Iterative Calculation Research Articles

The mechanical properties of Al3Sc single crystal investigated by nanoindentation using Hertzian elasticity theory method and Oliver-Pharr method

The crystal structure, orientation, reduced modulus, and hardness of Al3Sc single crystal were studied using X-ray diffraction (XRD), electron backscatter diffraction (EBSD) and nanoindentation techniques, combined with Hertzian elastic theory method (Hertz) and Oliver-Pharr method (O&P). Millimeter-sized Al3Sc single crystals were prepared using quasi-equilibrium solidification of hypereutectic Al-15(wt %) Sc alloy. The XRD results showed that the samples were composed of L12-Al3Sc and Al phases. The EBSD and nanoindentation results showed that for five Al3Sc single crystals with different orientations, the reduced moduli measured by Hertz method were 146.6 ± 0.4–148.3 ± 0.2 GPa; while measured by O&P method they were 147 ± 2–150 ± 3 GPa. The corresponding hardnesses were varied between 3.8 ± 0.1 and 3.9 ± 0.1 GPa. The Poisson's ratio and elastic constants were determined through iterative calculation based on the relationship between the reduced modulus and Young’s modulus at various orientations. The polycrystal elastic properties, bulk modulus, shear modulus and Young's modulus, were determined. The elastic constants c11, c12, and c44 were 179.2 ± 0.4, 44.1 ± 0.1, and 68.3 ± 0.3 GPa, respectively; the Poisson's ratio was 0.196 ± 0.001. The Young's modulus of five Al3Sc single crystals oriented in different directions was in the narrow range 161–164 GPa. The anisotropy factor of Al3Sc crystal was 1.011 ± 0.002, confirming that it is elastically isotropic. These results provide fundamental information for the research and development of the Al3Sc intermetallic compound and related alloys in future.

A dynamic one-dimensional model for simulating unsteady air-water stratified flow in sewer pipes.

Ventilation is paramount in sanitary and stormwater sewer systems to mitigate odor problems and avert pressure surges. Existing numerical models have constraints in practical applications in actual sewer systems due to insufficient airflow modeling or suitability only for steady-state conditions. This research endeavors to formulate a mathematical model capable of accurately simulating various operational conditions of sewer systems under the natural ventilation condition. The dynamic water flow is modeled using a shock-capturing MacCormack scheme. The dynamic airflow model amalgamates energy and momentum equations, circumventing laborious pressure iteration computations. This model utilizes friction coefficients at interfaces to enhance the description of the momentum exchange in the airflow and provide a logical explanation for air pressure. A systematic analysis indicates that this model can be easily adapted to include complex boundary conditions, facilitating its use for modeling airflow in real sewer networks. Furthermore, this research uncovers a direct correlation between the air-to-water flow rate ratio and the filling ratio under natural ventilation conditions, and an empirical formula encapsulating this relationship is derived. This finding offers insights for practical engineering applications.

Application graph theory to evaluate the stability of landslide slopes

Evaluation of the stability of slopes is a complex and important engineering task, the solution of which requires the analysis of a significant number of factors. Many different methods of slope stability calculation have been developed to solve this type of problem. However, two groups of methods - limit equilibrium methods and the finite element method (FEM) - have become the most widely used. However, these methods have certain disadvantages. Limit equilibrium methods are limited by the assumptions used during the calculation, including the hypothesis of a solid compartment, which does not allow analyzing the stress-strain state. The FEM of the elements does not make it possible to unambiguously localize the sliding surface of the slope, and the determination of the stability coefficient using the method of reducing the strength of the soil requires a large number of complex iterative calculations. The methods and approaches of graph theory can be used precisely to combat the shortcomings of FEM. The paper examines the basics of graph theory. The main methods of specifying graphs, as well as certain types of graphs with an indication of their key features, are presented. The concept of isomorphism of graphs and some features of their graphical representation are revealed. The article presents the basic idea of using graph theory to calculate the stability of slopes. The main questions that must be solved when applying graph theory to the given type of problem are outlined. Two methods of converting a mesh of finite elements into a graph are considered in detail. The advantages and disadvantages of the proposed methods are analyzed. The transformation of the calculation scheme of an imaginary slope with a given geometry, which was simulated in the LIRA-SAPR software complex, into graphs using the above methods is demonstrated. An overview of the approaches that can be used to create a graph weight function is given.

