Successive Approximation Scheme Research Articles

Evaluating the lifetime distribution parameters and reliability of products using successive approximation method

AbstractThe Weibull distribution is an extensively used statistical model for analyzing the reliability of mechanical and electrical components. Due to the complexity of the nonlinear equations and the scarcity of failure data, the common method may not provide satisfactory results of the reliability. In this case, a new approach for Weibull parameter estimation and reliability analysis, based on successive approximation schemes, is presented. The shape and scale parameters are estimated by maximizing the likelihood functions, and the location parameter is obtained by constructing an approximate correction model between it and the failure data. In order to show the performance of the proposed method, an extensive Monte‐Carlo simulation study is conducted. Simulation results show that the proposed method provides better estimates and efficient confidence intervals for Weibull parameters. In addition, the proposed method works well in presence of small sample sizes. Finally, two real examples are analyzed to illustrate the application of the proposed method.

Covert communications in STAR-RIS-aided rate-splitting multiple access systems

In this paper, an simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is deployed in the downlink rate-splitting multiple access (RSMA) covert system to enhance the covert communication performance. According to the RSMA transceiver mechanism, the messages for the covert user (Bob) and public user (Grace) are converted to the common and private streams at the legitimate transmitter (Alice) to realize downlink transmissions, while the STAR-RIS not only assists Alice in transmitting public messages to Grace but also protects the covert messages Alice sends to Bob by mixing up Warden (Willie). To characterize the covert performance of the considered STAR-RIS-aided RSMA (STAR-RIS-RSMA) system, We derive a closed expression for its detection error probability in the most favorable case for Willie, based on which a covert rate maximization problem is formulated. To maximize Bob’s covert rate while confusing Willie’s monitoring, the power allocation factor, common rate allocation factor, and STAR-RIS reflection/transmission beamforming are jointly optimized subject to Grace’s quality of service (QoS) requirements. The complex non-convex problem of maximizing covert rate, involving coupled system parameters, thus is split into three separate sub-issues: the allocation of transmit power, allocation of common rates, and STAR-RIS reflection/transmission beamforming, respectively. To obtain the rank-one constrained optimal solution for the sub-problem of optimizing the STAR-RIS reflection/transmission beamforming, a penalty-based successive convex approximation scheme is developed. Moreover, an alternative optimization (AO) algorithm is designed to determine the optimal solution for the sub-problem of optimizing the transmit power allocation, while the original problem is overall solved by a new AO algorithm. Simulation results corroborate the accuracy of the derived analytical results and demonstrate that the proposed STAR-RIS-RSMA scheme outperforms the benchmark scheme in achieving the covert rate.

Detecting the most probable transition pathway based on optimal control theory

Many natural systems exhibit transitions when external environmental conditions (such as complex noise) spark a shift to a new and sometimes quite different state. Therefore, detecting the most probable transition pathway between metastable states of a stochastic dynamical system is a significant topic. The most probable transition pathway can be treated as the minimizer of the associated Onsager-Machlup action functional. We convert this variational problem for computing the most probable transition pathway into a deterministic optimal control problem. One traditional approach for an optimal control problem is via Pontryagin's Maximum Principle, but it is challenging in high dimensional systems. In this paper, we devise a method to detect the most probable transition pathway for stochastic dynamical systems, by combining Pontryagin's Maximum Principle with a successive approximation scheme and a nested neural network technique. We validate our method with three stochastic dynamical systems, including a double well system, a Maier-Stein system, and a Nutrient-Phytoplankton-Zooplankton system. Specifically, in order to illustrate its effectiveness, we test the error and convergence of our method with an upper bound of training loss. Our work contributes to a better understanding of transition phenomena in complex systems under random fluctuations.

