An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Multi-Source Underwater DOA Estimation Using PSO-BP Neural Network Based on High-Order Cumulant Optimization

Due to the complex and changeable environment under water,the performance of traditional DOA estimation algorithms based on mathematical model,such as MUSIC,ESPRIT,etc.,degrades greatly or even some mistakes can be made because of the mismatch between algorithm model and actual environment model.In addition,the neural network has the ability of generalization and mapping,it can consider the noise,transmission channel inconsistency and other factors of the objective environment.Therefore,this paper utilizes Back Propagation(BP)neural network as the basic framework of underwater DOA estimation.Furthermore,in order to improve the performance of DOA estimation of BP neural network,the following three improvements are proposed.(1)Aiming at the problem that the weight and threshold of traditional BP neural network converge slowly and easily fall into the local optimal value in the iterative process,PSO-BP-NN based on optimized particle swarm optimization(PSO)algorithm is proposed.(2)The Higher-order cumulant of the received signal is utilized to establish the training model.(3)A BP neural network training method for arbitrary number of sources is proposed.Finally,the effectiveness of the proposed algorithm is proved by comparing with the state-of-the-art algorithms and MUSIC algorithm.

Time–frequency co-movement and risk connectedness among cryptocurrencies:new evidence from the higher-order moments before and during the COVID-19 pandemic

Analyzing comovements and connectedness is critical for providing significant implications for crypto-portfolio risk management.However,most existing research focuses on the lower-order moment nexus(i.e.the return and volatility interactions).For the first time,this study investigates the higher-order moment comovements and risk connectedness among cryptocurrencies before and during the COVID-19 pandemic in both the time and frequency domains.We combine the realized moment measures and wavelet coherence,and the newly proposed time-varying parameter vector autoregression-based frequency connectedness approach(Chatziantoniou et al.in Integration and risk transmission in the market for crude oil a time-varying parameter frequency connectedness approach.Technical report,University of Pretoria,Department of Economics,2021)using intraday high-frequency data.The empirical results demonstrate that the comovement of realized volatility between BTC and other cryp-tocurrencies is stronger than that of the realized skewness,realized kurtosis,and signed jump variation.The comovements among cryptocurrencies are both time-dependent and frequency-dependent.Besides the volatility spillovers,the risk spillovers of high-order moments and jumps are also significant,although their magnitudes vary with moments,making them moment-dependent as well and are lower than volatility connectedness.Frequency connectedness demonstrates that the risk connectedness is mainly transmitted in the short term(1–7 days).Furthermore,the total dynamic connectedness of all realized moments is time-varying and has been significantly affected by the outbreak of the COVID-19 pandemic.Several practical implications are drawn for crypto investors,portfolio managers,regulators,and policymakers in optimizing their investment and risk management tactics.

CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES

The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

Neighboring optimal guidance using higher-order dynamics approximation with application to orbital injection problem

Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its high computational efficiency and low resource usage.For more advanced scenarios,the existing methods still have a problem that the guidance accuracy and optimality will seriously degrade when the actual state largely deviates from the nominal trajectory.This is mainly caused by the approximate description of the first-order conditions in terms of total flight time and nonlinear constraints.To address this problem,a higher-order neighboring optimal guidance method is proposed.First,a novel total flight time updating strategy,together with a normalized time scale,is presented that transforms the optimal problem with free total flight time into a more tractable optimal problem with fixed total flight time.Then,using the vector partial derivative method,a higher-order approximation is adopted,instead of the first-order approximation,to accurately describe the nonlinear dynamical and terminal constraints,thus obtaining a polynomially constrained quadratic optimal problem.Finally,to numerically solve the polynomially constrained quadratic optimal problem,a Newton-type iterative algorithm based on the orthogonal decomposition is designed.Through the iterative solution within each guidance period,the corrections to control quantities and total flight time are generated.The proposed method is applied to a launch vehicle orbital injection problem,and simulation results show that it achieves high accuracy of orbital injection and optimality of performance index.

Batch-to-batch Optimization of Batch Crystallization Processes

It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an optimal performance when implemented to real processes. This study proposes a batch-to-batch optimization strategy for the estimation of uncertain kinetic.par.ameters in a batch crystallization process of potassium sulfate production. The knowledge of a crystal size distribution of the product at the end of batch operation is used in the proposed methodology. The updated kinetic parameters are applied for determining an optimal operating temperature policy for the next batch run.

MoM-based topology optimization method for planar metallic antenna design

The metallic antenna design problem can be treated as a problem to find the optimal distribution of conductive material in a certain domain. Although this problem is well suited for topology optimization method, the volumetric distribution of conductive material based on 3D finite element method (FEM) has been known to cause numerical bottlenecks such as the skin depth issue, meshed 'air regions' and other numerical problems. In this paper a topology optimization method based on the method of moments (MoM) for configuration design of planar metallic antenna was proposed. The candidate structure of the planar metallic antenna was approximately considered as a resistance sheet with position-dependent impedance. In this way, the electromagnetic property of the antenna can be analyzed easily by using the MoM to solve the radiation problem of the resistance sheet in a finite domain. The topology of the antenna was depicted with the distribution of the impedance related to the design parameters or relative densities. The conductive material (metal) was assumed to have zero impedance, whereas the non-conductive material was simulated as a material with a finite but large enough impedance. The interpolation function of the impedance between conductive material and non-conductive material was taken as a tangential function. The design of planar metallic antenna was optimized for maximizing the efficiency at the target frequency. The results illustrated the effectiveness of the method.

