State Estimation Moving Window Gradient Iterative Algorithm for Bilinear Systems Using the Continuous Mixed p-norm Technique

This paper studies the parameter estimation problems of the nonlinear systems described by the bilinear state space models in the presence of disturbances.A bilinear state observer is designed for deriving identification algorithms to estimate the state variables using the input-output data.Based on the bilinear state observer,a novel gradient iterative algorithm is derived for estimating the parameters of the bilinear systems by means of the continuous mixed p-norm cost function.The gain at each iterative step adapts to the data quality so that the algorithm has good robustness to the noise disturbance.Furthermore,to improve the performance of the proposed algorithm,a dynamicmoving window is designed which can update the dynamical data by removing the oldest data and adding the newestmeasurement data.A numerical example of identification of bilinear systems is presented to validate the theoretical analysis.

Robinson-Ursescu Theorem in p-normed Spaces

For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.

Simplified p-norm-like Constraint LMS Algorithm for Efficient Estimation of Underwater Acoustic Channels

在水下声学的隧道为由于可观的困难例如是最困难的繁殖媒介之一被认出：multipath，周围的噪音，时间频率选择褪色。包含在的稀少的利用在水下声学的隧道提供一个潜在的答案改进表演在水下声学的隧道评价。与经典 l 相比 0 并且 l 1 个标准限制 LMS 算法，限制 LMS 算法在我们的以前的调查建议了的 p-norm-like (l p ) 在隧道变化的存在展出更好的稀少利用性能，，它由 p 参数调节启用适应性到稀疏。然而，与 p-norm-like 限制 LMS 算法联系的十进制的指数的计算在实际申请提出可观的限制。在这份报纸， p-norm-like 限制 LMS 的简化变体与牛顿重复方法的雇用被建议接近十进制的指数的计算。数字模拟和在物理浅水隧道获得的试验性的结果与传统的标准限制 LMS 算法相比表明建议方法的有效性。

Formal Difference Analysis and Unification on p-Norm Distribution Density Functions

The cause of the formal difference of p-norm distribution density functions is analyzed, two problems in the deduction of p-norm formulating are improved, and it is proved that two different forms of p-norm distribution density functions are equivalent. This work is useful for popularization and application of the p-norm theory to surveying and mapping.

APPROXIMATE REPRESENTATION OF THE p-NORM DISTRIBUTION

In surveying data processing,we generally suppose that the observational errors distribute normally.In this case the method of least squares can give the minimum variance unbiased estimation of the parameters.The method of least squares does not have the character of robustness,so the use of it will become unsuitable when a few measurements inheriting gross error mix with others.We can use the robust estimating methods that can avoid the influence of gross errors.With this kind of method there is no need to know the exact distribution of the observations.But it will cause other difficulties such as the hypothesis testing for estimated parameters when the sample size is not so big.For non_normally distributed measurements we can suppose they obey the p _norm distribution law.The p _norm distribution is a distributional class,which includes the most frequently used distributions such as the Laplace,Normal and Rectangular ones.This distribution is symmetric and has a kurtosis between 3 and -6/5 when p is larger than 1.Using p _norm distribution to describe the statistical character of the errors,the only assumption is that the error distribution is a symmetric and unimodal curve.This method possesses the property of a kind of self_adapting.But the density function of the p _norm distribution is so complex that it makes the theoretical analysis more difficult.And the troublesome calculation also makes this method not suitable for practice.The research of this paper indicates that the p _norm distribution can be represented by the linear combination of Laplace distribution and normal distribution or by the linear combination of normal distribution and rectangular distribution approximately.Which kind of representation will be taken is according to whether the parameter p is larger than 1 and less than 2 or p is larger than 2.The approximate distribution have the same first four order moments with the exact one.It means that approximate distribution has the same mathematical expectation,variance,skewness and kurtosis with p _norm distribution.Because every density function used in the approximate formulae has a simple form,using the approximate density function to replace the p _norm ones will simplify the problems of p _norm distributed data processing obviously.

Global exponential p-norm stability of BAM neural networks with unbounded time-varying delays:A method based on the representation of solutions

This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.

