Newton Downhill Method Research Articles

Combined Effect of Fluid Cavitation and Inertia on the Pressure Buildup of Parallel Textured Surfaces

A mathematical model is developed to investigate the combined effect of fluid cavitation and inertia on the fluid pressure buildup of parallel textured surfaces. The fluid cavitation is analyzed using the Rayleigh–Plesset model, and the fluid inertia is analyzed with an averaged method. The finite element method and Newton-downhill method are employed to solve the governing equations. The numerical model is validated by comparing the experimental and numerical results, and the combined effect of fluid cavitation and inertia on the fluid pressure buildup is analyzed and discussed. The research indicates that the cavitation weakens the fluid inertia effect on the pressure distribution at the inlet area of textures. The fluid inertia greatly enhances the hydrodynamic effect and effectively limits the excessive extension of the low-pressure zone caused by cavitation. The fluid cavitation and inertia, especially their interaction, significantly affect the fluid pressure buildup and generate a net load-carrying capacity (LCC). The numerical model with the fluid inertia and cavitation is more time saving than the commercial CFD tools in solutions, which gives a novel and optional HD foundation for developing a more efficient and accurate THD or TEHD model by numerical programming.

Development of multiphase subchannel code with new numerical method in COSINE code package

A new subchannel code of COSINE code package with three-phase and eleven-equation was developed in the present study. The governing equations were spatially discretized with the staggered mesh and a semi-implicit time discrete scheme was adopted. The Newton downhill method was implemented to accelerate the convergence, and the hydraulic cell re-meshing method was used to mitigate non-physical water packing phenomena. The flow blockage test and the Pryor pressure test were used to assess the new numerical method, and some benchmarking tests, including cross flow, droplet entertainment, post-CHF and reflooding heat transfer, were used for the preliminary validation. The results show that the convergence method can significantly accelerate the convergence and the re-meshing method can eliminate the artificial pressure spike. It is also shown that the various thermal-hydraulics phenomena predicted by the present code are in good agreement with the reference results.

Nonlinear Bending of Sandwich Plates with Graphene Nanoplatelets Reinforced Porous Composite Core under Various Loads and Boundary Conditions

The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction.

Annular Directed Distributed Algorithm for Energy Internet

This article investigates an annular directed distributed double optimal algorithm to manage many we-energy frameworks in energy management of energy Internet (EI). The we-energy (WE) is an integrated energy hub containing varied energy devices of different functions including multi-energy production, consumption, and conversion. On this basis, all WE models cooperate to search for a minimum value of an objective function. Energy management in EI has two main goals. On the one hand, it needs to attain the optimality of economy with influence about the fluctuation of distributed renewable energy and randomness of terminal users. On the other hand, the EI should protect the privacy of terminal users well. Besides, discovering optimality value in the oscillation near convergence point, EI also needs a decrease in communication frequency and refraining of Zeno behavior. Zeno behavior means some operation is triggered infinite times in finite times of iteration. For realizing these proposes, this literature establishes an EI system that transfers cyber information in an annular directed path. The algorithm in this EI system adopts a novel annular distributed double-control price guiding strategy. In addition, this algorithm employs other two methods including the alternating direction method of multipliers method and the Newton-downhill method to optimize economy and reach convergence, respectively. Meanwhile, that algorithm adopts a small positive constant w to avoid Zeno behavior. The performance of that algorithm is demonstrated through simulation results. Moreover, the optimality, convergence analysis, and avoiding Zeno behaviors are strictly proved by convex optimization and the monotone-bounded convergence theorem.

Nondetection zone computation and analytics for unintentional islanding in a distribution grid

With the integration rate of distributed energy resources (DERs) increasing rapidly, the significance of unintentional islanding hazard evaluation has become progressively prominent for distribution network planning and operations. The nondetection zone (NDZ) could serve as an effective metric for evaluating the hazards of unintentional islanding, but the existing research is still not able to balance the engineering demands of accuracy, rapidity, and practicality for NDZ computation. In this paper, a new method for fast online computation of NDZ is proposed aiming at the inverter-based microgrid. First, the mathematical model and the uncertainty model of the NDZ are analyzed and established. Then, Newton's downhill method is implemented to iteratively compute the model above. Numerical results demonstrate that the proposed method can obtain the NDZ quickly, effectively, and robustly. The characteristics of NDZ when different control strategies coexist are revealed, and the influences of different load types on NDZ are indicated. Additionally, investigations of the impacts of unbalanced loads on NDZ are covered. Based on NDZ, this paper further calculates the unintentional islanding frequencies and designs precautionary islanding defensive countermeasures.

