Bernoulli Process Research Articles

A design parameter-free geometric Kullback-Leibler information control chart for monitoring Bernoulli processes

This paper considers a design parameter-free Kullback-Leibler information (KLI) control chart for monitoring the nonconforming proportion p of Bernoulli processes in Phase II. The chart statistic is derived from the Kullback-Leibler information based on a geometric distribution. Unlike conventional charts for Phase II, the proposed chart does not require design parameters. The users only need to determine a desired in-control average run length. The performance of conventional control charts deteriorates if the prespecified optimal design parameter is not appropriate for the actual size of the shift in the monitored quality characteristic. A design parameter-free approach prevents this situation, and the time needed to find the optimal design parameter can be saved as well. The performance of charts is evaluated by the average number of observations to signal under a specific shift in p, and the penalized relative mean index assesses the overall performance. The proposed chart has the best overall performance for detecting an upward shift in p compared with the cumulative count of conforming (CCC-r), Bernoulli cumulative sum (CUSUM), Bernoulli exponentially weighted moving average (EWMA), Bernoulli generalized likelihood ratio (GLR), geometric CUSUM, and binomial GLR charts. The KLI chart has decent performance for detecting a downward shift in p if the size of the shift is small. For detecting a possible shift in p to both sides, the overall performance of the KLI chart is better than those of the charts.

Quasi-Consensus of Time-Varying Multi-Agent Systems with External Inputs under Deception Attacks.

The quasi-consensus of a class of nonlinear time-varying multi-agent systems suffering from both external inputs and deception attacks is studied in this paper. This is different from a time-varying matrix, which is assumed to be bounded; further reasonable assumptions are supposed. In addition, impulsive deception attacks modeled with Bernoulli variables are considered. Sufficient conditions to achieve quasi-consensus are given, and the upper bounds of the error state related to the deception attacks is derived. Finally, a numerical simulation example is provided to show the validity of the obtained results.

Security control for nonlinear systems under quantization and Round-Robin protocol subject to deception attacks

This paper is concerned with the security control problem for the nonlinear systems with the effects of quantization, communication protocol and deception attacks based on the Takagi–Sugeno (T–S) fuzzy model. The measurement output and control input signals are quantized by dynamic quantizers simultaneously, and the quantized signals are transmitted through the communication channels scheduled by Round-Robin (RR) protocol. Moreover, two Bernoulli processes are utilized to characterize the deception attacks occurring on the different channels respectively. The mode-dependent observer-based controller and dynamic quantizers are designed such that the security in probability of the closed-loop system with the prescribed quadratic cost index can be guaranteed. Then, sufficient design conditions are obtained for the controller gains and quantizers’ parameters based on the linear matrix inequalities (LMIs) approach. In the end, a numerical example is carried out to demonstrate the validity of the proposed method.

Queueing Subject to Activity-Dependent Server Performance: Task-Assignment Control Policies for Utilization Rate Reduction

We consider a discrete-time system comprising a first-come-first-served queue, a nonpreemptive server, and a scheduler that assigns tasks from the queue to the server. New tasks enter the queue according to a Bernoulli process with a prespecified arrival rate. At each instant, the server is either working on a task or is available. The scheduler implements a task-assignment control policy that we seek to design. When the server is available and the queue is nonempty, the policy either assigns a new task to the server or allows it to remain available (to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rest</i> ). In addition to the aforementioned <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">availability</i> state, we assume that the server has an integer-valued <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">activity state</i> . The activity state is nondecreasing during work periods, and is nonincreasing otherwise. In a typical application of our framework, the server performance (understood as task completion probability) worsens as the activity state increases. In this article, we build on and transcend recent stabilizability results obtained for the same framework. Specifically, we establish methods to design task-assignment control policies, which we call scheduler policies for short, which not only stabilize the queue but also reduce the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">utilization rate</i> —understood as the infinite-horizon time-averaged portion of time the server is working. This article has a main theorem leading to two key results: 1) We put forth a tractable method to determine, using a finite-dimensional linear program (LP), the infimum of all utilization rates that can be achieved by scheduler policies that are stabilizing, for a given arrival rate. 2) We propose a design method, also based on finite-dimensional LPs, to obtain stabilizing scheduler policies that can attain a utilization rate arbitrarily close to the aforementioned infimum. We also establish structural and distributional convergence properties, which are used throughout this article, and are significant in their own right.

