基于实验的钛合金优化动态本构模型与有限元模拟

为确定钛合金材料的Johnson-Cook模型中5个待定本构参数,克服传统单因素分析法的弊端并提高参数识别效率和精度,采用拉丁超立方抽样、Spearman秩相关分析的参数敏感度整体分析方法,并在参数敏感度分析结果和基本遗传算法的基础上,建立了一种基于改进小生境算法、可疑峰值点判断策略和局域精确搜索技术的改进遗传算法,基于实验数据建立了精细的钛合金Johnson-Cook本构模型。采用隐式应力积分法将该模型嵌入到ABAQUS用户材料子程序UMAT中,并通过隐函数求导方法推导出一致切线刚度矩阵。通过ABAQUS有限元软件对钛合金材料的动态响应进行数值模拟分析,计算结果与已有的实验数据吻合良好,UMAT子程序的准确性得到验证,可用于钛合金材料的动态响应预测分析中。     

基于Sigma点全局迭代参数卡尔曼滤波的折线型本构模型参数识别

折线型本构模型控制参数少,物理意义明确,但其数学表达式复杂因而识别困难。针对折线型本构模型的参数识别,提出基于Sigma点变换的全局迭代参数卡尔曼滤波算法。所提方法以待识别参数作为状态向量,降低状态向量维度,减少计算量;基于Sigma点卡尔曼滤波避免求解雅克比(Jacobian)矩阵,实现非连续型函数本构模型的参数识别;通过设定目标函数进行全局迭代,以获得最优解。由于非线性系统下一时刻响应与历史路径有关,量测更新时由初始时刻计算到当前时刻。最后,在地震荷载下,将隔震支座系统简化为单自由度双线性模型,将桥墩简化为单自由度Takeda模型,根据该文所提出的方法理念,分别基于无迹卡尔曼滤波(unscented Kalman filter,UKF)、容积卡尔曼滤波(cubature Kalman filter,CKF)和球面单纯形径向容积正交卡尔曼滤波(spherical simplex-radial cubature quadrature Kalman filter,SSRCQKF)采样规则识别折线型本构模型参数。结果表明所提方法能够准确识别非线性参数,同时具有较强的鲁棒性,不同滤波器收敛过程及结果也有所差异。     

基于IHHO算法的光伏电池工程模型的参数辨识

针对HHO算法存在搜索过程调整不够灵活,不能针对性地进行阶段性搜索,有时会陷入局部最优使算法搜索精度相对较差等问题,提出了一种基于改进哈里斯鹰优化(IHHO)算法的参数辨识方法.对HHO算法进行了两项改进:引人柔性递减策略,在迭代初期扩大全局搜索范围,在迭代后期延长局部搜索时间,从而加强了初期的全局搜索能力和后期的局部...     

Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the Levenberg-Marquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.     

Assessing and ensuring parameter identifiability for a physically-based strain hardening model for twinning-induced plasticity

Physically-based strain hardening models have become important ingredients in metal forming simulations over the last years, since they allow for the modeling of multi-stage forming processes based on the evolution of physically meaningful internal variables. Although these models are physically-based, there are still many fitting parameters involved which have to be identified from experiments. As a matter of fact, for each physical effect that is included in the model, a separate equation with new fitting parameters is introduced, such that physically-based models tend to contain a large number of fitting parameters. Parameter estimation is often based on the macroscopic response of a specimen which is tested in compression, tension or shear at various strain rates and temperatures. It is not guaranteed that this macroscopic information suffices to estimate parameters in model equations that describe (sub-) microscopic phenomena, since the effect of one parameter on the course of strain hardening can be compensated by other parameters. Since such parameter correlations are hard to detect from the model equations alone, the parameter estimation process may be ill-conditioned, i.e. numerous parameter sets can be found for such models that deliver almost the same minimum value of the error function in the parameter identification process. Given that parameter estimation involves a series of costly experiments, methods are needed that allow for analyzing the identifiability of the model parameters before costly experiments are performed. In this paper, an approach is presented that analyzes model parameter dependencies and quantifies the identifiability of the model parameters. The model considered in this study calculates the flow stress based on the evolution of three dislocation densities and the evolution of deformation twins. The analysis shows that correlations between the model parameters exist and that it is not possible to determine all model parameters based on an experimental set of flow curves in a single curve fitting procedure. An adapted fitting strategy is presented in which fitting is performed step-wise so that in each fitting step, only identifiable parameters are estimated, allowing for successful parameter identification.     

