Constant Step Research Articles

Stochastic Primal–Dual Hybrid Gradient Algorithm with Adaptive Step Sizes

In this work, we propose a new primal–dual algorithm with adaptive step sizes. The stochastic primal–dual hybrid gradient (SPDHG) algorithm with constant step sizes has become widely applied in large-scale convex optimization across many scientific fields due to its scalability. While the product of the primal and dual step sizes is subject to an upper-bound in order to ensure convergence, the selection of the ratio of the step sizes is critical in applications. Up-to-now there is no systematic and successful way of selecting the primal and dual step sizes for SPDHG. In this work, we propose a general class of adaptive SPDHG (A-SPDHG) algorithms and prove their convergence under weak assumptions. We also propose concrete parameters-updating strategies which satisfy the assumptions of our theory and thereby lead to convergent algorithms. Numerical examples on computed tomography demonstrate the effectiveness of the proposed schemes.

Charger-Mediated Energy Transfer for Quantum Battery With Constant Time Dependent Step Function and Open System Approach

The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.

Design of Complex Vector Controller for High-Power Induction Machine Drive

In high-power drives of large commercial vehicles, the switching frequency of the inverter is always strictly limited to avoid high switching losses. In this paper, a high-performance complex vector controller in discrete domain is proposed to reduce the cross-coupling effect and improve control performance under low switching frequency. The discretization error of the induction motor model under different coordinate systems is explored, and a high-precision discrete induction motor model is proposed for the design of the complex vector controller and flux observer. In order to improve the dynamic response of the rotor flux linkage, the designed controller takes the current as the inner loop and the rotor flux linkage as the outer loop. Besides, the signal reconstruction strategy is proposed to solve the contradiction between the variable-step characteristics caused by synchronous modulation and the discretization process based on constant step size. Finally, the designed control strategy and analysis of the system are validly verified by simulation and experimental results.

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

A New Method to Evaluate Lower Esophageal Distension Capacity in Eosinophilic Esophagitis by Using Functional Lumen Imaging Probe (EndoFLIP™).

Endoluminal functional lumen impedance planimetry (EndoFLIPTM) has become the gold standard to evaluate esophageal distensibility, although the study itself and its analysis present challenges. We propose here a new method to assess lower esophageal distension capacity that overcomes several limitations of prior approaches, including incomplete and corrupted EndoFLIPTM recordings. Esophageal distension capacity was evaluated with a 16-channel EndoFLIPTM in 10 controls and 14 patients with eosinophilic esophagitis (EoE). Controls were evaluated once. EoE patients were evaluated at baseline and after at least six weeks of treatment with orodispersible budesonide tablets, 1 mg bd. Balloon volumes were increased by 5 mL stepwise, either reaching a maximum volume of 60 mL or a maximum balloon pressure of 60 mmHg. Recordings were analyzed with a homemade R script. The mean esophageal diameter at 60 mL, D (60 mL), was calculated or extrapolated depending on whether the 60 mL volume was reached. By fitting a Michaelis-Menten curve across all measured diameters throughout all constant volume steps, the mean D (60 mL) was estimated. For control subjects, the mean ± SD value of D (60 mL) was 17.08 ± 1.69 mm, and for EoE patients at baseline, D (60 mL) was 14.51 ± 2.68 mm. After six weeks of treatment of EoE patients, D (60 mL) significantly increased to 16.22 ± 1.86 mm (paired Wilcoxon signed test: p = 0.0052), although the values for control subjects were not reached. The estimated mean esophageal diameter at 60 mL is a good proxy for esophageal distension capacity, which correlates with clinical outcomes in EoE. The method presented in this study overcomes difficulties encountered during the standard measurement protocol, allowing the analysis of recordings from incomplete and corrupted registries.

Variable time steps in the numerical implementation of viscoelastic fractional models for laminated glass

Abstract We elaborate numerical approaches to calculate the rheological response of laminated glass beams, whose viscoelastic interlayer is modelled via fractional calculus. This mathematical description is very effective when the relaxation function of the polymer can be expressed by continuously connected branches of power-laws, as is the case for most materials used to laminate glass. The classical approach uses the Grünwald-Letnikov approximation of fractional derivatives, but it requires constant time steps, which would become very large to reasonably cover the entire observation time, thus losing accuracy. We propose to use the L1 algorithm with increasing time steps, which is well suited to the power law character of the relaxation function. This allows to follow the long-term creep response, providing a better approximation when needed. The method is implemented for beams laminated with viscolastic interlayers whose relaxation is described by four branches of power laws, to cover most practical cases. Numerical experiments shows its advantages over the Grünwald-Letnikov approach for characterizing the long-term structural response.

