Complicated Numerical Calculations Research Articles

Energy-saving mechanism of series–parallel hybrid transmissions — A dynamic programming method based on matrix operations

The economic evaluation of hybrid transmission is a complicated numerical calculation problem in the finite time domain. Currently, employing traditional dynamic programming methods to evaluate a single design scheme consumes a lot of time, making it arduous to effectively compare performance disparities across various design schemes. This paper introduces a dynamic programming method based on matrix operations, enabling the determination of maximum energy-saving potential in hybrid transmission while reducing the evaluation time for a single design scheme from hours to less than 10 s. It unifies the design variables, constraints, and optimization objectives for multi-gear and multi-mode series–parallel hybrid transmissions (MGMM-SPHTs) during economic evaluation. By solving the performance of tens of thousands of design schemes, it is found that increasing the number of engine direct drive gears from 1 to 2 enhances the economy and power performance of series–parallel hybrid transmissions. For the optimal design scheme of Type-B vehicles, this enhancement results in a 1.712% increase in energy-saving efficiency and a 30.5% increment in power performance. Furthermore, this paper elucidates the adaptive relationship between MGMM-SPHTs and different vehicle types, revealing the energy-saving mechanisms under varied design schemes. This paper holds the promise of offering theoretical underpinnings and methodological instruments for selecting technical routes and optimizing design parameters for MGMM-SPHTs.

A New Design Method for Class-E Power Amplifiers Using Artificial Intelligence Modeling for Wireless Power Transfer Applications

This paper presents a new approach to simplify the design of class-E power amplifier (PA) using hybrid artificial neural-optimization network modeling. The class-E PA is designed for wireless power transfer (WPT) applications to be used in biomedical or internet of things (IoT) devices. Artificial neural network (ANN) models are combined with optimization algorithms to support the design of the class-E PA. In several amplifier circuits, the closed form equations cannot be extracted. Hence, the complicated numerical calculations are needed to find the circuit elements values and then to design the amplifier. Therefore, for the first time, ANN modeling is proposed in this paper to predict the values of the circuit elements without using the complex equations. In comparison with the other similar models, high accuracy has been obtained for the proposed model with mean absolute errors (MAEs) of 0.0110 and 0.0099, for train and test results. Moreover, root mean square errors (RMSEs) of 0.0163 and 0.0124 have been achieved for train and test results for the proposed model. Moreover, the best and the worst-case related errors of 0.001 and 0.168 have been obtained, respectively, for the both design examples at different frequencies, which shows high accuracy of the proposed ANN design method. Finally, a design of class-E PA is presented using the circuit elements values that, first, extracted by the analyses, and second, predicted by ANN. The calculated drain efficiencies for the designed class-E amplifiers have been obtained equal to 95.5% and 91.2% by using analyses data and predicted data by proposed ANN, respectively. The comparison between the real and predicted values shows a good agreement.

Practical estimation method for extreme value distribution of von Mises stress in ship structure

This study presents a practical method for estimating the extreme value distribution of von Mises stress for ship structural strength evaluations. The previous methods of calculating this distribution require somewhat complicated numerical calculations, such as multi-dimensional integration. In contrast, the proposed method is based on an asymptotic approximation and can be easily calculated in a similar way to the conventional linear statistical prediction. A closed expression was derived in the case of stress components which have non-zero mean value. The formula is derived under approximations that reflect realistic stress conditions when ships are under severe sea states. Through a structural analysis of a whole ship, it was comprehensively verified that the proposed method has sufficiently high accuracy for structural strength evaluation. Furthermore, a parametric analysis was conducted to clarify its limit of applicability.

Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems

The article proposes and analyzes the optimal error estimates of a second-order backward difference formula (BDF2) numerical scheme for the semi-linear parabolic interface problems. The partially penalized immersed finite element (PPIFE) methods are used for the spatial discretization to resolve discontinuity of the diffusion coefficient across the interface. The classical extrapolation method is adopted to treat the nonlinear term, which effectively avoids the complicated numerical calculation of the nonlinearity. Our error analysis is based on the corresponding time-discrete system, which neatly splits the error into two parts: the temporal discretization error and the spatial discretization error. Since the spatial discretization error is independent of time step size τ, we can unconditionally derive the optimal error estimates in both L2 norm and semi-H1 norm, while previous works always require the coupling condition of time step and space size. Numerical experiments are given to confirm the theoretical analysis.

