Newton-Raphson Method Research Articles

Parameter estimation of inverse Weibull distribution under competing risks based on the expectation–maximization algorithm

AbstractA system consisting of interconnected components in series is under consideration. This research focuses on estimating the parameters of this system for incomplete lifetime data within the framework of competing risks, employing an underlying inverse Weibull distribution. While one popular method for parameter estimation involves the Newton–Raphson (NR) technique, its sensitivity to initial value selection poses a significant drawback, often resulting in convergence failures. Therefore, this paper opts for the expectation–maximization (EM) algorithm. In competing risks scenarios, the precise cause of failure is frequently unidentified, and these issues can be further complicated by potential censoring. Thus, incompleteness may arise due to both censoring and masking. In this study, we present the EM‐type parameter estimation and demonstrate its superiority over parameter estimation based on the NR method. Two illustrative examples are provided. The proposed method is compared with the existing Weibull competing risks model, revealing the superiority of our approach. Through Monte Carlo simulations, we also examine the sensitivity of the initial value selection for both the NR‐type method and our proposed method.

Integrated energy cyber–physical system fusion modeling and operation state analysis under the cooperative attack

With the increasingly close coupling between the cyber system and the physical system, cyber attacks have a significant impact on the physical system by attacking the cyber system. As a cyber–physical system with multiple energy sources, integrated energy cyber–physical system (IECPS) is facing the risk of cyber attacks. However, the research on IECPS is still in the direction of operation optimization at the physical level, which cannot meet the requirements of system security and stability analysis under cyber cooperative attacks. Firstly, this paper analyzes the interaction mechanism between the energy network composed of electricity, heat and gas and the cyber network in IECPS, and put forward a layered modeling method of IECPS to analyze the influence of abnormal information flow caused by cyber attacks on energy flow. Secondly, based on the energy circuit method (ECM), a hybrid calculation method of IECPS energy-information flow is proposed to solve the model. Then, the load shedding state of IECPS and the tampering process of system control commands after the fake data injection attack are analyzed by using the proposed calculation method. Finally, the simulation analysis is carried out in an integrated energy system composed of IEEE 39-node power grid, 6-node heating network and 7-node gas network. The results show that, compared with the traditional Newton–Raphson method, the proposed IECPS hybrid calculation method can better obtain the change results of energy flow in the steady-state scenario and the cyber cooperative attack scenario, and identify the high-risk branches in the system, which is of great significance to the safe and stable operation of the energy system.

Solving non-linearities of hyperelastic rubbery behaviour by the asymptotic numerical method: Highlighting with the case of a Hybrid Integral Approach (HIA) model

This paper presents mathematical modelling and simulation founded on an Asymptotic Numerical Method (ANM) for the rubber-like material hyperelastic behaviour. The basic models such as Mooney-Rivlin, and the Gent partial models and the Hybrid Integral Approach (HIA) model are considered. The HIA is a strong nonlinear model developed from the inverse Langevin function approximation is considered here for its efficiency. Explicit formulations of each model are presented as well as the associated asymptotic developments in the frame of the ANM. Various types of boundary conditions effects are analysed for each considered hyperelastic model. The effectiveness of the ANM compared to the Newton-Raphson method is demonstrated and particularly for the HIA model. We present as results stress-strain curves for the implementation of these different models where we specify the influence of the Imposed Displacement for tensile and compressive stresses when the structure is clamped and simply supported. In term of this study, we observe that the complete HIA model present the curves with the difference hardly perceptible when we vary results in term of stress-strain curves with different imposed Displacement. But when strain is high than 5%, the Mooney-Rivlin and the Gent partial models, presents the high disparities with different imposed Displacement. This observation justifying the limitations of partial models in term of characterisation of the behaviour law of hyperplastic materials.

