Quadratic Approach Research Articles

Optimal State Feedback-Integral Control of Fuel-Cell Integrated Boost Converter

Clean energy and reduction in carbon footprint have motivated the adoption of Fuel Cells as an alternative source of energy, merely having any detrimental byproducts. In this work, the control of the Proton-exchange membrane fuel cell (PEMFC) integrated boost converter has been carried out. State-feedback with integral-based controllers has been designed using the classical pole placement method and optimal linear quadratic regulator approach. The first method aims at achieving the desired performance. The second method also minimizes the error while optimizing the control effort. In this approach, the control energy required for attaining the time and frequency domain objective at steady state operation is also optimized. The same avoids the limitation of existing schemes by avoiding sub-optimal solutions. Both control techniques have been verified in terms of transient performance during the load disturbance using numerical simulations and experimentation. In addition, comparative state trajectories and overall efficiency analysis of the system are presented.

Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell

We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the “zero-energy-contribution” feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.

Improving thermodynamic profile retrievals from microwave radiometers by including radio acoustic sounding system (RASS) observations

Abstract. Thermodynamic profiles are often retrieved from the multi-wavelength brightness temperature observations made by microwave radiometers (MWRs) using regression methods (linear, quadratic approaches), artificial intelligence (neural networks), or physical iterative methods. Regression and neural network methods are tuned to mean conditions derived from a climatological dataset of thermodynamic profiles collected nearby. In contrast, physical iterative retrievals use a radiative transfer model starting from a climatologically reasonable profile of temperature and water vapor, with the model running iteratively until the derived brightness temperatures match those observed by the MWR within a specified uncertainty. In this study, a physical iterative approach is used to retrieve temperature and humidity profiles from data collected during XPIA (eXperimental Planetary boundary layer Instrument Assessment), a field campaign held from March to May 2015 at NOAA's Boulder Atmospheric Observatory (BAO) facility. During the campaign, several passive and active remote sensing instruments as well as in situ platforms were deployed and evaluated to determine their suitability for the verification and validation of meteorological processes. Among the deployed remote sensing instruments were a multi-channel MWR as well as two radio acoustic sounding systems (RASSs) associated with 915 and 449 MHz wind profiling radars. In this study the physical iterative approach is tested with different observational inputs: first using data from surface sensors and the MWR in different configurations and then including data from the RASS in the retrieval with the MWR data. These temperature retrievals are assessed against co-located radiosonde profiles. Results show that the combination of the MWR and RASS observations in the retrieval allows for a more accurate characterization of low-level temperature inversions and that these retrieved temperature profiles match the radiosonde observations better than the temperature profiles retrieved from only the MWR in the layer between the surface and 3 km above ground level (a.g.l.). Specifically, in this layer of the atmosphere, both root mean square errors and standard deviations of the difference between radiosonde and retrievals that combine MWR and RASS are improved by mostly 10 %–20 % compared to the configuration that does not include RASS observations. Pearson correlation coefficients are also improved. A comparison of the temperature physical retrievals to the manufacturer-provided neural network retrievals is provided in Appendix A.

Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation

In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based on the extrapolation/prediction-correction technique and the symplectic Runge-Kutta method in time, together with the standard Fourier pseudo-spectral method in space. We show that the scheme is linear, high-order, unconditionally stable and preserves the discrete momentum of the system. For the energy-preserving scheme, it is mainly based on the energy quadratization approach and the analogous linearized strategy used in the construction of the linear momentum-preserving scheme. The proposed scheme is linear, high-order and can preserve both the discrete mass and the discrete quadratic energy exactly. Numerical results are addressed to demonstrate the accuracy and efficiency of the proposed scheme.

