Stochastic polynomial optimization

ABSTRACT

This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre-type Moment-SOS relaxations are used to solve the sample average optimization. Properties of the optimization and its relaxations are studied. Numerical experiments are presented.     

Supply chain network design under the risk of uncertain disruptions

Facility disruptions in the supply chain often lead to catastrophic consequences, although they occur rarely. The low frequency and non-repeatability of disruptive events also make it impossible to estimate the disruption probability accurately. Therefore, we construct an uncertain programming model to design the three-echelon supply chain network with the disruption risk, in which disruptions are considered as uncertain events. Under the constraint of satisfying customer demands, the model optimises the selection of retailers with uncertain disruptions and the assignment of customers and retailers, in order to minimise the expected total cost of network design. In addition, we simplify the proposed model by analysing its properties and further linearise the simplified model. A Lagrangian relaxation algorithm for the linearised model and a genetic algorithm for the simplified model are developed to solve medium-scale problems and large-scale problems, respectively. Finally, we illustrate the effectiveness of proposed models and algorithms through several numerical examples.     

基于协同优化算法的流速仪检定系统设计

提出了一种小型轻便的流速仪检定系统的设计方案,并运用改进的多学科协同优化方法求解各学科设计变量的最优解。首先介绍了算法思想及改进措施,并根据系统设计要求建立了各学科的设计变量、目标函数和约束条件；其次,运用遗传算法求解各学科设计变量的最优解,并根据优化结果完善了系统的设计方案,同时运用计算机仿真等方法验证了优化结果的可行性。结果表明,优化后的检定系统满足流体力学效应、匀速运动时间、系统重量等设计要求,同时证明了协同优化算法解决多学科设计优化问题的有效性。     

A-site Ca2+ substitution induced polyvalent Cu cations and correlated polaron relaxations in colossal permittivity Li1-xCaxCuNb3O9

LiCuNb₃O₉ has been reported newly a colossal permittivity (CP) perovskite, in which the B-site NbO₆ octahedra play a bridging role in the polaron hopping. However, how the A-site modification affects the origin of the polarons and further the CP behaviours remains unexplored. To this end, A-site Ca²⁺ was incorporated to form Li_1-xCa_xCuNb₃O₉, and the local states, dielectric relaxations and conduction behaviours were comprehensively studied. The substitution induces the polyvalent Cu cations, i.e. Cu⁺/Cu²⁺/Cu³⁺. Bond valence sum calculations imply that Cu²⁺ and Cu³⁺ are underbonded, and Cu⁺ is overbonded, while B-site Nb⁵⁺ shows slightly different with theoretical pentavalence. All the compositions exhibit a similarly room-temperature CP response, but present two dielectric relaxations, i.e. T_R1:170–300 K and T_R2:260–400 K. Comprehensive investigations on universal dielectric response and bulk dc conductivity indicate that the T_R1 follows the variable-range-hopping where the electron hopping between the mixed Cu⁺/Cu²⁺, while T_R2 contributes from the Cu³⁺ nearest neighbor hopping.     

Influence of the stoichiometry,microstructure, and metallization method on the dielectric properties of 0.94 Na0.5Bi0.5TiO3-0.06 BaTiO3

The morphotropic composition of the lead-free solid solution between Na_0.5Bi_0.5TiO₃ and BaTiO₃ (0.94 Na_0.5Bi_0.5TiO₃-0.06 BaTiO₃ or NBT-6BT) is of particular interest for the next generation of high-temperature capacitors but remains plagued by the diversity of dielectric properties reported in the literature. In order to explain the apparent inconsistencies among the reported dielectric properties of NBT-6BT, we examine the influence of stoichiometry, phase separation, and metallization method. We show that the nominal stoichiometry has a crucial effect, since increasing the nominal Na/Bi ratio increases conductivity and dielectric losses (tan δ). It also increases the real part of the permittivity (ε’) and the frequency dispersion of both ε’ and tan δ, thereby altering the shape of the evolution with temperature of the dielectric properties. Moreover it increases the depolarization temperature (T_d) and decreases the temperature of maximum permittivity (T_m). Phase separation also occurs during the synthesis of NBT-6BT as Na evaporation leads to the formation of secondary Ba-containing phases. We report that these phases can have a positive impact on the dielectric properties: a moderate volume fraction (2.5 to 3.0%) and average grain surface (0.9 to 3.0 µm²) of these secondary Ba-containing phases increase the relative permittivity, decrease the dielectric losses, and increase the insulation resistance. We also show that the metallization method impacts the dielectric properties and therefore may contribute to the differences between various reports. The dielectric properties of NBT-6BT samples are measured during successive heating/cooling cycles and reveal that the permittivity value is lower during the first heating when silver paste, even cured, is used. These three components contribute to explaining the diversity of the reported dielectric properties of NBT-6BT.     

