Mixed Uncertainties Research Articles

Service Optimization of Internet of Manufacturing Things Based on Mixed Information Axioms

As a new intelligent manufacturing model, the Internet of Manufacturing Things (IOMT) based on the Internet of Things technology has a large amount of random, fuzzy, and uncertain information, which makes the optimization of manufacturing services face challenges. On the basis of fully considering the uncertain factors in the process of manufacturing service, a quality of service (QoS) optimization method based on mixed information axioms is proposed to solve the optimization problem of manufacturing service in the IOMT environment. The mixed uncertainty model is expounded with random variables to express the range of system and fuzzy variables to describe the design range. In order to select the best resource or sort, the fuzzy mathematics and the axiomatic theory of axiomatic design theory are combined to evaluate the coexistence of ambiguity and randomness of the QoS. Finally, the process of treatment and optimization in practical application by taking the example of a hydraulic pump product seeking service through the civil aircraft IOMT service platform is described. This example is given out to demonstrate the effectiveness of the proposed method by comparing with the traditional information axiom method, and this method extends the application scope of traditional information axioms.

Short-Term Line Maintenance Scheduling of Distribution Network With PV Penetration Considering Uncertainties

In this paper, the methodology for short-term line maintenance scheduling in distribution network with PV penetration is proposed, in which the mixed randomness and fuzziness of solar power generation concerning the available cloud amount forecasting, along with other random or fuzzy factors, such as electricity demand and component historical failure rate, are considered. First, based on the obtained historical data from NASA, the empirical mapping from cloud amount to solar irradiance can be established where the uncertainty is represented by combining randomness and fuzziness. Second, the short-term line maintenance scheduling of distribution network with uncertainties is modeled by using random fuzzy chance-constrained programming aiming at minimizing the pessimistic value in terms of economics and reliability subject to the chance constraints. Finally, a hybrid intelligent algorithm with two-layer optimization is implemented to solve the model. Simulation experiments are carried out on the IEEE 33-Bus and IEEE RBTS 2-Bus systems, and the results demonstrate the effectiveness of the proposed short-term line maintenance scheduling solution for distribution network with the mixed uncertainties of randomness and fuzziness.

An integrated QMU approach to structural reliability assessment based on evidence theory and kriging model with adaptive sampling

The objective of this paper is to propose an implementation framework of the quantification of margins and uncertainties (QMU) calculation for reliability and safety assessment of high-consequence systems in the presence of mixed (aleatory and epistemic) uncertainties. The aleatory and epistemic uncertainties are represented by a probability distribution and the Dempster–Shafer theory of evidence (DSTE), respectively. This study focuses on the need to alleviate the computational cost in terms of mixed uncertainties propagation, which is the core of the QMU process. The kriging model together with an adaptive sampling method is tailored to predict the responses of a system simulation model. The confidence factor (CF) for the QMU calculation is then evaluated by integrating the surrogate model and the DSTE analysis. The proposed approach is demonstrated by a numerical example to examine the computational efficiency. Finally, the proposed QMU framework is demonstrated via a simulation-based structural analysis of a pressure vessel with corrosion damage.

Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

SummaryEstimating the input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) white noise deconvolution estimators for a class of uncertain multisensor systems with mixed uncertainties, including uncertain‐variance multiplicative noises in measurement matrix, missing measurements, and uncertain‐variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time‐varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the CF algorithm, the WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust fused steady‐state white noise deconvolution estimators are also presented. A simulation example with respect to the multisensor IS‐136 communication systems shows the effectiveness and correctness of the proposed results.

Robust Kalman estimators for systems with mixed uncertainties

SummaryThis paper addresses the problem of designing robust Kalman estimators for uncertain systems with mixed uncertainties including the same uncertain‐variance multiplicative noise in state and measurement matrices, missing measurements, and uncertain‐variance linearly correlated measurement and process white noise. By introducing fictitious noise to compensate for multiplicative noise, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, on the basis of the worst‐case system with known conservative upper bounds of uncertain variances, the minimax robust time‐varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady‐state Kalman estimators are also presented, and 3 modes of convergence in a realization among the time‐varying and steady‐state robust Kalman estimators for the time‐varying and time‐invariant systems are presented and proved by the dynamic error system analysis method. A simulation example with application to autoregressive signal processing is also given to show the effectiveness and correctness of the proposed results.