Analytical solution to partial least squares

Partial least squares (PLS) is a widely used multivariate statistical technique, which can be used in neuroimaging, process monitoring, economics, etc. Because the standard PLS is trained by nonlinear iterative partial least squares (NIPALS) algorithm, which can only obtain the numerical solution rather than the analytical solution. Therefore, it is hard for the subsequent theoretical analysis in PLS and the iterative optimization process is computationally intensive. This paper proposes an analytical solution to take the place of NIPALS. This determination meaningfully contributes to future theoretical analysis of PLS. In addition, the analytical solution demonstrates that the selection of initial vector in NIPALS does not affect the PLS training results. Moreover, the analytical solution avoids the multiple iterative calculations, so the divergence of the calculation process will be avoided and the computation burden will be reduced significantly.

Optimizing power sharing and voltage control in DC microgrids using a novel adaptive droop control strategy based on current consensus algorithm

In DC microgrids, a contradiction between power equalization and bus voltage control exists under conventional droop control. To address this issue, this study proposes a current consensus algorithm-based adaptive droop control for hierarchical controlled DC microgrids. The strategy includes primary, secondary, and current-consensus algorithms. In the primary and secondary control layers, an improved droop control strategy is realized, where the secondary layer provides adaptive parameters for primary control. Also, a current consensus algorithm is suggested to ensure equal current sharing, where the iterative calculation results are sent as the input for two control layers. Based on the novel strategy, a small signal analysis is carried out to investigate the relationship between system stability and controller parameters. Finally, simulation and experiments are conducted to assess the effectiveness of the proposed control strategy in complex operating conditions such as resistive load step-change and plug-and-play situation. Experiment and simulation results indicate that the novel control strategy guarantees accurate bus voltage control with a maximum steady-state error of 1.58 % and simultaneously achieves power equalization regardless of line impedance differences and the abrupt change of system status. Moreover, the comparative experiment between the traditional droop control and the proposed strategy verifies the superiority of this novel method.

Calculation of second-order bearing capacity of members subjected to axial load and biaxial bending

The second-order effects of biaxial bending members involve dual non-linear problems, namely material nonlinearity and geometric nonlinearity. These problems typically require iterative calculations and cannot be solved manually. To address this issue, this paper founded upon the strain-based resolution of stress and internal forces, deduces the formula for calculating the load-bearing capacity of the cross-section. The elastoplastic second-order deformation is then calculated at the member level, and the final result is presented in the form of a dimensionless nomogram for calculating the second-order biaxial bending members. In this paper, the limit range of section strain is determined based on the constitutive relationship of concrete and reinforcement. This range is divided into three limited strain areas, which enable the calculation of section bearing capacity and limit curvature, and subsequently the second-order bearing capacity of the member. The results are in good agreement with experimental data. The dimensionless nomogram in this paper considers the complete parabolic and rectangular of concrete stress-strain relationship and the ideal elastoplastic constitutive relationship of reinforcement and the second-order effect. It does not require iteration. It can quickly calculate the reinforcement or check the section bearing capacity by hand. It can be used to check the calculation results of engineering software and provides ideas for the design method of member subjected to axial load and biaxial bending based on seismic restoring force.

Stochastic seismic acoustic impedance inversion via a Markov-chain Monte Carlo method using a single GPU card

Seismic acoustic impedance inversion plays an important role in understanding subsurface structures and obtaining subsurface properties. The stochastic approach is one of the methods used for impedance inversion, and it aims to produce more reliable results by accounting for modeling uncertainty. Stochastic inversion represents the uncertainty of a subsurface model as a probability distribution and uses this distribution to estimate model parameters. In this study, seismic acoustic impedance inversion was performed using a Markov-chain Monte Carlo approach, which is a sampling method used in the stochastic process. Utilizing Bayesian inference based on prior information and observed data, we implemented acceptance probabilities and performed acoustic impedance inversion for field data through iterative calculations. We employed a single GPU card to execute the inversion algorithm and conducted a comparative analysis with the results obtained using a cluster composed of multiple CPU cores. Through a computational speed analysis, the efficiency of the algorithm using a GPU was verified, while uncertainty analysis was employed for algorithm validation. Through these analyses, we confirmed the feasibility of applying our developed GPU algorithm to tasks that require the inversion of extensive data, such as high-resolution seismic exploration and CO2 storage monitoring.