MAESTRO-X: Distributed Orchestration of Rotary-Wing UAV-Relay Swarms

This work details a scalable framework to orchestrate a swarm of rotary-wing UAVs serving as cellular relays to facilitate beyond line-of-sight connectivity and traffic offloading for ground users. First, a Multiscale Adaptive Energyconscious Scheduling and TRajectory Optimization (MAESTRO) framework is developed for a single UAV. Aiming to minimize the time-averaged latency to serve user requests, subject to an average UAV power constraint, it is shown that the optimization problem can be cast as a semi-Markov decision process, and exhibits a multiscale structure: outer actions on radial wait velocities and terminal service positions minimize the longterm delay-power trade-off, optimized via value iteration; given these outer actions, inner actions on angular wait velocities and service trajectories minimize a short-term delay-energy cost; finally, rate adaptation is embedded along the trajectory to leverage air-to-ground channel propagation conditions. A novel hierarchical competitive swarm optimization scheme is developed in the inner optimization, to devise high-resolution trajectories via iterative pair-wise updates. Next, MAESTRO is eXtended to UAV swarms (MAESTRO-X) via scalable policy replication, enabled by a decentralized command-and-control network augmented with: (1) spread maximization to proactively position UAVs to serve future requests; (2) consensus-driven conflict resolution to orchestrate scheduling decisions based on delay-energy costs including queuing dynamics; (3) adaptive frequency reuse to improve spectrum utilization across the network; and (4) a piggybacking mechanism allowing UAVs to serve multiple ground users simultaneously. Numerical evaluations show that, for user requests of 10 Mbits, generated according to a Poisson arrival process with rate 0.2 req/min/UAV, single-agent MAESTRO offers 3.8× faster service than a high-altitude platform and 29% faster than a static UAV deployment; moreover, for a swarm of 3 UAV-relays, MAESTRO-X delivers data payloads 4.7× faster than a successive convex approximation scheme; and remarkably, a single UAV optimized via MAESTRO outclasses 3 UAVs optimized via a deep-Q network by 38%.

Existence and Finite-Time Stability Results for Impulsive Caputo-Type Fractional Stochastic Differential Equations with Time Delays

ABSTRACT This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelöf iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Grönwall-Bellman inequality. As an application, examples are provided to expound our theoretical conclusions.

A Secure Downlink Transmission Scheme for a UAV-Assisted Edge Network

As an extension of centralized cloud services in a space-air-ground integrated network, an unmanned aerial vehicle (UAV-)-enabled edge network brings computation as close ground terminals of need as possible. In this scenario, the UAV is considered a mobile base station (MBS) to achieve data forwarding and processing from cloud servers to terminals. Note that downlink signals from the MBS to ground terminals are vulnerable to passive wiretapping by a malicious node. We formulate an average secrecy rate maximization problem to tackle the wiretapping issue by simultaneously transmitting confidential information and artificial noise (AN). We decompose the problem into two subproblems, including the UAV transmit power allocation subproblem and the UAV trajectory subproblem. Then, we adopt the successive convex approximation scheme and the alternating optimization method to develop our iterative algorithm to achieve secure transmission. Simulation results demonstrate that the proposed scheme is significantly better than other benchmarks in UAV-enabled downlink communication secrecy performance.

Green resource allocation for mobile edge computing

We investigate the green resource allocation to minimize the energy consumption of the users in mobile edge computing systems, where task offloading decisions, transmit power, and computation resource allocation are jointly optimized. The considered energy consumption minimization problem is a non-convex mixed-integer non-linear programming problem, which is challenging to solve. Therefore, we develop a joint search and Successive Convex Approximation (SCA) scheme to optimize the non-integer variables and integer variables in the inner loop and outer loop, respectively. Specifically, in the inner loop, we solve the optimization problem with fixed task offloading decisions. Due to the non-convex objective function and constraints, this optimization problem is still non-convex, and thus we employ the SCA method to obtain a solution satisfying the Karush-Kuhn-Tucker conditions. In the outer loop, we optimize the offloading decisions through exhaustive search. However, the computational complexity of the exhaustive search method is greatly high. To reduce the complexity, a heuristic scheme is proposed to obtain a sub-optimal solution. Simulation results demonstrate the effectiveness of the developed schemes.