Passive Decentralized Fuzzy Control for Takagi-Sugeno Fuzzy Model Based Large-Scale Descriptor Systems

This paper presents a decentralized control problem for stabilizing the nonlinear large-scale descriptor (LSD) systems that use the proportional-plus-derivative state (PD) feedback scheme. The descriptor systems have a great focus on the research because they can contain more physical characteristics than standard state-space systems. At first, each nonlinear subsystem in the LSD system can be represented by Takagi-Sugeno (T-S) LSD systems with interconnections. In order to be more realistic, we additionally consider external disturbances and perturbations that affect the system. Our goal is to design a decentralized (DPD) fuzzy controller, such that the T-S LSD system is stable while the external disturbances and perturbations that affect the system. For the controller design process, sufficient conditions were developed based on the quadratic Lyapunov approach, PD feedback scheme, robust constraint, passivity constraint, and linear matrix inequality (LMI) sufficient criteria. At last, two numerical examples are given to show the application of the main results.

User Rate Optimization for Fronthaul-Constrained Cell-Free Massive MIMO-OFDM Systems: A Quadratic Transform-Based Approach

As a promising candidate for the future generations of mobile communication networks, the cell-free (CF) massive multiple-input multiple-output (mMIMO) networks have been shown to provide high spectral efficiency (SE) and more uniform signal coverage than cellular mMIMO networks, enabling smart cities more diverse application services. The fronthaul link in such networks, defined as the transmission link between the central processing unit and the access point, requires a high capacity, but is often constrained. Hence, the optimization of the user rate under the limited capacity of fronthaul is the key problem to be solved in a CF networks. In this paper, we consider the downlink transmission of CF mMIMO orthogonal frequency division multiplexing (OFDM) systems with constrained transmit power and fronthaul capacity. Based on the min-max and sum-max principles, quadratic transform-min max (QT-MM) and quadratic transform-sum max (QT-SM) optimization algorithms are proposed, respectively. Simulation results show that compared with the weighted minimum mean square error (WMMSE) algorithm, both of the proposed algorithms can effectively prevent very low user rates when the fronthaul capacity is limited. When the fronthaul link capacity constraint is high, the QT-SM algorithm has better rate performance than the distributed WMMSE-d algorithm and the centralized WMMSE-c algorithm.

Robust synchronization analysis of delayed fractional order neural networks with uncertain parameters

<abstract><p>This paper is concerned with the robust synchronization analysis of delayed fractional order neural networks with uncertain parameters (DFNNUPs). Firstly, the DFNNUPs drive system model and response system model are established. Secondly, using multiple matrix quadratic Lyapunov function approach and inequality analysis technique, the robust synchronization conditions are derived in the form of the matrix inequalities. Finally, the correctness of the theoretical results is verified by an example.</p></abstract>

Sustainable two stage supply chain management: A quadratic optimization approach with a quadratic constraint

Designing a supply chain to comply with environmental policy requires awareness of how work and/or production methods impact the environment and what needs to be done to reduce those environmental impacts and make the company more sustainable. This is a dynamic process that occurs at both the strategic and operational levels. However, being environmentally friendly does not necessarily mean improving the efficiency of the system at the same time. Therefore, when allocating a production budget in a supply chain that implements the green paradigm, it is necessary to figure out how to properly recover costs in order to improve both sustainability and routine operations, offsetting the negative environmental impact of logistics and production without compromising the efficiency of the processes to be executed. In this paper, we study the latter problem in detail, focusing on the CO 2 emissions generated by the transportation from suppliers to production sites, and by the production activities carried out in each plant. We do this using a novel mathematical model that has a quadratic objective function and all linear constraints except one, which is also quadratic, and models the constraint on the budget that can be used for green investments caused by the increasing internal complexity created by large production flows in the production nodes of the supply network. To solve this model, we propose a multistart algorithm based on successive linear approximations. Computational results show the effectiveness of our proposal. • We study the problem of minimizing the CO 2 emissions produced by transportation activities from suppliers to production facilities and by manufacturing activities carried out at each facility in a two-stage supply chain. • A novel mathematical model which has a quadratic objective function and all linear constraints but one is proposed. The nonlinear constraint is quadratic and models the restriction of the budget usable for green investments caused by the increasing inner complexity produced by large production flows in production nodes of the supply network. • To solve this model, we propose a multi-start algorithm based on successive linear approximations. • Computational results and a comparison with a commercial solver reveal the effectiveness of our proposal.