Damage Identification of Full-Scale Steel Truss Structure Based on Model Condensation and Mean-Value Normalization Regularization Techniques

Structural health monitoring and damage identification aim to detect the internal damage and evaluate the health conditions of the practical engineering structure, which has been the most popular research field for several decades. The sensitivity-based method incorporated with the regularization techniques is the classical and useful approach, and it can obtain accurate damage detection results. However, with the development of civil engineering structures, this classical method faces two problems: one is it is only applied to simple structures rather than full-scale structures, and second is the iterative calculation efficiency is lower. Therefore, aiming at these drawbacks, the two improvement strategies have been introduced to the original method for its enhancement in the application potential and computational efficiency. The proposed method has been verified based on two examples, i.e., a numerical steel truss with 144 elements and a full-scale experimental steel truss with 160 elements. The results prove that the proposed method has better efficiency and good application potential in the practical full-scale engineering structure.

Internal Congruences Modulo Powers of 5 for Partition k-Tuples with Odd Parts Distinct

Let pod − k ( n ) denote the number of partition k-tuples of n where the odd parts in each partition are distinct. By utilizing some q-series manipulations and iterative computations, we derive dozens of internal congruences modulo powers of 5 for pod − k ( n ) with 1 ≤ k ≤ 4 . For example, one result proved in the present paper is that for any n ≥ 0 and 2 ≤ m ≤ 12 , pod − 4 ( 5 N m n + 5 N m + 1 2 ) ≡ pod − 4 ( 5 m n + 5 m + 1 2 ) ( mod 5 m ) , where N m = 2 × 5 m − 2 + m . Further, we conjecture that these internal congruences exist in the corresponding internal congruence families modulo any powers of 5.

Dynamic iterative correction algorithm for designing diffractive optical elements

When utilizing the Gerchberg–Saxton (GS) algorithm to design diffractive optical elements, correction coefficients are introduced to improve the quality of the design results. The main design idea is to correct the target information dynamically during the iterative calculation process. The effectiveness of the proposed method is demonstrated through the verification of beam shaping and phase-type hologram designs. Compared to the traditional GS algorithm, the results of beam shaping show that the light intensity nonuniformity and the root-mean-square error (RMSE) of the shaped spot are reduced by an order of magnitude. The results of phase-type holograms show that the reconstructed image’s peak signal-to-noise ratio (PSNR) is improved by about 12 dB. Finally, the paper also discusses the selection of correction coefficients, providing insights into the selection of optimal design correction coefficients. The simulation and experimental results show that the improved algorithm proposed in this paper is not only simple in design but also highly efficient in obtaining a high-quality phase structure, which is of great help in designing high-quality diffractive optical elements.

Performance improvement evaluation of latent heat energy storage units using improved bi-objective topology optimization method

Latent heat thermal energy storage (LHTES) based on phase change materials is one of the key technologies to improve energy utilization efficiency and alleviate the mismatch between energy supply and demand. Heat storage capacity and charging/discharging rate are two core factors that determine the comprehensive performance of LHTES units. So a bi-objective transient topology optimization(TO) model is established to freely evolve the optimal structure and volume fraction of LHTES fins to maximize the heat transfer rate based on ensuring high storage capacity. The bi-objective optimization function coupling storage capacity and heat transfer rate is constructed by normalized SAW model. The TO model is formulated using variable density-based design variables of grid cells in physical governing equations, objective functions and constraints. Helmholtz PDE filtering and hyperbolic tangent projection methods are employed to achieve high-precision optimization solutions. Complex transient multi-physics field and bi-objective iterative calculations are performed using the transient adjoint-based sensitivity analysis method and GCMMA algorithm. Results demonstrate that the physical field dynamics response of the design variables at each iteration can more clearly exhibit the evolutionary direction and mechanism of seeking optimal structures. The Pareto frontier indicates TO model responds significantly to the changes in the bi-objective weight ratio ω1:ω2, which also reveals the physical mechanism of the trade-off game among fin topology formation, state parameters distribution and objective changes. Optimal configurations and its performance parameters change regularly with ω1:ω2 decreasing, and has an demonstrable performance mutations occurring at ω1 = 0.65(ω2 = 0.35). The scattered distribution and uniform multi-branch structure of TO fins are key factors in regulating the physical field state. Therefore, TO-fins LHTES exhibits extremely high heat transfer rate, and the charging/discharging time of traditional trapezoid fin LHTES is approximately three times longer than that of TO-fins LHTES under ω1:ω2 = 0.65:0.35.

