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.

Inverse approach to determine piston profile from impact stress waveform on given non-uniform rod

An essential problem in the design of mechanical impact systems is the impact of a piston on a rod. The impact of a semi finite cylindrical piston on a non uniform rod was studied. Based on wave mechanics and characteristic line theory, an inverse numerical approach to determine the piston profile was proposed, by means of which the geometry of an impact piston may be determined from the given stress waveform for a given rod profile. Numerical results show that the given stress waveform may be produced by means of the alternatives of design of piston and rod. There is good agreement between the experimental results and numerical results. [

IDENTIFICATION OF ELASTIC-PLASTIC MECHANICAL PROPERTIES FOR BIMETALLIC SHEETS BY HYBRID-INVERSE APPROACH

Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by experimental measurements. The present paper proposes a hybrid-inverse analysis method for the identification of the nonlinear material parameters of any individual component from the mechanical responses of a global composite. The method couples experimental approach, numerical simulation with inverse search method. The experimental approach is used to provide basic data. Then parameter identification and numerical simulation are utilized to identify elasto-plastic material properties by the experimental data obtained and inverse searching algorithm. A numerical example of a stainless steel clad copper sheet is consid- ered to verify and show the applicability of the proposed hybrid-inverse method. In this example, a set of material parameters in an elasto-plastic constitutive model have been identified by using the obtained experimental data.

Dynamic multifunctional metasurfaces:an inverse design deep learning approach

Optical metasurfaces(OMs)offer unprecedented control over electromagnetic waves,enabling advanced optical multiplexing.The emergence of deep learning has opened new avenues for designing OMs.However,existing deep learning methods for OMs primarily focus on forward design,which limits their design capabilities,lacks global optimization,and relies on prior knowledge.Additionally,most OMs are static,with fixed functionalities once processed.To overcome these limitations,we propose an inverse design deep learning method for dynamic OMs.Our approach comprises a forward prediction network and an inverse retrieval network.The forward prediction network establishes a mapping between meta-unit structure parameters and reflectance spectra.The inverse retrieval network generates a library of meta-unit structure parameters based on target requirements,enabling end-to-end design of OMs.By incorporating the dynamic tunability of the phase change material Sb2Te3with inverse design deep learning,we achieve the design and verification of dynamic multifunctional OMs.Our results demonstrate OMs with multiple information channels and encryption capabilities that can realize multiple physical field optical modulation functions.When Sb2Te3is in the amorphous state,near-field nano-printing based on meta-unit amplitude modulation is achieved for X-polarized incident light,while holographic imaging based on meta-unit phase modulation is realized for circularly polarized light.In the crystalline state,the encrypted information remains secure even with the correct polarization input,achieving double encryption.This research points towards ultra-compact,high-capacity,and highly secure information storage approaches.

Similarity measure of sedimentary successions and its application in inverse stratigraphic modeling

This paper presents a unique and formal method of quantifying the similarity or distance between sedimentary facies successions from measured sections in outcrop or drilled wells and demonstrates its first application in inverse stratigraphic modeling. A sedimentary facies succession is represented with a string of symbols, or facies codes in its natural vertical order, in which each symbol brings with it one attribute such as thickness for the facies. These strings are called attributed strings. A similarity measure is defined between the attributed strings based on a syntactic pattern-recognition technique. A dynamic programming algorithm is used to calculate the similarity. Inverse stratigraphic modeling aims to generate quantitative 3D facies models based on forward stratigraphic modeling that honors observed datasets. One of the key techniques in inverse stratigraphic modeling is how to quantify the similarity or distance between simulated and observed sedimentary facies successions at data locations in order for the forward model to condition the simulation results to the observed dataset such as measured sections or drilled wells. This quantification technique comparing sedimentary successions is demonstrated in the form of a cost function based on the defined distance in our inverse stratigraphic modeling implemented with forward modeling optimization.

Two optimization algorithms for solving robotics inverse kinematics with redundancy

The kinematic redundancy in a robot leads to an infinite number of solutions for inverse kinematics, which implies the possibility to select a 'best' solution according to an optimization criterion. In this paper, two optimization objective functions are proposed, aiming at either minimizing extra degrees of freedom (DOFs) or minimizing the total potential energy of a multilink redundant robot. Physical constraints of either equality or inequality types are taken into consideration in the objective functions. Since the closed-form solutions do not exist in general for highly nonlinear and constrained optimization problems, we adopt and develop two numerical methods, which are verified to be effective and precise in solving the two optimization problems associated with the redundant inverse kinematics. We first verify that the well established trajectory following method can precisely solve the two optimization problems, but is computation intensive. To reduce the computation time, a sequential approach that combines the sequential quadratic programming and iterative Newton-Raphson algorithm is developed. A 4-DOF Fujitsu Hoap-1 humanoid robot arm is used as a prototype to validate the effectiveness of the proposed optimization solutions.