UAV-Enabled Covert Wireless Data Collection

This work considers unmanned aerial vehicle (UAV) networks for collecting data covertly from ground users. The full-duplex (FD) UAV intends to gather critical information from a scheduled user (SU) through wireless communication and generate artificial noise (AN) with random transmit power in order to ensure a negligible probability of the SU’s transmission being detected by the unscheduled users (USUs). To enhance the system performance, we jointly design the UAV’s trajectory and its maximum AN transmit power together with the user scheduling strategy subject to practical constraints, e.g., a covertness constraint, which is explicitly determined by analyzing each USU’s detection performance, and a binary constraint induced by user scheduling. The formulated design problem is a mixed-integer non-convex optimization problem, which is challenging to solve directly, but tackled by our developed penalty successive convex approximation (P-SCA) scheme. An efficient UAV trajectory initialization is also presented based on the successive hover-and-fly (SHAF) trajectory, which also serves as a benchmark scheme. Our examination shows the developed P-SCA scheme significantly outperforms the benchmark scheme in terms of achieving a higher max-min average transmission rate (ATR) from all the SUs to the UAV.

Iterative approach for a class of fuzzy Volterra integral equations using block pulse functions

Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.

Питання міцності і стійкості неоднорідних конструкцій ракетно-космічної техніки при урахуванні пластичності і повзучості

Shell structures provide a compromise between strength and mass, which motivates their use in rocket and space hardware (RSH). High and long-term loads cause plastic and creep deformations in structural elements. RSH structures feature inhomogeneity: design inhomogeneity (polythickness, the presence of reinforcements, openings, etc.) and technological inhomogeneity (defects produced in manufacturing, operation, storage. and transportation, defects produced by unforeseen thermomechanical effects, etc.). These factors, which characterize structural inhomogeneity, are stress and strain concentrators and may be responsible for an early failure of structural elements and inadmissible shape imperfections. In inhomogeneous structures, different parts thereof are deformed by a program of their own and exhibit a different stress and strain level. In accounting for a physical nonlinearity, which is governed by plastic and creep deformations, the following approach to the determination of the stress and strain field is efficient: the calculation is divided into stages, and at each stage parameters that characterize the plastic and creep deformations developed are introduced: additional loads in the equilibrium equations or boundary conditions, additional deformations, or variable elasticity parameters (the modulus of elasticity and Poisson’s ratio). Successive approximation schemes are constructed: at each stage, an elasticity problem is solved with the introduction of the above parameters. Special consideration is given to the determination of the launch vehicle and launch complex life. This is due to damages caused by alternate high-intensity thermomechanical loads. The basic approach relies on the theory of low- and high-cycle fatigue. The plasticity and the creep of a material are the basic factors in the consideration of the above problems. This paper considers various aspects of the solution of RSH strength and stability problems with account for the effect of plastic and creep deformations.

URJA: Usage Jammer as a Resource Allocation for Secure Transmission in a CR-NOMA-Based 5G Femtocell System

In this article, a joint user pairing and secure resource allocation scheme for cognitive radio inspired nonorthogonal multiple access (CR-NOMA) femtocells in the presence of a jammer base station (JBS) is proposed. In the considered CR-NOMA-based femtocells, femto base stations (FBSs) serve their femto mobile station (FMS) by sharing the resource block (RB) with macromobile stations (MMSs), while the JBS in each femtocell secures the data rate of a weak user from the eavesdropping capability of the strong FMS. The strong FMS intercepts the data rate of the weak FMS using a successive interference cancellation technique to decode their own data as per the NOMA principle. The weak FMS protects its data from the strong eavesdroppers through the JBS. The JBS generates artificial noise to confuse the strong eavesdroppers. The problem of the joint user pairing and resource allocation is formulated as an optimization problem, whose main goal is to maximize the secure sum rate of the FMS while guaranteeing the secure data rate of the weak FMS and MMS. For RB allocation, CR at the FBS senses the best RB for its FMS using the Greedy approach. To optimize the power of the FBS and JBS, a successive convex approximation scheme with a low complexity is applied. Simulation results show that our proposed scheme provides an improvement in the secure sum rate of the FMS in comparison to the conventional NOMA and preexisting orthogonal multiple access schemes.