基于低秩块Hankel矩阵正则化的阵元故障MIMO雷达DOA估计

多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达在阵元故障时虚拟阵列输出数据矩阵会出现大量的整行数据丢失,由于阵列接收数据矩阵的不完整而导致对波达方向(Direction of Arrival,DOA)的估计性能恶化。大多数低秩矩阵填充算法要求缺失数据随机分布于不完整的矩阵中,无法适用于整行缺失数据的恢复问题。为此,提出了一种基于低秩块Hankel矩阵正则化的阵元故障MIMO雷达DOA估计方法。首先,通过奇异值分解(Singular Value Decomposition,SVD)降低虚拟阵列输出矩阵的维度,以减少计算复杂度。然后,对降维数据矩阵建立基于块Hankel矩阵正则化的低秩矩阵填充模型,在该模型中将MIMO雷达降维数据矩阵排列成块Hankel矩阵并施加Schatten-p范数作为正则项。最后,结合交替方向乘子法(Alternate Direction Multiplier Method,ADMM)求解该模型,获得完整的MIMO雷达降维数据矩阵。仿真结果表明,所提方法能够有效恢复降维数据矩阵中的整行数据缺失,具有较高的DOA估计精度和实时性,在阵元故障率低于50.0%时DOA估计精度优于现有方法。

具有p-Laplacian算子的分数阶问题共振正解的存在性

本文研究了具有p-拉普拉斯算子的分数阶微分方程在两种边界条件下的共振正解存在的问题.利用Leggett-Williams范型定理的方法,获得了一些新的存在性结果,推广了该类问题已有的研究结果.

A Perturbation Analysis of Low-Rank Matrix Recovery by Schatten p-Minimization

A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.

基于多重注意力和schatten-p范数的息肉分割网络

自动准确的息肉定位分割方法可以在结直肠癌病变早期及时地发现息肉,大大降低癌变几率。编解码结构作为近年来息肉分割中最主流的网络结构,已经得到了很大的改进,如提高模型捕获全局上下文特征和局部特征的能力,使用深层特征对浅层解码做指导。但是息肉形状和大小不一,在编码时,由于卷积特性容易过于陷入局部信息挖掘,而失去远程信息依赖关系;还有一些息肉图像存在对比度低、空间复杂的特性,导致息肉与背景两者极易混淆。本文提出了基于多重注意力和schatten-p范数的息肉分割网络。其中,轴向多重注意力模块利用轴向注意力补充图像中的远程上下文关系,同时补充对边缘、背景信息的关注以实现特征互补,在注意全局特征的同时加强对局部细节特征的捕捉;利用矩阵奇异值和矩阵隐含信息的关联性,引入schatten-p范数作约束,从矩阵角度分析数据,辅助模型辨别前景和背景。通过设置大量实验,证明了本文提出方法的有效性,并且MASNet在Kvasir-SEG数据集上对比不同的方法,取得了较好的分割结果。

面向矩阵秩函数准确估计的自表示子空间聚类方法

传统子空间聚类方法通常使用矩阵核范数代替矩阵秩函数进行低秩矩阵恢复,然而在目标优化过程中主要关注低秩矩阵大奇异值的影响,容易导致矩阵秩估计不准确的问题。为此,在分析矩阵奇异值长尾分布特点的基础上,提出使用基于截断Schatten-p范数的低秩子空间聚类模型。该模型充分考虑小奇异值对低秩矩阵恢复过程的贡献,利用小奇异值信息拟合矩阵奇异值的长尾分布,通过对矩阵秩函数进行准确估计以提升子空间聚类性能。实验结果表明,与现有加权核范数子空间聚类WNNM-LRR和近邻约束子空间聚类BDR算法相比,在Extended Yale B数据集上的聚类准确性分别提升了11%和8%,所提方法能够更好地拟合数据奇异值分布以及生成准确的相似度矩阵。

基于压缩感知理论的远震P波数据重建研究

本文将基于压缩感知理论的地震观测数据重建方法用于天然远震事件的P波到时处理之中,基于曲波(curvelet)变换,建立基于L_(1)范数的正则化反演模型,并采用迭代收缩阈值算法(ISTA)求解该模型。针对在内蒙古布设的流动地震台阵记录到的远震波形数据,对其进行稀疏采样,采用稀疏反演重建方法对欠采样数据进行重建,并拾取重建数据的P波到时,之后开展远震P波层析成像进行验证。研究结果表明,远震天然地震观测数据在曲波变换中表现出稀疏性,可利用压缩感知方法实现远震P波数据的完备化处理。基于内蒙古流动地震台阵数据三维P波成像也表明,基于压缩感知的数据重建技术可以提高地震层析成像的分辨率,且压缩感知采集技术在天然地震研究中具有潜在的应用价值。

考虑增材制造填充结构强度的拓扑优化方法

提出了一种针对给定薄壁外形的内填充结构拓扑优化方法,用于设计具有优化结构强度、满足增材制造几何要求的轻量化多孔填充结构.基于p范数函数计算结构最大应力近似值,并以最小化该值为优化目标,以提升填充结构强度.通过在优化模型中考虑局部体积约束,获得多孔填充构型,并进一步提出局部体积上限动态调整策略,提升优化过程稳定性,避免优化过程约束过强导致结构构型和应力响应突变甚至优化失败.此外,考虑了自支撑约束,保证优化所得填充结构自支撑,且支撑给定薄壁外形的悬空区域.引入了基于两场公式的优化模型,确保优化所得填充结构满足增材制造最小尺寸要求.数值算例表明,所提方法优化结果与以最小化柔度为目标的填充结构拓扑优化结果相比,在相同质量下结构强度得到了显著提升.在此基础上,在优化模型中考虑了柔度约束,讨论了填充结构刚度、强度的相互影响规律.

