techniques

The large-scale adoption of complex electromechanical systems (CMESs) renders it challenging to perform reliability assessments for such systems. In terms of the reliability evaluation of CMESs, previous studies generally assume that only binary states exist within the systems. However, owing to the stochastic failures and various operating characteristics of the system components, not only the good/bad states but also the performance levels within the system should be taken into account when analyzing the reliability of CMESs. Hence, we abstract the CMES as a multi-layer and multi-state network in which minimum maintenance units (MMUs) and three types of connections constitute nodes and edges in different layers. Furthermore, multi-state models for different MMUs in the CMES are developed based on universal generating functions (UGFs). Aggregation operators are then utilized to aggregate these UGFs to obtain the multi-state models. Subsequently, a cascading failure model is introduced to incorporate MMUs into the system reliability assessment. Thus, the effects of the operating mechanism and topological attributes can be considered in the reliability evaluation of the CEMS. Finally, the CRHX high-speed train system is used as an example to demonstrate the applicability and effectiveness of the proposed method in the reliability assessment of the CMES.

Short-Term Reliability Assessment of Integrated Power-Gas Systems With Hydrogen Injections Using Universal Generating Function

Injecting alternative gas (e.g., green hydrogen from wind generation) into the gas system is a promising way to decarbonize the energy sector. However, the fluctuating renewable generation could lead to time-varying alternative gas injections. Then, the gas composition in the gas system may become uncertain, increasing the short-term risk of the integrated power-gas systems during the operation. This paper proposes a short-term reliability assessment approach for IPGS with alternative gas injections. First, the multi-performance and multi-state universal generating functions (UGF) are constructed to efficiently model the short-term reliability of the power-to-gas facility and the wind farm, respectively. Then, a reliability management UGF operator is proposed to minimize both load shedding and gas security violation. A set of novel reliability indices is proposed to comprehensively assess the gas security violations under uncertain gas compositions. Moreover, an analytical short-term reliability assessment approach is proposed, where the state-based sequential approximation and state-based McCormick envelope techniques are tailored and embedded. By optimizing the solution order by the system states, the nonconvexities in the reliability management optimization problem can be handled tractably without increasing the computation burden. Finally, the IEEE 24 bus Reliability Test System and the Belgium gas system are used to validate the proposed approach.

Intuitionistic fuzzy approach to reliability assessment of multi-state systems

One of the major problems that one encounters within an engineering system is the assessment of its quality, or in other words, reliability. However, conventional reliability tends to ignore the fuzziness in the system, i.e., the lack of precision, vagueness, inaccuracy, or inadequacy in the information obtained. As a result, the integration of fuzzy sets into reliability theory has proven to be incredibly vital. Similarly, the universal generating function (UGF) technique has also been an asset in reliability assessment ever since its inception due to its simplicity. Here, a novel technique involving the intuitionistic fuzzy sets (IFS), specifically using the triangular intuitionistic fuzzy numbers (TIFN) and the UGF method, has been created for the reliability assessment of a fuzzy multi-state system (FMSS). This method is then applied to a system of wireless communication and its intuitionistic fuzzy reliability and availability are evaluated where each performance state and its probability are characterized by a TIFN. The obtained results are also represented graphically for better insights. This work is helpful in getting a clear picture of FMSS and thus, making them more reliable.

Reliability analysis of complex multi-state system based on universal generating function and Bayesian Network

In the complex multi-state system (MSS), reliability analysis is an important research content, both for equipment design, manufacturing, operation and maintenance. Universal Generating Function (UGF) is an essential method in reliability analysis, which efficiently obtains system reliability by a fast algebraic procedure. However, when structural relationships between subsystems or components are unclear or without explicit expressions, the UGF method is difficult to use or not applicable at all. Bayesian Network (BN) has a natural advantage in terms of reliability inference for the relationship without explicit expressions. When the number of components is extremely large, though, it has the defects of low efficiency. To overcome the respective shortcomings of UGF and BN, a novel reliability analysis method called UGF-BN is proposed for the complex MSS. In the UGF-BN framework, the UGF method is first used to analyze the bottom components with a large number. Then probability distributions obtained are taken as the input of BN. Finally, the reliability of the complex MSS is modeled by the BN method. This proposed method improves the computational efficiency, especially for the MSS with a large number of bottom components. Besides, the aircraft reliability-based design optimization based on the UGF-BN method is further studied with budget constraints on mass, power, and cost. Finally, two cases are used to demonstrate and verify the proposed method.

