Nonlinear Optimization Procedure Research Articles

Enhancing energy efficiency and comfort with a multi-domain approach: Development of a novel human thermoregulatory model for occupant-centric control

Occupant Centric Control (OCC) strategies aims to achieve a more personalized and comfortable indoor environment, translating occupants' comfort requirements into real environmental conditions. This strategy relies on a multilevel non-linear programming optimization procedure to determine optimal thermo-hygrometric setpoints. The objective is to minimize space heating and cooling requirements while addressing multi-domain comfort concerns related to individual thermal sensations and perceived air quality. To facilitate this process, this study adopts a novel Personal Comfort Model (PCM), incorporating physiological factors to predict occupants' thermal sensations and CO2 intakes. The PCM's reliable predictive capabilities are confirmed through validation with real experimental data from a test room at the University of Perugia. For detailed energy analyses, considering occupants' subjective comfort preferences, the PCM is seamlessly integrated into DETECt, an in-house building energy performance simulation tool developed by the University of Naples Federico II, for the design of advanced control algorithms and energy efficiency strategies. To effectively manage the HVAC system, a model predictive control is implemented, using the determined setpoints to ensure mechanical ventilation and maximize cost savings. The proof of concept for the developed methodology involves simulating experimental tests using the thermal model of the human body and the new facility management system, to be simulated and optimized by means of the enhanced building energy performance simulation tool, exploited for the design and operation of more occupant-centric and sustainable buildings. The proposed study demonstrates that through the developed OCC strategy enables a significant reduction in thermal discomfort (40 % and 60 % less than the occupation time for test 1 and test 2, respectively) compared to reference scenarios. Additionally, energy analysis reveals high efficiency, achieving savings of 12.8 % and 7.8 % of electricity consumed for HVAC system operation.

RMS Current Minimization in a SiC-Based Dual Active Bridge Converter Using Triple-Phase-Shift Modulation

This paper proposes an optimization approach targeting RMS current minimization in a dual active bridge (DAB) converter controlled by triple-phase-shift modulation. The proposed technique overcomes the drawbacks in the existing optimization solutions, namely, the high complexity of the time-domain optimization and low accuracy of the fundamental harmonic minimization. A finite-component harmonic model is employed in the optimization approach to calculate the current harmonic values in the converter. The total RMS current is approximated as the summation of dominant harmonics using the harmonic model. A numerical assessment technique is also proposed in this research that guarantees the accuracy of the adopted harmonic model. The proposed method ensures that the harmonic approximation error is less than a certain level over the operating range. The converter's optimal parameters are calculated through a standard nonlinear optimization procedure. The results are verified in the PLECS simulation environment and experimentally validated on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5\ kW$</tex-math></inline-formula> DAB converter. The prototype input and output voltage ranges are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$600\ V - 800\ V$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$200\ V - 450\ V$</tex-math></inline-formula> , respectively.

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. We demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

RRVPE: A Robust and Real-Time Visual-Inertial-GNSS Pose Estimator for Aerial Robot Navigation

Self-localization and orientation estimation are the essential capabilities for mobile robot navigation. In this article, a robust and real-time visual-inertial-GNSS(Global Navigation Satellite System) tightly coupled pose estimation (RRVPE) method for aerial robot navigation is presented. The aerial robot carries a front-facing stereo camera for self-localization and an RGB-D camera to generate 3D voxel map. Ulteriorly, a GNSS receiver is used to continuously provide pseudorange, Doppler frequency shift and universal time coordinated (UTC) pulse signals to the pose estimator. The proposed system leverages the Kanade Lucas algorithm to track Shi-Tomasi features in each video frame, and the local factor graph solution process is bounded in a circumscribed container, which can immensely abandon the computational complexity in nonlinear optimization procedure. The proposed robot pose estimator can achieve camera-rate (30 Hz) performance on the aerial robot companion computer. We thoroughly experimented the RRVPE system in both simulated and practical circumstances, and the results demonstrate dramatic advantages over the state-of-the-art robot pose estimators.

Photovoltaic single diode model parameter extraction by dI/dV-assisted deterministic method

In this work, a state-of-the-art deterministic method is proposed for photovoltaic single diode model parameter extraction from experimental current–voltage (I-V) curves. This new method takes advantage of the numerical derivative (dI/dV) information, such that a high-quality solution can be obtained by linear least squares technique. The solution can be further improved through a two-step nonlinear optimization procedure using the trust-region-reflective or Levenberg-Marquardt algorithm. Compared with previous methods, the proposed method has achieved the best accuracy with the lowest computation cost up till now in the benchmark test of two commonly-used case studies. When comparing the computation costs of different works, it is pointed out for the first time that not only the number of iteration steps but also the single-step computation complexity should be taken into account if different deterministic optimization algorithms are implemented. Furthermore, the robustness of the proposed method is verified through a large-scale dataset containing more than one million I-V curves, showing that the method can be used for realtime monitoring of photovoltaic modules. Finally, a MATLAB app is developed and freely provided to the public.

