Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.

Calculation of Mass Concrete Temperature Containing Cooling Water Pipe Based on Substructure and Iteration Algorithm

Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for evaluating the effectiveness of temperature control measures for mass concrete.One important measure for temperature control in mass concrete is the use of cooling water pipes.However,the mismatch of grids between large-scale concrete models and small-scale cooling pipe models can result in a significant waste of calculation time when using the finite element method.Moreover,the temperature of the water in the cooling pipe needs to be iteratively calculated during the thermal transfer process.The substructure method can effectively solve this problem,and it has been validated by scholars.The Abaqus/Python secondary development technology provides engineers with enough flexibility to combine the substructure method with an iteration algorithm,which enables the creation of a parametric modeling calculation for cooling water pipes.This paper proposes such a method,which involves iterating the water pipe boundary and establishing the water pipe unit substructure to numerically simulate the concrete temperature field that contains a cooling water pipe.To verify the feasibility and accuracy of the proposed method,two classic numerical examples were analyzed.The results showed that this method has good applicability in cooling pipe calculations.When the value of the iteration parameterαis 0.4,the boundary temperature of the cooling water pipes can meet the accuracy requirements after 4∼5 iterations,effectively improving the computational efficiency.Overall,this approach provides a useful tool for engineers to analyze the temperature control measures accurately and efficiently for mass concrete,such as cooling water pipes,using Abaqus/Python secondary development.

Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

Another SSOR Iteration Method

Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.

Iteration and evaluation of shale oil development technology for continental rift lake basins

By benchmarking with the iteration of drilling technology,fracturing technology and well placement mode for shale oil and gas development in the United States and considering the geological characteristics and development difficulties of shale oil in the Jiyang continental rift lake basin,East China,the development technology system suitable for the geological characteristics of shale oil in continental rift lake basins has been primarily formed through innovation and iteration of the development,drilling and fracturing technologies.The technology system supports the rapid growth of shale oil production and reduces the development investment cost.By comparing it with the shale oil development technology in the United States,the prospect of the shale oil development technology iteration in continental rift lake basins is proposed.It is suggested to continuously strengthen the overall three-dimensional development,improve the precision level of engineering technology,upgrade the engineering technical indicator system,accelerate the intelligent optimization of engineering equipment,explore the application of complex structure wells,form a whole-process integrated quality management system from design to implementation,and constantly innovate the concept and technology of shale oil development,so as to promote the realization of extensive,beneficial and high-quality development of shale oil in continental rift lake basins.

The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space

Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.

Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple

The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.

Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iteration(DTTV)algorithm,is developed.The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance.The admissibility of the iterative control law is analyzed.The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution.To implement the algorithm,neural networks are employed and a new implementation structure is established,which avoids solving the generalized Bellman equation in each iteration.Finally,the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm,where the mass and pendulum bar length are permitted to be time-varying parameters.The effectiveness of the developed method is illustrated by numerical results and comparisons.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

For linear time varying(LTV)multiple input multiple output(MIMO)systems with vector relative degree,an open‐closed‐loop iterative learning control(ILC)strategy is developed in this article,where the time interval of operation is iteration dependent.To compensate the missing tracking signal caused by iteration dependent interval,the feedback control is introduced in ILC design.As the tracking signal of many continuous iterations is lost in a certain interval,the feedback control part can employ the tracking signal of current iteration for compensation.Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense,the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity.Under the circumstance that the initial state varies around the desired initial state with a bound,as the number of iteration tends to infinity,the expectation of ILC tracking error can be driven to a bounded range,whose upper bound is proportional to the fluctuation.It is revealed that the convergence condition is dependent on the feed-forward control gains,while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains.As a special case,the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method.Finally,the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.

A Novel Method to Enhance the Inversion Speed and Precision of the NMR T_(2) Spectrum by the TSVD Based Linearized Bregman Iteration

The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.

