Distributed QoS multicast routing in networks with imprecise state information

The goal of quality-of-service （QoS） multicast routing is to establish a multicast tree which satisfies certain constraints on bandwidth, delay and other metrics. The network state information maintained at every node is often im- precise in a dynamic environment because of non-negligible propagation delay of state messages, periodic updates due to overhead concern, and hierarchical state aggregation. The existing QoS multicast routing algorithms do not provide satisfactory performance with imprecise state information. We propose a distributed QoS multicast routing scheme based on traffic lights, called QMRI algorithm, which can probe multiple feasible tree branches, and select the optimal or near-optimal branch through the UR or TL mode for constructing a multicast tree with QoS guarantees if it exists. The scheme is designed to work with imprecise state information. The proposed algorithm considers not only the QoS requirements but also the cost optimality of the multicast tree. The correctness proof and the complexity analysis about the QMRI algorithm are also given. In addition, we develop NS2 so that it is able to simulate the imprecise network state information. Extensive simulations show that our algorithm achieves high call-admission ratio and low-cost multicast trees with modest message overhead.

Structural Reliability Modeling Based on Imprecise Probability Theory under Insufficient Data

Traditional structural reliability analysis methods adopt precise probabilities to quantify uncertainties and they are suitable for systems with sufficient statistical data.However,the problem of insufficient data is often encountered in practical engineering.Thus,structural reliability analysis methods under insufficient data have caught more and more attentions in recent years and a lot of nonprobabilistic reliability analysis methods are put forward to deal with the problem of insufficient data.Non-probabilistic structural reliability analysis methods based on fuzzy set,Dempster-Shafer theory,interval analysis and other theories have got a lot of achievements both in theoretical and practical aspects and they have been successfully applied in structural reliability analysis of largescale complex systems with small samples and few statistical data.In addition to non-probabilistic structural reliability analysis methods,structural reliability analysis based on imprecise probability theory is a new method proposed in recent years.Study on structural reliability analysis using imprecise probability theory is still at the start stage,thus the generalization of imprecise structural reliability model is very important.In this paper,the imprecise probability was developed as an effective way to handle uncertainties,the detailed procedures of imprecise structural reliability analysis was introduced,and several specific imprecise structural reliability models which are most effective for engineering systems were given.At last,an engineering example of a cantilever beam was given to illustrate the effectiveness of the method emphasized here.By comparing with interval structural reliability analysis,the result obtained from imprecise structural reliability model is a little conservative than the one resulted from interval structural reliability analysis for imprecise structural reliability analysis model considers that the probability of each value is taken from an interval.

Imprecise Computation Based Real-time Fault Tolerant Implementation for Model Predictive Control

Model predictive control (MPC) could not be deployed in real-time control systems for its computation time is not well defined. A real-time fault tolerant implementation algorithm based on imprecise computation is proposed for MPC, according to the solving process of quadratic programming (QP) problem. In this algorithm, system stability is guaranteed even when computation resource is not enough to finish optimization completely. By this kind of graceful degradation, the behavior of real-time control systems is still predictable and determinate. The algorithm is demonstrated by experiments on servomotor, and the simulation results show its effectiveness.

A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification

This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the crosscorrelation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model,through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.

Bayesian Network Based Imprecise Probability Estimation Method for Wind Power Ramp Events

Although wind power ramp events(WPREs)are relatively scarce,they can inevitably deteriorate the stability of power system operation and bring risks to the trading of electricity market.In this paper,an imprecise conditional probability estimation method for WPREs is proposed based on the Bayesian network(BN)theory.The method uses the maximum weight spanning tree(MWST)and greedy search(GS)to build a BN that has the highest fitting degree with the observed data.Meanwhile,an extended imprecise Dirichlet model(IDM)is developed to estimate the parameters of the BN,which quantificationally reflect the ambiguous dependencies among the random ramp event and various meteorological variables.The BN is then applied to predict the interval probability of each possible ramp state under the given meteorological conditions,which is expected to cover the target probability at a specified confidence level.The proposed method can quantify the uncertainty of the probabilistic ramp event estimation.Meanwhile,by using the extracted dependencies and Bayesian rules,the method can simplify the conditional probability estimation and perform reliable prediction even with scarce samples.Test results on a real wind farm with three-year operation data illustrate the effectiveness of the proposed method.

Importance measures for imprecise probability distributions and their sparse grid solutions

For the imprecise probability distribution of structural system, the variance based importance measures (IMs) of the inputs are investigated, and three IMs are defined on the conditions of random distribution parameters, interval distribution parameters and the mixture of those two types of distribution parameters. The defined IMs can reflect the influence of the inputs on the output of the structural system with imprecise distribution parameters, respectively. Due to the large computational cost of the variance based IMs, sparse grid method is employed in this work to compute the variance based IMs at each reference point of distribution parameters. For the three imprecise distribution parameter cases, the sparse grid method and the combination of sparse grid method with genetic algorithm are used to compute the defined IMs. Numerical and engineering examples are em-ployed to demonstrate the rationality of the defined IMs and the efficiency of the applied methods.