Impact of time resolution on estimation of energy savings using a copula-based calibration in UBEM

Urban Building Energy modelling (UBEM) has emerged in the last decade as an important tool to accelerate energy transition in the building sector. To fulfil one of its major purposes - forecasting energy savings for potential energy conservation measures at an urban scale, several challenges are still to be addressed. Two key challenges include: 1) the need to calibrate models with a large number of unknown parameters across numerous buildings (either individually or through archetype representation); 2) the limited availability of high-resolution measured data, which raises concerns about calibrated models based solely on yearly values for accurate energy savings forecast. This study addresses these challenges using a case study of 35 buildings in a district in Stockholm, Sweden. Firstly, a new iterative Approximate Bayesian Computation (ABC) method for calibration is proposed, incorporating a copula-based sampling process at each iteration. Secondly, the new calibration process is applied with three different time resolutions to examine the impact of data resolution on forecasted energy usage, particularly when applied to a classical energy conservation measure. Results demonstrate the efficiency of the new method across the 35 buildings, facilitating the rapid population of a final joint distribution for the nine unknown parameters considered in each building. While the marginals may be strongly influenced by the time resolution, the forecasted energy consumption remains identical across the three analysed time resolutions. However, a noticeable difference is observed when the ECM pertains to a formerly unknown or known parameter.

An Ultralow-Power Real-Time Machine Learning Based fNIRS Motion Artifacts Detection.

Due to iterative matrix multiplications or gradient computations, machine learning modules often require a large amount of processing power and memory. As a result, they are often not feasible for use in wearable devices, which have limited processing power and memory. In this study, we propose an ultralow-power and real-time machine learning-based motion artifact detection module for functional near-infrared spectroscopy (fNIRS) systems. We achieved a high classification accuracy of 97.42%, low field-programmable gate array (FPGA) resource utilization of 38354 lookup tables and 6024 flip-flops, as well as low power consumption of 0.021 W in dynamic power. These results outperform conventional CPU support vector machine (SVM) methods and other state-of-the-art SVM implementations. This study has demonstrated that an FPGA-based fNIRS motion artifact classifier can be exploited while meeting low power and resource constraints, which are crucial in embedded hardware systems while keeping high classification accuracy.

A New Approach to the Use of Non-Primitive Variables in the Mechanics of Continuous Media

The problem of an approximate solution to hydrodynamic problems is the consideration of pressure. To exclude it from the equations, the transition to “non-primitive variables” (vortex and velocity vector divergence) is made. In this case, there are difficulties in the algorithmization of new equations for solving the inverse problem of hydrodynamics and a lot of internal iterative calculations. The object of this study includes equations in “non-primitive” variables. The research methods are based on the transformation without simplifications and assumptions of hydrodynamic equations into a form containing “non-primitive” variables and the demonstration of the possibilities of solving the equations. The GAMS programming language was used for approximate solutions for the first time. The aim of this paper is to demonstrate the possibility of solving the full equations in “non-primitive” variables for various conditions. The results showed the possibility of considering the compressibility of the medium when solving the inverse problem of hydrodynamics; the identity of solutions of the proposed system of equations and equations using the potential; and the possibility of using optimizing programming languages for hydrodynamics problems. The scientific novelty of this research consists of solving the full equations of hydrodynamics with the use of “non-primitive” variables but without the use of the current function. Doi: 10.28991/ESJ-2024-08-02-021 Full Text: PDF

A deep-learning-based compact method for accelerating the electrowetting lattice Boltzmann simulations