A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

基于整车路面谱的副车架开裂台架试验及仿真

针对前悬架稳定杆与副车架连接处在整车试验场耐久测试过程中出现的疲劳破坏问题,通过对稳定杆进行贴片标定,获得了试验场环境下稳定杆的连杆力和稳定杆扭转相对位移的强化耐久路谱,设计搭建了稳定杆副车架系统的物理台架,并按照耐久性规范进行了台架试验。试验结果表明:该台架试验装置能良好地再现整车耐久路试下的断裂位置,疲劳寿命相对于整车耐久路试的疲劳寿命偏差仅为2.5%。在此基础上,建立了稳定杆与副车架多体的仿真模型,设定了与系统试验台架相同的约束边界,通过虚拟迭代的方法及准静态有限元疲劳寿命分析法对系统进行了仿真分析。仿真得到稳定杆连杆力和稳定杆扭转相对位移信号,与测试结果进行对比分析可以看出,时域下相位和幅值重合度良好,频域下的PSD谱重合度较高,穿级计数载荷统计基本一致,载荷相对损伤均在1附近,相关风险位置处的仿真疲劳寿命与整车耐久试验寿命偏差比为6.25%,获得了较高精度的风险位置载荷,实现了耐久风险位置的复现。最后,基于仿真模型对副车架风险位置处进行了结构优化设计,改进后的方案顺利通过了后续的台架试验和整车耐久路试。

基于空时级联单脉冲的多目标高效参数估计算法

比幅单脉冲最大似然算法(ACM-ML)在进行目标参数估计时需要进行距离与速度的2维松弛迭代搜索,导致了计算效率低、运算量大的问题。针对上述问题,该文提出一种基于空时级联单脉冲的高效多目标参数估计算法(M-STCMP算法)。该算法将单脉冲概念引入脉冲域,利用时域单脉冲计算目标速度,避免了ACM-ML算法中对速度的迭代搜索,将2维松弛迭代搜索降为1维搜索,有效降低了计算复杂度。考虑时域单脉冲无法同时匹配分布在不同时域主波束的速度各异的多个检测目标,进一步利用目标信号的多普勒信息,在各多普勒单元分别进行时域单脉冲测速,并搜索目标距离值。最后为抑制目标间的信号泄露,将所有目标的估计参数进行级联迭代获得高精度参数估计值。理论分析和仿真结果验证了M-STCMP算法的有效性。

不同迭代重建算法在眼眶CT中的适用性研究

目的:探讨不同迭代重建算法在眼眶CT中的应用价值。方法:回顾性收集2024年1月至2024年3月首都医科大学附属北京同仁医院行眼眶CT检查的31例患者,分别使用混合迭代重建算法(iDose4)和全模型迭代重建算法(IMR)技术对图像进行标准算法和骨算法重建,对比分析不同重建算法图像的平均CT值、噪声(SD)、信噪比(SNR)、对比度噪声比(CNR)以及图像质量主观评分;采用随机区组方差分析比较不同算法重建图像间的客观指标差异;采用多个相关样本的秩和检验比较不同算法重建图像的主观评分差异。结果:不同标准算法重建图像的CT值、噪声、SNR、CNR差异均有统计学意义,与iDose4相比,IMR标准算法重建图像噪声降幅达25%~67%,SNR增加1.3~1.5倍,CNR增加2~3倍;与iDose4相比,IMR骨算法重建图像噪声降幅达70%~96%,SNR增加5~15倍,CNR增加4~31倍;不同骨算法及标准算法的图像质量评分差异均有统计学意义,标准算法IMR1-Brain Routine组评分最高5(4,5),骨算法iDose43 YD组评分最高5(5,5);两名观察者评分的一致性较强,加权Kappa系数0.644~1。结论:眼眶CT中推荐使用混合迭代重建技术iDose4 Level 3重建骨算法图像,使用全模型迭代重建技术IMR Level1重建标准算法图像。

滤波辨识(11):多变量CARARMA系统的滤波递阶广义增广迭代参数辨识

针对多变量受控自回归自回归滑动平均(M-CARARMA)系统,利用滤波辨识理念和递阶辨识原理,研究和提出了滤波递阶广义增广梯度迭代辨识方法、滤波递阶多新息广义增广梯度迭代辨识方法、滤波递阶递推广义增广最小二乘迭代辨识方法、滤波递阶多新息广义增广最小二乘迭代辨识方法等。这些滤波递阶广义增广迭代辨识方法可以推广到其它有色噪声干扰下的线性和非线性多变量随机系统中。

