ODE在整体自装卸车操作训练系统中的应用

开源动力学引擎(Open Dynamics Engine,ODE)是一个开源的多刚体动力学引擎。整体自装卸车是近年来发展起来的集装、卸、运功能于一体的新型集装化运输车辆,在军事后勤补给和民用方面发挥着重要的作用。详细介绍了利用ODE建立整体自装卸车操作训练系统动力学模型的方法和过程,并测试了表现效果。介绍了该动力学模型应用于某军用仓库真实训练系统的情况。

Continuous-Time Prediction of Industrial Paste Thickener System With Differential ODE-Net

It is crucial to predict the outputs of a thickening system,including the underflow concentration(UC)and mud pressure,for optimal control of the process.The proliferation of industrial sensors and the availability of thickening-system data make this possible.However,the unique properties of thickening systems,such as the non-linearities,long-time delays,partially observed data,and continuous time evolution pose challenges on building data-driven predictive models.To address the above challenges,we establish an integrated,deep-learning,continuous time network structure that consists of a sequential encoder,a state decoder,and a derivative module to learn the deterministic state space model from thickening systems.Using a case study,we examine our methods with a tailing thickener manufactured by the FLSmidth installed with massive sensors and obtain extensive experimental results.The results demonstrate that the proposed continuous-time model with the sequential encoder achieves better prediction performances than the existing discrete-time models and reduces the negative effects from long time delays by extracting features from historical system trajectories.The proposed method also demonstrates outstanding performances for both short and long term prediction tasks with the two proposed derivative types.

可重构的微分方程通用解算器研究和实现

基于经典微分方程数值解法四阶龙格-库塔法(fourth-order Runge-Kutta,RK4),文章提出一种可重构微分方程解算器(reconfigurable differential equation solver,RDES)。RDES采用可重构的计算原理,内部运算部件能够被映射为不同常微分方程(ordinary differential equation,ODE)的求解电路。RDES支持ODEs的快速批量求解,具有良好的通用性。几种实际应用的ODEs进行性能验证的实验结果表明,RDES能够求解不同结构、阶数、变量等条件的ODEs,且在批量计算中性能较通用处理器提升约10~120倍。

森林工程教学课堂融入高等数学知识的研究

针对学生缺少足够的高等数学知识解决工程实践中实际问题的现状,为了在森林工程课堂教学中将高等数学知识与工程实践更好地结合,基于实际的研究工作,对用于解决常微分方程的显式欧拉法、隐式欧拉法、改进欧拉法、龙格库塔法和ODE45方法进行了介绍和对比研究。结果表明,这些方法在解决常微分方程的数值解上是一致的,而且相互之间的误差很小。介绍了解决偏微分方程的PDE方法。在建模的过程中用到了有限元方法,在方程的列写过程中用到了矩阵方法,通过理论分析可以看出,矩阵表示的是实际问题与空间、时间的关系,因而可以从直观的角度去理解抽象的矩阵知识。这些方法可以很好地帮助森林工程领域的学生在今后的工作中建立数学模型并加以分析,从而加强解决实际工程问题的能力,也为森林工程课题今后的教学提供一定的参考。

考虑故障状态的LCC-HVDC建模方法研究

直流输电系统的参数设计和故障分析依赖于系统建模与仿真,常规详细模型的仿真需要借助实时数字仿真等设备,而现有的简化模型又难以保证故障状态下的准确性,亟需提出新的建模方法以减小简化模型的暂态误差,继而降低直流输电系统的仿真难度与投入成本。为此,文中提出一种基于电网换相换流器的高压直流输电(LCC-HVDC)的常微分方程(ODE)模型,并将开关函数扩展到兼顾故障运行状态。首先,基于开关函数理论推导出LCC-HVDC的ODE模型;接着分析了自然换相点偏移和换相失败对开关函数的影响,并以此提出一种考虑故障状态的开关函数调制策略;最后结合仿真算例,研究了ODE模型在多种故障状态下的运行特性,并计算对比了仿真误差与运行效率。仿真结果表明,文中ODE模型能够准确反映换流阀的各种故障状态,且具有误差小、效率高的优点。

Neural network as a function approximator and its application in solving differential equations

A neural network(NN) is a powerful tool for approximating bounded continuous functions in machine learning. The NN provides a framework for numerically solving ordinary differential equations(ODEs) and partial differential equations(PDEs)combined with the automatic differentiation(AD) technique. In this work, we explore the use of NN for the function approximation and propose a universal solver for ODEs and PDEs. The solver is tested for initial value problems and boundary value problems of ODEs, and the results exhibit high accuracy for not only the unknown functions but also their derivatives. The same strategy can be used to construct a PDE solver based on collocation points instead of a mesh, which is tested with the Burgers equation and the heat equation(i.e., the Laplace equation).