Estimation-Based and Dropout-Dependent Control Design for Aeroengine Distributed Control System with Packet Dropout

A novel estimation-based and dropout-dependent control design for distributed control systems of aeroengines with packet dropout is proposed. The packet dropout is described as an independent identically distributed (i.i.d.) Bernoulli process with known probability. The objective of the control system is to effectively and stably impel aeroengines. An inverse system is proposed to reconstruct the missing measurements, based on which, a hybrid adaptive Kalman filter (HAKF) is proposed to provide the estimated states for control design. A new state-feedback control design is developed with the estimated states and the actual states. For guaranteeing the stability of aeroengines, both the stability of HAKF and the new controlled system are analyzed and proved. The new design is applied to an aeroengine, HAKF has superior estimation accuracy which ensures the effectiveness, and the desired stability performance is achieved by controlled system in the presence of packet dropout.

Inflated Unit-Birnbaum-Saunders Distribution

The modeling different data behaviour like the human development index as a function of life expectancy, the water capacity of a reservoir with respect to a certain threshold, or the percentage of death rate of an infant before his or her first birthday, are situations which a researcher can face. It is noteworthy that these problems may have in common data with excessive zeros and ones. Then, it is essential to have flexible and accuracy models to fit data with these features. Given the relevance of data modeling with excessive zeros and ones, in this paper, a mixture of discrete and continuous distributions is proposed for modeling data with these behaviors. Additionally, the Unit-Birnbaum-Saunders distribution is considered with the aim to explain the continuous component of the model and the features of a Bernoulli process. The estimation of the parameters is based on the maximum likelihood method. Observed and expected information matrices are derived, illustrating interesting aspects of the likelihood approach. Finally, with practical applications by using real data we can show the advantage of using our proposal concerning the inflated beta model.

Despeckling by sparse sampling on Bernoulli process in single-shot digital holography

Despeckling by sparse sampling on Bernoulli process in single-shot digital holography

Observer‐based event‐triggered secure synchronization control for multi‐agent systems under false data injection attacks

AbstractIn this article, the observer‐based event‐triggered robust secure synchronization control problem is studied for multi‐agent systems (MASs) under a directed graph and false data injection (FDI) attacks. During the information transmission, both control signals and measurement signals may be changed by false data, and the Bernoulli processes are used to describe FDI attacks that occur randomly on the sensor‐to‐controller and the controller‐to‐actuator transmission channels. A new event‐triggered mechanism with the state estimation threshold is introduced to reduce the waste of network resources. Based on which, a resilient observer‐based control scheme is proposed to solve the secure mean‐square bounded synchronization problem of MASs caused by FDI attacks. The controller gain and observer gain are designed by utilizing the linear matrix inequality technique. Furthermore, the Zeno behavior is effectively eliminated and proved by using a contradiction method. Finally, a simulation result is presented to illustrate the effectiveness and applicability of the theoretical results by comparisons.

Design of Prediction-Based Controller for Networked Control Systems with Packet Dropouts and Time-Delay

A novel prediction-based controller design is proposed for networked control systems (NCSs) with stochastic packet dropouts and time-delay in their control channel. The sequence of packet dropouts, which are modelled as a Bernoulli process, is compensated by a zero-order holder (ZOH)-based module, whereas a state predictor is utilized for obtaining the predicted states at the time delayed. In view of dropout compensator and state predictor, a novel modified model predictive controller (MPC) is designed and proposed in the following procedures. Compared to cost function of a general model predictive controller, variables of states are substituted by the predicted ones as obtained from state predictor preliminarily. Then, a logical programming approach is applied to include all the possible circumstances in the prediction horizon. Consequently, the cost function is reformed as simultaneous minimax linear matrix inequalities (LMI) with constraints. As a result, toolbox YALMIP is employed in order to solve such minimax programming problem eventually. Simulation results are presented to show the feasibility and performance of proposed method.