Robust Kalman estimators for systems with multiplicative and uncertain-variance linearly correlated additive white noises

For linear discrete-time stochastic systems with mixed uncertainties including multiplicative and uncertain-variance linearly correlated additive white noises, this paper addresses the problem of designing robust Kalman estimators. By the fictitious noise-based Lyapunov equation approach, the system under consideration is converted into one with only uncertain noise variances. Based on the worst-case system with conservative upper bounds of actual noise variances, the minimax robust time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady-state Kalman estimators are also presented. An innovation test rule and a search technique of selecting the less-conservative upper bounds of actual noise variances are presented, by which the two classes of guaranteed robust accuracy Kalman estimators are presented. One class is robust Kalman estimators with improved robust accuracy, the other class is ones with the prescribed robust accuracy index. Three modes of convergence in a realization among the time-varying and steady-state robust Kalman estimators for the time-varying and time-invariant systems are presented and proved by the dynamic error system analysis (DESA) method. Two simulation examples applied to autoregressive (AR) signal processing and uninterruptible power system (UPS) show the effectiveness of the proposed results.

What measurements of neutrino neutral current events can reveal

We show that neutral current (NC) measurements at neutrino detectors can play a valuable role in the search for new physics. Such measurements have certain intrinsic features and advantages that can fruitfully be combined with the usual well-studied charged lepton detection channels in order to probe the presence of new interactions or new light states. In addition to the fact that NC events are immune to uncertainties in standard model neutrino mixing and mass parameters, they can have small matter effects and superior rates since all three flavours participate. We also show, as a general feature, that NC measurements provide access to different combinations of CP phases and mixing parameters compared to CC measurements at both long and short baseline experiments. Using the Deep Underground Neutrino Experiment (DUNE) as an illustrative setting, we demonstrate the capability of NC measurements to break degeneracies arising in CC measurements, allowing us, in principle, to distinguish between new physics that violates three flavour unitarity and that which does not. Finally, we show that NC measurements can enable us to restrict new physics parameters that are not easily constrained by CC measurements.

Extending Horsetail Matching for Optimization Under Probabilistic, Interval, and Mixed Uncertainties

This paper presents a new approach for optimization under uncertainty in the presence of probabilistic, interval, and mixed uncertainties, avoiding the need to specify probability distributions on uncertain parameters when such information is not readily available. Existing approaches for optimization under these types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Here, horsetail matching is extended for use with these types of uncertainties to overcome some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems, the design of a wing using a low-fidelity coupled aerostructural code, and the aerodynamic shape optimization of a wing using computational fluid dynamics analysis.

Mixed uncertainty based analytical target cascading: an approach for hierarchical multilevel optimization under probabilistic and interval mixed uncertainties

Analytical target cascading (ATC) has been extended to the probabilistic formulation to deal with the hierarchical multilevel optimization problem under uncertainty. However, only aleatory uncertainties can be handled by the probabilistic theory. Considering both aleatory and epistemic uncertainties exist in engineering design, a mixed uncertainty based analytical target cascading (MUATC) approach is proposed in this paper. The probability distribution and interval are used to represent the aleatory uncertainties and epistemic uncertainties, respectively. To figure out the mixed uncertainty propagation(MUP) problem, the reliability index approach based MUP (RIA-MUP) and performance measurement approach based MUP (PMA-MUP) are proposed firstly. Based on PMA-MUP, the MUATC method is established. MUATC firstly decouples the mixed uncertainty all-in-one (MUAIO) problem into deterministic optimization problem and mixed uncertainty analysis, and then hierarchically decomposes them into subproblems. All-in-one (AIO) mixed uncertainty analysis and hierarchically mixed uncertainty analysis methods are established to calculate the characteristic of the interrelated responses and shared variables. The accuracy and effectiveness of MUATC are demonstrated with three examples.

Study on location allocation of earthquake emergency service depot based on hybrid multi-attribute decision making

The aim of this paper is to propose a location model of earthquake emergency service depot on the basis of hybrid multi-attribute decision-making method. The advantage of the proposed method is that practical mixed uncertainty of location decision information is considered, and the corresponding factors that affect the location of transfer stations are contained. To solve the location problem, a hybrid multi-attribute decision procedure without information transformation is developed. Besides, a novel weighting method and aggregation process is given. Finally, a numerical example is provided to show the feasibility and validity of the proposed method.

