在区域综合能源系统中燃气轮机(gas turbine,GT)和电制气(power to gas,P2G)实现气网和电网的双向耦合。GT出力和P2G产气速率的频繁调整,会引起管道内天然气的压力、流量和管存的剧烈波动,造成与之相连的GT不稳定运行,进而可能引起电网...在区域综合能源系统中燃气轮机(gas turbine,GT)和电制气(power to gas,P2G)实现气网和电网的双向耦合。GT出力和P2G产气速率的频繁调整,会引起管道内天然气的压力、流量和管存的剧烈波动,造成与之相连的GT不稳定运行,进而可能引起电网的故障。该文采用适合分析区域能源系统天然气管道动态过程的特征线法求解描述其动态特性的偏微分方程组,计算压力、流量和管存随时间变化的动态数据,采用不定流动方向的环状结构天然气网作为仿真算例,验证算法的稳定性,并通过与热力学计算对比验证结果的正确性;GT的稳定运行依赖于稳定的供气,为平抑管道中天然气的波动,根据仿真结果,基于气网结构提出在与GT连接的管道分支节点处安装定出口压力压缩机的控制方案,与无压缩机的仿真结果作对比,证明控制方案正确性。展开更多
Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in te...Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and efficiency.Potentially,the optimization problem in the RFM is more difficult to solve than those that arise in traditional methods.Unlike the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving PDEs.In this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization problem.Based on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.展开更多
The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling w...The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.展开更多
区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供...区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供冷/热管道和供气管道动态偏微分方程的代数解析解。针对基于供冷/热系统质–量调节模式下管道能量传输时滞变量造成RIES的动态能流计算模型难以求解的问题,提出采用分段插值法获得供冷/热管道两端节点温度之间关系的近似表达式并加入动态最优能流计算模型中。此外,针对优化模型中供冷/热系统的流量与温度相乘的双线性项,提出一种能够缩紧松弛间隙的分段凸包络松弛方法将原混合整数非线性优化模型转化为混合整数二次约束规划模型,能够在保证计算精度的同时实现高效求解。最后以某个RIES算例进行分析,验证了所提方法的计算准确性和高效性,并与常用的质调节模式相比,表明在供冷/热系统质–量调节模式下能找到经济性更优的RIES运行点。展开更多
This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)metho...This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.展开更多
文摘在区域综合能源系统中燃气轮机(gas turbine,GT)和电制气(power to gas,P2G)实现气网和电网的双向耦合。GT出力和P2G产气速率的频繁调整,会引起管道内天然气的压力、流量和管存的剧烈波动,造成与之相连的GT不稳定运行,进而可能引起电网的故障。该文采用适合分析区域能源系统天然气管道动态过程的特征线法求解描述其动态特性的偏微分方程组,计算压力、流量和管存随时间变化的动态数据,采用不定流动方向的环状结构天然气网作为仿真算例,验证算法的稳定性,并通过与热力学计算对比验证结果的正确性;GT的稳定运行依赖于稳定的供气,为平抑管道中天然气的波动,根据仿真结果,基于气网结构提出在与GT连接的管道分支节点处安装定出口压力压缩机的控制方案,与无压缩机的仿真结果作对比,证明控制方案正确性。
基金supported by the NSFC Major Research Plan--Interpretable and Generalpurpose Next-generation Artificial Intelligence(No.92370205).
文摘Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and efficiency.Potentially,the optimization problem in the RFM is more difficult to solve than those that arise in traditional methods.Unlike the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving PDEs.In this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization problem.Based on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.
文摘The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.
文摘区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供冷/热管道和供气管道动态偏微分方程的代数解析解。针对基于供冷/热系统质–量调节模式下管道能量传输时滞变量造成RIES的动态能流计算模型难以求解的问题,提出采用分段插值法获得供冷/热管道两端节点温度之间关系的近似表达式并加入动态最优能流计算模型中。此外,针对优化模型中供冷/热系统的流量与温度相乘的双线性项,提出一种能够缩紧松弛间隙的分段凸包络松弛方法将原混合整数非线性优化模型转化为混合整数二次约束规划模型,能够在保证计算精度的同时实现高效求解。最后以某个RIES算例进行分析,验证了所提方法的计算准确性和高效性,并与常用的质调节模式相比,表明在供冷/热系统质–量调节模式下能找到经济性更优的RIES运行点。
基金the National Natural Science Foundation of China(Grant Nos.71961022,11902163,12265020,and 12262024)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant Nos.2019BS01011 and 2022MS01003)+5 种基金2022 Inner Mongolia Autonomous Region Grassland Talents Project-Young Innovative and Entrepreneurial Talents(Mingjing Du)2022 Talent Development Foundation of Inner Mongolia Autonomous Region of China(Ming-Jing Du)the Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region Program(Grant No.NJYT-20-B18)the Key Project of High-quality Economic Development Research Base of Yellow River Basin in 2022(Grant No.21HZD03)2022 Inner Mongolia Autonomous Region International Science and Technology Cooperation High-end Foreign Experts Introduction Project(Ge Kai)MOE(Ministry of Education in China)Humanities and Social Sciences Foundation(Grants No.20YJC860005).
文摘This paper is aimed at solving the nonlinear time-fractional partial differential equation with two small parameters arising from option pricing model in financial economics.The traditional reproducing kernel(RK)method which deals with this problem is very troublesome.This paper proposes a new method by adaptive multi-step piecewise interpolation reproducing kernel(AMPIRK)method for the first time.This method has three obvious advantages which are as follows.Firstly,the piecewise number is reduced.Secondly,the calculation accuracy is improved.Finally,the waste time caused by too many fragments is avoided.Then four numerical examples show that this new method has a higher precision and it is a more timesaving numerical method than the others.The research in this paper provides a powerful mathematical tool for solving time-fractional option pricing model which will play an important role in financial economics.