Modelling and Analysis of Constant False Alarm Rate Performance in Presence of Jamming Environments

A novel “Bernoulli experiment model” of constant false alarm rate (CFAR) is presented in order to analyze CFAR performance in jamming condition. In this model, target detection can be treated as a sequence of independent subevents, and the detection process equals to pick up target energy from an energy pool diluted with noise, interference, and jamming pulses. In a multiple-jammer case, each jammer contributes independently, and the content of the energy pool only relates to the corresponding jammer. Impacts of jammer factors, such as signal-to-interference ratio (SIR), jamming-to-interference ratio (JIR), the number of false targets in reference cells, and the number of false targets in a cell under test (CUT), are analyzed and compared in detail, and two jamming operation principles are deduced as an application. The deduction procedure and conclusions drawn from the model can also be utilized on similar occasions.

A stochastic process on a network with connections to Laplacian systems of equations

AbstractWe study an open discrete-time queueing network. We assume data is generated at nodes of the network as a discrete-time Bernoulli process. All nodes in the network maintain a queue and relay data, which is to be finally collected by a designated sink. We prove that the resulting multidimensional Markov chain representing the queue size of nodes has two behavior regimes depending on the value of the rate of data generation. In particular, we show that there is a nontrivial critical value of the data rate below which the chain is ergodic and converges to a stationary distribution and above which it is non-ergodic, i.e., the queues at the nodes grow in an unbounded manner. We show that the rate of convergence to stationarity is geometric in the subcritical regime.

Computational and Analytical Bounds for Multivariate Bernoulli Distributions

Building on a new but simple method to characterize multivariate Bernoulli variables with given means, we investigate their dependence structure. We evaluate on some computational examples whether the assumption of exchangeability is binding. This is useful in applications where exchangeability is a standard assumption, such as credit risk.

Controllability of Delayed Discret Fornasini-Marchesini Model via Quantization and Random Packet Dropouts

This research is devoted to Fornasnisi-Marchesini model (FM). More precisely, the investigation of the control problem for the second model discrete-time FM. The model takes into account the random packet loss and quantization errors in the network environment. So our modelling method has the potential to achieve a better stabilization effects. Random packet dropouts, time delays and quantization are taken into consideration in the feedback control problem simultaneously. Measured signals are quantized before being communicated. A logarithmic quantizer is utilized and quantized signal measurements are handled by a sector bound method. The random packet dropouts are modeled as a Bernoulli process. A control law model which depends on packet dropouts and quantization is formulated. Notably, we lighten the assumptions by using the Schur complement. Besides, both a state feedback controller and an observer-based output feedback controller are designed to ensure corresponding closed-loop systems asymptotically stability. Sufficient conditions on mean square asymptotic stability in terms of LMIs have been obtained. Finally, two numerical example show the feasibility of our theoretical results.

Partial-Update Kalman Filter for Permanent Magnet Synchronous Motor Estimates Under Intermittent Data

The partial-update Kalman filter (PKF) is an extension of the Schmidt Kalman filter, which can improve the capabilities of the conventional extended Kalman filter for handling model uncertainties and nonlinearities. Herein, we adapt the PKF to estimate the states and parameters of electric machines, particularly in cases with intermittent observations. To account for missing data within the filter, the arrival of new measurements is treated as a Bernoulli process. We show that the estimation error of the proposed filter remains bounded if the system satisfies mild assumptions. Moreover, we show that the prediction error covariance matrix is guaranteed to be bounded if the observation arrival rate has a lower bound. Hardware experiments validate this technique for a surface-mounted permanent magnet synchronous motor.

A Multi-Cluster-Based Distributed CDD Scheme for Asynchronous Joint Transmissions in Local and Private Wireless Networks

In this paper, a multiple cluster-based transmission diversity scheme is proposed for asynchronous joint transmissions (JT) in private networks. The use of multiple clusters or small cells is adopted to reduce the transmission distance to users thereby increasing data-rates and reducing latency. To further increase the spectral efficiency and achieve flexible spatial degrees of freedom, we consider that a distributed remote radio unit system (dRRUS) is installed in each of the clusters. A key characteristic of deploying the dRRUS in private networks is the associated multipath-rich and asynchronous delay propagation environment. Therefore, we consider asynchronous multiple signal reception at the remote radio units and propose an intersymbol interference free distributed cyclic delay diversity (dCDD) scheme for JT to achieve the full transmit diversity gain without requiring full channel state information of the private network. The spectral efficiency of the proposed dCDD-based JT is analyzed by deriving a new closed-form expression, and then compared with link-level simulations for non-identically distributed frequency selective fading over the entire network. Due to its distributed structure, the dRRUS relies on backhaul communications between the private network server and cluster master (CM), which is the main backhaul connection, and between the CM to remote radio units, which are the secondary backhaul connections. Thus, it is important for us to investigate the impact of reliability of main and secondary backhaul connections on the system. Our results show that the resulting composite backhaul connections can be accurately modeled by our proposed product of independent Bernoulli processes.

