Search Results (135)

Real-time pricing is an ideal pricing mechanism for regulating the balance of power supply and demand in smart grid. Considering the differences in electricity consumption risks among different types of users, a social welfare maximization model with user risk classification is proposed in this paper. Also, a smoothing Newton method is investigated for solving the proposed model. Firstly, the convexity of the model is discussed, which implies that the local optimum of the model is also the global optimum. Then, by transforming the proposed model into a smooth equation system based on the Karush–Kuhn–Tucker (KKT) conditions, we devise a smoothing Newton algorithm integrated with Powell–Wolfe line search criteria. The nonsingularity of the corresponding function’s Jacobian matrix is obtained to ensure the stability of the proposed algorithm. Finally, we give a comparison between the proposed model and the unclassified risk model and the proposed algorithm and the distributed algorithm for real-time pricing, time-of-use pricing, and fixed pricing, respectively. The numerical results demonstrate the effectiveness of the model and the algorithm. Full article

The prediction of structural damage through vibrational analysis is a critical task in the field of composite structures. Structural defects and damage can negatively influence the load-carrying capacity of the beam. Therefore, detecting structural damage early is essential to preventing catastrophic failures. This study addresses the challenge of predicting damage in composite concrete–steel beams using a vibration-based finite element approach. To tackle this complex task, a finite element model to a quasi-static analysis emulating a four-point pure bending experimental test was performed. Notably, the numerical model equations were carefully modified using the Newton–Raphson method to account for the stiffness degradation resulting from material strains. These modified equations were subsequently employed in a modal analysis to compute modal shapes and natural frequencies corresponding to the stressed state. The difference between initial and damaged modal shape curvatures served as the foundation for predicting a damage index. The approach effectively captured stiffness degradation in the model, leading to observable changes in modal responses, including a reduction in natural frequencies and variations in modal shapes. This enabled the accurate prediction of damage instances during construction, service, or accidental load scenarios, thereby enhancing the structural and operational safety of composite system designs. This research contributes to the advancement of vibration-based methods for damage detection, emphasizing the complexities in characterizing damage in composite structural geometries. Further exploration and refinement of this approach are essential for the precise classification of damage types. Full article

The paper addresses the dynamics modeling of underwater vehicles that are inertia propelled, i.e., they can move based upon the change of the amount of water in their water tanks and the motion of an internal mass, enabling maneuvers. Underwater vehicles of this type can be successfully applied in ocean scientific reconnaissance and exploration missions or for water pollution monitoring. Usually, dynamics modeling methods for them are based upon the Newton–Euler or Lagrange approaches modified to encompass variable mass. The main motivation of this research is to explore other modeling methods and compare them to those traditionally used. In this paper, modeling methods based on the Maggi and Boltzmann–Hamel approaches are presented and discussed with respect to their effectiveness in modeling, operation, and control applications. The resulting comparisons indicate that the traditional approaches are sufficient for the analysis of vehicle operation and performance in the realization of simple tasks; however, they become of limited application when the variable mass or constraints on vehicle dynamics or motion are added or complex maneuvers are required. In this regard, the Maggi or Boltzmann–Hamel approaches are more effective for dynamics modeling. The theoretical development is illustrated by examples of vehicle dynamics developed using the approaches we propose. Full article

The reasonable construction state of a cable-stayed bridge refers to the state achieved after construction is carried out according to a specific sequence of procedures, leading to the reasonable completion status the bridge. The corresponding construction states at each stage are considered as part of the reasonable construction state. For the optimization of the construction state of cable-stayed bridges with steel box girders, a method combining a multi-objective programming algorithm with a forward iteration method is proposed to determine a reasonable construction state based on the structural characteristics and optimization principles of such bridges. First, a multi-objective programming model was established, taking the bending moments of the main girder and pylon, as well as cable forces, as objective functions. The weighted square sum method, a type of evaluation function method, was then employed to convert the multi-objective programming model into an unconstrained single-objective quadratic programming model. Subsequently, the damped Newton method was utilized to solve the quadratic programming problem. By integrating this algorithm with the forward iteration method, the reasonable construction state of a large-span and double-tower steel box girder cable-stayed bridge was optimized. The influence of different objective functions on the optimization results was analyzed. The findings demonstrate that the proposed method produces a smooth structural configuration under the optimized construction state, with internal forces and normal stresses within a reasonable range. In the completed state derived from this construction state, internal forces, normal stresses, and cable forces are uniformly distributed, while the reactions at transition piers and auxiliary piers exhibit sufficient pressure reserves. The structural state under dead load achieved through this method closely aligns with the desired reasonable completed state. Full article