Deciphering the adsorption potential of a functionalized green hydrogel nanocomposite for aspartame from aqueous phase

Herein, a functionalized green hydrogel nanocomposite based on carboxymethylated gum tragacanth and nanobentonite (GTBCH) was designed via free-radical polymerization approach for the elimination of Aspartame (AS) from wastewater. The GTBCH fabrication was validated by Fourier Transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Transmission electron microscopy (TEM), scanning electron microscopy (SEM), and energy dispersive X-ray spectroscopy (EDX) techniques. Central composite design (CCD) was efficaciously applied to determine the quadratic polynomial approach for predicting the adsorption capacity (qe) of AS. The optimum sequestration conditions were dosage (0.8 g L‒1), agitation time (35 min) initial AS concentration (60 mg L−1), pH (6) and temperature (308 K). The CCD results revealed that dosage of GTBCH and initial concentration have greater impact on qe followed by pH, time, and temperature. The significant adsorption capacity (392.04 mg g−1), calculated from Langmuir model, could be attributed to the stronger interactions prevalent between AS and GTBCH. Diffusion investigations depicted the uptake of AS via surface adsorption, liquid film and intraparticle diffusion, respectively. Ionic strength and real water have minor effect on the adsorption capacity demonstrating electrostatic interaction has least impact in adsorption process. The pHzpc, FTIR and XPS investigations revealed hydrogen bonding, n-π and van der Waals interactions as the principal removal mechanisms. Robust design, high adsorption capacity, eco-friendly facets along with excellent reusability indicated the GTBCH as a competent adsorbent for AS decontamination from wastewater.

The exponential invariant energy quadratization approach for general multi-symplectic Hamiltonian PDEs

Many conservative systems in physical sciences can be described by multi-symplectic Hamiltonian PDEs (MS-HPDEs) admitting three important inherent properties named as multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we develop a novel strategy to systematically derive linearly implicit local energy-preserving schemes for general MS-HPDEs, which is named the exponential invariant energy quadratization approach (EIEQ). Such novel strategy is based on the exponential form of non-quadratic terms of the state function that can remove the bounded-from-below restriction, so it is more applicable than the traditional IEQ approach widely employed to construct linearly implicit schemes. Moreover, we provide a completely explicit discretization of the auxiliary variable combined with the nonlinear term, which obtains linearly implicit schemes of the constant coefficient, making their more effective than the IEQ schemes for rapid simulations. We also present the multiple EIEQ approach to improve the applicability of the EIEQ approach for MS-HPDEs with more non-quadratic terms. In addition, when periodic or homogeneous boundary conditions are considered, the proposed schemes are global energy-preserving and can be explicitly solved by using the fast Fourier transform. Finally, ample numerical tests are carried out to demonstrate the computational efficiency, conservation and accuracy of EIEQ schemes.

An advanced quadratic displacement approach for the analytical stress analysis of adhesive bonded joints

AbstractIn this work an advanced analytical model for the efficient prediction of stress distributions in the adhesive layer of bonded joints is presented. In order to better account for local deformation effects occurring in thicker adhesive layers, a quadratic‐extended displacement approach is introduced. The use of a general sandwich‐type model for the overlap region enables a wide applicability to the analysis of different joint shapes and load cases.

An energy stable linear numerical method for thermodynamically consistent modeling of two-phase incompressible flow in porous media

In this paper, we consider numerical approximation of a thermodynamically consistent model of two-phase flow in porous media, which obeys an intrinsic energy dissipation law. The model under consideration is newly-developed, so there is no energy stable numerical scheme proposed for it at present. This model consists of two nonlinear degenerate parabolic equations and a saturation constraint, but lacking an independent equation for the pressure, so for the purpose of designing efficient numerical scheme, we reformulate the model forms as well as the free energy function, and further prove the corresponding energy dissipation inequality. Based on the alternative reformulations, using the invariant energy quadratization approach and subtle semi-implicit treatments for the pressure and saturation, we for the first time propose a linear and energy stable numerical method for this model. The fully discrete scheme is devised combining the upwind approach for the phase mobilities and the cell-centered finite difference method. The unique solvability of numerical solutions and unconditional energy stability are rigorously proved for both the semi-discrete time scheme and the fully discrete scheme. Moreover, the scheme can guarantee the local mass conservation for both phases. We also show that the upwind mobility approach plays an essential role in preserving energy stability of the fully discrete scheme. Numerical results are presented to demonstrate the performance of the proposed scheme.

