Step Load Research Articles

Pressurized Water reactor power level control: A nonlinear generalized predictive control with extended Kalman filter method

Reactor power level control is an effective way to achieve load tracking of Pressurized Water Reactor (PWR) in a nuclear power station. A novel Nonlinear Generalized Predictive Control with Extended Kalman Filter (NGPC + EKF) is proposed to solve the problem that discrete predictive model mismatch in noisy environment. In this paper, an NGPC controller is developed to realize the reactor load tracking, and an EKF is used to estimate reactor states and suppress noise. Finally, the control methods of PID, MPC, NGPC and NGPC + EKF are compared by two simulation experiments, load tracking experiment and step response experiment. The load tracking experiment results show that NGPC + EKF method obtains better noise suppression ability and tracking effect. In the step response experiment, the proposed NGPC + EKF scheme is also proved to have better step response performance than others.

Description of step loads at high temperature creep of metallic materials

Abstract In metallic materials under high-temperature creep conditions, the damage evolution occurs. To describe it, Kachanov and Rabotnov proposed the concept of damage. In this paper, the damage parameter is defined as the relative change in material density, serving as an integral measure of damage. By incorporating the damage parameter and the mass conservation law, are we formulated interrelated kinetic equations for rate of creep deformation and the damage parameter. The case of variable loads is crucial both theoretically and practically, as most structural components typically operate under such conditions. Therefore, solutions of considered equations are derived for the case of two-stage loading. The received solutions and experimental results on the creep of titanium alloy under variable loads at 500°C were compared. There is a good agreement between the theoretical results and experimental data.

A Novel LQI Control Technique for Interleaved-Boost Converters

Hybrid electric vehicles (HEVs) and fuel cell electric vehicles (FCEVs) utilize boost converters to gain a higher voltage than the battery. Interleaved boost converters are suitable for low input voltage, large input current, miniaturization, and high-efficiency applications. This paper proposes a novel linear quadratic integral (LQI) control for the interleaved boost converters. First, the small-signal model of the interleaved-boost converter is derived. In the proposed method, an output voltage and a current signal error between two-phase input currents are selected to control not only the output voltage but also a balance between two-phase input currents. Furthermore, steady-state characteristics in terms of the output voltage and the input current are demonstrated by experiments and simulations using an experimental apparatus with a rated power of 700 W. The validity of the proposed method’s tracking performance and load response is demonstrated by comparing it with that of the conventional PI control. The tracking performance of the LQI control for the 40 V step response has a ten times faster response than that of the PI control. Also, the experimental results demonstrate that the proposed method maintains a constant output voltage for a 300 W load step while the PI control varies by 10 V during 70 ms. Additionally, the proposed method has an excellent disturbance rejection.

Modeling and Control of Multi‐Stack Fuel Cell Air System based on Nonlinear Model Predictive Control Method

Hydrogen is crucial for achieving SDGs by driving energy transition and combating climate change. Proton exchange membrane fuel cell technology, leveraging hydrogen, faces challenges in meeting high‐power demands. The multistack fuel cell system (MFCS) tackles this by integrating multiple substacks, yet its air supply needs meticulous control. Proportional integral derivative (PID) decoupling from single‐stack falls short of MFCS. This article proposes nonlinear model predictive control (NMPC) for optimized air flow and pressure decoupling. Modeling MFCS's air system and designing a predictive model, it is aimed to ensuring precise control of air flow and pressure in each substack. The decoupling experiments show that NMPC outperforms PID, accurately managing air flow and pressure and reducing load fluctuations. For air mass flow, NMPC cuts mean‐absolute error (MAE) by 64.56% and root‐mean‐square error (RMSE) by 81.36%. For pressure, MAE drops 81.23% and RMSE 83.59%. Comprehensive step load tests confirm NMPC's precise, dynamic regulation too, compared to PID, NMPC lowers average MAE for air mass by 20.67%, pressure by 32.22%. RMSE improvements of 31.08% and 33.23% highlight NMPC's strength. NMPC's quick response mitigates coupling issues, enhancing vehicle load adaptability.

Microscale Normal Compression Behaviors of Clay Aggregates: A Coarse-Grained Molecular Dynamics Study.