Mathematical Model and Solution Algorithm for Virtual Localization Problem

Introduction. The optimization placement problem refereed to virtual localization is studied. This problem is motivated by the need to optimize the production of parts from near-net shape blanks using CNC machines. The known algorithms for solving the virtual localization problem come down to determining the location parameters of the part CAD model inside the point cloud obtained by scanning the workpiece surface. The main disadvantage of such algorithms is the use of criteria that are insensitive to the intersection of the surfaces of the part and the workpiece. In order to prevent such errors in production conditions, it is necessary to involve a human operator in conducting operations based on virtual localization. In this way, the virtual localization problem of complex shape objects is of paramount importance. The purpose of the paper is to propose a new approach for solving the virtual localization problem. Results. A new mathematical model of the virtual localization problem based on the phi-function technique is proposed. We developed a solution strategy that combines algorithm of generating feasible starting points with non-linear optimization procedure. The testing of the proposed approach was carried out for a two-dimensional case. The computational results illustrated with graphical illustrations are provided that show the efficiency of the proposed algorithm. Conclusions. The obtained results show that the use of the phi-functions technique prevents the occurrence of erroneous solutions with the intersection of the workpiece surfaces. An algorithm for solving the problem of virtual localization in a two-dimensional formulation for the case when the part and the workpiece are convex polygons has been developed. For the considered test problems, the solution time did not exceed 2.5 sec, which fully meets the requirements of industrial use. In the future, it is planned to extend the proposed method to the cases when the CAD model of the part has an arbitrary shape and is formed by Boolean operations on geometric primitives. Keywords: polygonal domain, phi-function technique, virtual localization, CNC machining.

Topology optimization of nonlinear flexoelectric structures

Recent advances in nanotechnology have allowed for the manufacturing of nanostructures and nanodevices with optimized topologies that outperforms their traditional counterparts based on simple geometry in terms of efficiency and function. In this work, a novel nonlinear topology optimization procedure is developed to design optimal layouts of flexoelectric structures undergoing large displacement. The optimal material distribution is determined by optimizing the energy conversion efficiency. Two material properties such as the elasticity coefficient and the permittivity coefficient are interpolated through the solid isotropic material with a penalization approach via an energy interpolation scheme to overcome the numerical instability. Obtained results have revealed that accounting for the geometric nonlinearity leads to a different final optimal topology with a better energy converting efficiency as compared to the linear model. We also found the significant influences of size effects on the optimized structure emphasizing the importance of nonlocal elastic behavior in characterizing and designing micro-structures and flexoelectricity.

Efficient Metropolis-Hastings Robbins-Monro Algorithm for High-Dimensional Diagnostic Classification Models.

The expectation-maximization (EM) algorithm is a commonly used technique for the parameter estimation of the diagnostic classification models (DCMs) with a prespecified Q-matrix; however, it requires O(2 K ) calculations in its expectation-step, which significantly slows down the computation when the number of attributes, K, is large. This study proposes an efficient Metropolis-Hastings Robbins-Monro (eMHRM) algorithm, needing only O(K + 1) calculations in the Monte Carlo expectation step. Furthermore, the item parameters and structural parameters are approximated via the Robbins-Monro algorithm, which does not require time-consuming nonlinear optimization procedures. A series of simulation studies were conducted to compare the eMHRM with the EM and a Metropolis-Hastings (MH) algorithm regarding the parameter recovery and execution time. The outcomes presented in this article reveal that the eMHRM is much more computationally efficient than the EM and MH, and it tends to produce better estimates than the EM when K is large, suggesting that the eMHRM is a promising parameter estimation method for high-dimensional DCMs.

