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.     

Quality assurance and quality control of subgrade compaction using the dynamic cone penetrometer

The Dynamic Cone Penetrometer (DCP) is a device that is used in the construction industry for the assessment of in situ soil compaction quality. Over the past few decades, numerous correlations have been developed between the DCP test results and soil strength and stiffness parameters. This paper proposes a comprehensive set of criteria and recommendations for quality control (QC) of compacted subgrade that take into account the inherent statistical variability of DCP test results. For the development of the QC criteria, a new statistical methodology is used to extract representative test values from the raw field DCP test data. In order to use the proposed QC criteria, soils are first classified into two broad categories (fine-grained and coarse-grained) depending on their fabric and response to compaction efforts. Test results indicate that (i) for fine-grained soils, the DCP test values have good correlation with the plasticity index (PI), which is indicative of the type and amount of clay content of the soil and (ii) for coarse-grained soils, the DCP test values have good correlation with the optimum water content of the soil, which is directly related to its in situ density. DCP blow count correlation equations are presented for both soil categories. Recommendations for field DCP testing and data analysis are also provided to highlight the significance of the statistical distribution of the DCP test results in QC testing of compacted subgrade.     

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。     

高速率通信网络下时变系统的有限时域H∞控制

针对高速率通信网络和Round-Robin（RR）协议影响下网络化时变系统的有限时域[H∞]控制问题，考虑到系统中存在乘性噪声、随机时滞和量化效应，提出了一种基于观测器的有限时域[H∞]控制器的设计方法。利用李雅普诺夫稳定性理论和线性矩阵不等式（Linear Matrix Inequality，LMI）技术得到有限时域[H∞]控制器存在的充分条件。基于锥补线性化（Cone Complementarity Linearization，CCL）方法通过求解一组递归矩阵不等式得到观测器和控制器参数。所设计的控制器保证闭环网络化时变系统在给定的时域内稳定，且满足预定的[H∞]性能指标。数值仿真验证了所提方法的有效性。     

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.     

Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

The paper deals with the consensus problem in a leaderless network of agents that have to reach a common velocity while forming a uniformly spaced string. Moreover, the final common velocity (reference velocity) is determined by the agents in a distributed and leaderless way. Then, the consensus protocol parameters are optimized for networks characterized by a communication topology described by a class of directed graphs having a directed spanning tree, in order to maximize the convergence rate and avoid oscillations. The advantages of the optimized consensus protocol are enlightened by some simulation results and comparison with a protocol proposed in the related literature. The presented protocol can be applied to coordinate agents such as mobile robots, automated guided vehicles (AGVs) and autonomous vehicles that have to move with the same velocity and a common inter-space gap.      

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.