Optimal economic environmental power dispatch by using artificial bee colony algorithm

<span>Today, most power plants worldwide use fossil fuels such as natural gas, coal, and oil as the primary resource for energy reproduction primarily. The new term for economic environmental power dispatch (EEPD) problems is on the minimum total cost of the generator and fossil fuel emissions to address atmosphere pollution. Thus, the significant objective functions are identified to minimize the cost of generation, most minor emission pollutants, and lowest system losses individually. As an alternative, an Artificial Bee Colony (ABC) swarming algorithm is applied to solve the EEPD problem separately in the power systems on both standard IEEE 26 bus system and IEEE 57 bus system using a MATLAB programming environment. The performance of the introduced algorithm is measured based on simple mathematical analysis such as a simple deviation and its percentage from the obtained results. From the mathematical measurement, the ABC algorithm showed an improvement on each identified single objective function as compared with the gradient approach of using the Newton Raphson method in a short computational time.</span>

A comparative analysis of numerically simulated and experimentally measured static responses of a floating dock

ABSTRACT Two numerical methods, dynamic and static analyses, are proposed to calculate the static responses of a floating dock under different ballast water distributions. Model-scale experimental tests were conducted to compare with these numerical methods. The dynamic analysis includes a 6-degree-of-freedom (6-DOF) model, a hydrostatic force model and a hydrodynamic force model to simulate the dock's freely floating processes. The dock's equilibrium position is identified when the difference in the dock’s motions between two successive time steps is below a specified tolerance value. In the static analysis, the static equilibrium equations in draught, heel, and trim are solved using the Newton-Raphson method. Both dynamic and static results of the draughts at the four corners, heel, and trim are in good agreement with the corresponding experimental results, which shows the reliability of the proposed numerical methods. Moreover, the static analysis exhibits quicker convergence, requiring fewer iteration steps than the dynamic analysis.

Coating of micropolar fluid during non-isothermal reverse roll coating phenomena

Reverse roll coating is a high-speed coating process used in many applications. The single largest application for reverse roll coating is applying architectural paint to coils of sheet metal; however, in the converting industry reverse roll coating is used for some thermal coatings, adhesives, color laser paper receivers, wax coatings, magnetic coatings, vinyl dispersions for wallcovering, some specialty light sensitive applications, and many specialty products that require a high precision application process. This work presents a mathematical model for the steady flow of non-isothermal, incompressible, micropolar fluid in the metering nip of a reverse roll coater with velocity slip applied at both roll’s surfaces. Lubrication approximation theory (LAT) is utilized to reduce the complexity of the non-dimensional equations. Exact solutions for pressure gradient, velocity, and temperature are achieved. At the same time, numerical techniques (Simpson’s 3/8 rule with Newton Raphson method) are used to compute the pressure distribution, coating thickness, flow rate, and separation points. Effects of coupling number, slip parameter, microrotation, and velocity ratio on velocity, pressure, temperature, and pressure gradient are presented in graphs. It is observed from the current analysis that the intrinsic rotations of the fluid particles prove to be the controlling parameter of the pressure gradient, which significantly varies the coating thickness. Also, as a result of velocity slip, the flow rate declines and the coating thickness reduces as the fluid moves faster along the boundary walls.

Investigation of Frequency-Dependent Characteristics of Wire Rope under Tension Based on Transfer Function Method

Wire rope is a complex structure made by twisting wires of various sizes in the longitudinal direction. It is used to support or move engineering structures and is subject to various tensions. Dynamic properties are important parameters to evaluate the resistance to bending deformation and vibration reduction of various structures. They are affected by the magnitude of tension. In this study, an experimental method for measuring the frequency-dependent characteristics of wire rope under tension is proposed. The study analyzed flexural wave propagation employing a vibration transfer function. Experimental results showed that the transfer function of wire rope under tension is affected by tension and bending stiffness. The Newton–Raphson method was employed to numerically measure wavenumbers of the wire rope. The bending stiffness and loss factor were determined from the wavenumbers. Changes in the bending stiffness and loss factor as the tension increased were explained by the dynamic behavior of the structure under tension. As the tension increased, the bending stiffness increased, and the loss factor decreased. Hysteresis analysis indicated that the energy dissipation of wire rope is greater than that of a steel beam due to the friction between the wires. Statistical analysis confirmed a significant correlation between dynamic characteristics and tension in wire rope.

Complex fracture description and quasi-elastic energy development mathematical model for shale oil reservoirs

Reservoir numerical simulation is an important tool and method for the reasonable and efficient development of shale reservoirs. Accurate description of three-dimensional fractures in shale reservoir development is a necessary and sufficient condition to improve the accuracy and robustness of shale reservoir numerical simulation. This paper achieves precise characterization of complex fracture shapes and oil, gas and water flow by establishing an embedded discrete fracture model based on a non-structural network, which has advantages in the fine characterization of complex morphological fractures in the reservoir and the grid division of the reservoir. In the large matrix solution method, the Newton-Raphson method is used to linearize the nonlinear equations, the Jacobian matrix is ​​constructed, the ILU method is used for preprocessing, the conjugate gradient method is used to solve the linear equations, and the shale oil quasi-elasticity is established A fully implicit solution method for mathematical models of energy development.