Impact Force Reconstruction of Composite materials based on Improved Regularization Technology

In the structural health monitoring of composite materials, in order to solve the ill-posed problem of impact force reconstruction, regularization techniques are often used to deal with it. Due to the poor convergence of the traditional Tikhonov regularization method, in order to accurately reconstruct the time history of the impact force, this paper improves Tikhonov regularization method and constructs homotopy function with strong convergence. Since the optimal regularization parameters need to be found in the homotopy function, the Newton downhill method is used to find the optimal parameters and the homotopy function can be calculated, which can accurately reconstruct the time history of the impact force. In order to verify the universality of the method in this paper, impact hammers of different materials were used in the experiment in this paper to study and compare the reconstruction effect of impact time history of different impact hammers.

Research on Segmentation Experience of Music Signal Improved Based on Maximization of Negative Entropy

With the rapid growth of digital music today, due to the complexity of the music itself, the ambiguity of the definition of music category, and the limited understanding of the characteristics of human auditory perception, the research on topics related to automatic segmentation of music is still in its infancy, while automatic music is still in its infancy. Segmentation is a prerequisite for fast and effective retrieval of music resources, and its potential application needs are huge. Therefore, topics related to automatic music segmentation have important research value. This paper studies an improved algorithm based on negative entropy maximization for well-posed speech and music separation. Aiming at the problem that the separation performance of the negative entropy maximization method depends on the selection of the initial matrix, the Newton downhill method is used instead of the Newton iteration method as the optimization algorithm to find the optimal matrix. By changing the descending factor, the objective function shows a downward trend, and the dependence of the algorithm on the initial value is reduced. The simulation experimental results show that the algorithm can separate the source signal well under different initial values. The average iteration time of the improved algorithm is reduced by 26.2%, the number of iterations is reduced by 69.4%, and the iteration time and the number of iterations are both small. Fluctuations within the range better solve the problem of sensitivity to the initial value. Experiments have proved that the new objective function can significantly improve the separation performance of neural networks. Compared with the existing music separation methods, the method in this paper shows excellent performance in both accompaniment and singing in separated music.

The fractional Kelvin-Voigt model for circumferential guided waves in a viscoelastic FGM hollow cylinder

Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be more accurate. A thorough knowledge of the dispersive characteristics of such model is very essential to the application of guided wave testing technique. In this paper, the guided waves in a fractional Kelvin-Voigt viscoelastic FGM hollow cylinder with material changing in the thickness direction are investigated. The Weyl definition of fractional order derivatives and the extended Legendre polynomial approach are employed for the derivations of the governing equations. The presented approach has the advantage that the solution of the complex partial differential wave equations with variable coefficients is reduced to an eigenvalue problem, which overcomes the shortcomings of the existing iterative methods such as the Newton downhill method and improves computation efficiency. The previous methods for dealing with viscoelastic guided wave transform the wave equations into a matrix determinant problem solved by the iterative methods, which has a very slow calculation speed. Comparisons with the related studies are conducted to validate the correctness of the presented approach, and the convergence of the approach is discussed. The full three dimensional spectrum, phase dispersion curves and attenuation curves are illustrated for various fractional order viscoelastic FGM hollow cylinders. The influences of fractional order, grade field and radius-thickness ratio on dispersion and attenuation curves are illustrated. The difference of the dispersion characteristics between the viscoelastic model and the elastic one is discussed. The influences of fractional order on displacement distributions are also studied.

Improved Inversion Method for Multi-Regional Oil-Immersed Paper Resistivity in Transformer

Oil-paper insulation ageing of transformer has characteristics of spatial locality due to uneven temperature distribution. The transformer is sealed, it is difficult to obtain the local ageing state of oil-paper insulation by sampling directly. Currently, there are no effective detection method to detect the insulation state of local regions. The oil-immersed paper resistivity inversion method can nondestructively assess the local state of oil-paper insulation. However, the current inversion methods still have shortcomings and need to be improved. In this paper, combining the back propagation neural network (BPNN) and Newton downhill method (NDM), an improved inversion method is proposed to optimize the current inversion method, so as to reduce the effect of initial value on it and make calculated results converge better. Finally, a 3D 10 kV transformer model is established to verify the effectiveness of the proposed method. The resistivity calculated by the improved method show that the method can provide initial resistivity values for technicians and improve the convergence and accuracy of current inversion method, which is more suitable for extending to the engineering practice.