Given the limitations of micromechanical experiments and molecular dynamics simulations, the normal compression process of clay aggregates was simulated under different vertical pressures (P), numbers of particles, loading methods, and environments by a Gay-Berne potential model. On the basis of the variations of particle orientation and the distribution of stacks, the evolution of deformation and stresses was elucidated. The results showed that the effects of the pressure level and loading environment on the deformation were significant. In the range of 0.1-10 MPa, the changes in the void ratio were essentially the evolution of the distribution of stacks determined by attractive short-range van der Waals interactions. The deformation under constant pressure was larger than that under step loading. Because the interactions between clay particles were mainly controlled by mechanical force when in the range of 40-100 MPa, the void ratios under various loading conditions were consistent. It was also found that changes in three-dimensional stresses during compression were dependent on those of the distribution of stacks. In the vacuum environment, owing to the lateral movement of interlocked small stacks, the horizontal stress decreased. The lateral pressure coefficients (k) were greater in an atmospheric environment because the anisotropic particle orientation was relatively less obvious. In the range of 10-100 MPa, when the loading path became longer, k was similar in vacuum but became smaller in an atmosphere. If the initial loading pressure was increased, the number of large stacks sharply increased and the anisotropy was significant in a vacuum environment, which was less prone to lateral expansion. In contrast, more consistent particle arrangements were maintained in an atmosphere. This work will be conducive to explaining experimental observations of long-term ripening.

Secondary consolidation simulation of peat with vertical drains under time-dependent loading

Preloading with vertical drains is an effective ground improvement technique used to accelerate the consolidation process. Generally, embankments are constructed over a period, by increasing the fill height with time. Hence, it is not always realistic to analyse embankments as a single ramp loading or an instantaneous loading. Although many studies have been conducted to calculate the settlement variation under time-dependent loading, those methods are complex in practical applications and do not consider the secondary consolidation settlement, which is important for very soft organic soils. In this study, the original Barron consolidation theory is applied to calculate the variation of settlement, pore water pressure and degree of consolidation due to incremental step loading of embankments, constructed on compressible soft organic soil, stabilised with vertical drains (gravel compaction piles, sand compaction piles and prefabricated vertical drains). The settlement predictions are compared with the actual settlement monitoring data obtained during the construction of road embankments, and pore pressure variation is compared with the results obtained from a case study reported in the literature. The comparisons show that the results obtained from the proposed method match very well with the actual field measurements.

Feedback-linearization decoupling based coordinated control of air supply and thermal management for vehicular fuel cell system

The coordinated control of the coupled system of air supply and thermal management is one of the important ways to improve the efficiency of proton exchange membrane fuel cell (PEMFC) system. The novelty of this paper is to design a feedback-linearization decoupling based coordinated controller combining with active disturbance rejection control (ADRC) method. Aiming at strong coupling of air supply and thermal management system, we have proposed a three-dimensional particle swarm coordinated optimization algorithm to calculate the steady-state reference, then, a feedback-linearization decoupling controller is designed to achieve independent control of air flow, cathode pressure and temperature. Besides, aiming at time-varying, nonlinear interference, we have designed an ADRC based on the decoupled method to achieve better dynamic response and stability. The current step load test reveals that the overshoot and the average tracking error are much smaller under the air flow-pressure-temperature decoupling coordinated controller compared that under the proportional-integral-derivative (PID) controller and the air flow-pressure decoupling controller. The test results under different ambient temperatures indicate that the proposed coordinated strategy reduces the tracking error by over 10 %, the efficiency of fuel cell system is increased by 3.5%–4.5 %.

Physical start-up of the Nuclear Subcritical Facility “Neutron Source” of NSC KIPT

National Science Center “Kharkov Institute of Physics and Technology” jointly with the Argonne National Laboratory developed, designed and constructed the Subcritical Nuclear Facility “Neutron source based on the subcritical assembly driven by electron linear accelerator”. The article presents the main results obtained during the physical start-up of the plant, the program of which involved the staged loading of fuel assemblies into the core with subsequent measurements of its neutron-physical characteristics. In total, 37 fuel assemblies of WWR-M2 type were loaded into the facility core. The values o f the effective neutron multiplication factor keff and reactivity ρ of the subcritical assembly were measured after each loading step using the multiplication and area ratio methods. In addition, the neutron flux to electron current ratio method was tested for on-line reactivity monitoring. The investigations were performed when the accelerator was operated with 100 MeV electron beam energy, 2.7 μs electron pulse duration, 20 Hz pulse repetition rate and ≤ 40 mA beam pulse current. The obtained results were analyzed in terms of ensuring the facility nuclear safety at the next stage of its commissioning which is the pilot operation.

