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In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example.

This article addresses the simultaneous state and unknown input estimation problem for a class of discrete time-varying complex networks (CNs) under redundant channels and dynamic event-triggered mechanisms (ETMs). The redundant channels, modeled by an array of mutually independent Bernoulli distributed stochastic variables, are exploited to enhance transmission reliability. For energy-saving purposes, a dynamic event-triggered transmission scheme is enforced to ensure that every sensor node sends its measurement to the corresponding estimator only when a certain condition holds. The primary objective of the investigation carried out is to construct a recursive estimator for both the state and the unknown input such that certain upper bounds on the estimation error covariances are first guaranteed and then minimized at each time instant in the presence of dynamic event-triggered strategies and redundant channels. By solving two series of recursive difference equations, the desired estimator gains are computed. Finally, an illustrative example is presented to show the usefulness of the developed estimator design method.

OBJECTIVE Currently available ventricular assist devices provide continuous flow and do not adapt to the changing needs of patients. Physiological control algorithms have been proposed that adapt the pump speed based on the left ventricular pressure. However, so far, no clinically used pump can acquire this pressure. Therefore, for the validation of physiological control concepts in vivo, a system that can continuously and accurately provide the left ventricular pressure signal is needed. METHODS We demonstrate the integration of two pressure sensors into a tapered inflow cannula compatible with the HeartMate 3 (HM3) ventricular assist device. Selective laser melting was used to incorporate functional elements with a small footprint and therefore retain the geometry, function and implantability of the original cannula. The system was tested on a hybrid mock circulation system. Static and simulated physiological flow and pressure profiles were used to evaluate the combined pressure and flow sensing capabilities of the modified cannula. CONCLUSION The cannula prototypes enabled continuous pressure measurements at two points of their inner wall in the range of 100 and 200 mmHg. The developed, Bernoulli-based, two sensor model improved the accuracy of the measured simulated left ventricular pressure by eliminating the influence of flow inside the cannula. This method reduced the flow induced pressure uncertainty from up to 7.6 mmHg in single sensor measurements to 0.3 mmHg. Additionally, the two-sensor system and model enable the measurement of the blood flow through the pump with an accuracy of 0.140.04 L/min, without dedicated flow sensors.

Bernoulli multi-armed bandits are a reinforcement learning model used to optimize sequences of decisions with binary outcomes. Well-known bandit algorithms, including the optimal policy, assume that before a decision is made the outcomes of previous decisions are known. This assumption is often not satisfied in real-life scenarios. As demonstrated in this paper, if decision outcomes are affected by delays, the performance of existing algorithms can be severely affected. We present the first practically applicable method to compute statistically optimal decisions in the presence of outcome delays. Our method has a predictive component abstracted out into a meta-algorithm, PARDI, which significantly reduces the impact of delays on commonly used algorithms. We demonstrate empirically that PARDI-enhanced Whittle Index is nearly optimal for a wide range of Bernoulli bandit parameters and delays. In a wide spectrum of experiments it performed better than any other suboptimal algorithm, e.g., UCB1-Tuned and Thompson sampling. PARDI-enhanced Whittle Index can be used when computational requirements of the optimal policy are too high.

This article deals with an unreliable bulk arrival single server queue rendering two-heterogeneous optional repeated service (THORS) with delayed repair, under Bernoulli Vacation Schedule (BVS) and N-policy. For this model, the joint distribution of the server’s state and queue length are derived under both elapsed and remaining times. Further, probability generating function (PGF) of the queue size distribution along with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, numerical experiments have been carried out in support of the theory.

A novel input/output feedback linearization control method by utilizing nonlinear disturbance observer (NDOB) is proposed for a quadruple-tank liquid level (QTLL) system in this paper. Firstly, the mathematical model of QTLL system is established by using Bernoulli’s law and mass conservation. Secondly, in view of the nonlinear and coupling characteristics of the QTLL system, a input/output feedback linearization controller is designed. Then, a NDOB is proposed to estimate disturbances and applied to compensation control. Finally, simulation and experimental results show that the proposed strategy has better control performances than PID control and the disturbance observer-based sliding mode control (DOBSMC).

The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence. Another problem considered is that of constructing effective statistical tests for random number generators (RNG). Currently, effectiveness of statistical tests for RNGs is mainly estimated based on experiments with various RNGs. We find an asymptotic estimate for the p -value of an optimal test in the case where the alternative hypothesis is a known stationary ergodic source, and then describe a family of tests each of which has the same asymptotic estimate of the p -value for any (unknown) stationary ergodic source. This model appears to be acceptable for binary sequences generated by physical devices that are used in cryptographic data protection systems.