Wireless UAV Rotary Wing Communication with Ground Nodes Using Successive Convex Approximation and Energy Saving Mode

Communication with several ground nodes (GNs) is enabled through wireless communications by means of a rotary-wing unmanned aerial vehicle (UAV). For every GN, the requirements of communication throughput is satisfied while minimizing the communication and propulsion related energy thereby reducing the total energy consumption of the UAV. The total completion time of the mission, the GN time allocation for communication as well as the trajectory of UAV are optimized jointly to formulate the problem of energy minimization. The UAV rotary wing model of power consumption for propulsion power in a closed-form is also derived. The complexity of the problem increases with the involvement of several variables infinitely over time and the non-convex variables, making it challenging to be solved optimally. The hovering location sets are visited by the UAV and at each location, communication is established with the corresponding GNs. This simplified design for fly-hover-communicate is established for tackling the underlying issue. Convex optimization techniques and travelling salesman problem with neighborhood (TSPN) are leveraged for optimization of the trajectory that connects the hovering locations and the duration of hovering by means of the proposed algorithm design. Communication of the UAV during operation is considered as a general scenario. Discretization of the problem to its equivalent is done in the proposed novel path discretization technique by means of optimized variables of finite number. Further, a successive convex approximation (SCA) scheme is applied for obtaining a solution that is locally optimal. A comparison of the proposed design is performed with the benchmark schemes and it is found that they are outperformed based on numerical results.

Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise

In this paper, the existence of solution of stochastic fractional differential equations with L?vy noise is established by the Picard-Lindel?f successive approximation scheme. The stability of nonlinear stochastic fractional dynamical system with L?vy noise is obtained using Mittag Leffler function. Examples are provided to illustrate the theory.

High-Dimensional Nonconvex Stochastic Optimization by Doubly Stochastic Successive Convex Approximation

In this paper, we consider supervised learning problems over training sets in which the number of training examples and the dimension of feature vectors are both large. We focus on the case where the loss function defining the quality of the parameter we wish to estimate may be non-convex, but also has a convex regularization. We propose a Doubly Stochastic Successive Convex approximation scheme (DSSC) able to handle non-convex regularized expected risk minimization. The method operates by decomposing the decision variable into blocks and operating on random subsets of blocks at each step (fusing the merits of stochastic approximation with block coordinate methods), and then implements successive convex approximation. In contrast to many stochastic convex methods whose almost sure behavior is not guaranteed in non-convex settings, DSSC attains almost sure convergence to a stationary solution of the problem. Moreover, we show that the proposed DSSC algorithm achieves stationarity at a rate of O((log t)/t <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/4</sup> ). Numerical experiments on a non-convex variant of a lasso regression problem show that DSSC performs favorably in this setting. We then apply this method to the task of dictionary learning from high-dimensional visual data collected from a ground robot, and observe reliable convergence behavior for a difficult non-convex stochastic program.

Spectrum-Efficient Resource Allocation in Multi-Radio Multi-Hop Cognitive Radio Networks.