Research on the electrowetting of micro- and nanoscale droplets is essential for microfluidics and nanomaterials applications. A lattice-Boltzmann-electrostatics (LBES) method is an effective and accurate method for simulating this process. However, the electric potential field in each time step requires numerous iterative calculations to converge. Therefore, there is a trade-off dilemma between using high-density lattice fields to improve simulation refinement and low-density lattice fields to reduce computing costs in simulations. Fortunately, deep learning techniques can enhance the computing efficiency of electric potential fields, providing an efficient and accurate solution for electrowetting studies in fine-grained fields. In this study, a compact LBES (C-LBES), a computationally accelerated model for an electric potential field with spatiotemporal prediction capability, is developed by combining the advantages of a recurrent residual convolutional unit and a convolutional long-short-term memory unit. A loss function incorporating a geometric boundary constraint term and a self-cyclic prediction scheme are introduced according to the characteristics of the prediction task, which further improves the prediction accuracy of the model and the computing efficiency of the electric potential field. The model is validated with small datasets, and the results show that the C-LBES model with the self-cyclic prediction scheme improves the computing efficiency of the conventional LBES method by a factor of 10 and provides high-precision results when predicting a two-dimensional convergent electric potential field with a lattice size of (110, 160). In the generalization experiments, the average absolute error of the calculated results remains in the same order of magnitude as the accuracy experimental results.

Mapping of Aquifer Characteristics and Reservoir Protective Capacity Variation in Obafemi-Owode Local Government Area, Ogun State South-West Nigeria

Variation of Aquifer potential characteristics and its impacts on the groundwater subsurface protection of the aquiferous zone using electrical resistivity method was carried out at Obafemi-Owode Local Government Area, Ogun State South-West Nigeria with the principal purpose of assessing and rating aquifer protective capacity of the overburden units in the area. Twenty seven (27) vertical electrical sounding (VES) were conducted using Schlumberger configuration with the maximum electrode spacing of 100m at each point using Allied OMHEGA Resistivity meter. The data were interpreted using partial curve matching techniques and computer iteration program using WINRESIST. Parameters such as aquifer resistivity, aquifer thickness, overburden thickness, bedrock resistivity, reflection coefficient and longitudinal unit conductance were calculated and used for evaluating the groundwater yields and vulnerability of the aquiferous zone to contaminant seepages. The range of reflection coefficient is found to be between 0.02 and 0.98 while that of the protective capacity is between 0.00135 and 0.510. Groundwater potentials of the area were categorized as being high (overburden thickness 13m and reflection coefficient less than 0.8); medium (overburden thickness 13m and with reflection coefficient 0.8) and low (overburden thickness < 13m and reflection coefficient. Also, the study area shows a very poor, poor, and moderate protective capacity rating. Seven (7) VES stations have very poor protective capacity, eighteen (18) VES stations shows poor protective capacity and only two (2) VES stations shows a moderate protective capacity rating. Since the illustration the longitudinal conductance revealed the impermeability of the confining layers which is generally ˂ 1.0 Siemens; values ˃1.0 Siemens which indicates zones in which the confined aquifer is subject to protection by the overlying formation materials; these revelations in the study area were possible indications that the groundwater quality status may have been impaired which necessitated the urgent need for the groundwater to be randomly...

On the possibility of changing the trajectory of a projectile or rocket based on aerodynamic impact in the shock wave zone

A physical hypothesis is proposed that it is possible to change the design trajectory of the projectile on the basis of mechanical action on the entire volume of shockwave zones with a unilateral, asymmetric presence of the second projectile. Deviating from the original trajectory results in a positive result when it comes to a defensive task. A new semi-empirical model has been developed and compiled, which allows you to calculate the trajectory of the projectile taking into account the air resistance to movement. In the new model, it is recommended that only four easily detectable values​ ​ be used in upcoming experiments: the initial departure speed , the maximum altitude , the maximum flight range and the full time. The calculation scheme uses iterative calculations. On the basis of which the values ​ ​ of numerical coefficients in the semi-empirical model are specified. The physical idea that external powerful laser radiation can heat the side surface of the projectile and the entire zone of wave jumps of the seal is justified. On one side of the semi-plant, that is, it is one-way heating. The asymmetrical thermal state on both sides of the missile may cause the missile or projectile to deviate from the previously assigned heading. This circumstance is also in favor of the proposed idea.