A valve-based piezoelectric pump operated by three bending transducers is proposed in this work. The major features of the proposed pump are self-priming and high pressure. The structure and operation principle of the proposed pump are presented and analyzed in detail. The output displacement of the transducer can be obtained by Timoshenko beam theory; on this basis, the flowrate and pressure models of the pump are established based on gap flow theory and extended Bernoulli equation. A prototype of the pump is fabricated and the experimental system is established. The results indicate that the maximum output flowrate is 58.6 mL/min under the frequency of 160 Hz; and the maximum output pressure is 28.7 kPa at the frequency of 180 Hz; and the maximum output power is 6 mW at the backpressure of 12.5 kPa. Besides, the self-priming of the pump is 10.7 kPa; thus, there is no need to fill the pump during working process, which can bring a convenience to the operation of the pump.

We introduce multi-poly-Bernoulli–Carlitz numbers, function field analogues of multi-poly-Bernoulli numbers of Imatomi–Kaneko–Takeda. We explicitly describe multi-poly-Bernoulli Carlitz numbers in terms of the Carlitz factorial and the Stirling–Carlitz numbers of the second kind and also show their relationships with function field analogues of finite multiple zeta values.

A simply supported beam is examined for maximum deflection and stress under various loading conditions. Euler-beam Bernoulli's equation is used to calculate the theoretical results. ANSYS 15.0 is the primary software used for the computational analysis. Compared to the commercial software ANSYS 15.0, the current technique has shown a remarkable degree of accuracy. It has also been observed for deflection, the Element 2 node 188, gives a closer value in all cases. In the case of stress analysis, this inference is exactly the opposite. As such, it can be seen that when trying to determine if a solid structure has been deflected, the user can choose 2 nodes 188 element as a selection if other preferences are unavailable.

This article inspects the problem of robust synchronization for uncertain Markovian jumping complex interconnected neural networks with randomly occurring uncertainties and time delays. The uncertainties considered here occur randomly and are assumed to follow certain mutually uncorrelated Bernoulli distributed white noise sequences. The presence of sensor faults may cause degradation or even instability of the entire network. Therefore, control laws are designed with sensor faults to ensure the controlled synchronization of the complex interconnected neural networks. Three types of fault-tolerant controls are designed based on the Lyapunov stability theory and adaptive schemes which include passive and adaptive fault-tolerant control laws. By constructing a new Lyapunov-Krasovskii functional (LKF) and by using Jensen’s inequality with a free-weighting matrix approach, some new delay-dependent synchronization criteria are obtained in terms of linear matrix inequalities (LMIs). By using the Lyapunov stability theory, the existence condition for the adaptive controller that guarantees the robust mean-square synchronization of complex interconnected neural networks in terms of LMIs are derived. Finally, a numerical example is presented to demonstrate the performance of the developed approach.

This paper is concerned with the problem of dynamic output feedback control design for the cooperative adaptive cruise control (CACC) system with randomly occurring sensor saturations (ROSSs) subject to randomly occurring deception attacks (RODAs). The dynamics of the vehicle equipped with CACC system behave like a linear model in which the deviation of the position and velocity are chosen as the state variables. Sensor saturations and deception attacks are simultaneously taken into account, and two sets of Bernoulli random variables are utilized to characterize their nature of random occurrence. The main objective of this article is to develop a robust dynamic output feedback controller (RDOFC) such that, for all possible parameter uncertainties, sensor saturations as well as deception attacks, all the states can still be exponentially mean square stable and the $H_{\infty}$ performance index is guaranteed. In light of the Lyapunov stability theory, a sufficient condition of the desired controller is firstly constructed, then the controller parameters are obtained relying on the solutions to a set of linear matrix inequalities (LMIs). Finally, the three-car platoon system is evaluated to validate the usefulness of the developed algorithm.

A method for optimal actuator design in vibration control is presented. The optimal actuator, parametrized as a characteristic function, is found by means of the topological derivative of the LQR cost. An abstract framework is proposed based on the theory for infinite-dimensional optimization of both the actuator shape and the associated control problem. A numerical realization of the optimality condition is developed for the actuator shape using a level-set method for topological derivatives. A numerical example illustrating the design of actuator for Euler-Bernoulli beam model is provided.