Decomposition for a new kind of imprecise information system

In this paper, we first propose a new kind of imprecise information system, in which there exist conjunctions （∧＇s）, disjunctions （∨＇s） or negations （ ＇s）. Second, this paper discusses the relation that only contains ∧＇s based on relational database theory, and gives the syntactic and semantic interpretation for A and the definitions of decomposition and composition and so on. Then, we prove that there exists a kind of decomposition such that if a relation satisfies some property then it can be decomposed into a group of classical relations （relations do not contain ∧） that satisfy a set of functional dependencies and the original relation can be synthesized from this group of classical relations. Meanwhile, this paper proves the soundness theorem and the completeness theorem for this decomposition. Consequently, a relation containing ∧＇s can be equivalently transformed into a group of classical relations that satisfy a set of functional dependencies. Finally, we give the definition that a relation containing ∧＇s satisfies a set of functional dependencies. Therefore, we can introduce other classical relational database theories to discuss this kind of relation.

MERGING FUZZY STATISTICAL DATA WITH IMPRECISE PRIOR INFORMATION

Solving complex decision problems requires the usage of information from different sources. Usually this information is uncertain and statistical or probabilistic methods are needed for its processing. However, in many cases a decision maker faces not only uncertainty of a random nature but also imprecision in the description of input data that is rather of linguistic nature. Therefore, there is a need to merge uncertainties of both types into one mathematical model. In the paper we present methodology of merging information from imprecisely reported statistical data and imprecisely formulated fuzzy prior information. Moreover, we also consider the case of imprecisely defined loss functions. The proposed methodology may be considered as the application of fuzzy statistical methods for the decision making in the systems analysis.

An Interval-valued Approach to Calculation ofNonequilibriumThermodynamics with Imprecise Information

The research of the imprecision of a nonequilibrium thermodynamic system is justifiedby the structural and parametric uncertainties of such systems. The paper gives an interval-valuedformulation of the phenomenological equations and shows a realistic approach for studying the entropyproduction in Physical systems, the time trajectories of chemical reactions, etc. Using algorithms derivedfor special reaction systems, bundles of time trajectories with prescribed boundary possibility measuresare calculated.

Imprecise Probability Method with the Power-Normal Model for Accelerated Life Testing

We present a new nonparametric predictive inference(NPI)method using a power-normal model for accelerated life testing(ALT).Combined with the accelerating link function and imprecise probability theory,the proposed method is a feasible way to predict the life of the product using ALT failure data.To validate the method,we run a series of simulations and conduct accelerated life tests with real products.The NPI lower and upper survival functions show the robustness of our method for life prediction.This is a continuous research,and some progresses have been made by updating the link function between different stress levels.We also explain how to renew and apply our model.Moreover,discussions have been made about the performance.

Application of Sigma Metric Analysis to Evaluate the Performance of the Biochemistry Analytical System in a Medical Biology Laboratory in Côte d’Ivoire

Introduction: The Six Sigma methodology is an opportunity for a better understanding of the performance of analytical methods and for a better adaptation of the quality control management policy of the medical biology laboratory. Using the sigma metric, this study assessed the performance of the Biochemistry analytical system of a medical biology laboratory in Côte d'Ivoire. Methods: Six Sigma methodology was applied to 3 analytes (alanine aminotransferase, glucose and creatinine). Performance indicators such as measurement imprecision and bias were determined based on the results of internal and external quality controls. The sigma number was calculated using the total allowable error values proposed by Ricos et al. Results: For both control levels, ALT had a sigma number greater than 6 (7.6 for normal control and 7.9 for pathological control). However, low sigma numbers, less than or equal to 2 for creatinine (1.4 for normal control and 2 for pathological control) and less than 1 for glucose were found. Conclusion: This study revealed good analytical performance of ALT from the point of view of 6 sigma analysis. However, modifications to the overall quality control procedure for glucose and creatinine are needed to improve their analytical performance. The study should be extended to the entire laboratory’s analytes in order to modify the strategies of quality control procedures based on metric analysis for an overall improvement in analytical performance.

The First-Order Comprehensive Sensitivity Analysis Methodology (1st-CASAM) for Scalar-Valued Responses: I. Theory

This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently, exactly, and exhaustively, the first-order sensitivities of scalar-valued responses (results of interest) of coupled nonlinear physical systems characterized by imprecisely known model parameters, boundaries and interfaces between the coupled systems. The 1st-CASAM highlights the conclusion that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions defining the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems. Ongoing research will generalize the methodology presented in this work, aiming at computing exactly and efficiently higher-order response sensitivities for coupled systems involving imprecisely known interfaces, parameters, and boundaries.

RBF neural network regression model based on fuzzy observations

A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.