A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation

We carry out error estimates for a linear, second-order, unconditionally energy stable, semi-discrete time stepping scheme, which is based on the Lagrange Multiplier approach and could also be viewed as a special case of the invariant energy quadratization approach, for the modified phase field crystal equation. At each time step, the proposed scheme only requires solving several linear equations. Rigorous proofs are presented to demonstrate the unique solvability, mass conservation, and unconditional energy stability of the scheme. Various numerical experiments in 2D and 3D are performed to validate the accuracy, unconditional energy stability and mass conservation of the proposed numerical strategy.

Artificial Neural Networks Models Based on ARX and State Space Forms and Adaptive Control PID/LQR of Systems Based on Peltier Cells

To improve the performance of a thermal plant based on Peltier cell actuators, an online parametric estimation via artificial neural networks and adaptive controller is presented. The control actions are based on adaptive digital controller and an adaptive quadratic linear regulator approaches. The Artificial neural networks topology is based on ARX and NARX models, and its training algorithms, such as accelerated backpropagation and recursive least square. The Control strategies are design-oriented to adaptive digital PID controller and quadratic linear regulator framework. The proposal is evaluated on temperature control of an object that is inside of a chamber.

Projected Adaptive Cubic Regularization Algorithm with Derivative-Free Filter Technique for Box Constrained Optimization

An adaptive projected affine scaling algorithm of cubic regularization method using a filter technique for solving box constrained optimization without derivatives is put forward in the passage. The affine scaling interior-point cubic model is based on the quadratic probabilistic interpolation approach on the objective function. The new iterations are obtained by the solutions of the projected adaptive cubic regularization algorithm with filter technique. We prove the convergence of the proposed algorithm under some assumptions. Finally, experiments results showed that the presented algorithm is effective in detail.

A rapid exploratory assessment of vegetation structure and carbon pools of the remaining tropical lowland forests of Southwestern Nigeria

Vegetation composition and structural diversity are important for biodiversity conservation and forest carbon storage.. Less attention has been paid to tropical forest vegetation characteristics and the carbon stock across different pools in Nigeria. This study presents the results of a rapid assessment and exploratory estimate of the woody species composition, biomass and carbon stock of six plots in order to gain quantitative insight into the carbon pools in the lowland forests across Southwest (SW) Nigeria. Using plot level quadrat (25 × 25 m) approach, this study explores the structural characteristic and carbon stock potential of the tropical natural forest. . Woody species composition, density, girth-size, height, basal area, and carbon stock from five major pools and their impact on total carbon storage were determined. A total of 89 woody species with mean density of 770.67/ha were enumerated and species structural composition, biomass and carbon stock differed among the investigated plots. Plots III and IV had the highest total number of species and woody density. The species diversity also varies across the plots, and ranged between 2.01 in Plot VI to 2.91 in Plot III. Although majority of the species present in Plots I, II, IV, and VI have lower species importance value index and smaller girth sizes, there were still few individuals with high girth-size. Above and below ground pools suggest that the study area has the capacity of storing between 145.17 to 745.57 Mg C ha−1 of carbon. Carbon stock estimate of the aboveground pool (1,593.89 MgC/ha) was higher than the belowground pool (595.19 MgC/ha) and carbon contribution from litter (0.0203 MgC/ha) and herb (0.0067 MgC/ha) was quite low. Overall, these findings have shown that despite the ongoing anthropogenic disturbance, SW Nigeria tropical forest has considerable potential carbon sequestration.