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.     

A new strategy for assessing sensitivities in biochemical models

An integral part of any systems biology approach is the modelling and simulation of the respective system under investigation. However, the values of many parameters of the system have often not been determined or are not identifiable due to technical experimental difficulties or other constraints. Sensitivity analysis is often employed to quantify the importance of each of the model's parameters in the behaviour of the system. This approach can also be useful in identifying those parts of the system that are most sensitive with the potential of becoming drug targets. A problem of the commonly used methods of sensitivity analysis is that they constitute local methods meaning that they depend directly on the exact parameter space, which in turn is not known exactly. One way to circumvent this problem is to carry out sensitivity analysis over a wide range of values for all parameters, but this is handicapped by expensive computations when the systems are high dimensional. Another approach is to employ global sensitivity analysis, which in this context is mostly based on random sampling methods. In this paper we present an efficient approach that involves using numerical optimizing methods that search a wide region of parameter space for a given model to determine the maximum and minimum values of its metabolic control coefficients. A relevant example for drug development is presented to demonstrate the strategy using the software COPASI.     

镁合金AZ31D 热粘塑性模型的参数识别

通过联合实数编码遗传算法和一些经典的局部优化方法,构造了一种混合型的全局优化方法并用于开发一个专用的参数识别程序。使用这个专用程序进行了镁合金 AZ31D 的参数识别。变形试验和数值模拟结果的比较显示,本参数识别方法及其所得到的材料参数都是可用的。所得到的本构参数可用于镁合金零件热塑性成形的数值模拟。     

基于改进萤火虫算法的有限元模型修正

针对标准萤火虫算法后期收敛速度慢、收敛精度低、易陷入局部最优解的问题,提出了参数自适应策略的改进萤火虫算法,建立了基于改进萤火虫算法的有限元模型修正方法。通过隔代随机吸引度因子扩大了算法搜索路径,提升了算法遍历性,避免计算陷入局部最优;通过自适应步长因子使得算法寻优过程中能随迭代次数逐渐减少随机搜索范围,从而提高收敛速度。单、多峰测试函数计算结果表明,改进算法显著提高了收敛速率与收敛精度;简支梁数值算例与某刚构桥实桥有限元模型修正结果表明,简支梁参数最大误差由初始的66.7%降低至修正后的1.08%,刚构桥频率最大误差由14.47%降低至3.25%。所提方法具有良好的更新精度,适用于大型复杂结构的有限元模型修正。     

基于自适应混合近似模型的顶置武器站多柔体系统动力学优化研究

针对顶置武器站结构优化设计存在计算量大、优化效率低等问题,提出一种基于自适应混合近似模型的优化策略,引入分层设计空间缩减思想,在优化迭代过程中依次在构造的全局空间、聚类空间和重点空间内选取样本点更新混合近似模型,以同时提高模型的全局和局部预测能力。使用典型测试函数算例和某顶置武器站结构动力优化实例,验证了所提优化策略的有效性。顶置武器站结构动力优化结果表明:使用该方法获得的武器站炮口扰动目标函数减小了58.3%,各炮口扰动参数得到有效改善;与静态近似模型方法相比,该方法所得的炮口扰动目标函数优化结果降低了14.5%,所需调用武器站分析计算模型次数减少了47.4%。     

The two-level probabilistic description of the compressive constitutive parameters of concrete