Equalization Strategy for Multi-Battery Energy Storage Systems Using Maximum Consistency Tracking Algorithm of the Conditional Depreciation

The neglect of the history depreciation imbalance in the conventional equalization strategies may aggravate the lifetime depreciation of the multi-battery energy storage systems (MBESSs) and overuse the high-history-depreciation batteries (HHDBs). This paper proposes an equalization strategy using maximum consistency tracking algorithm of the conditional depreciation to solve the stated problem. Conditional depreciation is innovatively defined to evaluate the operation equitability of the MBESSs. The maximum consistency tracking algorithm consists of two searching levels: the global searching level and the range searching level. A sequential approximation method is utilized at the global searching level to find the variation range consisting of the most equitable conditional depreciation. The newton downhill method is adopted at the range searching level to find the exact value of the most equitable conditional depreciation. The proposed equalization strategy is validated by a hardware-in-the-loop simulation system. Test results show that the proposed equalization strategy minimizes the imbalance of batteries’ conditional depreciations and decreases the HHDBs’ sharing power. Compared to the conventional equalization strategies, the proposed equalization strategy will protect the HHDBs from intermittent overuse and extend the lifetime of the MBESSs.

A size-dependent model for beam-like MEMS driven by electrostatic and piezoelectric forces: A variational approach

A size-dependent model of a micro-electromechanical system (MEMS) actuated by both electrostatic and piezoelectric forces is proposed based on the modified couple stress. The governing equation and boundary conditions are derived with the help of the Hamilton principle and solved numerically by employing the Galerkin method and Newton downhill method. A material length scale parameter (MLSP) is incorporated in the model to capture the size effect in microstructures. An excellent agreement is found between the results of the present model and the experimental data, providing the validity of this model. The results reveal that the introduction of the MLSP stiffens the system and increases the pull-in voltage. The size-effect is significant when the dimension of the beam is comparable to the MLSP but it becomes smaller as the beam size increases. Besides, the static characteristic of the micro-switch is studied. It is found that the piezoelectric material attached on the beam can reduce the pull-in voltage remarkably, which may guide the design of the micro-structure when the system is on the order of micron or submicron.

Forward Displacement Analysis of Two Coupled Degree Nine-Link Barranov Truss Based on Hyper-Chaotic Newton Downhill Method

Forward Displacement Analysis of Two Coupled Degree Nine-Link Barranov Truss Based on Hyper-Chaotic Newton Downhill Method

Forward Displacement Analysis of Nine-Link Barranov Truss Based on Anti-Control of Chaos Newton Downhill Method

The anti-control of chaos Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with chaotic sequences, anti-control of chaos Newton downhill method based on utilizing anti-control of chaos in body motion system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given.The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

Displacement Analysis of the 4SPS-2CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 4SPS-2CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the Newton-downhill method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Synthesis of Planar Stephenson III Six-Link Mechanism for Function Generation Based on Hyper-Chaos Newton Downhill Method

The problem synthesis of planar Stephenson Ⅲ six-link mechanism for function generation all the while is a research difficult puzzle in mechanism fields. The hyper-chaos Newton downhill method finding all real solutions of nonlinear equations was proposed that is based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions. The numerical example of synthesis of planar Stephenson Ⅲ six-link mechanism for function generation with 11 accurate points was given. The result shows that most real solutions have been quickly obtained. The number of solutions is the most and the time-spending is the less than existing any other method and it proves the correctness and validity of the proposed method.

Forward Displacement Analysis of Non-Plane Two Coupled Degree Nine-Link Barranov Truss Based on Hyper-Chaotic Newton Downhill Method

The hyper-chaotic Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 33th non-plane 2-coupled–degree nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with hyper-chaotic sequences, hyper-chaotic Newton-downhill method based on utilizing hyper-chaotic discrete system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given. Comparison was also done with other finding solution method. The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

A fast synthesis algorithm of adaptive beams for smart antennas

AbstractAn amplitude approaching algorithm (AAA) for the pattern synthesis of adaptive arrays is presented in this paper. Furthermore, the algorithm is amended by the Newton downhill method. Simulations show that the main lobe and side lobe can be controlled efficiently, and the algorithm converges more quickly and steadily. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 503–507, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10804

Small-signal theory of a ridge-loaded ring-plane travelling-wave tube

The travelling-wave tube is an important high-power microwave amplifier. The ridge-loaded ring-plane slow-wave structure can provide high output power in a relatively broader bandwidth. Starting from the beam-present wave equation, the dispersion relation for the interaction between the electron beam and the symmetrical mode propagating in this slow-wave circuit is obtained in this paper by means of the variational method. Making use of the Newton downhill method the numerical results of small-signal gain and phase velocity are given. The influences of the radius and current of the electron beam, the acceleration voltage and the geometrical dimension of the slow-wave structure on the smallsignal gain and phase velocity are discussed. The instantaneous operating bandwidth can be estimated from the diagrams of the relation between the gain and the frequency. This paper provides a theoretical basis for designing the ridgeloaded ring-plane travelling-wave tube.