Multi‐state reliability assessment for shipboard hybrid turbine‐diesel generation system with redundancy and aging effects

AbstractComplex system structures, dynamic energy demands, and tough operating environment pose a huge challenge to reliability assessment and risk control. Taking multi‐state, redundant structure and aging impact into account, reliability assessment for shipboard hybrid turbine‐diesel generation system is studied. This work adopts a comprehensive method combining the Markov method and universal generating function (UGF): the Markov method is used for reliability modeling at the unit level, and then synthesized and calculated through UGFs to obtain system‐level reliability. Based on the above methodology, this work presents a multi‐state system (MSS) model with different configuration structures and failure rate types, then compares the availability evaluation results of the single power generation system, the hybrid power system with redundancy and aging effects. The results show that (1) redundant design effectively improves system availability to meet power supply requirements; (2) in the case of system aging and imperfect repair, redundant configuration and power distribution can significantly improve the availability of power supply to be almost unaffected by aging, and effectively reduce the risk of performance failure; and (3) when the redundancy is applied, the system power supply availability is not sensitive in the high‐value range of the redundant installed capacity ratio, but sensitive in the high‐value range of effective coefficient about power compensation control.

The Optimization of Working Time for a Consecutively Connected Production Line

Most factory production processes are completed by machines and workers on production lines. The operation schedule is arranged to reduce the cost of the enterprises to obtain the maximum economic profit for sustainable running. Previous studies usually investigated the working time while only considering the workers’ conditions. This study proposed a method to optimize the operation schedule by jointly considering the workers’ fatigue states and the operation states of machines. This method was proposed based on a system structure called the multistate consecutively connected system (MCCS), which has been widely applied in many areas, such as electronic communications. This structure is also an analogy of the production line. The corresponding model is constructed based on the universal generating function (UGF) since it is a powerful tool in modeling a consecutively connected system. The proposed model can be used to evaluate the different productivities of different types of workers in different states and to realize the screening of the whole scheme through simulation. According to the proposed method, we obtained the optimal operation schedule, including the working time, rest time and allocation strategy for a production line system. Some examples are provided to illustrate the proposed method.

Spatio-temporal evaluation of electricity price risk considering multiple uncertainties under extreme cold weather

The increasing frequency of long-lasting price spikes in electricity markets caused by extreme weather has brought unbearable economic burdens to both electricity consumers and retailers, attracting wide attention on price risk evaluation and prevention. However, the precise and comprehensive evaluation of price risks has been hindered by the lack of spatio-temporal feature analysis and multi-uncertainty fusion modeling, including random failures, rapid surges in electricity demands and natural gas prices under extreme cold weather. To address this, a spatio-temporal evaluation model of electricity price risk considering the synthetic effects of multiple uncertainties is proposed based on the universal generating function (UGF) technique. Firstly, the UGF representations of standardized probabilistic models for different uncertainty factors induced by freezing temperatures are developed. On this basis, the market price calculation (MPC) operator is proposed to obtain the probabilistic model of the electricity market by aggregating these UGFs. Moreover, the spatio-temporal price risk indices are proposed to comprehensively evaluate the market risk level. Furthermore, the impact analysis based on sensitivity calculation is introduced to identify the most critical factor from multiple uncertainties. Case studies demonstrate that the extremely high price risks mainly occur during severe icing intervals and locate in the region away from major energy resources. Moreover, the surge in electricity demand is identified as the major factor for extremely high electricity prices. The findings can provide effective references for risk prevention and hedging for market operators and participants.

Modular battery energy storage system design factors analysis to improve battery-pack reliability

Traditional battery energy storage systems (BESS) are based on the series/parallel connections of big amounts of cells. However, as the cell to cell imbalances tend to rise over time, the cycle life of the battery-pack is shorter than the life of individual cells. New design proposals focused on modular systems could help to overcome this problem, increasing the access to each cell measurements and management. During the design of a modular battery system many factors influence the lifespan calculation. This work is centred on carrying out a factor importance analysis to identify the most relevant variables and their interactions. The analysis models used to calculate the reliability of the batteries are the state of health (SoH) and the Multi-State System (MSS) analysis with the Universal Generating Function (UGF), while electronic devices reliability is approximated using constant failure rate achieved with FIDES guide. Thus, it is determined numerically that module redundancy, cell capacity, module voltage and their interactions are the most determinant design characteristics.

Reliability evaluation of balanced systems with common bus performance sharing considering balance degree base on battery storage systems

To solve the problem of inconsistency of batteries, many people have studied the the battery system with the automatic balancing mechanism which can be regarded as a balanced system. In this paper, a reliability evaluation model for balanced systems with common bus performance sharing considering the degree of balance is proposed. The balance degree of the system is represented by the difference in performance between the components. If the performance difference between components exceeds the balance degree threshold, the system is unbalanced and performance sharing is required to redistribute performance through a common bus. This paper also takes into account transfer capacity limits. When the output performance exceeds the maximum transmission capacity, the performance transmission is performed according to the maximum limit to achieve the best balance. The criterion for system failure is that the balance is still out of balance after performance sharing or the total system performance is lower than the specified requirements. Firstly, by solving the Markov equation, the steady-state probability of component performance levels under the long-term operation of the system is obtained, and then the reliability of the system is evaluated by UGF (Universal generating function) method. Finally, a numerical example is carried out to illustrate the effectiveness of the method.