This letter focuses on time-critical multiagent systems over the finite-time interval [ $0,T$ ). Specifically, we propose a distributed control algorithm that guarantees agents to approach a time-varying command at time $T$ with reduced information exchange. The key feature of the proposed algorithm allows $T$ to be user-defined, where it neither depends on the initial conditions of agents nor unknown but bounded time rate of change of the command. Furthermore, an event-triggered approach is utilized to reduce agent-to-agent information exchange. Predicated on a time transformation approach, the proposed algorithm defined over the finite-time interval [ $0,T$ ) is first transformed to an equivalent form over the infinite-time interval [ $0,\infty $ ) through a strictly increasing and continuously differentiable function that guarantees solutions in both time intervals being equivalent. Over the infinite-time interval [ $0,\infty $ ), we then use a quadratic energy function, the Bernoulli equation, and the comparison principle to establish stability and convergence properties of our algorithm.

Machines consume intensive energy in some production systems. Although substantial efforts have been devoted to performance analysis, continuous improvement, and design of production systems, the research on reducing the energy consumption in these systems is limited. In this article, the problem of minimizing the energy consumed by machines in the two-machine Bernoulli serial line, which has been formulated as nonlinear programming with production rate constraint, is investigated. Specifically, structural characteristics and optimality conditions of the problem are analyzed, and two nonlinear algebraic optimality equations are established. To solve the optimality equations, their properties are explored, and an effective algorithm based on the binary search method is developed. Furthermore, the sensitivity of the optimal solution with respect to system parameters is quantitatively analyzed. Based on the sensitivity analysis, some useful insights on the optimal objective value are extracted.

The pivotal aim of present work is to design and implement an effective numerical approach, the iterative reproducing-kernel algorithm, to provide numerical solutions to the fractional Riccati and Bernoulli differential equations in the Caputo-Fabrizio sense. To achieve this, we develop an advanced operational algorithm based on creating a complete orthonormal function system utilizing the reproducing-kernel function in order to formulate the solution in the form of uniformly convergent Fourier series. Additionally, error and stability analysis of the proposed method are studied in the appropriate space W 2 , 2 ( Δ ) . On the other hand, some meaningful numerical applications are included to demonstrate the feasibility and reliability of this approach under the qualitative effect of the Caputo-Fabrizio fractional derivative. In numerical viewpoints, the achieved results using the proposed approach indicate a high level of accuracy and rare technical skills, which qualifies it to deal with many fractional models emerging in various mathematical and physical disciplines within the frame of Caputo-Fabrizio derivatives.

This paper is concerned with the fixed-time quasi-synchronization of coupled memristive neural networks (CMNNs). The communication channel is subject to the deception attack described by the Bernoulli stochastic variable. To reduce signal transmissions, a dual-channel event-triggered mechanism is proposed. In each channel of sensor to controller and controller to actuator, an event-triggered mechanism is designed. Compared with the single event-triggered mechanism in the communication loop, the main difficulties lie in how to deal with the problems of packet scheduling and network attacks. By using Lyapunov method combining with a new proposed lemma, some sufficient conditions are derived to guarantee the leader-following quasi-synchronization of CMNNs. The Zeno behaviour is excluded for the designed dual-channel event-triggered mechanism. The influence of the event-triggered mechanism on the estimation of settling time is discussed. Three numerical examples are provided to show the effectiveness of the theoretical results.

In this article, we analyze the secrecy rate of a physical-layer security (PLS) algorithm using antenna subset modulation (ASM), which requires significantly lower complexity and cost compared to fully digital beamforming. All of the existing studies on the ASM-based PLS provide only approximate secrecy rate by treating random selection of two subsets of antennas for each symbol as independent and identically distributed Bernoulli random variables. To clarify its limitation, we first show that such widely adopted approximation incurs a significant error in the secrecy rate compared to the true value. In addition, we propose a new mathematical approach to derive the exact and closed-form expression for secrecy rate without any approximation. We also show the system optimization using our exact analysis in line with the simulation results, while the existing approximate analysis results in a considerable error.

In this article, a piezoelectric active proportional regulation valve with high differential pressure is proposed based on a bending transducer. The output flowrate of the valve can be accurately controlled by a bending transducer. The configuration design and driving principle of the valve are presented and analyzed. The static analyses are performed to determine the structural parameters of the valve and deduce its transient overflow gap. On this basis, the overall flowrate model of the valve is established using the theory of circumferential flow and extended Bernoulli equation. The effects of differential pressure and driving voltage on output flowrate are clarified. A prototype of the valve is manufactured and the experimental setup is also established to evaluate the performances of the valve. The results indicate that the proportional regulation of the valve can be achieved by changing the driving voltage; the valve displacement and response time under no liquid-loading condition are 16.16 μ m and 340 μ s at the voltage of 300 Vp-p; the maximum output flowrate is 286.3 mL/min under the differential pressure of 344.75 kPa, and the leakage level is 0.11%; the maximum cut-off pressure of 275.8 kPa can be realized; the corresponding input power is 185 mW.

