Multistep Methods Research Articles

Current Profiling Control for Torque Ripple Reduction in the Generating Mode of Operation of a Switched Reluctance Motor Drive

The benefits of utilizing Switched Reluctance Motor (SRM) drives in traction applications can be realized fully by improving the electromagnetic performance of the machine in the generating mode of operation. This is because the generating capability of an SRM drive could be utilized for regenerative braking and also for the machine to generate power for the vehicle while the engine is in operation. In this paper, a current profiling-based control strategy is proposed to reduce the torque ripple in an SRM drive in the generating mode. The reference current profile is determined using a multi-step computation method to minimize torque ripple and maximize the average torque. The reference current profile is derived based on the reference torque command by utilizing the torque–current–angle look up table. The flux linkage characteristics of the SRM are considered when deriving the phase reference current profile. Then, the performance of the proposed profiling method, analytical linear and cubic torque sharing functions (TSFs), and the average torque optimization scheme are compared using simulation results. Finally, an experimental correlation is performed to validate the efficacy of the proposed control scheme.

Comparison of Adams-Bashforth-Moulton and Dormand-Prince Methods in Lengyel-Epstein Reaction Model Forming Zinc Oxide Nanostructures

This study adopts a numerical approach in the Lengyel-Epstein reaction model for forming zinc oxide (ZnO) nanostructures. It aims to determine the optimal approximation technique to analyze the growth of ion concentrations in ZnO nanostructures. For this purpose, ordinary differential equations are developed using the Dormand-Prince method in the Lengyel-Epstein reaction model. The results obtained from this technique are compared with the results obtained from the Adams-Bashforth-Moulton (ABM) method. After a comparative analysis of both methods, the results showed that the ABM method performs better than the Dormand-Prince method. The accuracy and stability of the ABM method are higher than those of the Dormand-Prince method. Furthermore, error analysis for both methods confirms that the results obtained from the former are more optimized. Moreover, this method also validates the results obtained from the experimental procedure by using the aqueous chemical growth (ACG) method to form the nanostructures of ZnO.

A New Methodology for the Development of Efficient Multistep Methods for First–Order IVPs with Oscillating Solutions IV: The Case of the Backward Differentiation Formulae

A theory for the calculation of the phase–lag and amplification–factor for explicit and implicit multistep techniques for first–order differential equations was recently established by the author. His presentation also covered how the approaches’ efficacy is affected by the elimination of the phase–lag and amplification–factor derivatives. This paper will apply the theory for computing the phase–lag and amplification–factor, originally developed for implicit multistep methods, to a subset of implicit methods, called backward differentiation formulae (BDF), and will examine the impact of the phase–lag and amplification–factor derivatives on the efficiency of these strategies. Next, we will show you the stability zones of these brand-new approaches. Lastly, we will discuss the results of numerical experiments and draw some conclusions about the established approaches.

RiskPath: Explainable deep learning for multistep biomedical prediction in longitudinal data.

Predicting individual and population risk for disease outcomes and identifying persons at elevated risk is a key prerequisite for targeting interventions to improve health. However, current risk stratification tools for the common, chronic diseases that develop over the lifecourse and represent the majority of disease morbidity, mortality and healthcare costs are aging and achieve only moderate predictive performance. In some common, highly morbid conditions such as mental illness no risk stratification tools are yet available. There is an urgent need to improve predictive performance for chronic diseases and understand how cumulative, multifactorial risks aggregate over time so that intervention programs can be targeted earlier and more effectively in the disease course. Chronic diseases are the end outcomes of multifactorial risks that increment over years and represent cumulative, temporally-sensitive risk pathways. However, tools in current clinical use were constructed in older data and utilize inputs from a single data collection step. Here, we present RiskPath, a multistep deep learning method for temporally-sensitive biomedical risk prediction tailored for the constraints and demands of biomedical practice that achieves very strong performance and full translational explainability. RiskPath delineates and quantifies cumulative multifactorial risk pathways and allows the user to explore performance-complexity tradeoffs and constrain models as required by clinical use cases. Our results highlight the potential for developing a new generation of risk stratification tools and risk pathway mapping in time-dependent diseases and health outcomes by leveraging powerful timeseries deep learning methods in the wealth of biomedical data now appearing in large, longitudinal open science datasets.