Calculating critical temperature and critical exponents by self-similar approximants

Abstract Self-similar approximation theory allows for defining effective sums of asymptotic series. The method of self-similar factor approximants is applied for calculating the critical temperature and critical exponents of the O(N)-symmetric φ 4 field theory in three dimensions by summing asymptotic ε expansions. This method is shown to be essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

Seismic performance assessment of corroded RC columns based on data-driven machine-learning approach

Corrosion of steel reinforcements is a major factor that will adversely affect the seismic performance of the reinforced concrete (RC) columns. This paper investigates the application of machine learning (ML)-based approach for seismic failure mode and maximum bearing capacity prediction for corroded RC columns. A comprehensive database consisting of 180 cyclic tests of corroded RC columns are collected. Six ML algorithms including three single learning methods (k-Nearest neighbors, Decision tree, Artificial neural network) and three ensemble learning methods (Random forest, AdaBoost, CatBoost) are selected to develop the predictive model. The performance of the six models are evaluated and the application of ML-based approaches for life-cycle seismic performance assessment of RC column is demonstrated with a case-study column. The results show that the Random forest and CatBoost models have the best performance for seismic failure mode prediction with an accuracy of 89%. The best model for bearing capacity prediction is the CatBoost model which has a R2 of 0.92, and the CatBoost model is superior to the traditional mechanism-based code models for bearing capacity prediction. The ML-based models can conveniently predict the seismic failure mode and bearing capacity of RC columns in its life-cycle context without complicated numerical simulations or theoretical calculations.

Self-similar sequence transformation for critical exponents

Self-similar sequence transformation is an original type of nonlinear sequence transformations allowing for defining effective limits of asymptotic sequences. The method of self-similar factor transformations is shown to be regular. This method is applied for calculating the critical exponents of the O(N)-symmetric φ4 theory in three dimensions by summing asymptotic ε expansions. It is shown that this method is straightforward and essentially simpler than other summation techniques involving complicated numerical calculations, while enjoying comparable accuracy.

Analytical quantitative semiclassical approach to the Lo Surdo–Stark effect and ionization in two-dimensional excitons

Using a semi-classical approach, we derive a fully analytical expression for the ionization rate of excitons in two-dimensional materials due to an external static electric field, which eliminates the need for complicated numerical calculations. Our formula shows quantitative agreement with more sophisticated numerical methods based on the exterior complex scaling approach, which solves a non-hermitian eigenvalue problem yielding complex energy eigenvalues, where the imaginary part describes the ionization rate. Results for excitons in hexagonal boron nitride and the $A-$exciton in transition metal dichalcogenides are given as a simple examples. The extension of the theory to include spin-orbit-split excitons in transition metal dichalcogenides is trivial.

A unifying identity for the work of cluster formation in heterogeneous and homogeneous nucleation theory.

A unifying identity is derived relating the reversible work of cluster formation (W) and its molecular number content (n) and surface work (Φ) components, each ratioed to the corresponding values for a spherical capillary drop of critical size in classical nucleation theory. The result is a relationship that connects these ratios: fW = -2fN + 3fS, where fW = W/W*CNT, fN = n/n*CNT, and fS = Φ/Φ*CNT. Shown to generalize two early thermodynamic relationships of Gibbs, the new result is demonstrated here for Fletcher's model of heterogeneous nucleation, resulting in a unified treatment of condensation on flat and curved substrates and smooth passage to the homogeneous limit. Additional applications are made to clusters of non-critical as well as critical size and to a molecular-based extension of classical nucleation theory based on the Kelvin relation. The new identity serves as a consistency check on complicated theoretical expressions and numerical calculations and can be used to guide the construction of theory and interpretation of measurements.