Electrochemical performance and distribution of relaxation times analysis of tungsten stabilized La0·5Sr0·5Fe0·9W0·1O3-δ electrode for symmetric solid oxide fuel cells

W-doped La_0·5Sr_0·5Fe_0·9W_0·1O_3-δ (LSFW) was prepared and evaluated as a symmetric electrode for solid oxide fuel cells (SSOFCs). Phase and structural stability of LSFW under both reducing and oxidizing atmospheres was studied. The oxygen reduction reaction (ORR) and hydrogen oxidation reaction (HOR) mechanisms were investigated by using electrochemical impedance spectra (EIS) and distribution of relaxation times (DRT). Electrode polarization resistance (R_p) of LSFW are 0.08 and 0.16 Ω cm² in air and wet hydrogen at 800 °C, respectively. DRT results indicate that the rate-limiting step of LSFW at 800 °C in cathodic conditions and anodic conditions are related to oxygen diffusion and hydrogen adsorption/diffusion, respectively. A La_0·8Sr_0.2Ga_0.8Mg_0·2O_3-δ (LSGM) electrolyte-supported single cell using LSFW electrodes shows a maximum power density of 617.3 mW cm⁻² at 800 °C with considerable stability and reversibility, which enables LSFW a promising SOFCs symmetric electrode material.     

Effects of hydrocarbon impurities,vibrational relaxation,and boundary-layer-induced pressure rise on the ignition of H2–O2‒Ar mixtures behind reflected shock waves

The results of an experimental and theoretical study of the ignition of H₂–O₂?Ar mixtures behind reflected shock waves are reported. The experiments are performed with mixtures containing from 0.15 to 8.0% H₂ and from 0.75 to 2.0% O₂ at temperatures of 980–1800 K and a total gas concentration of (1.0 ± 0.1) × 10^?5 mol/cm³. The progress of the process is monitored by recording the time evolution of the pressure behind the reflected shock wave and the intensity of the chemiluminescence of electronically excited OH1 radicals (λ = 308 ± 2.5 nm). A numerical model capable of predicting the effects of additional factors, such as hydrocarbon impurities, the vibrational relaxation of the test mixture, and boundary-layer-induced pressure rise, is developed and used to simulate our own and published experimental data on the ignition of H₂–O₂?Ar mixtures. It is demonstrated that the best agreement between experimental and theoretical results is achieved when all the additional factors are taken into account. A sensitivity analysis shows that the effects of the vibrational relaxation of the test mixture and the presence of hydrocarbon impurities are significant only for lean mixtures, whereas the influence of the boundary-layer-induced pressure rise is important across a wide range of stoichiometries at long ignition delay times. Additionally, an analytical model is developed, which takes into account the finite time of the chain?propagation reactions O + H₂ and OH + H₂. The predictions of the numerical and analytical models are demonstrated to be in close agreement for a wide range of mixture compositions and experimental conditions.     

Understanding CO2 electrochemical reduction kinetics of mixed-conducting cathodes by the electrical conductivity relaxation method

Electrochemical reduction reaction is an important approach to utilize CO₂ and convert it into valuable products. Exceptional reaction kinetics at a high temperature of solid oxide electrolysis cells (SOECs) attracts particular attention. In this work, we propose to investigate CO₂-RR kinetics using a new theoretical method based on the electrical conductivity relaxation (ECR) technique on a typical mixed-conducting Sr₂Fe_1.5Mo_0.5O_6-δ (SFM) electrode. Three kinetic parameters that are commonly adopted in the typical electrochemical test experiments consisting of overpotential, current density and area-specific resistance (ASR) are derived. The overpotential resulted from the difference in the oxygen partial pressure is caused by the change of CO₂ partial pressure, while current density from the surface reaction rate constant. Accordingly, area-specific resistance, as well as overpotential-current density relationship, can be derived. We believe that this work brings a new method to study the kinetic process of CO₂ electrolysis and to evaluate the electrocatalyst activity of developed new electrode materials as well as to benefit the designing of novel electrode electrocatalysts for highly efficient solid oxide electrolysis cells.     

Mixed convection flow of a Maxwell nanofluid with Hall and ion‐slip impacts employing the spectral relaxation method

This article investigates the Hall and ion‐slip impacts on the mixed convection flow of a Maxwell nanofluid over an expanding surface in a permeable medium. The impacts of Brownian movement and thermophoresis parameters, Soret, Dufour, viscous dissipation, chemical reaction, and suction parameters, are, moreover, considered. Using the similitude changes, the partial differential equations with regard to the momentum, energy, and concentration equations are transformed to an arrangement of nonlinear ordinary differential equations, which are handled numerically utilizing a spectral relaxation method (SRM). The impacts of noteworthy physical parameters on the velocities, thermal, and concentration distributions are investigated graphically. Moreover, the numerical values of skin‐friction coefficients, local Nusselt number, and Sherwood number for different values of the mixed convection parameter $\left(\gamma \right),$ Deborah number $\left(\lambda \right),$ Hall parameter $({\beta }_{\mathrm{H}}),$ ion‐slip parameter $({\beta }_{\mathrm{i}}),$ Dufour number (Du), and Soret number $\left(\mathit{Sr}\right)$ are computed and tabulated. It is discovered that ascent in Deborah number reduces both the stream and transverse velocity profiles, while the inverse pattern is seen with augmentation in the mixed convection parameter. In addition, inverse patterns of the stream and transverse velocity profiles are seen with expansion in magnetic, Hall, and ion‐slip parameters. Besides this, the temperature and concentration disseminations decline with augmentation in Dufour number and chemical reaction parameters, respectively. It is likewise seen that both the skin‐friction coefficients lessen with expansion in Deborah number, and they ascend with upgrade in blended convection and ion‐slip parameters, while the opposite condition is noticed with augmentation in Hall parameter. Furthermore, the reverse trends of local Nusselt and Sherwood numbers are discovered with expansion in the Dufour and Soret numbers.