Determination of Soil Hydraulic Properties from Infiltration Data Using Various Methods

In the present study, the determination of soil saturated hydraulic conductivity (Ks) and soil sorptivity (S) from one-dimensional vertical infiltration data of eight different soils were investigated using three methodologies. Specifically, the nonlinear optimization procedure with the help of the Excel Solver application using six different two-parameter infiltration equations, as described by Valiantzas, Haverkamp et al. (complete, two and three approximate expansions), Talsma and Parlange and Green and Ampt; the linearization method of cumulative infiltration data by Valiantzas and the method of Latorre et al. were used. The results showed that, in almost all cases, the relative errors in the prediction of S were smaller than those of Ks. The nonlinear optimization procedure using the Valiantzas equation gave the best prediction of S and Ks, with relative errors up to −12.49% and 13.61%, respectively. The two-term approximate expansion of Haverkamp gave the highest relative errors in both S and Ks. The various forms of the Haverkamp equation (complete and three approximate expansion), as well as the Latorre method, gave good predictions of S and Ks in fine-textured soils. In all forms of the Haverkamp equation, when parameter β was considered as an additional adjustment parameter, no improvement in the prediction of the S and Ks values was achieved, so the constant value β = 0.6 was proposed. The relative errors in the prediction of S and Ks resulting from the linearization method of the cumulative infiltration data were similar to those of the Valiantzas equation by the nonlinear optimization procedure. The accuracy in estimating the S and Ks parameters from each equation depends on its infiltration time validity and the soil type.

Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect

The conventional target for self-excited galloping/flutter control of a civil structure often focuses on the critical wind speed. In the present work, a nonlinear control target is introduced, i.e., to ensure that the vibration amplitude is lower than a threshold value (pre-specified according to the expected structural performance) before a target wind speed. Unlike the conventional control target, the nonlinear one can take into account the underlying large-amplitude vibrations before the critical state and/or the structural safety redundancy after the critical state. To obtain the most economical TMD parameters that enable the nonlinear target, an optimization procedure involving nonlinear aeroelastic effect is developed for galloping control based on the quasi-steady aeroelastic force model, and for flutter control based on a nonlinear unsteady model. Three numerical examples involving the galloping/flutter control of different cross-sections are analyzed to demonstrate the different results designed by the conventional and nonlinear targets. It is demonstrated that the nonlinear target and optimization procedure can lead to more economical design results than the conventional ones in the galloping/flutter control for a structure with relatively large post-critical safety redundancy, and they are more reliable than the conventional ones for a structure that may experience large-amplitude vibrations before the critical wind speed. These superiorities of the nonlinear control target and new optimization procedure suggest that they may be utilized in the TMD parameter optimization for galloping/flutter control of structures in a wide domain of engineering fields.

A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

Abstract We present a constitutive model for particle-binder composites that accounts for finite-deformation kinematics, nonlinear elasto-plasticity without apparent yield, cyclic hysteresis, and progressive stress-softening before the attainment of stable cyclic response. The model is based on deformation mechanisms experimentally observed during quasi-static monotonic and cyclic compression of mock Plastic-Bonded Explosives (PBX) at large strain. An additive decomposition of strain energy into elastic and inelastic parts is assumed, where the elastic response is modeled using Ogden hyperelasticity while the inelastic response is described using yield-surface-free endochronic plasticity based on the concepts of internal variables and of evolution or rate equations. Stress-softening is modeled using two approaches; a discontinuous isotropic damage model to appropriately describe the softening in the overall loading-unloading response, and a material scale function to describe the progressive cyclic softening until cyclic stabilization. A nonlinear multivariate optimization procedure is developed to estimate the elasto-plastic model parameters from nominal stress-strain experimental compression data. Finally, a correlation between model parameters and the unique stress-strain response of mock PBX specimens with differing concentrations of aluminum is identified, thus establishing a relationship between model parameters and material composition.

Polarimetric Model-Based Decomposition with Refined Double-Bounce Orientation Angle and Scattering Model

Oriented manmade targets can produce significant cross-polarization power. The scattering mechanism interpretation of them is still challenging. Within the framework of traditional scattering models, the scattering mechanism of oriented manmade targets will be interpreted as volume scattering. Recently, many advanced approaches have been proposed to mitigate the cross-polarization terms of the coherency matrix or distribute the power of cross-polarization to new scattering models, such as orientation angle compensation and multiple scattering components decomposition. Among these methods, the general model-based decomposition with physically meaningful double-bounce and odd-bounce scattering models has been proposed by modeling their independent orientation angles and becomes a widely accepted method. However, the two vital parameters of generalized scattering models: double- and odd-bounce orientation angles are derived through nonlinear optimization procedure. These generalized models lead to a heavy computation burden for parameters inversion. In this paper, we disclose the latent relationship between the double-bounce orientation angle and polarization orientation angle by data fitting experiments. With this simplified relationship, a refined double-bounce scattering model is established. Then, the odd-bounce orientation angle can be derived through equations. In this way, the nonlinear optimization procedure can be converted to a linear solution. A fast generalized model-based decomposition is developed thereafter. The main contribution of this work is to inherit the generalized models while speeding up the parameter calculation procedure. The comparison studies are carried out with X-band airborne PiSAR, L-band spaceborne ALOS-2, and C-band spaceborne Radarsat-2 PolSAR datasets. Compared with the state-of-the-art approaches, the proposed decomposition achieves improved interpretation performance from both visual and quantitative investigations especially for oriented built-up areas.

