电动汽车锂离子电池健康状态(state of health,SOH)的精准预测对行车安全与电池管理系统优化具有重要意义.然而,现有方法普遍面临两大挑战:其一,依赖大量健康特征导致信息冗余与计算复杂度过高;其二,SOH时间序列的强非线性与非平稳性使...电动汽车锂离子电池健康状态(state of health,SOH)的精准预测对行车安全与电池管理系统优化具有重要意义.然而,现有方法普遍面临两大挑战:其一,依赖大量健康特征导致信息冗余与计算复杂度过高;其二,SOH时间序列的强非线性与非平稳性使传统神经网络易出现预测漂移和趋势振荡.基于此,本文提出一种融合KAN(Kolmogorov-Arnold)表示理论的混合神经网络—Kan Former,用于高精度SOH预测.该网络由局部特征提取、全局特征提取与预测输出三大模块构成:局部特征提取模块利用KAN的平滑插值能力有效捕捉细粒度信息,全局特征提取模块结合Transformer的复杂关系建模能力实现跨时间尺度的信息整合,预测输出模块借助KAN的非线性拟合优势生成精准预测结果.该模型一方面有效缓解了数据非线性与非平稳性导致的漂移与振荡问题,另一方面实现了平均15.32%的训练速度提升.在Michigan Formation,HNEI,NASA三个公开电池老化数据集上的验证结果表明,Kan Former在均方误差(MSE)、平均绝对误差(MAE)和决定系数(R^(2))上分别达到了0.0045,0.041,0.978(Michigan数据集)与0.00055,0.0175,0.996(HNEI数据集),显著优于现有主流方法,充分说明其在SOH预测中的高准确性和强泛化能力.展开更多
The Reynolds-averaged Navier-Stokes(RANS)technique enables critical engineering predictions and is widely adopted.However,since this iterative computation relies on the fixed-point iteration,it may converge to unexpec...The Reynolds-averaged Navier-Stokes(RANS)technique enables critical engineering predictions and is widely adopted.However,since this iterative computation relies on the fixed-point iteration,it may converge to unexpected non-physical phase points in practice.We conduct an analysis on the phase-space characteristics and the fixed-point theory underlying the k-ε turbulence model,and employ the classical Kolmogorov flow as a framework,leveraging its direct numerical simulation(DNS)data to construct a one-dimensional(1D)system under periodic/fixed boundary conditions.The RANS results demonstrate that under periodic boundary conditions,the k-ε model exhibits only a unique trivial fixed point,with asymptotes capturing the phase portraits.The stability of this trivial fixed point is determined by a mathematically derived stability phase diagram,indicating the fact that the k-ε model will never converge to correct values under periodic conditions.In contrast,under fixed boundary conditions,the model can yield a stable non-trivial fixed point.The evolutionary mechanisms and their relationship with boundary condition settings systematically explain the inherent limitations of the k-ε model,i.e.,its deficiency in computing the flow field under periodic boundary conditions and sensitivity to boundary-value specifications under fixed boundary conditions.These conclusions are finally validated with the open-source code OpenFOAM.展开更多
We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
基金Project supported by the National Natural Science Foundation of China(Nos.12372214 and U2341231)。
文摘The Reynolds-averaged Navier-Stokes(RANS)technique enables critical engineering predictions and is widely adopted.However,since this iterative computation relies on the fixed-point iteration,it may converge to unexpected non-physical phase points in practice.We conduct an analysis on the phase-space characteristics and the fixed-point theory underlying the k-ε turbulence model,and employ the classical Kolmogorov flow as a framework,leveraging its direct numerical simulation(DNS)data to construct a one-dimensional(1D)system under periodic/fixed boundary conditions.The RANS results demonstrate that under periodic boundary conditions,the k-ε model exhibits only a unique trivial fixed point,with asymptotes capturing the phase portraits.The stability of this trivial fixed point is determined by a mathematically derived stability phase diagram,indicating the fact that the k-ε model will never converge to correct values under periodic conditions.In contrast,under fixed boundary conditions,the model can yield a stable non-trivial fixed point.The evolutionary mechanisms and their relationship with boundary condition settings systematically explain the inherent limitations of the k-ε model,i.e.,its deficiency in computing the flow field under periodic boundary conditions and sensitivity to boundary-value specifications under fixed boundary conditions.These conclusions are finally validated with the open-source code OpenFOAM.
基金Supported by NSFC (No.12031006)Fundamental Research Funds for the Central Universities of China。
文摘We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