AC/DC hybrid distribution networks with power electronic transformers (PETs) as distribution hubs are in line with the future development direction of the AC/DC hybrid distribution network. Unlike traditional transformers, power electronic transformers introduce new node types and may transform the network topology from radial to ring structures. These changes render traditional power flow calculation methods inadequate for achieving satisfactory results in AC/DC hybrid networks. In addition, existing commercial power flow calculation software packages are mainly based on the traditional AC power flow calculation method, which have limited support for the DC network. Especially when the DC network is coupled with the AC network, it is difficult to achieve a unified calculation of its power flow. To address these challenges, this paper proposes a novel power flow calculation method for ring AC/DC hybrid distribution networks with power electronic transformers. The proposed method is based on the alternating iterative method to ensure compatibility with mature AC power flow calculation programs in commercial software, thereby improving the feasibility of engineering applications. Firstly, the steady-state power flow calculation model of PET is constructed by analyzing that the working principle and control modes of power electronic transformer are proposed based on the source-load attributes of its connected subnetworks. According to the characteristics of the power electronic transformer, AC distribution network, and DC distribution network, a hybrid alternating iteration method combining the high computational accuracy of the Newton–Raphson (NR) method with the high efficiency of the Zbus Gaussian method in dealing with ring networks is proposed. On this basis, the power flow calculation model of the AC/DC hybrid distribution network with power electronic transformers is established. Finally, the simulation of the constructed 44-node ring AC/DC hybrid distribution network example is carried out. The simulation results show that the proposed method can not only converge reliably when the convergence accuracy is 1 × 10⁻⁶ p.u., but also ensure that the voltage magnitudes of all nodes are above 0.96 p.u. whose maximum offset value is 0.789% when the outputs of the connected distributed generations fluctuate, which verifies the effectiveness and accuracy of the proposed method. Full article

A local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already studied in the literature under different types of conditions, such us Newton’s, and Steffensen’s, and Kurchatov’s methods, the Secant method, and other methods. This study is carried out under generalized conditions for first-order divided differences, as well as first-order derivatives. Both in the local case and in the semi-local case, the error estimates, the radii of the region of convergence, and the regions of the solution’s uniqueness are determined. A numerical majorizing sequence is constructed for studying semi-local convergence. The approach of restricted convergence regions is used to develop a convergence analysis of the considered method. The new approach allows a comparison of the convergence of different methods under a uniform set of conditions. In particular, the assumption of generalized continuity used to control the divided difference provides more precise knowledge on the location of the solution as well as tighter error estimates. Moreover, the generality of the approach makes it useful for studying other methods in an analogous way. Numerical examples demonstrate the applicability of our theoretical results. Full article

In the present study, an extension of the idea of dynamic neurons is proposed by replacing the weights with a weight function that is applied simultaneously to all neuron inputs. A new type of artificial neuron called an integral neuron is modeled, in which the total signal is obtained as the integral of the weight function. The integral neuron enhances traditional neurons by allowing the signal shape to be linear and nonlinear. The training of the integral neuron involves finding the parameters of the weight function, where its functional values directly influence the total signal in the neuron’s body. This article presents theoretical and experimental evidence for the applicability and convergence of standard training methods such as gradient descent, Gauss–Newton, and Levenberg–Marquardt in searching for the optimal weight function of an integral neuron. The experimental part of the study demonstrates that a single integral neuron can be trained on the logical XOR function—something that is impossible for single classical neurons due to the linear nature of the summation in their bodies. Full article