Sufficient Conditions for Instability of the Subgradient Method with Constant Step Size

Sufficient Conditions for Instability of the Subgradient Method with Constant Step Size

Controlling a generalized Fokker–Planck equation via inputs with nonlocal action

This paper concerns an optimal control problem (P) related to a generalized Fokker–Planck equation. Basic properties of the solutions to the generalized FP equation are derived via a semigroup approach in the space H−1(Rd). Problem (P) is proven to be deeply related to a stochastic optimal control problem (PS) for a McKean–Vlasov equation. The existence of an optimal control is obtained for the deterministic problem (P). The existence of an optimal control is established for an approximating optimal control problem (Ph) related to a backward Euler approximation of the generalized FP equation (with a constant discretization step h). One proves under additional hypotheses that “(Ph) converges to (P)” in a certain sense. First order necessary conditions for (Ph) are derived as well.

ON THE SUPPRESSION OF VIBRATIONS IN ELASTIC LINKS OF A THREEMASS ELECTRIC DRIVE SYSTEM

The main reason for failures of technological mechanisms is associated with the failure of elements of the electric drive system. One of the main reasons for the malfunction of electric drive elements is the presence of vibrations in the elastic links of the mechanical part of the electric drive. Such phenomena mainly occur during transient processes of starting and stopping an electric drive, as well as under the influence of a load that is variable in nature. From the above, it is obvious that suppression of vibrations in the elastic links of the mechanical part is of practical interest. The most promising studies aimed at studying and suppressing vibrations in the elastic links of a three-mass electric drive system are analyzed. A comparative analysis of these studies shows that they consider the operating features of individual specific electric drive systems, which cannot provide a complete understanding of a comprehensive solution to the problem of ensuring the suppression of vibrations, arising in the mechanical part for various reasons. That is why it is necessary to evaluate the possibilities of suppressing elastic vibrations of the electric drive system, taking into account all its links. The goal of this work is to propose an approach for suppressing vibrations in the elastic links of a three-mass electric drive system. The change in the elastic moment under various characteristics of the load created by the mechanism is considered, in particular, in cases of constant moment, exponential and step laws of change. The capabilities of proportional-integral (PI) and proportional-integral-derivative (PID) controllers for suppressing oscillations are analyzed. It is substantiated that although the system stabilizes with a PID controller in a short time, it does not provide the expected result and therefore it is recommended to use a controller with a fuzzy logic due to its simple control and rather high efficiency. The results obtained can be successfully used to improve the reliability of a three-mass electric drive system.

Optimal test plans for accelerated life tests based on progressive type-I censoring with engineering applications

In reliability engineering studies, the accelerated life tests with optimal test design that balances cost constraints is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are typically modelled with this characteristic. Comparative optimal test plans for accelerated life tests are developed in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we compare, under cost restriction with a specified budget, optimum multiple constant stress and step stress accelerated life tests based on progressive-type-I censoring. The goal is to assess the advantage provided by step-stress testing over constant-stress testing. In order to conduct an accelerated life test effectively, stress durations need to be carefully specified during the design stage due to limited resources in engineering practice. The estimated accuracy of the parameters of interest and the expense of the experiment are directly impacted by the stress durations. Under a prespecified budget and cost constraints, this article examines the optimal stress durations based on D-, E-, T-, C-, R-, and P-optimal criteria. These criteria are also contrasted together. We illustrate the application of the optimal durations using numerical and simulation examples. A study is conducted to determine how sensitive the optimal duration is to model parameter misspecification.

Cyclic stress accelerated life test method for mechatronic products

AbstractThe reliability requirements for mechatronics continue to increase. Traditional life test methods make it difficult to obtain the data required to assess or predict the reliability of these mechatronic products within a reasonable time. Accelerated life tests can speed up the failure process of the product by using accelerated stress conditions. And then test data is obtained to predict the reliable life of the product under normal service conditions through modeling and analysis. The test efficiency of the accelerated life tests is higher than that of the life test. So, the method of accelerated life tests has become a solution for life and reliability prediction of highly reliable and long‐life mechatronic products. However, mechatronic products usually undergo cyclic stress during service. The use of cyclic stress as an accelerating stress in accelerated life tests can provide a realistic representation of service conditions and achieve higher test efficiency. Cyclic stress accelerated life test is an accurate and efficient solution for predicting the life and reliability of such mechatronic products. Current relative research is focused on constant stress, step stress and sequential stress accelerated life tests. A great challenge in engineering is modeling and analysis of cyclic stresses accelerated life tests. In this paper, we first describe the cyclic stress accelerated life test profile and its key parameters, then propose model assumptions and establish a modelling and analysis method for cyclic stress accelerated life test data, followed by an illustrative example to apply and validate the proposed method. The research results can provide technical support for the life and reliability assessment of mechatronic products under cyclic stress service conditions.