On the behaviors of solutions of a nonlinear diffusion system with a source and nonlinear boundary conditions

We study the global solvability and unsolvability of a nonlinear diffusion system with nonlinear boundary conditions in the case of slow diffusion. We obtain the critical exponent of the Fujita type and the critical global existence exponent, which plays a significant part in analyzing the qualitative characteristics of nonlinear models of reaction-diffusion, heat transfer, filtration, and other physical, chemical, and biological processes. In the global solvability case, the key components of the asymptotic solutions are obtained. Iterative methods, which quickly converge to the exact solution while maintaining the qualitative characteristics of the nonlinear processes under study, are known to require the presence of an appropriate initial approximation. This presents a significant challenge for the numerical solution of nonlinear problems. A successful selection of initial approximations allows for the resolution of this challenge, which depends on the value of the numerical parameters of the equation, which are primarily in the computations recommended using an asymptotic formula. Using the asymptotics of self-similar solutions as the initial approximation for the iterative process, numerical calculations and analysis of the results are carried out. The outcomes of numerical experiments demonstrate that the results are in excellent accord with the physics of the process under consideration of the nonlinear diffusion system.

Integrated Active and Reactive Power Control Methods for Distributed Energy Resources in Distribution Systems for Enhancing Hosting Capacity

Recently, there has been a significant increase in the integration of distributed energy resources (DERs) such as small-scale photovoltaic systems and wind turbines in power distribution systems. When the aggregated outputs of DERs are combined, excessive reverse current may occur in distribution lines, leading to overvoltage issues and exceeding thermal limits of the distribution lines. To address these issues, it is necessary to limit the output of DERs to a certain level, which results in constraining the hosting capacity of DERs in the distribution system. In this paper, coordination control methodologies of DERs are developed and executed to mitigate the overvoltage and overcurrent induced by DERs, thereby increasing the hosting capacity for DERs of the distribution system. This paper proposes three coordinated approaches of active and reactive power control of DERs, namely Var Precedence, Watt Precedence, and Integrated Watt and Var Control. The Var and Watt Precedence prioritizes reactive power for voltage (Q–V) and active power for current (P–I) to address network congestion, thereby enhancing hosting capacity. Conversely, the Integrated Var and Watt Precedence propose a novel algorithm that combines four control indices (Q–V, P–V, Q–I, and P–I) to solve network problems while maximizing hosting capacity. The three proposed methods are based on the sensitivity analysis of voltage and current to the active and reactive power outputs at the DER installation locations on the distribution lines, aiming to minimize DER active power curtailment. Each sensitivity is derived from linearized power equations at the operating points of the distribution system. To minimize the computation burden of iterative computation, each proposed method decouples active and reactive power and proceeds with sequential control in its own unique way, iteratively determining the precise output control of distributed power sources to reduce linearization errors. The three proposed algorithms are verified via case studies, evaluating their performance compared to conventional approaches. The case studies exhibit superior control effectiveness of the proposed DER power control methods compared to conventional methods when issues such as overvoltage and overcurrent occur simultaneously in the distribution line so that the DER hosting capacity of the system can be improved.

AC-Winding-Resistance Calculation of Toroidal Inductors with Solid-Round-Wire and Litz-Wire Winding Based on Complex Permeability Modeling

This paper has investigated a method for calculating the frequency-dependent winding resistance of toroidal inductor windings with Litz-wire as well as solid-round wire. The modified Dowell’s model is employed to address the effectiveness for inductor windings with the low and high filling factors. To overcome the limitation of this model, especially for a winding densely wound around the core, an alternative approach based on the complex permeability and iterative calculations is proposed. For the calculated AC-resistance factor of five inductors with different numbers of turns, layers with the same wire diameters are compared with that of FEA, and the three air-core toroidal windings are manufactured and tested within the frequency where the self-resonance can be neglected. The proposed model demonstrates the versality of the AC-resistance calculation of both solid- and Litz-wire windings within an error of 15% across a wide range of frequencies up to 1 MHz, compared with FEA.