Bem2d.jl: A quadratic co-location two-dimensional boundary element approach to quasi-static faulting problems with gravity and non-planar topography

Linear elastic boundary element models are commonly used tools to understand the mechanics of earthquake cycle processes and their contribution to the growth of tectonic structures. Here we describe a two-dimensional plane strain linear elastic boundary element approach to earthquake cycle and tectonic processes based on the displacement discontinuity method. This approach integrates an analytic solution for coincident interactions using three node quadratic elements and the classic particular integral approach to uni-directional gravity. Three node quadratic elements are more accurate than classical constant displacement elements and enable the exact representation displacements, stresses and tractions on elements subject to slip gradients. We demonstrate the recovery of analytic solutions and illustrate the combined effects of faulting and gravitational body forces in the presence of topographic relief.

An Optimal Scheduling and Planning of Campus Microgrid Based on Demand Response and Battery Lifetime

Existing electricity supply systems face several challenges, including increasing energy prices with greenhouse gas (GHG) emissions and fossil fuel depletion. These issues have a significant impact on all power system stakeholders, including customers/prosumers, utilities, and microgrid operators. Renewable energy incorporation and different energy managing strategies such as demand-side management (DSM), demand response (DR), and others may help to overcome these limitations. Campus microgrids are among the largest energy consumers in the United States, with high energy expenditures. This article presents a new energy management (EMS) system for a university campus microgrid with onsite solar PV and ESS that operates in a grid exchange scenario. The suggested EMS not only lowers power consumption costs by prolonging storage life; however, it also guarantees grid stability through limiting and shifting loads using price-based and incentive-based demand response methods. ESS is utilized as a stand-by energy reserve to maintain the microgrid system stability and to assist the utility network in the event of a power outage. In MATLAB, a quadratic approach is used to solve the proposed framework. According to the findings, the suggested EMS decreases the prosumer's operating cost and increasing self-consumption, minimizes peak load from the national grid, and encourages campus stakeholders and energy controllers to engage in large-scale ESS installations and distributed generation (DG).

Robust Resource Allocation for Two-Tier HetNets: An Interference-Efficiency Perspective

The heterogeneous network (HetNet) is a promising network for beyond 5G to improve network capacity and spectral efficiency by developing low-power small cells within macro networks. Therefore, appropriate resource allocation schemes should be designed to balance between data rates and the cross-tier interference among different cells. To improve system robustness and also reduce the harmful interference to macrocell users (MUs), in this paper, we maximize the total interference efficiency (IE) (i.e., the ratio of the sum data rates of femtocell users (FUs) to the total cross-tier interference from femtocell base stations (FBSs) to MUs) with imperfect channel state information in a two-tier orthogonal frequency division multiple access based HetNet by jointly optimizing the transmit power of the FBS and the subcarrier allocation factor. Meanwhile, the outage rate constraint of each FU, the outage interference constraint of each MU, the maximum transmit power constraint of the FBS, and the subcarrier assignment constraint are considered simultaneously. The considered problem belongs to a mixed-integer non-linear programming problem and thus is NP-hard. The original problem with uncertain parameters is transformed into a deterministic and convex one solved by using the quadratic transformation approach, the variable relaxation approach, and Lagrange dual theory. The feasible region analysis and robust sensitivity are provided. Simulation results demonstrate that the proposed scheme has a lower interference to the MU and higher IE by comparing it with the traditional schemes.

Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential

AbstractWe consider numerical approximations for a modified phase field crystal model with a strong nonlinear vacancy potential. Based on the invariant energy quadratization approach and stabilized strategies, we develop linear, unconditionally energy stable numerical schemes using the first‐order Euler method, the second‐order backward differentiation formulas and the second‐order Crank–Nicolson method, respectively. We rigorously prove the unconditional energy stability, the mass conservation of these three numerical schemes and carry out error estimates in time for the first‐order numerical scheme. Various numerical experiments in 2D and 3D are carried out to validate the accuracy, energy stability, mass conservation, and efficiency of the proposed schemes.