Development of a Critical Edge-Based Adaptive Toolpath Strategy to Improve Geometrical Accuracy of Incrementally Formed Titanium Implants

Incremental sheet forming has become increasingly popular due to its advantages over traditional metal forming processes, including flexibility, low setup cost, and enhanced formability. It holds great potential for manufacturing asymmetrical components, particularly biomedical implants like cranio-facial implants. However, a significant drawback of this technique is a lack of geometrical accuracy in the produced parts. This research aims to enhance the geometric accuracy of a patient-specific frontal cranial implant by introducing a novel tool path strategy called the adaptive tool path strategy (ATP). The ATP dynamically adjusts step sizes by selectively removing slices based on local curvature requirements. The proposed strategy begins with slicing a CAD model at an extremely fine step depth (0.01 mm) to generate the initial dataset. Subsequently, slices are strategically eliminated to conform to desired curvature specifications. The manufacturing process utilizes commercially pure titanium grade 2 alloy, which is incrementally formed into the desired implant shape using both the traditional constant step depth method and the new adaptive tool path strategy. The produced parts are then scanned using high resolution 3D scanners and a detailed comparison is made between the final geometries and the design geometry. The assessment includes evaluating the forming depth, analysing bending due to spring back, and measuring geometric deviations. Furthermore, numerical simulations are conducted to assess the estimation capabilities of finite element analysis in predicting the forming process. The results demonstrate that the ATP tool path strategy significantly reduces spring back, indicated by a nearly 30 % decrease in the angle of bend along the critical edge. Moreover, the root mean square deviation is reduced by 11 %. Importantly, the experimental results aligned with the patterns observed in the numerical simulations, validating the findings obtained through the study.

A Method of Anti-Windup PID Controller for a BLDC-Drive System

This research aims to enhance control systems for Brushless DC (BLDC) motors by introducing Proportional-Integral-Derivative (PID) control as a straightforward yet reliable solution, known for its precision, quick responsiveness, and stability. Emphasizing its suitability for BLDC motor speed control, the study addresses PID controller windup challenges, highlighting anti-windup techniques crucial for maintaining system stability. The primary focus is on improving the performance of an anti-windup PID controller for BLDC motor speed control in electric vehicles. Through simulations and analyses, the research aims to minimize steady-state error and overshooting, contributing to overall operational efficiency. Practical implementation involves optimizing the PID anti-windup controller's gain using the MATLAB PID Tuner and implementing it in the Arduino IDE. Experimental tests, which cover constant and varying step function scenarios, are conducted on the designed hardware. Results show the PID anti-windup controller's superiority, exhibiting significantly lower overshoot values of 5.42% and 3.35% compared to 13.26% and 23.76%, respectively. Despite its higher control action, the traditional PID controller displays a more pronounced overshoot. This research is a significant step toward advancing control systems for electric vehicles and optimizing BLDC motor performance in practical applications.