Improvement of Voltage profile by Integrating Renewable Generation Units at weak bus locations of the System

The Grid consists of higher rating sources and transmission system that supports local loads. The grid operates at voltages in the range of 66kV-132kV and transmits power in MW to smaller or longer distance locations. Due to higher rating power system the power quality issues are also more. For our consideration an IEEE 14 bus interconnected system is represented as grid operating at higher rated values. The weak bus of the interconnected system is determined by Fast voltage stability index (FVSI) and load flow analysis using Newton-Raphson method available in MATLAB software. The weak buses are integrated with renewable power generation units like PV plant and wind farm improving the bus characteristics. This paper presents a comparative analysis with and without the RGUs in the system. Improvisation of the parameters like power loss, reduced conventional power consumption, power factor and voltage magnitudes are validated through time domain simulations.

Dynamical Modeling and Dynamic Characteristics Analysis of a Coaxial Dual-Rotor System

The dual-rotor structure is the primary excitation source of aero-engine vibration. It is essential to study the dynamical model and analyse the dynamic characteristics such as critical speed and the unbalanced response for rotor system dynamics. The coaxial dual-rotor support scheme of an aero-engine was introduced in the previous work, and the physical model with a high-speed flexible inner rotor of a sizeable length-diameter ratio has been designed. Then a finite element dynamic model based on the Timoshenko beam elements and rigid body kinematics of the dual-rotor system is modelled, with the Newmark-β method and Newton-Raphson method used for the numerical calculation to study the dynamic characteristics of the system. Three different simulation models, including beam-based FE (1D finite element) model, solid-based FE (3D finite element) model, and TM (transfer matrix) model, were designed to study the characteristics of mode and the critical speed characteristic of the dual-rotor system. The unbalanced response of the dual-rotor system was analysed to study the influence of mass unbalance on the rotor system. The effect of different disc unbalance phases and different speed ratios on the dynamic characteristics of the dual-rotor system were investigated in detail. The experimental result shows that the beam-based FE model is effective and suitable for studying the dual-rotor system. Conflict of Interest Statement The authors declare no conflicts of interest.

Interactive Rendering of Caustics using Dimension Reduction for Manifold Next-Event Estimation

Specular surfaces, like water surfaces, create caustics by focusing the light being refracted or reflected. These caustics are very important for scene realism, but also challenging to render: to compute them, we need to find the exact path connecting two points through a specular reflective or refractive surface. This requires finding the roots of a complicated function on the surface. Manifold-Exploration methods find these roots using the Newton-Raphson method, but this involves computing path derivatives at each step, which can be challenging. We show that these roots lie on a curve on the surface, which reduces the dimensionality of the search. This dimension reduction greatly improves the search, allowing for interactive rendering of caustics. It also makes implementation easier, as we do not need to compute path derivatives.

Characterization of Rectangular Waveguides Loaded E-Plane Dielectrics Using the Newton-Raphson Method

Homogeneous metallic waveguides have long been used to carry high powers. They are often filled with inhomogeneous, isotropic dielectrics to reduce their size and cut-off frequencies. To characterize these inhomogeneous rectangular waveguides made of homogeneous and isotropic media, the Newton-Raphson method is used in this article. Frequency of cutoff, attenuation, and power flow distribution are all properties of the EM wave that are highly dependent on the physical structure and composition within the guide. This article presents the characterization of an inhomogeneous and isotropic rectangular guide. The analysis of this type of guide is based on the Borgnis potential method for determining the components of the electric field E and the magnetic field H, to obtain the guide's dispersion equations. The modes that were found to exist in these waveguides are hybrid, meaning that they have both axial E- and H-fields. Numerical resolution of these equations using the Newton-Raphson method obtains the guide's propagation constants. A MATLAB program is used to plot these dispersion curves. The propagation constant increases as a function of frequency, and the d/a ratio influences the dispersion curves. Increasing the relative permittivity of the dielectric leads to an increase in the ratio of the propagation constant in the z direction to the wave number.