TC21合金在不同温度下进行连续多步置氢处理时的显微组织及室温力学性能

利用OM、XRD、TEM以及压缩试验等方法研究TC21钛合金经不同温度连续多步置氢处理后的显微组织及室温力学性能。结果表明:当氢处理温度超过1073 K时,α相的尺寸明显降低,β相成为主要相。随着氢处理温度的升高,δ氢化物的含量呈先增加后逐渐降低的趋势。当氢处理温度超过1073 K时,TC21钛合金在室温压缩变形过程中出现应变软化现象,且该现象随氢处理温度的升高而越来越显著。随着氢处理温度的升高,TC21钛合金的极限变形率呈先降低后增加的趋势。当氢处理温度为1123 K时,TC21钛合金的极限变形率比原始合金增加67.51%。

基于深度学习的图像重建算法在下肢动脉病变CTA诊断中的研究

目的 探讨基于深度学习的图像重建算法对下肢动脉病变CT血管成像(Computed Tomography Angiography,CTA)的诊断价值。方法 回顾性收集2021年6月至2022年2月于我院就诊的51例下肢动脉狭窄或闭塞患者的CTA检查资料(65条下肢动脉)。分别基于深度学习的图像重建(Deep Learning Image Reconstruction,DLIR)算法和混合迭代重建(Hybrid Iterative Reconstruction,HIR)算法对CTA图像进行重建,以HIR法为参照进行质量评估;两位医师在不同重建算法下对血管狭窄的部位和程度进行评估,并采用Kappa检验观察者间一致性;以数字减影血管造影作为“金标准”比较HIR法和DLIR法诊断下肢动脉中度和重度狭窄的效能。结果与HIR法相比,DLIR法图像质量的噪声显著降低(Z膝上动脉=8.36,Z膝下动脉=9.46,Z足背动脉=7.19,均P<0.001),信噪比(Z膝上动脉=-7.32,Z膝下动脉=-7.91,Z足背动脉=-8.45,P<0.001)及对比噪声比(Z膝上动脉=-8.66,Z膝下动脉=-9.21,Z足背动脉=-8.52,均P<0.001)显著提高。DLIR法对动脉狭窄或闭塞程度的识别和评估均显示出更高的观察者间一致性(Kappa=0.86)。与HIR法相比,DLIR法的图像对膝下动脉重度狭窄的敏感度(72.2%vs.94.4%)、特异性(78.7%vs.95.7%),足背动脉中度狭窄的特异性(86.0%vs.97.7%)及重度狭窄的敏感度(50.0%vs.87.5%)均显著提高(P<0.05)。结论 DLIR算法可有效改善下肢动脉的CTA图像质量,并获得更优的诊断效能。

滤波辨识(12):多变量OEARMA系统的滤波辅助模型递阶广义增广迭代参数辨识

针对多变量输出误差自回归滑动平均(M-OEARMA)系统,即多变量Box-Jenkins系统,利用滤波辨识理念和辅助模型辨识思想,研究和提出了滤波辅助模型递阶广义增广梯度迭代辨识方法、滤波辅助模型递阶多新息广义增广梯度迭代辨识方法、滤波辅助模型递阶递推广义增广最小二乘迭代辨识方法、滤波辅助模型递阶多新息广义增广最小二乘迭代辨识方法等。这些滤波辅助模型递阶广义增广迭代辨识方法可以推广到其它有色噪声干扰下的线性和非线性多变量随机系统中。

基于幂指数法的地震模拟振动台频域前馈补偿方法

针对地震模拟振动台受到系统和试件非线性等因素影响,导致波形再现精度不高的问题,提出基于幂指数法的地震模拟振动台频域前馈补偿方法以提高振动台的控制效果,通过数值仿真和实际振动台试验对该方法的控制性能进行研究。研究结果表明:基于幂指数法的地震模拟振动台频域前馈补偿方法能够快速收敛,迭代次数较少,可以大幅提高振动台的波形复现精度,能够提高振动台的控制性能。

316LN不锈钢真空电子束焊接工艺试验

本文对30mm的316LN不锈钢进行了真空电子束焊试验。随后对典型工艺参数下焊缝组织在常温及77K低温下焊接接头的力学性能进行了研究。微观组织SEM观察的结果表明,316LN的电子束焊接接头均不同程度地出现了气孔。力学性能测试结果表明,77K下接头的强度系数为83%,室温下接头的强度系数则达87%。此外,显微维氏硬度测试结果表明,接头区硬度约为母材的80%。