p-Norm Broad Learning for Negative Emotion Classification in Social Networks

Negative emotion classification refers to the automatic classification of negative emotion of texts in social networks.Most existing methods are based on deep learning models,facing challenges such as complex structures and too many hyperparameters.To meet these challenges,in this paper,we propose a method for negative emotion classification utilizing a Robustly Optimized BERT Pretraining Approach(RoBERTa)and p-norm Broad Learning(p-BL).Specifically,there are mainly three contributions in this paper.Firstly,we fine-tune the RoBERTa to adapt it to the task of negative emotion classification.Then,we employ the fine-tuned RoBERTa to extract features of original texts and generate sentence vectors.Secondly,we adopt p-BL to construct a classifier and then predict negative emotions of texts using the classifier.Compared with deep learning models,p-BL has advantages such as a simple structure that is only 3-layer and fewer parameters to be trained.Moreover,it can suppress the adverse effects of more outliers and noise in data by flexibly changing the value of p.Thirdly,we conduct extensive experiments on the public datasets,and the experimental results show that our proposed method outperforms the baseline methods on the tested datasets.

基于截断p-shrinkage范数的航空发动机数据重构

针对航空发动机传感器的数据缺失问题,提出基于张量奇异值阈值(TSVT)的张量重构模型LRTC-PTNN,对航空发动机的传感器数据进行重构。LRTC-PTNN模型运用截断pshrinkage范数的方式代替原始张量迹范数作为张量秩的凸包络,并根据TSVT的特性,计算了传感器之间的相关性,选取传感器截面作为重构精度最佳的数据输入方向,使用交替乘子法实现LRTCPTNN算法。选取NASA提供的PHM2008数据集进行实验,对数据集进行标准化,并在重构后进行恢复,将多个时间序列个数相近的发动机传感器数据构建为高维张量的形式,设置2种传感器的数据缺失场景进行实验,结果表明:重构后数据的均方根误差和平均绝对百分比误差范围分别为2.10~13.13和0.32~1.49,LRTC-PTNN模型优于现有的基线模型,且在极端情况下有较强的鲁棒性。

Hardy-Littlewood截断极大算子的L^(p)范数的连续性

研究截断极大算子M^(b)_(a)的L_(p)(R^(n))→L_(p)(R^(n))范数的连续性。首先,分别给出‖M^(b)_(a)‖L_(p)(R^(n))→L_(p)(R^(n))关于参数θ=b/a的左右连续性,然后证明‖M^(b)_(a)‖L_(p)(R^(n))→L_(p)(R^(n))在无穷远处的连续性。

On Complete Hypersurfaces with Constant Mean Curvature and Finite L^p-norm Curvature in R^(n+1)

By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite L^n-norm curvature in R^1＋1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n＋1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite L^1-norm curvature in R^1＋1 are considered.

基于改进HHO算法的碳交易价格组合预测研究

为提高碳交易价格预测精度,建立了多策略改进哈里斯鹰算法的碳交易价格组合预测模型。一方面对碳交易价格序列的高频和低频序列分别建立ARIMA模型和指数平滑模型,通过加和对碳交易价格进行预测。另一方面综合考虑碳交易价格的经济指标和技术指标,通过Pearson相关系数筛选出6个与下一日碳交易价格高度相关的变量作为解释变量,建立多策略改进哈里斯鹰优化极限学习机模型(THHO_ELM)。最后,对模型I和模型II建立基于l_(p)范数的组合预测模型。结果表明,组合预测模型优于单一的分类模型。

关于矩阵的Schatten p-范数的注记

利用矩阵奇异值分解、柯西不等式及Schatten p-范数的酉不变性,讨论了矩阵主对角线元素与矩阵Schatten p-范数之间的关系.利用正交投影的性质及分块矩阵的主对角块组成的准对角矩阵可以表示成其凸组合,刻画了分块矩阵与其主对角块p-范数之间的关系.利用分块矩阵的技巧、矩阵的谱分解及Schatten p-范数的特性,深入讨论了矩阵与其伴随换位子Schatten p-范数之间的关系.利用了正规矩阵的特性及Frobenius范数的特性,给出了矩阵的绝对值及换位子之间Frobenius范数的界.所得结果细化和深化的矩阵Schatten p-范数的已有结果.