Reliability Modeling and Optimization of Circular Multi-State Sliding Time Window System with Sequential Demands

This paper proposes a new model of circular multi-state sliding time window system with sequential demands (named CMSTWS-SD). This model is an extension of the multi-state sliding window systems with considering temporal window width defined by the required completion time. For the proposed model, the system contains n multi-state elements (MEs) arranged in circular structure, and any ME can be designated as the starting point for completing the pre-specified sequential tasks. The system function depends on its capability of completing the sequential tasks within the required mission time from any possible starting points. The reliability model of the CMSTWS-SD is formulated by investigating the performance assignment schemes of each elements group starting on different MEs and adopting the extended universal generating function (UGF) technique. We suggest an approach of states aggregation to reduce the computational burden caused by the raising number of system states. Furthermore, we develop a dynamic programming algorithm for determining the optimal performance assignment scheme with minimum completion time. Since the sequence of MEs strongly affects the system reliability of considered CMSTWS-SD, we further study the optimal element sequencing problem. Numerical experiments of the system reliability evaluation and the element sequencing optimization are conducted for illustration.

Reliability optimization of multi-state networks in a star configuration with bi-level performance sharing mechanism and transmission losses

A multi-state star network with bi-level performance sharing mechanism is studied. According to the proposed topology, the network consists of a main node, which occupies the central position in the network, and n terminal nodes, which are directly connected to the central part through primary transmission lines with limited capacities. Each terminal node contains groups of components connected to a secondary common bus with a specific transmission capacity. Also, each group has a demand to satisfy. The groups within the same terminal node are able to share their surplus performance through a secondary common bus while the different terminal nodes may also share surplus performance with the main node through their primary transmitters. An adverse feature of real performance sharing systems is transmission loss that has to be taken into account if accurate reliability estimates are sought. To address this problem, the present study considers transmission loss at two levels. Network reliability is, then, calculated using a universal generating function (UGF)-based method while the best component allocation to maximize network reliability is also determined. The proposed method is eventually validated through a numerical example and a case study.

Research on Reliability Modelling for Heavy CNC Machine Tools under Uncertain Variables Based on Universal Generating Function

Due to the lack of historical data, the inability to carry out a large number of reliability tests on the machine tool, the lack of reliability information collected, and the change of the working environment of the machine tool, there are a lot of uncertainties in the machine tool. In the existing research, only unilateral uncertainty factors are usually considered, while in practical problems, random uncertainty and cognitive uncertainty exist at the same time. Therefore, in this study, the random uncertainty and cognitive uncertainty in the system are characterized by random variables, fuzzy variables, probability box variables, and interval variables. For the structural function with more variables, the dimension is reduced first, and then the reliability model of the universal generating function (UGF) is established. Taking the heavy CNC machine tool as an example, the structural reliability analysis model of the fatigue strength of the milling shaft based on the UGF is constructed. The local sensitivity analysis and global sensitivity analysis of the variables affecting the fatigue strength of the milling shaft are carried out, and the factors that have the greatest impact on the fatigue strength of the milling shaft are obtained. The case study shows the effectiveness of the method proposed in this study.

Reliability analysis of m-out-of-r-within-k-out-of-n system

A binary-state m-out-of-r-within-k-out-of-n:G model is proposed and the reliability of the model is estimated with the help of Universal Generating Function (UGF). In the proposed system, the subsystems are connected in k-out-of-n:G type configuration. The subsystems are also a combination of m-out-of-r:G type. The elements of the subsystem consist of components connected in series. The components cannot be divided further and taken as an individual unit. The reliability function and absolute reliability of the proposed model are evaluated from the UGF technique.

Reliability Evaluation of Multi-State Systems With Common Bus Performance Sharing Considering Performance Excess

In a multi-state system with common bus performance sharing, the residual performance of any sub-unit can be shared to other sub-units with insufficient performance by the common bus with stochastic sharing capacity. This study extends the reliability evaluation model by considering both the minimum and maximum requirements of elements, which should not only meet the random minimum requirements of each single element, but also require that there should be no excess performance. The reliability of the multi-state system (MSS) is estimated by using the Universal Generating Function (UGF) technique. Illustrative example is presented to illustrate the procedures. In addition, the genetic operator is used to obtain the optimal location of the components with maximum reliability.