This paper studies the thermomechanical low-velocity impact behaviors of geometrically imperfect nanoplatelet-reinforced composite (GRC) beams considering the von Kármán nonlinear geometric relationship. The graphene nanoplatelets (GPLs) are assumed to have a functionally graded (FG) distribution in the matrix beam along its thickness, following the X-pattern. The Halpin–Tsai model and the rule of mixture are employed to predict the effective Young modulus and other material properties. Dividing the impact process into two stages, the corresponding impact forces are calculated using the modified nonlinear Hertz contact law. The nonlinear governing equations are obtained by introducing the von Kármán nonlinear displacement–strain relationship into the first-order shear deformation theory and dispersed via the differential quadrature (DQ) method. Combining the governing equation of the impactor’s motion, they are further parametrically solved by the Newmark-β method associated with the Newton–Raphson iterative process. The influence of different types of geometrical imperfections on the nonlinear thermomechanical low-velocity impact behaviors of GRC beams with varying weight fractions of GPLs, subjected to different initial impact velocities, are studied in detail. Full article

This paper investigates the design and stability of Traub–Steffensen-type iteration schemes with and without memory for solving nonlinear equations. Steffensen’s method overcomes the drawback of the derivative evaluation of Newton’s scheme, but it has, in general, smaller sets of initial guesses that converge to the desired root. Despite this drawback of Steffensen’s method, several researchers have developed higher-order iterative methods based on Steffensen’s scheme. Traub introduced a free parameter in Steffensen’s scheme to obtain the first parametric iteration method, which provides larger basins of attraction for specific values of the parameter. In this paper, we introduce a two-step derivative free fourth-order optimal iteration scheme based on Traub’s method by employing three free parameters and a weight function. We further extend it into a two-step eighth-order iteration scheme by means of memory with the help of suitable approximations of the involved parameters using Newton’s interpolation. The convergence analysis demonstrates that the proposed iteration scheme without memory has an order of convergence of 4, while its memory-based extension achieves an order of convergence of at least $7.993$, attaining the efficiency index $7.{993}^{1/3}\approx 2$. Two special cases of the proposed iteration scheme are also presented. Notably, the proposed methods compete with any optimal j-point method without memory. We affirm the superiority of the proposed iteration schemes in terms of efficiency index, absolute error, computational order of convergence, basins of attraction, and CPU time using comparisons with several existing iterative methods of similar kinds across diverse nonlinear equations. In general, for the comparison of iterative schemes, the basins of iteration are investigated on simple polynomials of the form $z^n-1$ in the complex plane. However, we investigate the stability and regions of convergence of the proposed iteration methods in comparison with some existing methods on a variety of nonlinear equations in terms of fractals of basins of attraction. The proposed iteration schemes generate the basins of attraction in less time with simple fractals and wider regions of convergence, confirming their stability and superiority in comparison with the existing methods. Full article

Understanding energy demands and costs is important for policy makers and the energy sector, especially in the context of residential heating and cooling systems. To estimate the thermal demand of a residential house, a grey-box modelling method with a resistance–capacitance (RC) analogy was implemented. The architectural properties used to parameterize the grey-box model were derived from a house used for research purposes in Vaughan, Ontario, Canada (TRCA-House A). The house model accounts for solar irradiance on exterior building surfaces, thermal conductivity through all surfaces, solar heat gains through windows, and thermal gains from ventilation. Two parallel short- and long-term calibrations were performed such that model outputs reflected the real-world operation of the house as best as possible. To define the unknown model parameters (such as the conductivity of building materials and some constant parameters), a hybrid optimization scheme including a genetic algorithm (GA) and the Quasi-Newton algorithm was introduced and implemented using Bayesian approximation and Markov Chain Monte Carlo (MCMC) methods. The temperature outputs from the model were compared to the data retrieved from TRCA-House A. The final iteration of the model had an RMSE for interior zone temperature estimation of 0.22 °C when compared to the retrieved interior zone temperature data from TRCA-House A. Furthermore, the annual heating and cooling energy consumption values are within 1.50% and 0.08% of target values, respectively. According to these preliminary results, the introduced model and optimization techniques could be adjusted for different types of housing, as well as for smart control applications on both a short- and long-term basis. Full article