Potato Beetle Detection with Real-Time and Deep Learning

In this study, deep learning methods were used to detect potato beetles (Leptinotarsa decemlineata) on potato plants. High-resolution images were taken of fields with the help of a drone. Since these images were large in size, each one was divided into six equal parts. Then, according to the image, the potato beetles were divided into three classes: adult, late-stage potato beetle, and no beetles. A data set was created with 3000 images in each class, making 9000 in total. Different filters were applied to the images that made up the data set. In this way, problems that may have arisen from the camera in real-time detection were minimized. At the same time, the accuracy rate was increased. The created data set was used with six different deep learning models: MobileNet, InceptionV3, ResNet101, AlexNet, DenseNet121, and Xception. The deep learning models were tested with Sgd, Adam, and Rmsprop optimization methods and their performances were compared. In order to evaluate the success of the models more accurately, they were tested on a second data set created with images taken from a different field. As a result of this study, the highest accuracy of 99.81% was obtained. In the test results from a second field that did not exist in the data set, 92.95% accuracy was obtained. The average accuracy rate was 96.30%.

Rice Yield Estimation Using Machine Learning and Feature Selection in Hilly and Mountainous Chongqing, China

To investigate effective techniques for estimating rice production in hilly and mountainous areas, in this study, we collected yield data at the field level, agro-meteorological data, and Sentinel-2/MSI remote sensing data in Chongqing, China, between 2020 and 2023. The integral values of vegetation indicators from the rice greening up to heading–filling stages were determined using the Newton–trapezoidal integration method. Using correlation analysis and importance analysis of permutation features, the effects of agro-meteorological variables and vegetation index integrals on rice yield were assessed. The chosen characteristics were then combined with three machine learning techniques—random forest (RF), support vector machine (SVM), and partial least squares regression (PLSR)—to create six rice yield estimate models. The results showed that combined vegetation indices were more effective than indices used in separate development phases. Specifically, the correlation coefficients between the integral values of eight vegetation indices from rice greening up to heading–filling stages and rice yield were all above 0.65. By introducing agro-meteorological factors as new independent variables and combining them with vegetation indices as input parameters, the predictive capability of the model was evaluated. The results showed that the performance of PLSR remained stable, while the prediction accuracies of SVM and RF improved by 13% to 21.5%. After feature selection, the inversion performance of all three machine learning models improved, with the RF model coupled with variables selected during permutation feature importance analysis achieving the optimal inversion effect, which was characterized by a coefficient of determination of 0.85, a root mean square error of 529.1 kg/hm2, and a mean relative error of 5.63%. This study provides technical support for improving the accuracy of remote sensing-based crop yield estimation in hilly and mountainous regions, facilitating precise agricultural management and informing agrarian decision making.

Intelligent computing applications to study the tri-hybrid nanofluid past over the stretched surface

In this study, a recurrent neural network with the Levenberg-Marquardt backpropagation algorithm is used to examine the effects of various parameters on cooling mechanisms involving tri-hybrid nanofluid consisting of Al2O3, Cu, TiO2 and magnetohydrodynamic stagnation point flow. This research focus on nanofluid in the existence of an asymmetrically stretched disc in water, which plays an imprortant role for understanding heat transfer in addition to the dynamics of momentum and thermal boundary surface. Transform the complex partial differential system through suitable similarity transformations into the ordinary differential equations for numerical computing. These equations have been solved numerically by using the Adams method in Mathematica to generate datasets for various parameters.The current study demonstrates that the velocity profile rises with higher magnetic, velocity slip, and mass suction parameters. The fluid thermal level tends to decrease with an increase in mass suction parameters, whereas an increase in the magnetic parameter and Eckert number raises the fluid’s thermal level. Furthermore, it is noticed that the flow resistance and internal friction of the fluid are proportional to the viscosity parameter. The proposed scheme has shown its effectiveness in a wide range of scenarios and cases. This was achieved by comparing the mean square error metric for the squeezing flow tri-hybrid nanofluid problem with the obtained results. In addition, various statistical measures like state transitions, fitness assessments, error histograms, and regression analyses, provide further evidence of the solver’s robustness and reliability. The excellent agreement between the reference datasets and refined numerical solutions through the scheme showcases the method’s effectiveness, achieving remarkable accuracy levels ranging from 10-6 to 10-12.

Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules.

We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm, in which the multiplication of Ĥ-k to the reference wave function is replaced by the Fourier transformed multiplication of e-iλĤ, as a function of the integration parameters and the iteration power k for various systems, including H2, LiH, BeH2 and the notorious H4 molecule at square geometry. We further consider the possibility of employing the Gaussian-quadrature rule as an alternate integration method and compared it to the results employing trapezoidal integration. The Q-Inv algorithm is compared to the inverse iteration method using the Ĥ-1 inverse (I-Iter) and the exact inverse by lower-upper decomposition. Energy values are evaluated as the expectation values of the Hamiltonian. Results suggest that the Q-Inv method provides lower energy results than the I-Iter method up to a certain k, after which the energy increases due to errors in the numerical integration that are dependent on the integration interval. A combined Gaussian-quadrature and trapezoidal integration method proved to be more effective at reaching convergence while decreasing the number of operations. For systems like H4, in which the Q-Inv cannot reach the expected error threshold, we propose a combination of Q-Inv and I-Iter methods to further decrease the error with k at lower computational cost. Finally, we summarize the recommended procedure when treating unknown systems.

