Distributed Fault Estimation for Nonlinear Systems With Sensor Saturation and Deception Attacks Using Stochastic Communication Protocols

This paper is aimed at the distributed fault estimation issue associated with the potential loss of actuator efficiency for a type of discrete-time nonlinear systems with sensor saturation.For the distributed estimation structure under consideration,an estimation center is not necessary,and the estimator derives its information from itself and neighboring nodes,which fuses the state vector and the measurement vector.In an effort to cut down data conflicts in communication networks,the stochastic communication protocol(SCP)is employed so that the output signals from sensors can be selected.Additionally,a recursive security estimator scheme is created since attackers randomly inject malicious signals into the selected data.On this basis,sufficient conditions for a fault estimator with less conservatism are presented which ensure an upper bound of the estimation error covariance and the mean-square exponential boundedness of the estimating error.Finally,a numerical example is used to show the reliability and effectiveness of the considered distributed estimation algorithm.

Distributed Dynamic Load in Structural Dynamics by the Impulse-Based Force Estimation Algorithm

This paper proposes a novel approach for identifying distributed dynamic loads in the time domain.Using polynomial andmodal analysis,the load is transformed intomodal space for coefficient identification.This allows the distributed dynamic load with a two-dimensional form in terms of time and space to be simultaneously identified in the form of modal force,thereby achieving dimensionality reduction.The Impulse-based Force Estimation Algorithm is proposed to identify dynamic loads in the time domain.Firstly,the algorithm establishes a recursion scheme based on convolution integral,enabling it to identify loads with a long history and rapidly changing forms over time.Secondly,the algorithm introduces moving mean and polynomial fitting to detrend,enhancing its applicability in load estimation.The aforementioned methodology successfully accomplishes the reconstruction of distributed,instead of centralized,dynamic loads on the continuum in the time domain by utilizing acceleration response.To validate the effectiveness of the method,computational and experimental verification were conducted.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

Archimedean copula estimation of distribution algorithm based on artificial bee colony algorithm

The artificial bee colony （ABC） algorithm is a com- petitive stochastic population-based optimization algorithm. How- ever, the ABC algorithm does not use the social information and lacks the knowledge of the problem structure, which leads to in- sufficiency in both convergent speed and searching precision. Archimedean copula estimation of distribution algorithm （ACEDA） is a relatively simple, time-economic and multivariate correlated EDA. This paper proposes a novel hybrid algorithm based on the ABC algorithm and ACEDA called Archimedean copula estima- tion of distribution based on the artificial bee colony （ACABC） algorithm. The hybrid algorithm utilizes ACEDA to estimate the distribution model and then uses the information to help artificial bees to search more efficiently in the search space. Six bench- mark functions are introduced to assess the performance of the ACABC algorithm on numerical function optimization. Experimen- tal results show that the ACABC algorithm converges much faster with greater precision compared with the ABC algorithm, ACEDA and the global best （gbest）-guided ABC （GABC） algorithm in most of the experiments.

Combinations of Estimation of Distribution Algorithms and Other Techniques

This paper summaries our recent work on combining estimation of distribution algorithms （EDA） and other techniques for solving hard search and optimization problems： a） guided mutation, an offspring generator in which the ideas from EDAs and genetic algorithms are combined together, we have shown that an evolutionary algorithm with guided mutation outperforms the best GA for the maximum clique problem, b） evolutionary algorithms refining a heuristic, we advocate a strategy for solving a hard optimization problem with complicated data structure, and c） combination of two different local search techniques and EDA for numerical global optimization problems, its basic idea is that not all the new generated points are needed to be improved by an expensive local search.

An improved estimation of distribution algorithm for multi-compartment electric vehicle routing problem

The multi-compartment electric vehicle routing problem(EVRP)with soft time window and multiple charging types(MCEVRP-STW&MCT)is studied,in which electric multi-compartment vehicles that are environmentally friendly but need to be recharged in course of transport process,are employed.A mathematical model for this optimization problem is established with the objective of minimizing the function composed of vehicle cost,distribution cost,time window penalty cost and charging service cost.To solve the problem,an estimation of the distribution algorithm based on Lévy flight(EDA-LF)is proposed to perform a local search at each iteration to prevent the algorithm from falling into local optimum.Experimental results demonstrate that the EDA-LF algorithm can find better solutions and has stronger robustness than the basic EDA algorithm.In addition,when comparing with existing algorithms,the result shows that the EDA-LF can often get better solutions in a relatively short time when solving medium and large-scale instances.Further experiments show that using electric multi-compartment vehicles to deliver incompatible products can produce better results than using traditional fuel vehicles.

Distribution of chlorophyU a and estimation of primary productivity in the eastern waters of Balingtang Channel in summer

Oceanographical features on both sides of Balingtang Channel (17°55′-20°06′N, 122°55′-126°57′E) were comprehensively investigated on board of R/V "Experiment 3" in June. 1984. The pre-sent paper reports the chlorophyll data collected and primary productivity estimated there. Water sam-ples were taken with a glass bottle of Model HQMat the depth of 0, 10. 25, 50, 75, 100 and 150m, separately. Chlorophyll was determined according to the spectrophotometry proposed by UNESCO(1966) and calculated with the trichromatic equations of Jeffrey-Humphrey(1975). Estimations ofprimary productivity were carried out using a simplified equation (Q = 1.5) given by Cadee(1975).