Conventional multi-rotors with limited deformation capability are unable to meet the traversal capability of complex and narrow environments. In order to solve the above problems, a novel type of deformable quadrotor with a two-degree-of-freedom arm, named QTDA, is proposed. Firstly, the overall structural design of the QTDA is introduced, and its movement strategy is analyzed. Secondly, the Newton–Euler equations based on a quaternion are utilized to model the omnidirectional dynamics and kinematics of the system. Next, to tackle the multi-actuator control problem, a pseudo-inverse control allocation method is developed, along with an analysis of control allocation singularities. Furthermore, non-singular terminal sliding mode position control law and non-singular terminal sliding mode attitude control law based on a quaternion are designed. Finally, simulations are conducted to verify the effectiveness of the proposed control methods. The results demonstrate the QTDA’s ability to traverse both narrow horizontal and vertical environments, thereby validating the effectiveness of the approach presented in this paper. Full article

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product’s lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method. Full article

The Lorentz force magnetic levitation gim2bal stabilized platform (LFMP), as a new generation of high-precision turntable for maglev satellites, can meet the requirements of future spacecraft for ultra-high attitude pointing accuracy and stability. To solve the problem of three-module multi-body attitude control under maneuvering conditions, the platform subsystem is first dynamically modeled based on the second type of Lagrangian equation, and the payload subsystem is dynamically modeled based on the Newton–Euler method. Secondly, a multi-loop control system is designed, consisting of high-precision and fast attitude pointing control for the payload, position tracking control for the platform subsystem, and tracking control for the maglev module. The final simulation results verified the feasibility and effectiveness of the payload-centered control method. An evaluation of the stability with a specific model has been performed, and the attitude accuracy of the payload is within 0.00002° and the attitude stability is within 0.00005°/s. Full article

In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used to describe complex filtration processes such as fluid movement in horizontal wells in fractured geological formations. To construct the numerical method, a high-order approximation formula for the fractional derivative in the sense of Caputo is applied, and a combination of the finite difference method with the finite element method is used. The article proves the uniqueness and continuous dependence of the solution on the input data in differential form, as well as the stability and convergence of the proposed numerical scheme. The linearization of nonlinear terms is carried out by the Newton method, which allows for achieving high accuracy in solving complex problems. The research results are confirmed by a series of numerical tests that demonstrate the applicability of the developed method in real engineering problems. The practical significance of the presented approach lies in its ability to accurately and effectively model filtration processes in shale formations, which allows engineers and geologists to make more informed decisions when designing and operating oil fields. Full article

The development of reusable liquid rocket turbopumps has gradually highlighted the disadvantages of rolling bearings, particularly the contradiction between long service life and high rotational speed. It is critical to explore a feasible bearing scheme offering a long wear life and high stability to replace the existing rolling bearings. In this study, liquid nitrogen is adopted to simulate the ultra-low temperature environment of liquid rocket turbopumps, and theoretical evaluations of the lubrication performance of thrust-type foil bearings in liquid nitrogen are conducted. A link-spring model for the bump foil structure and a thin-plate finite element model for the top foil structure are established. The static and dynamic characteristics of the bearings are analyzed using methods including the finite difference method, the Newton–Raphson iteration method, and the finite element method. Detailed analysis includes the effects of factors such as rotational speed, fluid film thickness, thrust disk tilt angle, and the friction coefficient of the bump foil interface on the static and dynamic characteristics of thrust-type foil bearings. The research results indicate that thrust-type foil bearings have a good load-carrying capacity and low frictional power consumption. The adaptive deformation of the foil structure increases the fluid film thickness, preventing dry friction due to direct contact between the rotor journal and the bearing surface. When faced with thrust disk tilt, the direct translational stiffness and damping coefficient of the bearing do not undergo significant changes, ensuring system stability. Based on the results of this study, the exceptional performance characteristics of thrust-type foil bearings make them a promising alternative to rolling bearings for the development of reusable liquid rocket turbopumps. Full article