A Simple Fuzzy PI Control of Dual-Motor Driving Servo System

Aiming at the control problem of dual-motor driving servo system, in order to avoid the complicated numerical calculation of complicated control algorithm, we presented a simple fuzzy PI controller for the first time. Firstly, we explained system control principle. In view of the shortcomings of current-error negative feedback, we used speed-error negative feedback synchronous driving control strategy. Then we theoretically analyzed dual-motor synchronous driving system in detail. We proposed the conditions of dual-motor driving servo system synchronous operation for step signal and ramp signal, respectively. Finally, we presented a simple fuzzy PI controller, by combining fuzzy controller with PI controller. We analyzed the fuzzy PI control system and found it was stable. We considered two cases in simulation tests comparing fuzzy PI control with PI control. Simulation results show that fuzzy PI control has better adaptability than conventional PI control, validating the effectiveness and efficiency of the proposed control strategy.

Comparison of Rigorous Design Procedure with Approximate Design Procedure for Variable Sampling Plans Indexed by Quality Loss

Traditional acceptance sampling plans have focused on the proportion of nonconforming items as an attribute criterion for quality. In today’s modern quality management under high quality production environments, the reduction of the deviation from a target value in a quality characteristic has become the most important purpose. In consequence, various inspection plans for the purpose of reducing the deviation from the target value in the quality characteristic have been investigated. In this case, a concept of the quality loss evaluated by the deviation from the target value has been accepted as the variable evaluation criterion of quality. Further, some quality measures based on the quality loss have been devised; e.g. the process loss and the process capability index. Then, as one of inspection plans based on the quality loss, the rigorous design procedure for the variable sampling plan having desired operating characteristics (VS-OC plan) indexed by the quality loss has been proposed by Yen and Chang in 2009. By the way, since the estimator of the quality loss obeys the non-central chi-square distribution, the rigorous design procedure for the VS-OC plan indexed by the quality loss is complicated. In particular, the rigorous design procedure for the VS-OC plan requires a large number of the repetitive and complicated numerical calculation about the non-central chi-square distribution. On the other hand, an approximate design procedure for the VS-OC plan has been proposed before the proposal of the above rigorous design procedure. The approximate design procedure for the VS-OC plan has been constructed by combining Patnaik approximation relating the non-central chi-square distribution to the central chi-square distribution and Wilson-Hilferty approximation relating the central chi-square distribution to the standard normal distribution. Then, the approximate design procedure has been devised as a convenient procedure without complicated and repetitive numerical calculations. In this study, through some comparisons between the rigorous and approximate design procedures, the applicability of the approximate design procedure has been confirmed.

대용량 에너지 저장장치용 2세대 고온 초전도 코일의 특성해석

대용량 초전도 에너지저장장치(Superconducting Magnetic Energy Storage, SMES)용 초전도 권선을 제작하기 위해서는 높은 자장특성을 가고 있는 2세대 고온초전도 (2nd Generation High-Temperature Superconductor, 2G HTS) 선재를 사용하는 것이 효율적이다. 자기에너지 저장 밀도를 높이기 위해서는 권선에 높은 전류밀도를 인가해야 하는데, 도체의 평면에 수직 방향으로 인가되는 자속밀도가 커지면 임계전류가 작아지는 2세대 HTS 선재의 특성상 토로이드 형태의 권선을 구성하는 것이 일반적이다. 이러한 고온초전도 권선을 설계하기 위해서는 권선 특성의 정확한 해석이 필요한데 이를 위해 유한요소법을 사용한 프로그램을 이용하여 해석이 가능하나 토로이드 형태의 권선은 대칭성의 문제로 3차원 해석을 해야만 하며, 이는 모델링에 많은 어려움과 높은 컴퓨터 사양, 그리고 매우 긴 계산 소요시간이 필요함을 의미한다. 본 논문에서는 이러한 문제점을 해결하기 위해 분석적이고 통계적으로 고온 초전도 코일에서 작용하는 최대 수직자장과 저장된 에너지를 결정하는데 이해하기 쉽고 효율적으로 계산하는 방법을 제시했다. 이 방법은 현저한 시간단축과 효율적인 설계를 할 수 있는 새로운 계산 방법으로 기존의 유한요소법에 의해 소요되는 계산 시간에 비해 1/1000정도로 계산시간 단축을 할 수 있었다. Large scale superconducting magnetic energy storage (SMES) system requires very high magnetic energy density in its superconducting coils to enhance the energy capacity and efficiency of the system. The recent high temperature superconducting (HTS) conductors, so called 2G conductors, show very good performance under very high magnetic field so that they seem to be perfect materials for the large scale SMES coils. A general shape of the coil system with the 2G HTS conductor has been a tor oid, because the magnetic field applied perpendicularly to the surface of the 2G HTS conductor could be minimized in this shape of coil. However, a toroid coil requires a 3-dimensional computation to acquire the characteristics of its critical current density - magnetic field relations which needs very complicated numerical calculation, very high computer specification, and long calculation time. In this paper, we suggested an analytic and statistical calculation method to acquire the maximum magnetic flux density applied perpendicularly to the surface of the 2G HTS conductor and the stored energy in the toroid coil system. Although the result with this method includes some errors but we could reduce these errors within 5 percent to get a reasonable estimation of the important parameters for design process of the HTS toroid coil system. As a result, the calculation time by the suggested method could be reduced to 0.1 percent of that by the 3-dimensional numerical calculation.