Design for a Crane Metallic Structure Based on Imperialist Competitive Algorithm and Inverse Reliability Strategy

Uncertainties in parameters such as materials, loading, and geometry are inevitable in designing metallic structures for cranes. When considering these uncertainty factors, reliability-based design optimization （RBDO） offers a more reasonable design approach. However, existing RBDO methods for crane metallic structures are prone to low convergence speed and high computational cost. A unilevel RBDO method, combining a discrete imperialist competitive algorithm with an inverse reliabil- ity strategy based on the performance measure approach, is developed. Application of the imperialist competitive algorithm at the optimization level significantly improves the convergence speed of this RBDO method. At the reli- ability analysis level, the inverse reliability strategy is used to determine the feasibility of each probabilistic constraint at each design point by calculating its a-percentile per- formance, thereby avoiding convergence failure, calcula- tion error, and disproportionate computational effort encountered using conventional moment and simulation methods. Application of the RBDO method to an actual crane structure shows that the developed RBDO realizes a design with the best tradeoff between economy and safety together with about one-third of the convergence speed and the computational cost of the existing method. This paper provides a scientific and effective design approach for the design of metallic structures of cranes.

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.

Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions

The Bayesian inversion method is a stochastic approach based on the Bayesian theory.With the development of sampling algorithms and computer technologies,the Bayesian inversion method has been widely used in geophysical inversion problems.In this study,we conduct inversion experiments using crosshole seismic travel-time data to examine the characteristics and performance of the stochastic Bayesian inversion based on the Markov chain Monte Carlo sampling scheme and the traditional deterministic inversion with Tikhonov regularization.Velocity structures with two different spatial variations are considered,one with a chessboard pattern and the other with an interface mimicking the Mohorovicicdiscontinuity(Moho).Inversions are carried out with different scenarios of model discretization and source–receiver configurations.Results show that the Bayesian method yields more robust single-model estimations than the deterministic method,with smaller model errors.In addition,the Bayesian method provides the posterior probabilistic distribution function of the model space,which can help us evaluate the quality of the inversion result.

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.

基于迭代自适应的短孔径逆合成孔径雷达成像方法

针对合成孔径时间短、逆合成孔径雷达数据成像质量差的问题,本研究提出一种基于迭代自适应恢复缺失数据(missing-data iterative adaptive processing approach,MIAA)的短孔径数据的逆合成孔径雷达(inverse synthetic aperture radar,ISAR)超分辨率成像方法。该方法利用MIAA对ISAR回波数据的方位向进行扩展,从而增加数据的方位向长度,提高成像质量。仿真和实测均表明该方法能够有效扩展回波数据的方位向长度,提高短孔径条件下的成像质量。

High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions

The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.

联合均值和散度逆高斯回归模型的参数估计

逆高斯回归模型可用于分析正偏态数据,人们通常研究解释变量对其均值参数的影响,但往往忽略了对其散度参数的影响,文章则基于解释变量对均值和散度都有影响的前提,针对联合均值和散度逆高斯回归模型,探讨模型参数的极大似然估计问题。MM算法在优化问题上具有分离参数、降低目标函数的维度、简化求解过程等优点,将MM算法应用于联合均值和散度逆高斯回归模型,能将多元似然函数彻底分解为一系列一元函数之和,从而绕开了参数估计中的矩阵求逆问题。模拟研究表明,当数据量达到100时就能得到很好的估计效果;实证分析表明,理论研究在实际应用中具有可行性。