Free Standing Electrodes: From Roll Product to 41-Layer Pouch Cells

Processes to produce free standing electrodes for Lithium-Ion Batteries (LIB), using lithium iron phosphate (LFP) as active material for the cathode and artificial graphite for the anode, are being developed. The production of these electrodes is realized by using a slot die to produce a liquid film which solidifies in a precipitation bath and is wound up after moving through washing baths. This procedure consumes significantly less energy compared to conventional coating processes, as the drying needs are reduced, and the electrodes have a broader spectrum of use cases due to their high flexibility.In this work, the development process of the manufacturing procedures of pouch cells using free standing electrodes will be presented. This includes the characterization of the electrodes, usability trials with research pilot line equipment, and cycling tests of built pouch cells of up to more than 7 Ah per device.The screening of electrodes through cycling in coin cells showed a specific discharge capacity of > 120 mAhg-1 for 50 cycles at 0.2C.This innovative and sustainable electrode production process required adjustments throughout the whole production process of a LIB, starting with the slot die geometry to reduce thick edges of the released film. The electrodes’ surfaces were investigated regarding homogeneity and roughness using a digital microscope. Gas adsorptioneasurements showed the specific surface of cathodes at around 3.6 m²g-1. Challenges during calendaring of the free-standing electrodes included thickness deviations of the pristine electrodes and uneven tension throughout the width of the samples.After laminating the free-standing electrodes with current collectors, they were electrochemically and mechanically analysed. Therefore, additional adjustments had to be made to attach tabs on multiple layers of these flexible electrodes through a single ultrasonic welding spot. All electrodes were successfully processed inside a dry room (dew point < -40 °C) using industrially relevant pilot scale equipment (punching, stacking, electrolyte filling, sealing).The manufactured pouch cells all showed an initial OCV of around 400 mV and were formed prior to cycling. During three formation cycles at 0.1C, followed by a constant Voltage step, the two-layered pouch cells showed a specific discharge capacity of . These cells reached roughly 90 mAhg-1 of discharge capacity after 20 cycles at 0.2C, but higher C-rates reduced the capacity and cell life significantly. Measuring the cells’ resistance after cycling at 3.3 V using 10 measurement points at 1 kHz revealed the high inner resistance of > 2 Ohm. Post-mortem analysis revealed lithium deposition throughout the whole surface of the anode. In the following upscaling process, the number of layers was increased to 11 layers (2 Ah cells) and 41 layers (7 Ah cells). These pouch cells showed similar performances, specific discharge capacities of around 110 mAhg-1 during formation, but with decreased cycling capabilities at C-rates higher than 0.1C. The main cause for this behaviour is the high inner resistance of these cells.In this work we demonstrate that free-standing electrodes can be handled at pilot scale in a comparable manner as conventionally coated electrodes. The produced cells were all successfully cycled but showed higher inner resistances and lower capacities at high C-rates (> 0.5C). The proof-of-concept was therefore achieved, further improvement of the cell performance will be focused on in the future. Figure 1

Read/write fence-free work-stealing with multiplicity

It has been shown that any nonblocking algorithm for work-stealing in the standard asynchronous shared memory model of computation must use expensive Read-After-Write synchronization patterns or atomic Read-Modify-Write instructions. Algorithms for relaxations of work-stealing have been proposed, which only partially avoid this impossibility result. In restricted models of computation, work-stealing algorithms have been designed that avoid Read-After-Write patterns and atomic Read-Modify-Write instructions.This paper considers work-stealing with multiplicity, a relaxation in which every task is taken by at least one process, and any process can take any task at most once. We study two variants of the relaxation, for each variant designing a Read/Write wait-free algorithm in the standard asynchronous shared memory model. The two algorithms are devoid of Read-After-Write synchronization patterns in all their operations, and additionally, the algorithm for the second variant has constant step complexity and is fence-free. Namely, no specific ordering among the algorithm's instructions is required beyond what is implied by data dependence. To our knowledge, these are the first algorithms for relaxations of work-stealing possessing all these properties. The algorithms are also solutions to relaxed versions of single-enqueuer multi-dequeuer queues. The theoretical results are complemented with an experimental evaluation showing that the benefits of relaxed work-stealing vary depending on the application, concretely on the complexity of the work associated with each task.

Hydraulic and thermal performances of micro pin fin heat sink with increasing pin fin height

This study investigates numerically the impacts of pin fins (PF) with varying height on the pressure drop ΔP, the bottom average temperature Tbw, the Nusselt number Nu and the thermal performance factor η of a micro pin fin heat sink (MPFHS). Three groups of PF structure characterized by a different height increase mode are introduced: Case 1: structure with constant height step, Case 2: structure with increasing height step, and Case 3: structure with decreasing height step. The findings in this work show that ΔP and Nu increase but Tbw decreases with the increasing height step for Case 1 and with the increasing increment of the height step for Case 2 and Case 3. When comparing their thermal and hydraulic performances, Case 2 demonstrates the best thermal performances, whereas Case 3 has the best hydraulic performance when the total height steps of PFs in all three kinds of heat sink are kept constant. Furthermore, this study finds that the PF with increasing height can always enhance η of the MPFHS compared to PF with uniform height. This finding validates the performance advantage of the PF with increasing height and offers the potential technique for the optimization design of MPFHS.