Effects of disk surface roughness on static flying characteristics of air bearing slider by using a combined method of Reynolds equation and rough disk surface

Reynolds equation was modified with adding the surface roughness parameters to analyze the effects of disk surface roughness on the static flying characteristic of an air bearing slider. However, the modification demands the complicated mathematical expressions and related knowledge of physics and mathematics. In this paper, a combined method of Reynolds equation without introducing the roughness parameters and rough disk surface is proposed to investigate the effects of disk surface roughness on the static flying characteristics of an air bearing slider, it is different from those models of modified Reynolds equation introducing the disk surface roughness used by many researchers. More importantly, this method avoids the complicated numerical calculation resulted from the mathematical expressions including the Peklenik parameter $$\gamma$$ź and roughness Ra. By using an Ω air bearing slider, we investigated the effects of disk surface roughness on the static flying characteristics of this slider, the results show that the Peklenik parameter $$\gamma$$ź and roughness Ra have a significant influence on the pressure distribution, the load carrying capacity and the location of the pressure centre.

Multivariable Generalized Predictive Control Design: Application for Couple of DC Motors

The paper presents method for design stable generalized predictive controller in the frequency domain and its application on model of couple DC motors. The frequency domain predictive methods are easier for application and can improve performance of control circuit. This way the presented predictive control method can be used in practice on real devices like FPGA without needs of complicated numerical calculations. Numerical results based on identification of real process are given to illustrate the effectiveness of the proposed method

Comparison of Analytical Solutions to Evaluate Aquifer Response to Arbitrary Stream Stage

Groundwater table response to arbitrarily varied stream stage is a practical engineering issue related to stream-aquifer interaction processes. A one-dimensional (1D) linear Boussinesq equation is invariably used in the interpretation. Previous studies have emphasized the employment of convolution integration and pulse or function fitting methods to solve this problem. Consequently, complicated mathematical derivations and numerical calculations are involved during an analysis. In this paper, we transformed the previously published solutions into an easily solved formation to investigate this problem. Then the solution is solved based on the trapezoidal method and applied in cases. The solution fits favorably with the previous classic solutions in the simulations of groundwater table responses to sinusoidal, linear, and unit step rise varied stream stages. This approach was also applied to interpret groundwater table fluctuations induced by typical flood waves and field measured stream stage fluctuations. The developed approach performs well compared with those solved numerically by function fitting methods and modular finite-difference flow model (MODFLOW). This analytical solution potentially provides a rapid and simple way to estimate aquifer responses to any type of stream stage variation.

APPROXIMATE MODEL FOR UNIVERSAL BROADBAND ANTIREFLECTION NANO-STRUCTURE

In this work, we investigate the efiect of broadband antire∞ection of a medium by a layer of embedded nano-cavities arranged near the surface. It is shown that this structure is versatile and allows near 100% transmittance in a wide spectral range practically for any dielectric material. The approximate model of nano-structured layer is suggested that allows to determine the parameters of the system necessary for achieving antire∞ection of any a priori given media without complicated numerical calculations. The transmission spectrum of a medium modifled by such a structure is entirely deflned by a radius and a depth of bedding of the nano-porous layer.