Active Distribution Network Expansion Planning Integrating Practical Operation Constraints

This paper proposes a mathematics model of active distribution network expansion planning (DNEP) integrating the practical operation constraints, which are the OLTC (On-Load Tap Changer) tap adjusting frequency and substation voltage variation. Distributed Generation (DG) curtailment, load curtailment, OLTC tap adjustment, and reactive power compensation are considered as the active management schemes. The expansion model allows alternatives to be considered for new wiring, DG installation, new substation, and substation expansion. The DNEP problem is a mixed integer non-linear programming problem, active management, and uncertainties, especially with the DG integration make the DNEP problem much complex. In order to find the suitable algorithm, this paper converts the DNEP problem to a Second-Order Cone Programming (SOCP) model through distflow equations and constraints relaxation. A modified 33-bus application example is used to verify the proposed model with different active management scenarios.

A novel uncertainty analysis method for composite structures with mixed uncertainties including random and interval variables

This paper is aimed at proposing a novel uncertainty analysis approach based on polynomial chaos expansion method for composite structures, where mixed uncertainties including normal random and interval variables can be considered simultaneously. Firstly, existing uncertain elastic parameters in composites can be separately dealt with as normal random and interval variables according to the amount of available information and the uncertain response analysis problem with mixed uncertainties is proposed. Then some traditional uncertainty analysis methods are introduced, whose purpose is to point out the shortcomings or deficiencies for given approaches. Furthermore, the basic knowledge for polynomial chaos expansion (PCE) method and a novel uncertainty analysis method on the basis of PCE method for composite structures with mixed uncertainties are explained in details, where the polynomial coefficients are viewed as quadratic polynomial functions of interval variables. Finally, two numerical examples are carried out to account for the validity and feasibility of the developed method. The results show that the developed PCE method can be efficiently applied in uncertainty analysis of composite structures.

Integrated material-financial supply chain master planning under mixed uncertainty

This paper develops a bi-objective mixed possibilistic-stochastic model for a comprehensive supply chain master planning problem. The model integrates physical/material and financial tactical plans by accounting for the reciprocal effects of supply chain's functions and flows. Given the existence of several sources of uncertainty and the uncertainty level of input data, a mixture of fuzzy and random fuzzy variables is incorporated into the model. Appropriate methods are then tailored to convert the original uncertain model into a deterministic counterpart. To demonstrate the applicability of the developed model, an illustrative example is provided. Sensitivity analyses are performed on the critical parameters of the developed model and its solution methodology to provide useful managerial insights. Also, a novel performance comparison method is devised to compare the original random fuzzy model against its fuzzy and deterministic counterparts. The results demonstrate the superiority of the proposed random fuzzy model over its counterparts.

A New MCP Method of Wind Speed Temporal Interpolation and Extrapolation Considering Wind Speed Mixed Uncertainty

In this paper, a missing wind speed data temporal interpolation and extrapolation method in the wind energy industry was investigated. Given that traditional methods have previously ignored part of mixed uncertainty of wind speed, a concrete granular computing method is constructed and a new Measure–Correlate–Predict (MCP) method of wind speed data temporal interpolation and extrapolation considering all mixed uncertainties is proposed, based on granular computing theory by adopting the cloud model method, support vector regression method, artificial neural network, genetic algorithm, and fuzzy c-means clustering algorithm as tools. The importance of considering mixed wind speed uncertainty and the suitability of using granular computing method are illustrated, and wind speed mixed uncertainty analysis is implemented, then, recommended values and estimation tools for wind speed measurement uncertainty and combined uncertainty are provided. An interpolation case of two practical meteorological sites in central Southern China was used to implement and validate the method proposed in this paper. The following conclusions are reached: (a) by using the method proposed in this paper, mixed uncertainty of wind speed can be considered, comparing to other MCP methods used for purposes of comparison, a better estimation of the wind speed is provided, and most evaluation metrics employed in this analysis were superior to other methods, that is to say, the accuracy of the wind resource assessment improved, and the risks of wind farm construction were reduced; (b) granular computing method is suitable for the issue of wind speed data interpolation and extrapolation considering wind speed mixed uncertainty; (c) mixed uncertainty of wind speed can be divided into three levels, and recommended values of granularity are minimum interval of records, 0.3–0.8 m/s, and 1–3 m/s, respectively.

Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements

For multisensor uncertain systems with mixed uncertainties, including multiplicative noises in state and process noise transition matrices, uncertain-variance multiplicative and additive white noises, and missing measurements, this paper addresses the problem of designing robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman predictors. By introducing fictitious noises, the system under study is converted into a system with only uncertain noise variances. According to the minimax robust estimation principle, which is based on the worst-case system with conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman predictors are presented in a unified framework. Using the Lyapunov equation, the robustness of these predictors is proven in the sense that the actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using an information filter, they are proven to have the same robust and actual accuracies. The complexity analysis shows that when the number of sensors is larger, the WMF algorithm more significantly reduces the computational burden than the CF algorithm. The corresponding robust fused steady-state Kalman predictors are also presented. The three modes of convergence in a realization among the time-varying and steady-state robust fused Kalman predictors are proposed and proven using the dynamic error system analysis method. Two simulation examples, autoregressive moving average signal processing and an uninterruptible power system, demonstrate the effectiveness of the proposed methods.