The multi-hop cognitive radio network (CRN) has attracted much attention in industry and academia because of its seamless wireless coverage by forming multi-hop links and high spectrum utilization of cognitive radio (CR) technology. Using multi-slot statistical spectrum status information (SSI), this work investigates the average spectrum efficiency (SE) of a multi-radio multi-hop (MRMH) CRN where each hop is permitted to use different spectra and long-distance hops can reuse the same idle primary user (PU) spectrum. Faced with the modeled SE problem, which is a complex non-convex fractional mixed integer nonlinear programming (MINLP) problem, the optimal spectrum and power allocation for multi-hop links in multi-slot and multi-channel scenarios can be obtained with the proposed successive multi-step convex approximation scheme (SMCA). As shown through computational complexity and simulation analysis, SMCA can obtain an approximate lower bound of the optimal solution for the modeled SE problem with a lower computational cost. Furthermore, some potential relationships between network performance and spectrum idle rate can be easily discussed with SMCA, which can provide some sensible deployment strategies for the MRMH CRN in future multi-slot scenarios.

Secure SWIPT for Directional Modulation-Aided AF Relaying Networks

Secure wireless information and power transfer based on directional modulation is conceived for amplify-and-forward relaying networks. Explicitly, we first formulate a secrecy rate maximization (SRM) problem, which can be decomposed into a twin-level optimization problem and solved by a one-dimensional (1D) search and semidefinite relaxation (SDR) technique. Subsequently, in order to reduce the search complexity, we formulate an optimization problem based on maximizing the signal-to-leakage-AN-noise-ratio (Max-SLANR) criterion, and transform it into a SDR problem. In addition, the relaxation is proved to be tight according to the classic Karush-Kuhn-Tucker (KKT) conditions. Finally, to reduce the computational complexity, a successive convex approximation (SCA) scheme is proposed to find a near-optimal solution. The complexity of the SCA scheme is much lower than that of the SRM and the Max-SLANR schemes. Simulation results demonstrate that the performance of the SCA scheme is very close to that of the SRM scheme in terms of its secrecy rate and bit error rate, but much better than that of the zero forcing scheme.

Rate-Distortion Performance and Incremental Transmission Scheme of Compressive Sensed Measurements in Wireless Sensor Networks.

We consider a Wireless Sensor Network (WSN) monitoring environmental data. Compressive Sensing (CS) is explored to reduce the number of coefficients to transmit and consequently save the energy of sensor nodes. Each sensor node collects N samples of environmental data, these are CS coded to transmit values to a sink node. The M CS coefficients are uniformly quantized and entropy coded. We investigate the rate-distortion performance of this approach even under CS coefficient losses. The results show the robustness of the CS coding framework against packet loss. We devise a simple strategy to successively approximate/quantize CS coefficients, allowing for an efficient incremental transmission of CS coded data. Tests show that the proposed successive approximation scheme provides rate allocation adaptivity and flexibility with a minimum rate-distortion performance penalty.

Existence of Solutions of Stochastic Fractional Integrodifferential Equations

In this paper, a general class of stochastic fractional integrodifferential equations is investigated. The Picard-Lindel ¨of successive approximation scheme is used to establish the existence of solutions. The uniqueness of the solution is also studied under suitable conditions.

On the mathematical modelling of cellular (discontinuous) precipitation

Cellular precipitation is a dynamic phase transition in solid solutions (such as alloys) where a metastable phase decomposes into two stable phases : an approximately planar (but corrugated) boundary advances into the metastable phase, leaving behind it interleaved plates (lamellas) of the two stable phases.The forces acting on each interface (thermodynamic, elastic and surface tension) are modelled here using a first-order ODE, and the diffusion of solute along the interface by a second-order ODE, with boundary conditions at the triple junctions where three interfaces meet. Careful attention is paid to the approximations and physical assumptions used in formulating the model.These equations, previously studied by approximate (mostly numerical) methods, have the peculiarity that $v,$ the velocity of advance of the interface, is not uniquely determined by the given physical data such as $c_0$, the solute concentration in the metastable phase. It is hoped that our analytical treament will help to improve the understanding of this.We show how to solve the equations exactly in the limiting case where $v=0$. For larger $v$, a successive approximation scheme is formulated. One result of the analysis is that there is just one value for $c_0$ at which $v$ can be vanishingly small.

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.