Optimum estimation of missing values in randomized complete block design by genetic algorithm

Missing data are a part of almost all research, and we all have to decide how to deal with it from time to time. There are a number of alternative ways of dealing with missing data. The problem of handling missing data has been treated adequately in various real world data sets. Several statistical methods have been developed since the early 1970s, when the manipulation of complicated numerical calculations became feasible with the advancement of computers. The purpose of this research is to estimate missing values by using genetic algorithm (GA) approach in a randomized complete block design (RCBD) table and to compare the computational results with three other methods, namely, particle swarm optimization (PSO), Artificial Neural Network (ANN), approximate analysis and exact regression method. Furthermore, 30 independent experiments were conducted to estimate missing values in 30 RCBD tables by GA, PSO, ANN, exact regression and approximate analysis methods. Computational results indicated that the best answer (in the last 10-chromosome population) obtained by GA is frequently the same as the missing value, with the mean value being close to the missing observation. It is concluded that GA provides much better estimation than the other methods. The superiority of GA is shown through lower error estimations and also Pearson correlation experiment. Therefore, it is suggested to utilize GA approach of this study for estimating missing values for RCBD.

Landau Model of the Phase Transitions for Description of Commensurate Polar Smectic Structures

Calculations of polar structures with frustration interaction are often difficult and require complicated numerical calculations. A simple approach based on Landau model is given to describe the manifold of commensurate structures. The power of the used method is shown on the example of polar liquid crystals. Our approach allows to perform analytical study that shows the nature of formation of different structures. In spite of its simplicity this approach is fruitful. Fluctuation of the modulus of the order parameter leads to decrease in the energy and formation of stable phases with six, three, five and ten layer periodicity. Results of analytical studies correlate with experimental data and numerical calculations.

Scaling to generalize a single solution of Richards' equation for soil water redistribution

Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of water flow in unsaturated soils. In this study, a new method is developed to scale RE for the soil water redistribution process. Two similarity conditions are required: similarity in the shape of the soil water content profiles as well as of the water flux density curves. An advantage of this method is that it is not restricted to a specific soil hydraulic model - hence, all such models can be applied to RE. To evaluate the proposed method, various soil textures and initial conditions were considered. After the RE was solved numerically using the HYDRUS-1D model, the solutions were scaled. The scaled soil water content profiles were nearly invariant for medium- and fine-textured soils when the soil profile was not deeply wetted. The textural range of the soils in which the similarity conditions are held decreases as the initial conditions deal with a deeply wetted profile. Thus, the scaling performance was poor in such a condition. This limitation was more pronounced in the coarse-textured soils. Based on the scaling method, a procedure is suggested by which the solution of RE for a specific case can be used to approximate solutions for many other cases. Such a procedure reduces complicated numerical calculations and provides additional opportunities for solving the highly nonlinear RE as in the case of unsaturated water flow in soils.

분포형 강우유출모형 병렬화 처리기법 적용

Distributed Models have relative weak points due to the amount of computer memory and calculation time required for calculating water flow using a numerical analysis based on kinematic wave theory when compared to the conceptual models used so far. Typically, the distributed models have been mainly applied to small basins. It was necessary to decrease the resolution of the grid to make it applicable for large scale watersheds, and because it would take up too much time to calculate using a higher resolution. That has been one of the more difficult factors in applying the model for actual work. In this paper, MPI (Message Passing Interface) technique was applied to solve the problem of calculation time as it is one of the demerits of the distributed model for performing physical and complicated numerical calculations for large scale watersheds. The comparison studies were performed a single domain and a divided small domain in Yongdam Dam watershed in case of typoon `Ewiniar` at 2006. They were compared to analyze the application effects of parallelization technique. As a result, a maximum of 10 times the amount of calculation time was saved but keeping the level of quality for discharge by using parallelization code rather than a single processor.