Investigate Thermodynamic and Kinetic Degradation of Lithium-Ion Batteries through a Combined Experimental and Modeling Approach

With the significant cost reduction of Li-ion battery (LIB) (85% in the past 10 years), 50-fold growth in market penetration of the technology has been projected through to 2030 for modern transportation and renewable energy integration [1]. LIB is a high energy density, high round-trip efficiency, high reliability energy storage device [2]. Different from Internal Combustion Engine, as a power generator, LIB pack is sealed in a certain container and its status need to be estimated by additional diagnostic instruments with specific electrochemical performance data. The traditional methods to estimate State of Charge (SOC) and State of Health (SOH) include current integration method and open circuit voltage method, which are time-consuming (over 1 day) and rely on historical information of the system [3]. Impedance spectroscopy technique can capture both thermodynamic and kinetic information of the LIB in a relatively short time, however, it is difficult and sometimes unreliable to interpret the data by using a simplified equivalent circuit method (ECM). In our recent publication [4], we also find that nonideality effect caused by interaction among high concentration Li ions could lead to nonlinear transport and kinetic parameters as a function of SOC. In this research work, we would like to use the perturbation form of a physics-based LIB model considering the nonideality feature of the cell to deconvolute the electrochemical impedance spectroscopy (shown in Fig.1) of a LIB coin cell operating under different SOCs and different number of cycles. After proper status evaluation of beginning of life (BOL) of the cell, parasitic side reactions, the solid electrolyte interface (SEI) formation in anode and cathode, are included as the indicators of degradation. A nonlinear optimization procedure will be used to identify the parameters associated with the cell capacity loss in each electrode, solid/liquid interface reaction, Li-ion diffusion, ohmic resistance, etc. The results will map out the cell capacity loss caused by thermodynamic degradation and deteriorated reaction kinetics and diffusivity caused by the growth of the SEI layers during cycling. It will provide important guidance in designing fast and accurate LIB real-time diagnostic devices.

Topology optimization of multi-material structures with elastoplastic strain hardening model

The paper presents a new multi-material topology optimization method with a novel adjoint sensitivity analysis that can accommodate not only multiple plasticity but also multiple hardening models for individual materials in composite structures. Based on the proposed method, an integrated framework is developed which details the nonlinear finite element analysis, sensitivity analysis and optimization procedure. The proposed method and framework are implemented and illustrated by three numerical examples presented in this paper. An in-depth analysis of the numerical results has revealed the significant impact of the selection of plasticity and hardening model on the results of topology.

An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

We present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

Modeling the Reaction and Transport Mechanism for Total Petroleum Hydrocarbon Using Selected Linear and Nonlinear Error Functions

In this article, field pilot study was undertaken to examine the transport mechanism for total petroleum hydrocarbon remediation in varying concentration using pseudo first order, pseudo second order and intra particle diffusion kinetic models in land farming treatment. Soil samples were artificially contaminated in varying concentration of 1,000 mg/kg (low), 3,000 mg/kg (medium) and 5,000 mg/kg (high) and treated using organic and inorganic fertilizers for a period of 150days which is the duration for effective remediation treatment. The results from the treated samples were subjected to kinetics studies while coefficient of determination (R2) was applied on the residual total petroleum hydrocarbon (TPH) after 150 days of treatment, pseudo first order had R2 values of 0.7898 (low), 0.6776 (medium) and 0.6131 (high). Pseudo second order had R2 values of 0.9737 (low), 0.9467 (medium), 0.7863 (high) while intra particle diffusion had R2 values of 0.9940 (low), 0.9821 (medium) and 0.9489 (high) respectively. The results indicate that intra particle diffusion model best described the kinetics mechanism of TPH remediation using land farming treatment; but when the alteration in the error structure associated with transforming a nonlinear kinetic equation into linear equation is minimized using nonlinear regression optimization procedure, pseudo first order emerged as the best kinetic model having the least sum of errors as 0.000270 (low), 0.000185 (medium) and 0.000278 (high).