Comparative Study of Parameter Extraction from a Solar Cell or a Photovoltaic Module by Combining Metaheuristic Algorithms with Different Simulation Current Calculation Methods

In this paper, single-diode model (SDM) and double-diode model (DDM) parameters of the French RTC solar cell and the Photowatt PWP 201 photovoltaic (PV) module were extracted by combining five metaheuristic algorithms with three simulation current calculation methods (i.e., approximation method, Lambert W method and Newton–Raphson method), respectively. It was found that the parameter-extraction accuracies of the Lambert W (LW) method and the Newton–Raphson (NR) method are always approximately equal and higher than that of the approximation method. The best RMSEs (root mean square error) obtained by using the LW or the NR method on the solar cell and the PV module are 7.72986 × 10−4 and 2.05296 × 10−3 for SDM parameter extraction and 6.93709 × 10−4 and 1.99051 × 10−3 for DDM parameter extraction, respectively. The latter may be the highest parameter-extraction accuracy reported on the solar cell and the PV module so far, which is due to the adoption of more reasonable DDM parameter boundaries. Furthermore, the convergence curves of the LW and the NR method basically coincide, with a convergence speed faster than that of the approximation method. The robustness of a parameter-extraction method is mainly determined by the metaheuristic algorithm, but it is also affected by the simulation current calculation method and the parameter-extraction object. In a word, the approximation method is not suitable for application in PV-model parameter extraction because of incorrect estimation of the simulation current and the RMSE, while the LW and NR methods are suitable for the application for accurately calculating the simulation current and RMSE. In terms of saving computation resources and time, the NR method is superior to the LW method.

The Optimal Infrastructure Design for Grid-to-Vehicle (G2V) Service: A Case Study Based on the Monash Microgrid

The electrification of the transport sector has emerged as a game changer in addressing the issues of climate change caused by global warming. However, the unregulated expansion and simplistic approach to electric vehicle (EV) charging pose substantial risks to grid stability and efficiency. Intelligent charging techniques using Information and Communication Technology, known as smart charging, enable the transformation of the EV fleets from passive consumers to active participants within the grid ecosystem. This concept facilitates the EV fleet’s contribution to various grid services, enhancing grid functionality and resilience. This paper investigates the optimal infrastructure design for a smart charging system within the Monash microgrid (Clayton campus). We introduce a centralized Grid-to-Vehicle (G2V) algorithm and formulate three optimization problems utilizing linear and least-squares programming methods. These problems address tariff structures between the main grid and microgrid, aiming to maximize aggregator profits or minimize load fluctuations while meeting EV users’ charging needs. Additionally, our framework incorporates network-aware coordination via the Newton–Raphson method, leveraging EVs’ charging flexibility to mitigate congestion and node voltage issues. We evaluate the G2V algorithm’s performance under increasing EV user demand through simulation and analyze the net present value (NPV) over 15 years. The results highlight the effectiveness of our proposed framework in optimizing grid operation management. Moreover, our case study offers valuable insights into an efficient investment strategy for deploying the G2V system on campus.

Integration of multiple distributed solar PV (DSP) into the grid: The case of the distribution network in Freetown, Sierra Leone

The optimal integration of distributed solar photovoltaic (DSP) is a transformative engineering method that is key in contributing to a sustainable and resilient energy future, especially when countries seek to increase the proportion of renewables in their energy mix to reduce carbon emissions. This paper presents a power flow-based approach that makes use of Newton Raphson's method in the ETAP tool to integrate multiple DSPs into both the existing and expanded Freetown distribution networks. The study determined the network's hosting capacities and optimal points of injection for the reduction of active power loss and improvement of bus voltage profiles. The study showed that the existing Freetown distribution network had a hosting capacity of 34.6 MW with an active power loss reduction of 0.967 MW while the expanded Freetown distribution network had a hosting capacity of 59.57 MW with an active power loss reduction of 5.12 MW. Before the injection of the DSPs into both networks, most of the bus voltages were not within acceptable limits. However, with the intervention of the injected DSPs, bus voltages considerably improve. The study showed that the expanded Freetown distribution network is better for DSPs integration compared to the existing Freetown distribution network. To evaluate the impacts of the injected DSPs and to validate the model used, four network scenarios were considered. The study used an analytical approach, considering future load growth and an evolving grid to integrate DSPs for long-term planning. The study will inform policymakers, utilities, etc., about the potential of integrating DSPs.