Distribution Estimation with Smoothed Auxiliary Information

Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable, A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.

Improved Estimation of Distribution Algorithm for Solving Unrelated Parallel Machine Scheduling Problem

Scheduling problem is a well-known combinatorial optimization problem.An effective improved estimation of distribution algorithm(IEDA) was proposed for minimizing the makespan of the unrelated parallel machine scheduling problem(UPMSP).Mathematical description was given for the UPMSP.The IEDA which was combined with variable neighborhood search(IEDA_VNS) was proposed to solve the UPMSP in order to improve local search ability.A new encoding method was designed for representing the feasible solutions of the UPMSP.More knowledge of the UPMSP were taken consideration in IEDA_ VNS for probability matrix which was based the processing time matrix.The simulation results show that the proposed IEDA_VNS can solve the problem effectively.

Robust multi-task distributed estimation based on generalized maximum correntropy criterion

False data injection(FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion(GMCC-DLMS)for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work,it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm.

Distributed Secure State Estimation of Multi-Agent Systems Under Homologous Sensor Attacks

This paper addresses the problem of distributed secure state estimation for multi-agent systems under homologous sensor attacks.Two types of secure Luenberger-like distributed observers are proposed to estimate the system state and attack signal simultaneously.Specifically,the proposed two observers are applicable to deal with the cases in the presence and absence of time delays during network communication.It is also shown that the proposed observers can ensure the attack estimations from different agents asymptotically converge to the same value.Sufficient conditions for guaranteeing the asymptotic convergence of the estimation errors are derived.Simulation examples are finally provided to demonstrate the effectiveness of the proposed results.

An Ellipsoidal Set-Membership Approach to Distributed Joint State and Sensor Fault Estimation of Autonomous Ground Vehicles

This paper is concerned with the problem of distributed joint state and sensor fault estimation for autonomous ground vehicles subject to unknown-but-bounded(UBB)external disturbance and measurement noise.In order to improve the estimation reliability and performance in cases of poor data collection and potential communication interruption,a multisensor network configuration is presented to cooperatively measure the vehicular yaw rate,and further compute local state and fault estimates.Toward this aim,an augmented descriptor vehicle model is first established,where the unknown sensor fault is modeled as an auxiliary state of the system model.Then,a new distributed ellipsoidal set-membership estimation approach is developed so as to construct an optimized bounding ellipsoidal set which guarantees to contain the vehicle’s true state and the sensor fault at each time step despite the existence of UBB disturbance and measurement noises.Furthermore,a convex optimization algorithm is put forward such that the gain matrix of each distributed estimator can be recursively obtained.Finally,simulation results are provided to validate the effectiveness of the proposed approach.

E-Bayesian estimation for competing risk model under progressively hybrid censoring

This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Distributed Privacy-Preserving Fusion Estimation Using Homomorphic Encryption

The privacy-preserving problem for distributed fusion estimation scheme is concerned in this paper.When legitimate user wants to obtain consistent information from multiple sensors,it always employs a fusion center(FC)to gather local data and compute distributed fusion estimates(DFEs).Due to the existence of potential eavesdropper,the data exchanged among sensors,FC and user imperatively require privacy preservation.Hence,we propose a distributed confidentiality fusion structure against eavesdropper by using Paillier homomorphic encryption approach.In this case,FC cannot acquire real values of local state estimates,while it only helps calculate encrypted DFEs.Then,the legitimate user can successfully obtain the true values of DFEs according to the encrypted information and secret keys,which is based on the homomorphism of encryption.Finally,an illustrative example is provided to verify the effectiveness of the proposed methods.

A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

With the application of phasor measurement units(PMU)in the distribution system,it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration.How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration.According to the concept of efficient frontier,a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors,statistical characteristics of the pseudo measurements,and reliability of the measurement instrument.The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system.Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed,and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.

Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for the Gamma Cumulative Distribution Function with Known and Integer Scale Parameter

Uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameter. This paper applies Rao-Blackwell and Lehmann-Scheffeé Theorems to deduce the uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameters. The paper closes with an example comparing the empirical distribution function with the UMVUE estimates.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

Distributed computations for large-scale networked systems using belief propagation

This paper introduces several related distributed algorithms,generalised from the celebrated belief propagation algorithm for statistical learning.These algorithms are suitable for a class of computational problems in largescale networked systems,ranging from average consensus,sensor fusion,distributed estimation,distributed optimisation,distributed control,and distributed learning.By expressing the underlying computational problem as a sparse linear system,each algorithm operates at each node of the network graph and computes iteratively the desired solution.The behaviours of these algorithms are discussed in terms of the network graph topology and parameters of the corresponding computational problem.A number of examples are presented to illustrate their applications.Also introduced is a message-passing algorithm for distributed convex optimisation.

Distributed Trimmed Hill Estimator

Proceeded from trimmed Hill estimators and distributed inference, a new distributed version of trimmed Hill estimator for heavy tail index is proposed. Considering the case where the number of observations involved in each machine can be either the same or different and either fixed or varying to the total sample size, its consistency and asymptotic normality are discussed. Simulation studies are particularized to show the new estimator performs almost in line with the trimmed Hill estimator.