A mixed-integer linear programming model for solving fuzzy stochastic resource constrained project scheduling problem

This paper addresses resource-constrained project scheduling problem with mixed uncertainty of randomness and fuzziness (FS-RCPSP). The activity durations are considered to be fuzzy random variables. A resource flow network based mathematical model with fuzzy random variables is presented. Then, this model is transformed into a mixed-integer linear programming model with crisp variables. The CPLEX 12.6.0.1 solver in AIMMS (2014) is employed for applying the proposed model to solve 960 benchmark instances generated from the well-known sets J30 and J60 in PSPLIB. The computational results are encouraging and indicate the ability of the proposed model to handle the FS-RCPSP.

Highly efficient evaluation of a gas mixer using a hollow waveguide based laser spectral sensor.

This paper aims to provide a fast, sensitive, and accurate characterization of a Mass Flow Controller (MFC) based gas mixer. The gas mixer was evaluated by using a hollow waveguide based laser spectral sensor with high efficiency. Benefiting from the sensor's fast response, high sensitivity and continuous operation, multiple key parameters of the mixer, including mixing uncertainty, linearity, and response time, were acquired by a one-round test. The test results show that the mixer can blend multi-compound gases quite efficiently with an uncertainty of 1.44% occurring at a flow rate of 500 ml/min, with the linearity of 0.998 43 and the response time of 92.6 s. The results' reliability was confirmed by the relative measurement of gas concentration, in which the isolation of the sensor's uncertainty was conducted. The measured uncertainty has shown well coincidence with the theoretical uncertainties of the mixer, which proves the method to be a reliable characterization. Consequently, this sort of laser based characterization's wide appliance on gas analyzer's evaluations is demonstrated.

Global sensitivity analysis under mixed uncertainty based on possibilistic moments

Global sensitivity analysis under mixed uncertainty based on possibilistic moments

Uncertainty representation and quantification for a nonlinear rotor/stator system with mixed uncertainties

A rotor-to-stator coupled system usually exhibits complicated dynamic behaviors due to its nonlinear nature. Moreover, the inherent uncertainty (aleatory uncertainty) and many undetermined factors either brought by manufacturing process or due to the lack of knowledge (epistemic uncertainty) make the analysis of system response a challenging task. Existing studies on rotor uncertainties are mostly focused on the stochastic variables, yet pay less attention to other forms of uncertain variables such as intervals. However, some physical parameters (e.g. friction coefficient) can be hardly assigned one specific probability distribution and often available in interval forms. To deal with this, the concept of likelihood is extended from classical discrete point value to interval variable in the presence of mixed uncertainties. A likelihood-based approach is carried out for the mixed uncertainties representation and quantification. In addition, a new single loop sampling algorithm is developed to reduce the computation cost. This framework could be applied in the field of industry manufacturing and mounting, especially take effect in risk assessment and product maintaining. A series of numerical cases are demonstrated for validation and comparison.

The Shortest Path Problem on a Time-Dependent Network With Mixed Uncertainty of Randomness and Fuzziness

The uncertainty of travel times on a time-dependent network is conventionally considered as randomness or fuzziness. However, sometimes, randomness or fuzziness cannot describe the uncertainty of the travel times on the time-dependent network. In this paper, we introduce a random fuzzy time-dependent network (RFTDN), in which travel times of a time-dependent network are represented as mixed uncertainty of randomness and fuzziness. With these conditions, the resulting RFTDN is far more complex when compared with the known networks. The complexity stems from estimating the length of a path, which is a basic and core issue when analyzing a network. To address this problem, we propose an optimized method that is suitable to cope with the shortest path problem of the RFTDN. The proposed method is realized by means of random fuzzy simulation and a new repair-based genetic optimization. Random fuzzy simulation is used to estimate the random fuzzy functions that describe the length of arcs, whereas the repair-based genetic algorithm is presented for finding the shortest path on the network. Furthermore, the proposed repair-based genetic operators are demonstrated their effectiveness by analyzing running time. A numerical example is also provided to show the robustness of the proposed approach.