Asymptotic approximations of Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions. For each polynomial there are two approximations derived with one having enlarged region of validity.

Computational fluid dynamics (CFD) has been used successfully in cardiovascular system research to analyze the physiological processes inside vessels. We evaluated the hydraulic information of urine through the lower urinary tract in a patient with posterior urethral valve (PUV) before and after valve ablation by CFD. A set of models of the lower urinary tract were developed based on geometrical data obtained by cystoscopy and voiding cystourethrography. Simulated assumptions and conditions were applied according to prior studies and urodynamic results. We used Fluent CFD 19.0 (Ansys Inc., USA) to compute the velocity and pressure of the fluid regions. The simplification of Bernoulli's formula was applied afterward to calculate the hydraulic energy of different positions. The urine flow rates of the NORMALst, the PUVst, and the POSTst at 5000 Pa were 18.08 ml/s, 11.14 ml/s, and 12.16 ml/s, respectively. Precipitous pressure change was observed around the valve in the PUVst, and the abnormal change was concentrated in the dilated urethra in the POSTst. Major energy dissipations were generated around the valve and the dilated urethra in the PUVst. The energy loss that occurred in the dilated urethra did not improve after the operation. Our findings are probably indicative of the hydrodynamics changes in the dilated urethra in PUV and need to be confirmed through more improved CFD models in the future. CFD may revolutionize pediatric urologists' perception in the management of urinary disease.

In the static analysis of beam-column systems using matrix methods, polynomials are using as the shape functions. The transverse deflections along the beam axis, including the axial- flexural effects in the beam-column element, are not adequately described by polynomials. As an alternative method, the element stiffness matrix is modeling using stability parameters. The shape functions which are obtaining using the stability parameters are more compatible with the system’s behavior. A mass matrix used in the dynamic analysis is evaluated using the same shape functions as those used for derivations of the stiffness coefficients and is called a consistent mass matrix. In this study, the stiffness and consistent mass matrices for prismatic three-dimensional Bernoulli-Euler and Timoshenko beam-columns are proposed with consideration for the axial-flexural interactions and shear deformations associated with transverse deflections along the beam axis. The second-order effects, critical buckling loads, and eigenvalues are determined. According to the author’s knowledge, this study is the first report of the derivations of consistent mass matrices of Bernoulli-Euler and Timoshenko beam-columns under the effect of axially compressive or tensile force.

Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.

Experimental tests were conducted on a rectangular flume with different grid-type dam grid sizes, channel slopes and debris flow bulk density. We use the Bernoulli equation of energy conservation to deduce a formula to calculate debris-flow discharge. By combining the flume experiments with dimensional analysis methods, we mainly consider the bulk density of the debris flow, grid size of the grid-type dam, and flume slope to establish the discharge-coefficient correction formula and propose a method of calculating debris-flow discharge through a grid-type dam. The practical value of the formulas was illustrated using the Niwan gully, a tributary of Bailong River in Gansu province, China, as an example, which can be used as a reference in further practical engineering applications.

A mirror-image rotating piezoelectric energy harvester is proposed, and it can adapt to 2.8 m/s — 13.6 m/s wind speed. It is arranged by the mirror image of two piezoelectric elements, so it has multiple resonant frequencies. The multiple resonant frequencies make the bandwidth of the energy harvester be broadened. The force applied on the piezoelectric beam is aperiodic and an evaluable analytical model is established based on Fourier series and superposition principle. The influence of the system parameters on the piezoelectric beam is deduced by the Bernoulli beam formula of axial direction, and a prototype is made for experiment and application. The results show that when the distance between the two magnets is kept at 15 mm, the torsion angle of the blades is 15°, three blades are selected, and the height of each blade is 50 mm, the power generation effect is optimal, and the power can reach 12.5 mW. Under the optimal power, it only takes 100s to charge the capacitor of 220 μF to 15V, the prototype can directly power 98 light emitting diodes (LEDs) and make the calculator work. This technology can also be extended for harvesting water energy.

In the classical form, the Poisson Multi-Bernoulli Mixture (PMBM) filter uses a PMBM density to describe target birth, surviving, and death, which does not model the appearance of spawned targets. Although such a model can handle target birth, surviving, and death well, its performance may degrade when target spawning arises. The reason for this is that the original PMBM filter treats the spawned targets as birth targets, ignoring the surviving targets’ information. In this paper, we propose a Kullback-Leibler Divergence (KLD) minimization based derivation for the PMBM prediction step, including target spawning, in which the spawned targets are modeled using a Poisson Point Process (PPP). Furthermore, to improve the computational efficiency, three approximations are used to implement the proposed algorithm, such as the Variational Multi-Bernoulli (VMB) filter, the Measurement-Oriented marginal MeMBer/Poisson (MOMB/P) filter, and the Track-Oriented marginal MeMBer/Poisson (TOMB/P) filter. Finally, simulation results demonstrate the validity of the proposed filter by using the spawning model in these three approximations.

Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a likelihood ratio between two models as a measure for indicating change. The first model is a single bernoulli variable while the second model divides the stored data in two segments, and models each segment with its own bernoulli variable. Finding the optimal split can be done in \( \mathcal {O} \mathopen {}\left( n\right) \) time, where n is the number of entries since the last change point. This is too expensive for large n. To combat this we propose an approximation scheme that yields \((1 - \epsilon )\) approximation in \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log ^2 n\right) \) time. The speed-up consists of several steps: First we reduce the number of possible candidates by adopting a known result from segmentation problems. We then show that for fixed bernoulli parameters we can find the optimal change point in logarithmic time. Finally, we show how to construct a candidate list of size \( \mathcal {O} \mathopen {}\left( \epsilon ^{-1} \log n\right) \) for model parameters. We demonstrate empirically the approximation quality and the running time of our algorithm, showing that we can gain a significant speed-up with a minimal average loss in optimality.

The chapter reviews fundamental theories, formulas, solution methods, and a set (toolbox) of MATLAB functions for static analysis of Euler–Bernoulli beams. The system requirements for the MATLAB toolbox—a PC with Win 98SE/NT/2000 and XP or Mac with OS 9.x and up, and the software MATLAB (version 5.x and up) installed on the computer. A fundamental problem in the static analysis of Euler-Bernoulli beams is stated as the given external loads and boundary disturbances that determines the beam response (displacement, rotation, bending moment, and shear force), which is governed by a given equation and boundary conditions. There are many solution methods available for the static analysis of Euler-Bernoulli beams. The chapter presents three analytical solution methods for the beam problem—method of singularity functions, the boundary value approach, and distributed transfer function method (DTFM). The MATLAB functions are developed based on the distributed transfer function method, which is an exact analytical modeling and solution method for many one-dimensional distributed systems including bars, shafts, strings, and beams.

The paper deals with the limit behavior of a compound Poisson process with switching between a finite number of sequences of i.i.d. random variables. The switching is provided by Bernoulli’s random variables. Under suitable normalization, the limit process is a Brownian motion with switching variance.

In IEEE 802.15.4 standard for low-power low-range wireless communications, only one channel is employed for transmission which can result in increased energy consumption, high network delay and poor packet delivery ratio (PDR). In the subsequent IEEE 802.15.4-2015 standard, a Time-slotted Channel Hopping (TSCH) mechanism has been developed which allows for a periodic yet fixed frequency hopping pattern over 16 different channels. Unfortunately, however, most of these channels are susceptible to high-power coexisting Wi-Fi signal interference and to possibly some other ISM-band transmissions. This interference manifests itself in the form of the presence/absence of other devices with either or both static and dynamic channel selection policies. In order to isolate channels with undesirable conditions, blacklisting mechanisms are defined to adapt the channel hopping process. However, the existing solutions which form blacklists unrealistically assume that the statistical model of the external interference remains fixed, and do not vary over time. In this paper, we realistically assume that the impact of external interferes on 802.15.4 may generally follow a non-stationary pattern, and accordingly formulate the adaptive channel hopping problem as a Dynamic Multi-Armed Bernoulli Bandit (Dynamic MABB) process from the machine learning theory. We then propose an online learning algorithm with track-ability properties for computing an adaptive hopping policy. Simulations confirm that when the statistics of the external interference has a switching regime, the proposed solution outperforms the previous schemes in terms of both energy efficiency as well as two important KPIs for TSCH-based networks, i.e., PDR and latency.

Summary Accept-reject-based Markov chain Monte Carlo algorithms have traditionally utilized acceptance probabilities that can be explicitly written as a function of the ratio of the target density at the two contested points. This feature is rendered almost useless in Bayesian posteriors with unknown functional forms. We introduce a new family of Markov chain Monte Carlo acceptance probabilities that has the distinguishing feature of not being a function of the ratio of the target density at the two points. We present two stable Bernoulli factories that generate events within this class of acceptance probabilities. The efficiency of our methods relies on obtaining reasonable local upper or lower bounds on the target density, and we present two classes of problems where such bounds are viable: Bayesian inference for diffusions, and Markov chain Monte Carlo on constrained spaces. The resulting portkey Barker’s algorithms are exact and computationally more efficient that the current state of the art.