OPTIMAL CONTROL OF BRAKING MOMENT FOR A WHEEL AND TYRE

in the design of the antiskid braking system (ABS) of an aircraft, the braking moment is one of the most important parameters, because it influences not only the deceleration and the taxiing distance of an aircraft, but also the strength and the fatigue life of the landing gear. Furthermore, the determination of braking moment will be concerned in the reasonableness of the demands proposed for the material design of a brake. For this reason, through setting up the mechanical model of a wheel and tyre under taxiing and braking, dynamic simulations on the optimal closed-loop control of braking moment are carried out by means of the nonlinear control theory. The simulation results show that the difference between the real output of the ABS and the expected one can tend to the minimum under the optimal control. And also, this optimal control can guarantee the braking moment to change smoothly.

Optimal seismic retrofit model for steel moment resisting frames with brittle connections

Based on performance-based seismic engineering, this paper proposes an optimal seismic retrofit model for steel moment resisting frames（SMRFs） to generate a retrofit scheme at minimal cost. To satisfy the acceptance criteria for the Basic Safety Objective（BSO） specified in FEMA 356, the minimum number of upgraded connections and their locations in an SMRF with brittle connections are determined by evolutionary computation. The performance of the proposed optimal retrofitting model is evaluated on the basis of the energy dissipation capacities, peak roof drift ratios, and maximum interstory drift ratios of structures before and after retrofitting. In addition, a retrofit efficiency index, which is defined as the ratio of the increment in seismic performance to the required retrofitting cost, is proposed to examine the efficiencies of the retrofit schemes derived from the model. The optimal seismic retrofit model is applied to the SAC benchmark examples for threestory and nine-story SMRFs with brittle connections. Using the retrofit efficiency index proposed in this study, the optimal retrofit schemes obtained from the model are found to be efficient for both examples in terms of energy dissipation capacity, roof drift ratio, and maximum inter-story drift ratio.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

IMPEDANCE THEORY AND BANDWIDTH OPTIMIZATION OF THE TWIN-LOOP ANTENNA

The Twin-Loop Antenna(TLA)has been widely used because of itsbroadband property and simply feeding,and some modified structures have been devel-oped from its prototype by Chinese engineers.But the exact design theory for TLA accord-ing to the impedance calculation has not yet been published.In this paper,the impedanceof loop in a TLA is analysed and computed by using the method of moments,and the de-sign formulae and a two-step optimization program for extending the bandwidth of inputimpedance of TLA are detailed.An example of optimized design shows that the bandwidthcan be increased up to 36.4% for VSWR≤1.10,which is wider than the bandwidth of ra-diation pattern.

DIRECTIVITY OPTIMIZATION OF CURVED SURFACE DIPOLE ANTENNAS

Based on the calculation of the characteristic parameters by moment method, the curved surface dipoles are optimized by an optimization method, the maximum directivities of some V-curved and Gauss-curved surface dipoles are given.

Reliability-based concurrent subspace optimization method

To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

A Derivative-Free Optimization Algorithm Using Sparse Grid Integration

We present a new derivative-free optimization algorithm based on the sparse grid numerical integration. The algorithm applies to a smooth nonlinear objective function where calculating its gradient is impossible and evaluating its value is also very expensive. The new algorithm has: 1) a unique starting point strategy;2) an effective global search heuristic;and 3) consistent local convergence. These are achieved through a uniform use of sparse grid numerical integration. Numerical experiment result indicates that the algorithm is accurate and efficient, and benchmarks favourably against several state-of-art derivative free algorithms.

市场激励型环境规制与区域绿色创新效率——基于产业结构优化的中介作用和财政分权的调节作用

市场激励型环境规制是解决环境治理负外部性、推进区域绿色创新效率的重要途径。以2005~2020年省级面板数据为研究对象,采用系统广义矩模型(GMM)法检验市场激励型环境规制对区域绿色创新效率的影响效应及作用机理。结果表明:市场激励型环境规制能够显著促进区域绿色创新效率的提升;从影响机制来看,市场激励型环境规制可以通过促进产业结构合理化和产业结构高级化显著促进区域绿色创新效率的提升。此外,有效的财政分权环境能够正向调节市场激励型环境规制与区域绿色创新效率的关系。

基于火箭简化模型的多状态模型修正研究

火箭发射过程中燃料的不断减少导致火箭结构不断变化,结构的固有频率和模态振型也会随之变化。针对有限元模型的不准确性,以截面惯性矩为修正参数,不同状态下数值仿真结果与试验测试结果的误差最小为目标函数,建立多状态模型修正的优化模型。通过灵敏度分析和一阶泰勒展开对目标函数进行显式化处理,并利用序列线性规划求解得到设计变量的最优解。同时对于多状态结构,以多截面简支梁模型为例,利用锤击法对简支梁进行试验,设计磁吸重物方案模拟多状态模型,以单截面简支梁试验的前4阶频率为目标函数建立优化模型,经过修正将多截面简支梁模型修正为单截面简支梁模型,并且符合截面惯性矩与面积的比例,验证了多状态模型修正方法的准确性。

基于影响矩阵和精英遗传算法的斜拉桥索力优化

由于传统索力优化方法不能自动优化和兼顾全桥结构性能,以及与智能优化算法相结合后存在计算量大、耗时长、效率低和收敛速度慢等缺点,以Ansys和Matlab分别作为结构计算器和主控程序,以最小弯矩能为控制目标,将影响矩阵和精英保留策略引入到遗传算法中,实现成桥阶段的索力优化.该方法能够同时兼顾主梁与主塔的受力特性,而且影响矩阵的应用可以解决每一代都需要有限元评估的问题,大大减少了计算量.与传统的影响矩阵法相比,所提方法在吸取影响矩阵法优点的基础上,还考虑参数迭代过程,可在结构的关键截面添加特殊的约束要求,使得优化过程更加符合实际,而精英保留策略的引入可以提高进化迭代收敛的速度与进化过程的稳定性.最后,通过一个实际工程应用验证了所提方法的可行性.