The constitutive model of concrete is the critical basis for the nonlinear analyses of concrete structures. Due to the fact that the mechanical behavior of concrete exhibits remarkable randomness, the probabilistic modeling of the key parameters of the concrete constitutive model is of paramount significance. In the present study, a two-level probabilistic model is proposed to describe the dependent random constitutive parameters based on the compressive test results of several batches of concrete specimens of different strength grades. Both the local probabilistic dependence, i.e., the dependence of the parameters of intra-batch specimens, and the global probabilistic dependence, i.e., the dependence of the parameters of inter-batch specimens, are captured by the proposed method. To this end, the constitutive parameters of concrete are first standardized by their means and coefficients of variation (COVs). In this way, the local dependence can be represented by the same copula model for the concrete of different strength grades. The global dependence is expressed as the empirical formulae in terms of the means and COVs of the parameters. The full probabilistic model can then be obtained by synthesizing the local and global dependence models. The effectiveness of the proposed approach is demonstrated by comparing the generated samples with the test results. To illustrate the effect of the probabilistic dependence of the compressive constitutive parameters on the structural evaluation result, the nonlinear stochastic dynamic response analysis of a reinforced concrete frame is carried out. The results indicate that the probabilistic dependence of the constitutive parameters of concrete has a non-negligible effect on the structural response and reliability, and should be reasonably considered in practice.     

基于IALO算法的蓄电池参数辨识

合理的等效电路模型及准确的模型参数对蓄电池荷电状态(SOC)的准确估计具有重要影响。针对蓄电池三阶Thevenin等效电路模型,基于改进蚁狮优化算法,提出了一种模型参数辨识方法。引入混沌Logistic映射初始化,使初始化群体遍及解空间,有利于寻找全局最优解;引入自适应惯性权重加随机柯西变异策略,有效提高了算法收敛速度;引入精英反向学习策略,有效提高了群体的多样性,避免算法陷入局部最优解。5个测试函数的测试结果表明:相比于蚁狮优化算法、粒子群算法与樽海鞘优化算法,改进蚁狮优化算法收敛速度更快,精度更高。对蓄电池三阶Thevenin等效电路模型进行参数辨识,结果表明:改进蚁狮优化算法相比蚁狮优化算法具有更高的辨识精度。     

求解垂直互补问题的一种修正非光滑Levenberg-Marquardt算法

本文提出了一种求解垂直互补问题的修正非光滑Levenberg-Marquardt算法.与以往算法相比,该算法不但采用了新的微分形式取代了B-微分,还运用了一种LM参数的自适应调整策略以确保每次迭代时LM步不至于过小,从而保证了算法的快速收敛.最后,数值实验表明了算法的有效性.     

A consistent formulation for the integration of combined plasticity and creep

Within the context of the consistent tangent update, this paper outlines a stress update algorithm for combined creep and plasticity. The algorithm is implicit, providing unconditional stability, and utilizes local Newton iteration to solve SCALAR forms of the coupled constitutive equations for the creep and plastic strain increments. The tangent for the local iteration is obtained accurately providing quadratic convergence at the Gauss point level. Quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep. Further, combination with an automatic time-stepping scheme provides an efficient, stable, accurate and robust computational algorithm. The algorithm has been implemented in the general purpose FE package LUSAS¹.     

PBX炸药粘弹性损伤本构模型参数敏感度分析

建立了基于拉丁超立方抽样和Spearman秩相关系数的本构模型参数敏感度分析方法,实现对PBX炸药粘弹性损伤本构模型参数敏感度的整体性分析。以PBX炸药柱体压缩的分析为例,采用该方法确定了各本构参数对端面载荷值的敏感度及排序。并分析了抽样样本量,以及载荷加载速率对本构参数的敏感度的影响。同相关文献结果进行比较,证实了该方法的可行性。该文的方法可在参数识别中提前预测各参数对实验结果的敏感度,为本构模型参数识别中缩减待识别参数和选择合适的模拟实验提供理论基础。     