Lagrangian Finite Element Model Formulation and Experimental Validation of the Laser Impact Weld Process for Ti/Brass Joining

Information on the flyer deformation during laser impact welding (LIW) is an important aspect to consider when high reliability of the welded components is required. For this reason, accurate numerical models simulating thermal and mechanical aspects are needed. In the present work, the cross-section morphology during LIW of Ti/Brass joints at varying laser pulse energies is modeled by a 2D finite element (FE) model. A hydrodynamic plasma pressure model able to describe the evolution of the pressure load step by step, taking into account the progressive deformation of the flyer, was implemented. Hence, this paper proposes an alternative method to the conventional node concentrated forces or predefined velocity as flyer boundary conditions. The levels of the equivalent plastic strain (PEEQ), shear stress, and critical flyer velocity at the collision point were used as reference parameters to predict the success of the welding bond, distinguishing the welded area from the unwelded area. The model was validated by comparison with the experimental data, which showed the effectiveness of the proposed FE code in predicting the cross-section morphology of the welded materials. Moreover, practical industrial information such as variation in the flyer impact velocity, collision angle, and process temperatures was predicted by varying the process laser pulse energy according to the basic principle of the process.

Influence of mass conservation cavitation boundary on transient performance of water-lubricated bearings

Given the current research gap regarding cavitation phenomena and startup conditions in water-lubricated bearings (WLBs), this study offers an innovative approach by integrating the mass conservation boundary condition proposed by Jakobsson, Floberg, and Olsson (known as the JFO boundary condition) with a transient mixed lubrication model of WLBs. It also considers the impact of elastic deformation and surface roughness peaks, thus establishing a transient startup model of WLBs that incorporates the cavitation effect. Furthermore, the dynamic behaviors of this boundary condition are contrasted with the commonly used Reynolds boundary condition during the startup process of the bearings, as well as under eccentric and step load impacts. The findings demonstrate that the JFO boundary condition, accounting for cavitation effects, significantly influences the transient performance of WLBs. The presence of a cavitation region diminishes the damping of the bearing system following step load impacts, leading to increased overshoot and adjustment time while weakening the system's self-adjusting ability against step loads. This study offers valuable insights for theoretical analysis of ship propulsion systems operating under complex conditions.

Comparison of batch and continuous multi-column capture of monoclonal antibodies with convective diffusive membrane adsorbers

Protein A affinity membrane adsorbers are a promising alternative to resins to intensify the manufacturing of monoclonal antibodies. This study examined the process performance of convective diffusive membrane adsorbers operated in batch and continuous multi-column mode. Therefore, three different processes were compared regarding membrane utilization, productivity, and buffer consumption: the batch process, the rapid cycling parallel multi-column chromatography process, and the rapid cycling simulated moving bed process. The influence of the monoclonal antibody loading concentration (between 0.5 g L-1 and 5.2 g L-1) and the loading flow rate (between 1.25 MV min-1 and 10 MV min-1) on the monoclonal antibody binding behavior of the membrane adsorber were studied with breakthrough curve experiments. The determined breakthrough curves were used to calculate the monoclonal antibody dynamic binding capacity, the duration of the loading steps for each process, and the number of required membrane adsorbers for the continuous processes rapid cycling parallel multi-column chromatography and rapid cycling simulated moving bed. The highest productivity for the batch (176 g L-1 h-1) and rapid cycling parallel multi-column chromatography process (176 g L-1 h-1) was calculated for high monoclonal antibody loading concentrations and low loading flow rates. In contrast, the rapid cycling simulated moving bed process achieved the highest productivity (217 g L-1 h-1) for high monoclonal antibody loading concentrations and loading flow rates. Furthermore, due to the higher membrane utilization, the buffer consumption of the rapid cycling simulated moving bed process (1.1 L g-1) was up to 1.9 times lower than that of the batch or rapid cycling parallel multi-column chromatography operation (2.1 L g-1).

