Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second-and Fourth-Order Gradient Plasticity Models

To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band （ASB） are predicted. The calculated results of the second- and fourth- order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the sec- ond-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively.

A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.

Fractional Order Modeling of Human Operator Behavior with Second Order Controlled Plant and Experiment Research

Modeling human operator's dynamics plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behavior, a new kind of fractional order mathematical model for human operator in single-input single-output (SISO) systems is proposed. Compared with the traditional models based on the commonly used quasilinear transfer function method or the optimal control theory method, the proposed fractional order model has simpler structure with only few parameters, and each parameter has explicit physical meanings. The actual data and experiment results with the second-order controlled plant illustrate the effectiveness of the proposed method. © 2014 Chinese Association of Automation.

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.

Modelling of Energy Storage Photonic Medium by Wavelength-Based Multivariable Second-Order Differential Equation

Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium.The existence of this medium demands certain mathematical constraints,which have been derived in detail.Using reverse modelling,a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point.A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium,despite scattering,absorption,fluorescence,heat generation,and other nonlinear mechanisms.The energy and velocity functions are thus singly and doubly differentiable with respect to wavelength.The solution of the resulting second-order differential equation in two variables proves that energy storage or energy flotation occurs inside a medium with a refractive index satisfying the described mathematical constraints.The minimum-value-normalized refractive index profiles of the modelled optical medium for transformed wavelengths both inside the medium and for vacuum have been derived.Mathematical proofs,design equations,and detailed numerical analyses are presented in the paper.

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.

Fritz John Duality in the Presence of Equality and Inequality Constraints

A dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situation, is formulated which uses Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and does not require a constraint qualification. Various duality results, namely, weak, strong, strict-converse and converse duality theorems are established under suitable generalized convexity. A generalized Fritz John type dual to the problem is also formulated and usual duality results are proved. In essence, the duality results do not require any regularity condition if the formulations of dual problems uses Fritz John optimality conditions.

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.

浮式风力机若干特征动力学问题综述

总结浮式风力机类型及其对应的特征动力学问题,针对浮式风力机气动荷载、水动荷载的计算方法以及结构动力学、控制动力学典型问题进行论述。讨论了气动—水动—结构—伺服耦合分析的难点,重点分析了二阶波浪力、畸形波等非线性波浪荷载、流荷载及涡激运动对浮式风力机特征动力响应的影响。阐述了浮式风力机动力学研究的试验方法、数值仿真方法、样机测试方法,并对模型试验技术的相似理论、气动模型的实现和难点以及数值仿真的频域方法、时域方法和分析工具进行了归纳对比。研究表明:浮式风力机多场、多体耦合动力分析机理及相关技术仍不成熟,气动荷载、高阶非线性波浪荷载耦合模型的建立是动力学问题研究的重点,数值仿真及模型试验是浮式风力机动力响应研究的主要方法,样机测试技术的积累将促进设计标准的完善及浮式风电的产业化发展。

基于超螺旋二阶滑膜的汽车主动悬架控制方法研究

汽车悬架的控制效果直接影响汽车的稳定性和舒适性,针对一阶滑模控制在主动悬架控制中存在的抖振和控制精度问题,基于汽车二自由度1/4主动悬架模型,提出了一种基于超螺旋二阶滑模控制的汽车主动悬架控制方法。在控制器前端串联一个负加速度反馈回路来调节悬架性能,并使用扩展的超螺旋观测器实时补偿系统的未知内部动态。为了验证控制方法的可行性,通过仿真进行对比分析。仿真结果表明,相比于一阶滑膜控制,该方法解决了悬架未知非线性动态的多目标控制问题,能更有效地改善汽车稳定性和舒适性。

基于二阶价值梯度模型强化学习的工业过程控制方法

为了实现对高延时、非线性和强耦合的复杂工业过程稳定准确的连续控制,提出了一种基于二阶价值梯度模型强化学习的控制方法。首先,该方法在模型训练过程中加入了状态价值函数的二阶梯度信息,具备更精确的函数逼近能力和更高的鲁棒性,学习迭代效率更高;其次,通过采用新的状态采样策略,可以更高效地利用模型进行策略学习。最后,通过在OpenAI的Gym公共实验环境和两个工业场景的仿真环境的实验表明:基于二阶价值梯度模型对比传统的基于最大似然估计模型,环境模型预测误差显著降低;基于二阶价值梯度模型的强化学习方法学习效率优于现有的基于模型的策略优化方法,具备更好的控制性能,并减小了控制过程中的振荡现象。可见该方法能有效地提升训练效率,同时提高工业过程控制的稳定性和准确性。

基于HPPC-FFRLS的锂电池等效模型参数在线辨识

目的为了实现锂离子动力电池的高精度状态监测与分析,方法针对锂离子动力电池二阶RC等效电路模型的参数在线辨识展开研究。搭建锂离子动力电池二阶RC等效电路模型;利用开路电压法与安-时积分算法相结合的方式进行电池荷电状态(SOC)评估;通过HPPC测试实验数据进行等效电路模型的离线参数辨识;以离线辨识结果作为系统状态初值,结合带遗忘因子的递推最小二乘算法(FFRLS)对锂离子动力电池二阶RC等效电路模型参数进行在线辨识;利用Simulink搭建电池状态监测和充放电控制仿真系统,对基于在线辨识参数的模型进行仿真测试;利用可编程电源和电子负载搭建实验平台。结果对比在线辨识参数的系统仿真输出、离线辨识参数的系统仿真输出和实验数据,结果表明:基于HPPC-FFRLS在线辨识的模型仿真输出的误差相对于HPPC实验法减小了50%;在线辨识策略克服了环境温度、电池老化、充放电倍率等因素对参数的影响;仿真初期系统波动明显减小,等效模型系统动态跟踪具有更高的精度,鲁棒性更好。结论基于HPPC-FFRLS的锂电池等效模型在线辨识保证了模型参数的有效性,简化运算量的同时提高了模型精度。