Novel dynamic evidential Petri net for system reliability analysis

This paper proposes a novel dynamic Petri net (PN) model based on Dempster-Shafer (D-S) evidence theory, and this improved evidential Petri net (EPN) model is used in knowledge inference and reliability analysis of complex mechanical systems. The EPN could take epistemic uncertainty such as interval information, subjective information into account by applying D-S evidence quantification theory. A dynamic representation model is also proposed based on the dynamic operation rules of the EPN model, and an improved artificial bee colony (ABC) algorithm is employed to proceed optimization calculation during the complex systems' learning process. The improved ABC algorithm and D-S evidence theory overcome the disadvantage of extremely subjective in traditional knowledge inference efficiently and thus could improve the accuracy of the EPN learning model. Through a simple numerical case and a satellite driving system analysis, this paper proves the superiority of the EPN and the dynamic knowledge representation method in reliability analysis of complex systems.

Quasi-Bayesian software reliability model with small samples

In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information of experts＇ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued probabilities to clearly quantify experts＇ prior beliefs on possible intervals of the parameters of the probability distributions is presented. The model integrates experts＇ judgments with statistical data to obtain more convincible assessments of software reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda （JM） model using maximum likelihood （ML）.

Overall profit Malmquist productivity index under data uncertainty

The calculation of the overall profit Malmquist productivity index(MPI)requires precise and accurate information on the input,output,input-output prices of each decision making unit(DMU).However,in many situations,some inputs and/or outputs and input-output prices are imprecise.As such,we consider the overall profit MPI problem when the input,output,and input-output prices are imprecise and vary over intervals,showing that method(MCM 54:2827–2838,2011)has some shortfalls.To remedy these shortfalls,we propose another method for measuring the overall profit MPI when the inputs,outputs,and price vectors vary over intervals.That is,to calculate the overall profit efficiency intervals,cone-ratio data envelopment analysis models can be applied to the incorporated information as weight restrictions.Further,we provide a new approach to calculating the upper bound of the overall profit efficiency of each DMU.A numerical example is provided for illustrating the proposed method.

Assessment of Sustainable Regional Development Policies： A Case Study of Jambi Province, Indonesia

This paper presents a study of sustainable regional development using multi-criteria analysis. The aim of this paper is to provide an evaluation framework that can be used for the assessment of sustainable regional development using multi criteria linked to development scenarios set by stakeholders. This study was carried out in Jambi Province in Indonesia where balancing sustainable development is constrained by the fact that conservation areas make up the majority of the region. The study employs four alternative policy scenarios for regional sustainable development： （1） business as usual; （2） development based on regional competitiveness; （3） development based on local resources; and （4） regional development based on non-extractive scenario. These four scenarios were assessed using the FLAG Model and the Imprecise Decision Model. Results from analysis show that development policy scenarios based on utilization of local resources and non-extractive economic activities are the most sustainable way of regional development. The study shows the trade-off among policy scenarios must be faced by policy makers in the region either to pursue high economic growth at the cost of the environment or vice versa.

The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model

This work illustrates the application of the 1st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

A Note on Standard Goal Programming with Fuzzy Hierarchies: A Sequential Approach

In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it has been assumed that the normalized deviations should lie between zero and one. In some cases, this assumption may not be valid. Therefore, additional constraints must be incorporated into the model to ensure that the normalized deviations should not exceed one. This modification is illustrated by the given numerical example.

Assessment of quality control system by sigma metrics and quality goal index ratio: A roadmap towards preparation for NABL

AIM To study sigma metrics and quality goal index ratio(QGI). METHODS The retrospective study was conducted at the Clinical Biochemistry Laboratory, PGIMS, Rohtak, which recently became a National Accreditation Board for Testing and Calibration of Laboratories accredited lab as per the International Organization for Standardization 15189:2012 and provides service to a > 1700-bed tertiary care hospital. Data of 16 analytes was extracted over a period of one year from January 2017 to December 2017 for calculation of precision, accuracy, sigma metrics, total error, and QGI. RESULTS The average coefficient of variation ranged from 2.12%(albumin) to 5.42%(creatinine) for level 2 internal quality control and 2%(albumin) to 3.62%(high density lipoprotein-cholesterol) for level 3 internal quality control. Average coefficient of variation of all the parameters was below 5%, reflecting very good precision. The sigma metrics for level 2 indicated that 11(68.5%) of the 16 parameters fall short of meeting Six Sigma quality performance. Of these, five failed to meet minimum sigma quality performance with metrics less than 3, and another six just met minimal acceptable performance with sigma metrics between 3 and 6. For level 3, the data collected indicated eight(50%) of the parameters did not achieve Six Sigma quality performance, out of which three had metrics less than 3, and five had metrics between 3 and 6. QGI ratio indicated that the main problem was inaccuracy in the case of total cholesterol, aspartate transaminase, and alanine transaminase(QGI > 1.2), imprecision in the case of urea(QGI < 0.8), and both imprecision and inaccuracy for glucose.CONCLUSION On the basis of sigma metrics and QGI, it may be concluded that the Clinical Biochemistry Laboratory, PGIMS, Rohtak was able to achieve satisfactory results with world class performance for many analytes one year preceding the accreditation by the National Accreditation Board for Testing and Calibration of Laboratories. Aspartate transaminase and alanine transaminase required strict external quality assurance scheme monitoring and modification in quality control procedure as their QGI ratio showed inaccuracy.