Numerical integration of mechanical forces in center-based models for biological cell populations

Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method and comparing five different integration methods. We investigate the gain in using single rate time stepping based on local estimates of the numerical errors for the forward and backward Euler methods of first order accuracy and a Runge-Kutta method and the trapezoidal method of second order accuracy. Properties of the analytical solution such as convergence to steady state and conservation of the center of gravity are inherited by the numerical solutions. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for a model system in numerical experiments. We conclude, for example, that the multirate forward Euler method performs better than the Runge-Kutta method for low accuracy requirements but for higher accuracy the latter method is preferred. Only with frequent cell divisions the method with a fixed time step is the best choice.

Accelerating the Speed of Convergence for High-Order Methods to Solve Equations

This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.

A multi-step on-policy deep reinforcement learning method assisted by off-policy policy evaluation

A multi-step on-policy deep reinforcement learning method assisted by off-policy policy evaluation

A 4-Stage Runge-Kutta Type Method for Solution of Stiff Ordinary Differential Equations

In this paper, a 2 step implicit block hybrid linear multistep method was reformulated into a 4-stage block hybrid Runge-Kutta Type Method via the butcher analysis. The method can be used to solve first order stiff ordinary differential equations. A numerical example solved with the proposed method showed a better result in comparison with an existing method.

Microstructure and tribological behavior of Al–TiC composite strips fabricated by a multi-step densification method

This study aims to enhance the tribological properties of automotive applications by examining the effects of TiC content on the microstructure, mechanical properties, and wear behavior. This study investigates the production of Al–TiC composite strips using a novel multi-step densification process combining mechanical alloying and hot rolling with TiC concentrations ranging from 0 to 12 vol%. The novelty of this work lies in its comprehensive approach to developing and analyzing Al–TiC composite strips using a multistep densification method. This study integrates microstructural analysis, mechanical property evaluation, and detailed tribological behavior assessment under different wear loads (5–25 N). A key innovation is the application of the Abbott Firestone method to analyze worn surfaces, providing insights into optimal wear conditions. The study reveals that increasing the TiC content to 12 vol% significantly improves densification, hardness (up to 268.8% increase), and wear resistance (up to 95% improvement at a 5N load). Dry ball-on-flat sliding wear tests at loads of 5–25N demonstrate that TiC particles hindered complete delamination wear in the composite strips. The Abbott Firestone method analysis of worn surfaces indicated an optimal exploitation zone in the Al-6 vol% TiC composite at both low and high wear loads. This comprehensive approach provides valuable insights into optimizing Al–TiC composites for enhanced performance in automotive components that require improved wear resistance.

A high order multi step method for solving system of fractional differential equations

The primary objective of this research paper is to present an advanced method utilizing quadratic interpolation to address the challenges encountered in solving a system of fractional initial value problems. By employing this high-order technique, we aim to improve the accuracy and efficiency of numerical computations associated with fractional differential equations. In our proposed methodology, we strive to enhance the conventional block-by-block approach by mitigating the interdependence of unknown solutions at each block iteration, except for the initial two steps. This modification aims to maintain the favorable stability characteristic inherent in block-by-block schemes, while effectively reducing coupling effects. We meticulously examine the convergence properties of the proposed method and conduct a rigorous analysis of the associated errors that prove that the numerical solution convergence to the true solution with an order of 3 + β when the parameter 0 < β ≤ 1. To substantiate the theoretical claims put forth in our research, we present a series of numerical examples. These examples serve as empirical evidence to demonstrate the effectiveness and practical applicability of the proposed method. The presented method superiority over alternative approaches is highlighted through a comprehensive comparison of the numerical results.

A time-series deep learning model for predicting concrete shrinkage and creep verified with in-situ and laboratory test data

This paper proposed a time series prediction method for concrete shrinkage and creep based on deep learning and the accuracy of the method was verified by field tests. Based on the experiment data in the Northwestern University (NU database), a deep learning model considering the material, environment, and history was constructed by integrating Gated Recurrent Units and Self-Attention mechanism (GSA model). To validated the model, short-term indoor and outdoor field tests of concrete shrinkage and creep were conducted. The proposed GSA model outperformed the LSTM model for both creep and shrinkage predictions. Moreover, the comparison between the GSA model prediction and the outdoor test data indicated that the model can accurately capture the real-time outdoor temperature and humidity variation through historical data. To predict the ten-year shrinkage and creep of concrete, a recursive multi-step method was proposed to extrapolate the short-term predictions of the GSA model. The effectiveness of the recursive multi-step method was validated against the long-term test data in the NU database. Overall, the proposed GSA model demonstrated high accuracy in both short-term and long-term predictions.