Inverse Design of a Graphene-Based Quantum Transducer via Neuroevolution

We introduce an inverse design framework based on artificial neural networks, genetic algorithms, and tight-binding calculations, capable to optimize the very large configuration space of nanoelectronic devices. Our non-linear optimization procedure operates on trial Hamiltonians through superoperators controlling growth policies of regions of distinct doping. We demonstrate that our algorithm optimizes the doping of graphene-based three-terminal devices for valleytronics applications, monotonously converging to synthesizable devices with high merit functions in a few thousand evaluations (out of $\simeq 2^{3800}$ possible configurations). The best-performing device allowed for a terminal-specific separation of valley currents with $\simeq 96$\% ($\simeq 94\%)$ $K$ ($K'$) valley purity. Importantly, the devices found through our non-linear optimization procedure have both higher merit function and higher robustness to defects than the ones obtained through geometry optimization.

Modeling and prediction of the 2019 coronavirus disease spreading in China incorporating human migration data.

This study integrates the daily intercity migration data with the classic Susceptible-Exposed-Infected-Removed (SEIR) model to construct a new model suitable for describing the dynamics of epidemic spreading of Coronavirus Disease 2019 (COVID-19) in China. Daily intercity migration data for 367 cities in China were collected from Baidu Migration, a mobile-app based human migration tracking data system. Early outbreak data of infected, recovered and death cases from official source (from January 24 to February 16, 2020) were used for model fitting. The set of model parameters obtained from best data fitting using a constrained nonlinear optimisation procedure was used for estimation of the dynamics of epidemic spreading in the following months. The work was completed on February 19, 2020. Our results showed that the number of infections in most cities in China would peak between mid February to early March 2020, with about 0.8%, less than 0.1% and less than 0.01% of the population eventually infected in Wuhan, Hubei Province and the rest of China, respectively. Moreover, for most cities outside and within Hubei Province (except Wuhan), the total number of infected individuals is expected to be less than 300 and 4000, respectively.

An Empirical Stochastic Volatility Model for Bitcoin Price Range Forecasting

By applying a Heston-like stochastic volatility model to an empirical returns-based drift-diffusion model, we show by extensive backtesting that we can improve Bitcoin price forecast accuracy for investment horizons of 7, 30, 45, and 60 days. In particular, we can improve median forecasts and also extreme tail forecasts simultaneously by applying a nonlinear parameter optimization procedure to find stochvol model parameters and by targeting the optimization to fit to historical data. The stochastic volatility model as solved provides additional backtest accuracy versus the baseline empirical drift-diffusion model, and forecasts from a tuned stochvol model are notably different than an associated baseline model, especially at the more extreme percentiles. Since contemporary daily returns on DOGE coin were noted to be mostly orthogonal to other high market cap crypto currencies, the model was tested and tuned on a 1 day forecast DOGE coin backtest, with positive results.

Modeling the Reaction and Transport Mechanism for Total Petroleum Hydrocarbon Using Selected Linear and Nonlinear Error Functions

In this article, field pilot study was undertaken to examine the transport mechanism for total petroleum hydrocarbon remediation in varying concentration using pseudo first order, pseudo second order and intra particle diffusion kinetic models in land farming treatment. Soil samples were artificially contaminated in varying concentration of 1,000 mg/kg (low), 3,000 mg/kg (medium) and 5,000 mg/kg (high) and treated using organic and inorganic fertilizers for a period of 150days which is the duration for effective remediation treatment. The results from the treated samples were subjected to kinetics studies while coefficient of determination (R&lt;sup&gt;2&lt;/sup&gt;) was applied on the residual total petroleum hydrocarbon (TPH) after 150 days of treatment, pseudo first order had R&lt;sup&gt;2&lt;/sup&gt; values of 0.7898 (low), 0.6776 (medium) and 0.6131 (high). Pseudo second order had R2 values of 0.9737 (low), 0.9467 (medium), 0.7863 (high) while intra particle diffusion had R&lt;sup&gt;2&lt;/sup&gt; values of 0.9940 (low), 0.9821 (medium) and 0.9489 (high) respectively. The results indicate that intra particle diffusion model best described the kinetics mechanism of TPH remediation using land farming treatment; but when the alteration in the error structure associated with transforming a nonlinear kinetic equation into linear equation is minimized using nonlinear regression optimization procedure, pseudo first order emerged as the best kinetic model having the least sum of errors as 0.000270 (low), 0.000185 (medium) and 0.000278 (high).