Analysis of signature reliability of ring-shaped network system

PurposeThe purpose of this paper is to design a ring network topology system and alter it into a series–parallel type framework. Then, reliability of the framework is analysed and authors also discussed the signature to analyse the most sensitive component.Design/methodology/approachThis study presents a ring-shaped network system where this type of topology forms a single continuous pathway for signals through every node. In this study, a system consists of ring network topology is generalized in the series–parallel mixed configuration and reliability characteristics are evaluated with the assistance of universal generating function (UGF) technique. The system consists of wires, repeaters, components or computers and power supply. The wires and repeaters are in series, so, if they fail the whole system will fail and the signals will not go further. The components or computers are connected to each other in parallel configuration. So, the whole system will not fail until the last computer is working. There is also a two-unit power supply system which has one unit in a standby mode. On the failure of first power supply, the second one will start functioning and the whole system fails on the failure of both power supply.FindingsBy the assistance of UGF technique, reliability function of the framework is evaluated. Also, Barlow–Proschan index and expected lifetime for the designed system is estimated by considering a numerical example for the general ring-shaped network system.Originality/valueUGF technique is very effective for estimating the reliability of a system with complex structure and having two performance rates, i.e. completely failed and perfectly working, or more than two, i.e. multi-state performance. This technique enables to estimate every components contribution in the working and failure of the whole system. A general model of ring-shaped network system is taken and generalized algorithm is drawn for the system. Then a particular numerical example is solved for illustrating the use of this technique.

Availability Evaluation of Multi-Tenant Service Function Chaining Infrastructures by Multidimensional Universal Generating Function

The Network Function Virtualization (NFV) paradigm has been devised as an enabler of next generation network infrastructures by speeding up the provisioning and the composition of novel network services. The latter are implemented via a chain of virtualized network functions, a process known as Service Function Chaining. In this paper, we evaluate the availability of multi-tenant SFC infrastructures, where every network function is modeled as a multi-state system and is shared among different and independent tenants. To this aim, we propose a Universal Generating Function (UGF) approach, suitably extended to handle performance vectors, that we call Multidimensional UGF. This novel methodology is validated in a realistic multi-tenant telecommunication network scenario, where the service chain is composed by the network elements of an IP Multimedia Subsystem implemented via NFV. A steady-state availability evaluation of such an exemplary system is presented and a redundancy optimization problem is solved, so providing the SFC infrastructure which minimizes deployment cost while respecting a given availability requirement.

On Birnbaum type 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. This paper introduces, for two multistate components, Joint Birnbaum-Reliability Achievement Worth (JBRAW), Joint Birnbaum-Reliability Reduction Worth (JBRRW), Joint Birnbaum-Reliability Fussell-Vesely measure (JBRFV) and analogues joint risk importance measures for the multistate system. A steady state performance level distribution with restriction to the component’s states is used to obtain the introduced measures. Universal generating function (UGF) technique is applied for the evaluation of proposed joint importance measures. An illustrative example is provided.

An Efficient Universal Generating Function-Based Analyzing Approach for Multistate System with Imperfect Coverage Failure

A system with more than two states is called a multistate system (MSS), and such systems have already become a general trend in the arena of complex industrial products and/or systems. Fault-tolerant technology often plays a very important role in improving the reliability of an MSS. However, the existence of imperfect coverage failure (ICF) in a work-sharing group (WSG) decreases the reliability of MSS. A method is proposed to assess the reliability and sensitivity of an MSS with ICF. The components in a WSG can cooperate so as to improve overall efficiency by increasing performance levels. Using the technique of the universal generating function (UGF), a component’s UGF expression with ICF can be incorporated in two steps. During the computation of the system’s UGF, an algorithm based on matrix (ABM) is developed to reduce the computational complexity. Consequently, indices of reliability can be easily calculated based on the UGF expression of an MSS. Sensitivity analysis can help engineers judge which WSG should be eliminated first under various resource limitations. Examples illustrate and validate this method.

Reliability Assessment of Multi-State Phased Mission Systems With Common Bus Performance Sharing Subjected to Epistemic Uncertainty

In many real situations, because of the lack or inaccuracy of data, it is difficult to evaluate the performance levels and state probabilities of multistate components with precise values. Thus, the reliability evaluation of systems is always affected by the epistemic uncertainty. Existing research on epistemic uncertainty just focuses on simple multistate systems, without considering the phased mission and performance sharing characteristics of systems. Besides, the impact of transmission loss and performance storage on reliability needs to be considered in the modeling of performance sharing systems. In this article, considering the epistemic uncertainty, transmission loss, and performance storage simultaneously, an efficient reliability evaluation method for multi-state phased mission systems with common bus performance sharing is proposed. The transmission loss during the processes thatperformance sharing between subsystems and transferring between phases is considered in the system model. A modified Markov model combined with the mass function is adopted to measure the precise belief degree of component states at any given moment. Then, the belief universal generating function (UGF) method based on the Dempster—Shafer evidence theory is utilized to evaluate the uncertainty of the system instantaneous availability. Finally, two case studies are carried out to demonstrate the effectiveness of the proposed method and explore the dynamic system availability under epistemic uncertainty.