Nonlinear vibrations, bifurcations and chaos of piezoelectric composite lattice sandwich plate with four simply supported edges

This paper is devoted to investigate the nonlinear dynamics, bifurcation and chaos of the piezoelectric composite lattice sandwich plate with 1:3 internal resonance. Galerkin method is used to discretize the nonlinear partial differential governing equations of motion into the ordinary differential equations. The multi-scale method is used to obtain the modulation equations of the piezoelectric composite lattice sandwich plate in the polar coordinates and Cartesian coordinates in the primary and parametric resonances, respectively. Using Newton-Raphson method, the bifurcation diagrams of the steady-state equilibrium solution are obtained for the modulation equation with the change of the system parameters. The stability of the steady-state equilibrium solution is analyzed for the modulation equation. The existence of the static bifurcations, such as the saddle-node bifurcation, pitchfork bifurcation and Hopf dynamic bifurcations are found. The complex nonlinear jump phenomena caused by the existence of the multiple nonlinear steady-state solution regions are analyzed in detail. Fourth-order Runge-Kutta method is used to continue tracing the nonlinear periodic solution of the modulation equation in Cartesian coordinates. The time-history diagram, phase portrait and Poincaré map are obtained for the piezoelectric composite lattice sandwich plate in the nonlinear resonance. The dynamic process of the nonlinear periodic solution is described for the modulation equation from the limit cycle oscillation to the chaotic attractor in detail.

Forward solution of shield tunneling pose based on the Newton–Raphson method

To achieve precise control of the shield tunneling pose, obtaining a real-time shield pose state during the excavation process is necessary to achieve closed-loop feedback control of the shield pose. This study proposes a forward solution method to address the high cost and low efficiency of direct measurement methods, such as using lasers and gyroscopes, for measuring shield pose. This method relies on the real-time measurement of the strokes of hydraulic thrust cylinders during shield tunneling. Based on the inverse kinematics of the shield machine, the Newton–Raphson method was used to calculate the shield tunneling pose. Accordingly, a forward solution algorithm for shield pose was developed using MATLAB, and the effectiveness of the proposed method was verified through an example analysis. The results demonstrated the high computational efficiency of the method, proving its potential application in real-time control systems for shield tunneling poses.

Numerical Analysis of the Blade Coating Process Using Non‐Newtonian Nanofluid with Magnetohydrodynamic (MHD) and Slip Effects

AbstractThe coating process is widely used in various industries to enhance the production quality and efficiency. This study gives a comprehensive analysis of non‐isothermal blade coating of non‐Newtonian nanofluid incorporating magnetic, thermophoresis, and Brownian effects. The mathematical equations derived from mass, momentum, and energy conservation laws are initially streamlined by means of lubrication approximation theory (LAT). Subsequently, these dimensionless equations are solved in dimensionless form numerically using fourth order Runge–Kutta and Newton–Raphson methods. This study includes the effects of the slip parameter, magnetohydrodynamic (MHD) and other material parameters on the coating thickness (), blade load, velocity, temperature, concentration, and pressure profiles through graphs and tables. The velocity of molten polymer increases near the substrate while it decreases near the blade surface as the slip parameter increases. The temperature distribution increases as the Brinkman number rises, with the maximum temperature occurring in the nip region of the flow. The coating thickness and load‐carrying force for both plane and exponential coater increase with higher values of the magnetohydrodynamic (MHD) parameter.

Evaluating Performance and Grid Impacts of On-Grid Rooftop PV System: Case Study of A Mosque

This study presents a load flow analysis of on-grid rooftop PV installed at Masjid Tablighiyah, Bukittinggi, Indonesia. The analysis was conducted using the Newton-Raphson method and simulated using ETAP software. Two scenarios was explored for the analysis: i) connecting the PV into 20 kV bus, and ii) connecting into 380 V bus. Results obtained showed that grid voltage are meeting the utility standards, with all bus voltages are within ±5% threshold. However, certain nodes have moderately low voltages, suggesting a potential need for pre-emptive measures during peak demand. The power factor performance falls within acceptable ranges (84-91%), indicating reasonable system efficiency. However, there is still needed for continuous monitoring to prevent degradation from harmonic-producing loads. In addition, substation transformers and distribution feeders show ample capacity for future expansions as electricity loads grow. The findings provide a robust baseline for additional grid integration studies, emphasizing the need for further enhancements at weaker nodes to ensure sustained stability and reliability in future demand conditions.

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.