关节角参数化结合接近矢量可行方向的五自由度机械臂逆运动学求解

五自由度的机械臂无法达到任意位姿,采用传统的位姿描述方式进行逆运动学求解时,极易产生无解的情况。文中以一种适用于清洁、喷涂、焊接等作业的、由4个旋转关节和1个移动关节构成的五自由度机械臂为例,建立运动学模型并进行逆运动学分析,在此基础上,提出一种关节角参数化结合接近矢量可行方向的逆运动学求解方法。该方法基于自由度约束的末端位姿描述,先通过关节角参数化将末端执行器的运动空间由三维降为二维,再采用几何法分析末端执行器在不同目标位置(远端、中间端、近端)时的接近矢量的可行方向,从而避免参数盲目取值,确保运动学逆解的存在,然后根据运动连续性和各关节的运动范围从中筛选出最优解。路径规划仿真结果表明,实际路径与规划路径非常吻合,关节运动平稳,证明了所提方法的可行性和准确性。文中研究的五自由度机械臂具有一定的代表性,逆运动学求解方法计算复杂度低,求解过程较为简便,求解思路可为欠自由度机械臂的逆运动学求解提供借鉴。

常州市基于网格监测的臭氧污染过程分析

为研究常州市2022年6月14-21日的臭氧连续超标过程,利用EKMA曲线分析此次污染过程中臭氧生成对其前体物VOCs和NO_(x)的敏感性,通过反距离权重插值算法对网格化数据进行插值对该污染过程进行分析。结果表明:常州市臭氧及其前体物存在明显的日变化特征。6月臭氧超标天的臭氧与温度呈正相关,与相对湿度呈负相关。常州市臭氧处于强VOCs控制区,削减VOCs会使当地臭氧生成潜势逐步降低;不当削减NO_(x)排放反而会使当地臭氧生成潜势上升。6月14-18日,江苏省呈区域型污染,常州市温度偏高有利于臭氧生成;19-20日臭氧污染气团不断向西移动,臭氧高值区处于常州市;21日主导风向转为东南风,常州本地臭氧生成叠加周边区域影响,致使常州市臭氧仍处于高值。

Two 3-D multi-cascade co-design inverse methods based on streamline curvature approach and Clebsch formulation for single-stage centrifugal compressors

Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage centrifugal compressors.These two three-dimensional methods and a typical quasi-threedimensional streamline curvature through-flow inverse method were employed to design the same subsonic high-speed single-stage centrifugal compressors.The compressor performances were simulated by a commercial Reynolds averaged Navier-Stokes(RANS) equations solver.The studies show that two three-dimensional codesign methods are reasonable and feasible.It was found that : firstly the blade camber angle designed by the three-dimensional methods was larger than that designed by the quasi-three-dimensional method;and secondly with regard to two three-dimensional methods with different boundary conditions,the co-design result differences between the diffusers were small,but those between the deswirlers were relatively large.

Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach

The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.

Convergence analysis of an incremental approach to online inverse reinforcement learning

Interest in inverse reinforcement learning (IRL) has recently increased,that is,interest in the problem of recovering the reward function underlying a Markov decision process (MDP) given the dynamics of the system and the behavior of an expert.This paper deals with an incremental approach to online IRL.First,the convergence property of the incremental method for the IRL problem was investigated,and the bounds of both the mistake number during the learning process and regret were provided by using a detailed proof.Then an online algorithm based on incremental error correcting was derived to deal with the IRL problem.The key idea is to add an increment to the current reward estimate each time an action mismatch occurs.This leads to an estimate that approaches a target optimal value.The proposed method was tested in a driving simulation experiment and found to be able to efficiently recover an adequate reward function.

基于有限元逆算法的板料成形模拟拉深筋的灵敏度优化

基于有限元逆算法和灵敏度优化的BFGS(Broyden-Fletcher-Goldfarb-Shanno)算法,提出一种以成形极限曲线和起皱极限曲线作为目标函数,优化拉深成形中的拉深筋位置和大小的拉深筋灵敏度优化算法。优化算法综合考虑冲压件成形过程中起皱和破裂对成形性的影响因素,比只考虑板厚变化更能准确地反映板料的成形性,而且基于逆算法的灵敏度优化算法计算速度很快,可以应用于大型复杂冲压件的工艺参数优化过程模拟。通过两个典型的零件验证了该算法的优化结果符合实际工艺。

板料冲压成形快速分析软件FASTAMP

基于先进的有限元逆算法研制开发了具有独立版权的板料冲压成形快速分析软件FASTAMP,与传统的增量法CAE软件有很大的区别,可以进行快速的优化设计和成形性模拟,主要面向产品设计、工艺设计与模具设计人员.该软件具有一套完整的、独立的前后处理系统,其中包括标准的CAD数据接口、曲面编辑和曲面网格生成器.