A New Circulant Preconditioned GMRES Method for Solving Ordinary Differential Equation

The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases.

家蚕嗅觉蛋白研究进展

嗅觉系统在家蚕的宿主植物定位、可食性鉴别和交配产卵等生理活动过程中起着重要作用。家蚕对外界气味分子的识别过程有多种蛋白参与,主要包括气味结合蛋白(OBPs)、信息素结合蛋白(PBPs)、化学感受蛋白(CSPs)、气味受体(ORs)、气味降解酶(ODE)等。本文以家蚕嗅觉蛋白研究为重点,综述了OBPs、CSPs与ODE方面的研究进展,旨在为家蚕及其他昆虫的嗅觉研究提供参考。

Local parameter identification with neural ordinary differential equations

The data-driven methods extract the feature information from data to build system models, which enable estimation and identification of the systems and can be utilized for prognosis and health management(PHM). However, most data-driven models are still black-box models that cannot be interpreted. In this study, we use the neural ordinary differential equations(ODEs), especially the inherent computational relationships of a system added to the loss function calculation, to approximate the governing equations. In addition, a new strategy for identifying the local parameters of the system is investigated, which can be utilized for system parameter identification and damage detection. The numerical and experimental examples presented in the paper demonstrate that the strategy has high accuracy and good local parameter identification. Moreover, the proposed method has the advantage of being interpretable. It can directly approximate the underlying governing dynamics and be a worthwhile strategy for system identification and PHM.

Perturbation by Decomposition:A New Approach to Singular Initial Value Problems with Mamadu-Njoseh Polynomials as Basis Functions

This paper focuses on the application of Mamadu-Njoseh polynomials(MNPs)as basis functions for the solution of singular initial value problems in the second-order ordinary differential equations in a perturbation by decomposition approach.Here,the proposed method is an hybrid of the perturbation theory and decomposition method.In this approach,the approximate solution is slihtly perturbed with the MNPs to ensure absolute convergence.Nonlinear cases are first treated by decomposition.The method is,easy to execute with well-posed mathematical formulae.The existence and convergence of the method is also presented explicitly.Resulting numerical evidences show that the proposed method,in comparison with the Adomian Decomposition Method(ADM),Homotpy Pertubation Method and the exact solution is reliable,efficient and accuarate.

Tau-Collocation Approximation Approach for Solving First and Second Order Ordinary Differential Equations

This paper presents Tau-collocation approximation approach for solving first and second orders ordinary differential equations. We use the method in the stimulation of numerical techniques for the approximate solution of linear initial value problems (IVP) in first and second order ordinary differential equations. The resulting numerical evidences show the method is adequate and effective.

HPLC-CAD法测定替诺福韦酯类前药ODE-TFV中ODE残留量

目的：建立测定替诺福韦十八烷氧乙基单酯衍生物（ODE-TFV）中十八烷氧乙醇（ODE）含量的高效液相色谱-电喷雾检测器（HPLC-CAD）的方法。方法：采用Agilent ZORBAX XDB-C8柱（4.6 mm×75 mm,3.5μm）,以0.1 mol·L-1醋酸铵缓冲液（pH 4.0）为流动相A,乙腈为流动相B,梯度洗脱,流速约为1.0 mL·min-1,柱温40℃;采用电喷雾检测器（charged aerosol detector,CAD）,雾化室温度30℃,采样频率10 Hz;进样量10μL。结果：本法的线性范围为0.1000~10.00μg·mL-1（r=0.9999,n=6）,最低检测限为50.00 ng·mL-1;最低定量限为100.0 ng·mL-1;方法平均回收率（n=9）为99.8%。结论：本文建立的方法能满足ODE-TFV原料药中ODE残留量监控的需要。