Impact of ABT based control strategies on ALFC and AVR in DFIG-integrated interconnected power systems

To maintain a stable electricity supply in interconnected power grids, effective frequency and voltage regulation are required. Interconnected power systems use Automatic Load Frequency Control (ALFC) and Automatic Voltage Regulator (AVR) for this purpose. The integration of renewable sources, such as Doubly Fed Induction Generators (DFIGs), creates challenges for such control loops. This study investigates the impact of using various Frequency-Linked Pricing (FLP)-based operating strategies under Availability-Based Tariff (ABT) on combined ALFC and AVR in a two-area interconnected power system with DFIGs. FLP-based operating strategies under ABT react to frequency changes through price signals, which can act faster compared to traditional AGC methods that rely on communication between control centers. This quicker response helps maintain frequency and voltage during load disturbances. Most of the earlier research focused mostly on using only a single type of FLP-based operating strategy under ABT within the ALFC loop, neglecting the combined ALFC-AVR interaction. This work addresses this gap by evaluating three FLP-based operating strategies under ABT along with the traditional approach for their impact on frequency and voltage under step load disturbance. Simulation studies conducted in MATLAB 2022a demonstrate the effectiveness of the proposed strategies, providing valuable insights for improving frequency and voltage control in modern power systems. The investigation reveals that the strategy that considers the difference between the actual and reference values of the unscheduled interchange (UI) charge and the marginal cost of generation to produce the control command outperforms the other strategies and restores the frequency and voltage to their nominal values.

Geometrically nonlinear bending analysis of laminated thin plates based on classical laminated plate theory and deep energy method

This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.

Experimental study on peak shaving during preheating combustion for different coal ranks: Thermal modification and variable load operation

With the large-scale integration of renewable energy into the power grid, coal-fired power plants shoulder an enormous burden of peak shaving. In this study, the variable load characteristics of different coal ranks were extensively investigated on a 40 kWth down-fired test platform. Moreover, the preheating modification of fuel at ultra-low loads was investigated. A comprehensive evaluation coefficient (Eph) was established to characterize the reactivity of different coal ranks at wide loads. The determination criterion of combustion stability for variable load processes was modified. The results show that the preheating modification of different coal ranks was significant, especially for lower-activity coals such as anthracite and lean coals. The minimum loads after modification were 25 %, 25 %, 35 % and 40 % for ARG (lignite), SM (bituminous), RG (lean coal) and SH (anthracite), respectively. Furthermore, the preheating modification had a positive effect on increasing the variable load rate, which was positively correlated with Eph for different coal ranks. The maximum variable load rates after modification for ARG, SM, RG and SH were 2.78 %/min, 3.13 %/min, 1.79 %/min and 1.15 %/min, which corresponded to the optimum load steps of 25–30 %. The response rate of NO and N2O with time in the low-rank coal is faster than that in the high-rank coal during the variable load process, which is consistent with the trend of the variable load rate. In addition, the conversion of nitrogen oxides decreases and then increases with load, and the inflection points corresponding to AGB, SM, RG and SH are 40 %, 38 %, 70 % and 80 %, respectively. The NOx emissions were less than 335 mg/m3 (@6 % O2) for the different coal ranks during load changes.

Solving nonlinear structural problems by associating line-search and path-following techniques

The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line-search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence.

Convergence-Related Serviceability Limit States of Segmental Tunnel Rings: Lessons Learned from Structural Analysis of Real-Scale Tests

An extended hybrid method for the analysis of the symmetric structural behavior of segmental tunnel linings is proposed. Their deformations cannot be determined by the traditional hybrid methods when the convergences are close to the serviceability limit states (SLSs). Two real-scale tests are employed for the validation of the proposed method. It involves structural analysis that is based on transfer relations. They represent analytical solutions of the linear theory of thin circular arches, and they contain the symmetric mode of rigid-body displacements. The method is termed hybrid because it is based on two types of input, namely the external loading and experimental data of displacements monitored during the test. It is termed extended because, additionally, the vertical and horizontal convergences are employed to produce more accurate structural deformations than obtained by the traditional hybrid method. The latter is found to be unsuitable for structural analysis after sudden failure has occurred in the vicinity of segmental interfaces. At the respective load steps, the structures were in convergence-related serviceability class C, referring to endangered serviceability. The local failures occurring at these load steps resulted in a rapid increase in the structural deformations and fast attainment of the SLS. If, in convergence-related serviceability class C, local failures at segmental interfaces are detected, the strengthening of the structure is necessary. This cannot be delayed to the attainment of serviceability class D, i.e., to reaching the SLS.