Numerical discretization of initial–boundary value problems for PDEs with integer and fractional order time derivatives

This paper is mainly concerned with introducing a numerical method for solving initial–boundary value problems with integer and fractional order time derivatives. The method is based on discretizing the considered problems with respect to spatial and temporal domains. With the help of finite difference methods, we transformed the studied problem into a set of fractional differential equations. Then, we implemented the fractional Adams method to solve this set in order to provide approximate solutions to the main problem. This combination results in an algorithm that can efficiently and accurately solve a general class of integer and fractional order initial–boundary value problems, such that it does not need to solve large systems of linear equations. In addition, we discussed the stability of the proposed scheme. Three illustrative examples are numerically solved to reveal the effectiveness and validity of the proposed technique.

An Investigation on the Effect of TiC Additive on the Microstructural and Mechanical Properties of Ultra-High Temperature ZrB2-SiC-Based Ceramic Composite by Multi-Step Spark Plasma Sintering Method

An Investigation on the Effect of TiC Additive on the Microstructural and Mechanical Properties of Ultra-High Temperature ZrB2-SiC-Based Ceramic Composite by Multi-Step Spark Plasma Sintering Method

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations

Addressing the Challenge of a Simultaneous Destructive Assay of Plutonium and Uranium: Highly Precise, Robust, Universal, and Reagent-Free Differential Pulse Voltametric Method Development in Biodegradable Methanesulfonic Acid Medium.

The destructive assay of bulk uranium and plutonium, a cornerstone for chemical quality control and nuclear material accounting of fuel matrices, mandates robust and precise methodologies. Despite ongoing research, simultaneous, matrix independent determination of U and Pu has eluded solution owing to inherent limitations in aqueous acid medium, viz., coexistence of multiple oxidation states, coupled electrochemical reactions, smaller potential window, and requirement for multistep sample preconditioning and tedious electrode modification. The present study addresses this challenge wherein non-aqueous methanesulfonic acid (MSA) served the dual role of solvent and analyte media with a bare glassy carbon (GC) electrode. Fuel matrices, viz., (U, Pu)C, (U, Pu)O2, PuO2, UO3, UO2, and U3O8, were quantitatively dissolved in biodegradable MSA, without using any additives. Redox speciation of the analytes, U and Pu, in MSA was probed by ultraviolet-visible spectrophotometry and electrometry, revealing the absence of electrocatalytic regeneration and stabilization of single oxidation state, viz., U(VI) and Pu(IV), along with relevant redox-energetic (electron transfer and reversibility) and kinetic data. Bidentate coordination of MSA with the U analyte was indicated by X-ray absorption spectroscopy studies and was corroborated by density functional theory-based investigations, providing the optimized structure, viz., [UO2(MSA)2] and [Pu(MSA)4], binding modes and energy, partial charges, and molecular orbital diagrams. Based on these insights, the feasibility of differential pulse voltammetry (DPV)-based assay method development for U and Pu separately and in different U/Pu ratios, representing assorted fuel matrices, was probed. Analytical figures of merit for both U and Pu (detection limit of ∼10-5 M, precision of ∼0.2%, accuracy of ∼0.2%, high sensitivity, repeatability, and non-influence of relevant interferences) were determined, method validated employing actual fuel samples, and compared with the established, multi-step biamperometry method. Hence, a universal, simultaneous U and Pu destructive assay method in non-aqueous MSA media based on DPV with a commercial GC electrode was demonstrated.

Prime number-based multistep measurement for separation of roundness errors

Roundness measurement is critical in manufacturing, as it ensures that products conform to precise design specifications. However, traditional multistep measurements for roundness error separation are time-consuming and limited in their ability to separate specific Fourier components. In this study, we propose a novel combined multistep measurement method with prime numbers that overcomes these limitations. We demonstrate this method through three experimental cases, achieving high levels of Fourier components in error separation with a limited number of measurements. Our method combines two ( p and q) or three ( p, q, and r) steps of prime numbers to achieve high levels of Fourier components for error separation, compared to traditional multistep measurements that require more steps. In the first experimental case, we use a 2-step and 5-step measurement to achieve traditional multistep measurement in ten steps. In the second case, we use 3-step and 5-step measurements, and in the third, we combine the 2-step, 3-step, and 5-step measurements. We achieve roundness deviations (RONt) of 12.7, 7.8, and 9.9 nm, respectively, and maximum En-values of 0.8, 0.8, and 0.7, respectively. Our proposed combined multistep measurement method using prime numbers has practical applications in manufacturing, as it reduces the time and resources required for roundness error separation while achieving a higher level of Fourier components. Our results demonstrate the effectiveness of our method and its potential to revolutionize roundness measurement in industry.