SHOCKS ON PUBLIC SPENDING AND ECONOMIC GROWTH IN FRAGILE STATES

This paper focuses on fragile States, and look deeply how shocks on public spending affect private production, economic growth and households' welfare. The paper provides an explanation of a source of growth and technological progress in unstable countries. The increasing of public expenditures enhances the private production and households' consumption. One innovation of this paper is in the way to introduce shocks into economy. In fragile States, shocks are random variables that follow a Bernoulli process, which appear on public spending and affect the rest of economy.

Monte Carlo Study of Online Cleaning Cycles of Hydrogenerator Heat Exchangers

Related to an innovative cleaning device for cleaning hydrogenerator heat exchangers that does not require the interruption of generation (turning off the turbines), this article discusses two alternative schemes to estimate the minimum number of cleaning cycles required to ensure that all tubes of the heat exchanger will be visited at least once by the cleaning artifacts used by the conceived online cleaning system. The technique makes use of abrasive sponge balls transported by the cold working fluid of the exchanger to remove scale that accumulates inside the exchanger tubes during its operation. The main purpose of this study is to guide the hydrogenerator field operator in setting up the automation system of the exchanger cleaning system. In a first attempt, a negative binomial probability distribution function was investigated to estimate the number of tries needed to obtain a number of success events, with equal probability of success, after running a number of Bernoulli's experiments, where the last is considered the success case. Getting closer to the physical reality of the problem studied, a Monte Carlo method simulation, making use of a high number of repetitions (10 x 106), appeared to be a consistent mathematical formulation to anticipate the smallest number of cleaning cycles meeting the posed assumption.

Analysis of a Discrete-Time Queueing Model with Disasters

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

A robust variational autoencoder using beta divergence

The presence of outliers can severely degrade learned representations and performance of deep learning methods and hence disproportionately affect the training process, leading to incorrect conclusions about the data. For example, anomaly detection using deep generative models is typically only possible when similar anomalies (or outliers) are not present in the training data. Here we focus on variational autoencoders (VAEs). While the VAE is a popular framework for anomaly detection tasks, we observe that the VAE is unable to detect outliers when the training data contains anomalies that have the same distribution as those in test data. In this paper we focus on robustness to outliers in training data in VAE settings using concepts from robust statistics. We propose a variational lower bound that leads to a robust VAE model that has the same computational complexity as the standard VAE and contains a single automatically-adjusted tuning parameter to control the degree of robustness. We present mathematical formulations for robust variational autoencoders (RVAEs) for Bernoulli, Gaussian and categorical variables. The RVAE model is based on beta-divergence rather than the standard Kullback–Leibler (KL) divergence. We demonstrate the performance of our proposed β-divergence-based autoencoder for a variety of image and categorical datasets showing improved robustness to outliers both qualitatively and quantitatively. We also illustrate the use of our robust VAE for detection of lesions in brain images, formulated as an anomaly detection task. Finally, we suggest a method to tune the hyperparameter of RVAE which makes our model completely unsupervised.

H ∞ asynchronous synchronisation control for Markovian coupled delayed neural networks with missing information

This paper first studies asynchronous synchronisation control problem for Markovian coupled neural networks with missing information. As information exchanges among neural networks, which can help achieving synchronisation, are conducted via a generally unprotected communication network with limited bandwidth, nodes' state information and the synchronised state information may not be available to node i, and a Bernoulli process is used to model this phenomenon. Furthermore, considering that the amount of information needs to be transmitted is decided by the coupling relationship, missing information rate is assumed to be node- and coupling dependent. By introducing another nonhomogeneous Markov chain with transition probability matrix depending on coupling mode, the asynchronous synchronisation controller is designed, which can describe complex asynchronous switch phenomenon between system and controller modes and covers mode-dependent controller and mode-independent one as two special cases. Three sufficient conditions respectively guaranteeing the global synchronisation and the global synchronisation of the addressed networks are obtained, and then the asynchronous synchronisation controller design method is proposed. Finally, an illustrative example with results demonstrating the effectiveness of the given controller design approach is provided.