Digital backpropagation based on binary logarithmic step size distribution for fibre non‐linearity compensation

AbstractCapacity crunch has become critical in recent years as commercial communication systems approach their theoretical data rate limits. This work presents a low‐complexity digital backpropagation (DBP) implementation approach based on step size distribution that uses a binary logarithmic step size method to achieve high data rate optical transmission. The proposed scheme shows performance improvements (∆Q) of 2.36, 1.19, and 0.71 dB over linear compensation, constant step size (CSS) DBP, and logarithmic step size DBP techniques in a 2400 km 112 Gbit/s DP‐16 quadrature amplitude modulation (QAM) system, respectively. At 13 dBm, a high performance (Q) of 10.9 dB (BER = 2.25 × 10−4) is achieved, above the 3.80 × 10−3 hard‐decision forward error correction (HD‐FEC) limit, using the proposed scheme. Also, the allowable transmission distance is extended by 960 km at the HD‐FEC limit over the linear compensation technique. The optimization achieves a 38% saving in the number of DBP calculation steps compared to the CSS DBP, which considerably reduces the computational cost since a few steps are required for effective non‐linearity compensation.

The continuous stochastic gradient method: part I–convergence theory

In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function requires some form of integration, e.g., expected values. Since approximating the integration by a fixed quadrature rule can introduce artificial local solutions into the problem while simultaneously raising the computational effort, stochastic optimization schemes have become increasingly popular in such contexts. However, known stochastic gradient type methods are typically limited to expected risk functions and inherently require many iterations. The latter is particularly problematic, if the evaluation of the cost function involves solving multiple state equations, given, e.g., in form of partial differential equations. To overcome these drawbacks, a recent article introduced the CSG method, which reuses old gradient sample information via the calculation of design dependent integration weights to obtain a better approximation to the full gradient. While in the original CSG paper convergence of a subsequence was established for a diminishing step size, here, we provide a complete convergence analysis of CSG for constant step sizes and an Armijo-type line search. Moreover, new methods to obtain the integration weights are presented, extending the application range of CSG to problems involving higher dimensional integrals and distributed data.

PEM-based random vibration analysis under service-braking conditions on an irregular track

PurposeAccording to relevant research, non-uniform speed has a significant impact on the vehicle-track systems. Up to now, research work on it is still very limited. In this paper, the PEM is adopted to further transform it into a deterministic process to solve the vehicle’s problem of running at a non-uniform speed.Design/methodology/approachThe multi-body vehicle model has 10 degrees of freedom and the track is regarded as a finite long beam supported by lumped sleepers and ballast blocks. They are connected via linear Hertz springs. The vertical track irregularity is a Gaussian stationary process in the space domain. It is transformed into a uniformly modulated nonstationary random process in the time domain with respect to the non-uniform vehicle speed. By solving the equation of motion of the coupled vehicle-track system with the pseudo-excitation method, the pseudo-response and consequently the power spectral density and the standard deviation of the structural response can be obtained.FindingsTwo kinds of vehicle braking programs are taken in the numerical example and some beneficial conclusions are drawn.Originality/valueThe pseudo-excitation method (PEM) was used to perform the random vibration analysis of a coupled non-uniform speed vehicle-track system. Transforming the track irregularity into a uniformly modulated nonstationary random process in time domain with respect to the non-uniform vehicle speed was undertaken. The pseudo-response of the coupled system is solved by applying the Newmark algorithm with constant space integral steps. The random vibration transfer mechanism of the coupled system is fully discussed.

A coupled 3D thermo-mechanical peridynamic model for cracking analysis of homogeneous and heterogeneous materials

This paper proposes a variable timestep-strategy that can speed up the peridynamic modeling of thermomechanical cracking in both homogeneous and heterogeneous materials. A piecewise continuous time-step variation function is incorporated into the peridynamic framework that dynamically adjusts the time-step size, which ranges from a small value to a maximum value that remains below the critical stable time-step. The advantages of this variable timestep strategy are threefold: (1) The exceptional computational efficiency of this approach is mainly manifested in enabling peridynamic simulation that is 20 times faster compared to that employing a constant time step; (2) Taking advantage of the proposed method, both two- and three-dimensional peridynamic modeling of thermomechanical deformation and crack propagation has been demonstrated to be of great accuracy and robustness; (3) Facilitated with this variable timestep strategy, we achieve a remarkable advancement in peridynamics to capture intricate 3D crack patterns with complex topological structures in homogeneous specimens subjected to water quenching. Furthermore, the effects of the temperature difference, specimen geometrical configurations and the initial water entry velocity on the crack patterns of the specimens under water quenching are systematically explored.