Fast analysis approach for instability problems of thin shells utilizing ANNs and a Bayesian regularization back-propagation algorithm

Abstract This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

Nonlinear analysis of laminated composite shells with piezoelectric patches under displacement‐dependent pressure loads

AbstractIn this paper, the three‐dimensional stress field in nonlinear laminated composite shells with piezoelectric patches subjected to displacement‐dependent loads is analyzed. To solve the problem, the geometrically exact (GeX) hybrid‐mixed four‐node solid‐shell element has been developed. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms are taken exactly at the element nodes. The laminated solid‐shell element formulation is based on the choice of an arbitrary number of sampling surfaces (SaS) parallel to the middle surface and located at the Chebyshev polynomial nodes within the layers, in order to introduce the displacements and electric potentials of these surfaces as unknown functions. The outer surfaces and interfaces are also included into a set of SaS. Due to analytical integration utilized to evaluate the tangent stiffness matrix, the proposed GeX piezoelectric solid‐shell element under nonconservative loading exhibits superior performance in the case of coarse meshes and allows the use of only one load step in all considered benchmark problems. Therefore, it can be recommended for the large deformation analysis of doubly curved laminated composite shells with piezoelectric patches, since the SaS formulation allows one to find three‐dimensional solutions of electroelasticity with a prescribed accuracy.

Data‐driven predictive control of perturbed buck converters using a modified iterative feedback tuning algorithm

AbstractThe most challenging aspect of utilizing model predictive controllers (MPCs), particularly those involving power electronic applications, is the extraction of a model that accurately represents the behavior of the studied system. Concerning the use of power electronic applications, as long as an MPC is used, adjusting the controller parameters brings difficulties. In addition, as the number of elements increases, it becomes harder to get the best control law out of the model. To do away with the need for model extraction, this study presents an offline data‐driven approach in conjunction with the MPC that can optimally adjust the MPC parameters based on the iterative feedback tuning (IFT) algorithm called the iterative feedback predictive controller (IFPC). The proposed method eliminates concerns regarding selecting an optimal number of algorithm iterations, thereby reducing operating costs, by introducing a modified IFT called feedback‐based IFPC (FIFPC) while simultaneously achieving optimal MPC parameters. The proposed method is applied to a constant voltage load (CVL) connected less‐than‐ideal buck converter, that is, one with perturbed filter elements and variable loads. A robust stability analysis (RSA) is performed under normal operating conditions to investigate the robustness behavior of the proposed controller. Simulation studies are presented to evaluate the proposed controller under different scenarios, such as step and abrupt load changes and measurement noise, compared with the well‐known model‐based and data‐enabled predictive controller (DeePC) approaches in the MATLAB/Simulink environment.

Experimental investigation of fracture mechanism in organically modified silica-based coating applied on austenitic stainless steel AISI 904L under monotonic and very high cycle fatigue loading

Surface morphology significantly influences the fatigue life of the metallic materials. Therefore, improving surface performance is important for economic and safety applications. Silica-based coatings are anticipated to protect the metallic materials under synergistic operating conditions, such as fatigue and corrosion. However, pure inorganic silica-based coatings are brittle and fail to protect metallic materials. The properties of the sol–gel coatings can be determined by optimizing synthesis factors, such as synthesis steps, precursors, solvents, and catalysts. Organically modified silica-based sol–gel coatings were synthesized using 3-glycidoxypropyl trimethoxysilane and 3-aminopropyltriethoxysilane as precursors, with ethanol as the solvent. The resulting coating was named EtOH. This coating was applied on the surface of stable austenitic stainless steel AISI 904L with the dip coating method. The fracture behavior of the coating during monotonic loading has been studied by interrupted tensile tests at different load steps and examined closely with scanning electron microscopy. On the other hand, very high cycle fatigue experiments were conducted using an ultrasonic fatigue testing system at load frequency of 20 kHz on coated specimens to investigate the fracture behavior of the coating during cyclic loading. Three different kinds of fracture due to stress relaxation in the coating and at its interface with substrate were observed in monotonic loading. The same kinds of stress relaxation were observed in cyclic loading with the difference being that the range of experienced elongation in cyclic tests was significantly smaller. Therefore, the fracture in cyclic loading were concentrated in the vicinity of macro crack. The application of organically modified coatings could suppress the persistent slip bands and result in increased fatigue life for coated specimens.