改进的 QPSO 算法在自融资投资组合中的应用

针对量子粒子群优化 (Quantum Particle Swarm Optimization, QPSO) 算法的缺陷,提出了一种基于 L$\acute{\rm e}$vy 飞行策略和混合概率分布的改进量子粒子群优化 (Hybrid Quantum Particle Swarm Optimization, HQPSO) 算法。在算法的设计中,借助 L$\acute{\rm e}$vy 飞行策略对粒子位置的迭代公式进行更新,用于改善算法的局部收敛精度,增强其全局探索能力。另外,考虑到迭代后期的早熟问题,在势阱模型中引入了指数分布和正态分布相结合的混合概率分布,帮助算法及时逃离局部最优。基于 16 个基准函数的测试结果表明,HQPSO 算法在收敛精度和鲁棒性上比其他几种算法表现更好。最后,将改进的 QPSO 算法应用到自融资投资组合模型的求解中,其数值结果与差分进化、粒子群优化算法和量子粒子群优化算法相比,HQPSO 算法展现出更好的可比性和优越性。     

Exploiting intrinsic fluctuations to identify model parameters

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non‐identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non‐identifiable. The authors present a method to identify model parameters that are structurally non‐identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one‐dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system''s behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration‐death, gene expression and Epo‐EpoReceptor interaction, that this resolves the non‐identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.Inspec keywords: biochemistry, physiological models, stochastic processes, measurement errors, fluctuations, parameter estimationOther keywords: model parameter identification, deterministic framework, biochemical system, steady state, transient state, stochastic modelling framework, objective function, immigration‐death model, gene expression, Epo–EpoReceptor interaction, stochastic fluctuations, measurement noise     

半固态流变行为模型及应用

半固态成形是21世纪最具潜力的先进制造技术之一.分析了国内外半固态变形行为研究进展,重点阐述了近似单相本构关系模型、两相本构关系模型、宏观-微观耦合本构关系模型的特点及应用,特别是笔者提出的宏观-微观耦合本构关系模型反映了工艺参数和微观组织参数对半固态流变应力的影响.同时,笔者将新型宏观-微观耦合本构关系模型应用于Al-4Cu-Mg合金半固态反挤压过程的有限元数值模拟,获得了工艺参数对应力应变、温度、晶粒尺寸、液相体分数和挤压载荷等的影响规律,数值模拟结果与半固态实验结果基本一致.     

基于蝙蝠算法优化的变分模态分解的转子裂纹检测方法

针对转子裂纹故障特征难于提取,提出了一种基于蝙蝠算法(BA)优化参数的变分模态分解(VMD)诊断转子裂纹故障的方法。将蝙蝠算法应用于变分模态分解,对变分模态分解中参数K和惩罚因子α进行全局寻优,用BA搜索VMD的最优(α,K)组合,迭代过程采用局部极小包络熵为适应度值。仿真分析的结果表明,BA-VMD方法能很好的完成VMD参数K和α的自适应获取,且在抗模态混叠和抗噪声干扰方面的具有明显优势,最后采用BA-VMD方法对裂纹转子的位移信号进行了实验分析,分析结果表明,采用BA-VMD方法处理后的频谱能充分反映出信号的频率特征,且通过频率结构特征很容易识别出转子裂纹的故障特征。     

正交各向异性孔板的材料参数识别

结合优化技术和边界元分析,针对正交各向异性孔板进行了材料参数的识别。材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与边界元计算相应的位移之差的平方和。采用Levenberg-Marquardt方法解极小化目标函数的问题,其中灵敏度的计算是基于离散的边界元代数矩阵方程对识别材料参数的求导。数值算例中,首先把边界元计算正交各向异性圆孔方板位移的结果与解析解进行比较,两者符合良好;然后采用本文提出的方法识别正交各向异性圆孔方板的材料参数。数值算例表明本文提出的方法是有效的。