AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

Entanglement and Volume Monogamy Features of Permutation Symmetric N-Qubit Pure States with N-Distinct Spinors: GHZ and States

We explore the entanglement features of pure symmetric N-qubit states characterized by N-distinct spinors with a particular focus on the Greenberger-Horne-Zeilinger (GHZ) states and , an equal superposition of W and obverse W states. Along with a comparison of pairwise entanglement and monogamy properties, we explore the geometric information contained in them by constructing their canonical steering ellipsoids. We obtain the volume monogamy relations satisfied by states as a function of number of qubits and compare with the maximal monogamy property of GHZ states.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

Role of Metacognition in Mathematical Problem Solving Process of Permutations and Combinations--Basic Study for CAI Software Development

When solving a mathematical problem, we sometimes encounter a situation where we can not reach a correct answer in spite of acquiring knowledge and formula necessary for the solution. The reason can be attributed to the lack in metacognitive abilities. Metacognitive abilities consist of comparing the difficulty of problem with own ability, proper plan of solution process, and conscious monitoring and control of solution process. The role and importance of metacognitive ability in mathematical problem solving of permutations and combinations was explored. Participants were required to solve five practical problems related to permutations and combinations. For each problem, the solution process was divided into： （1） understanding （recognition） of mathematical problem; （2） plan of solution; （3） execution of solution. Participants were also required to rate the anticipation whether they could solve it or not, and to rate the confidence of their own answer. According to the total score of five problems, the participants were categorized into the group of the high test score and the group of the low test score. As a result, at the plan and the execution processes, statistically significant differences were detected between the high and the low score groups. As for the rating on the anticipation of result and the confidence of own answer, no significant differences were found between both groups. Moreover, the relationship between the score of plan process and the score of execution process was statistically correlated. In other words, the more proper the plan process was conducted, the more proper solution the participants reached. In such a way, the importance of metacognitive ability in the solving process, especially the plan ability, was suggested.

Singly Covered Minimal Elements of Linked Partitions and Cycles of Permutations

Linked partitions were introduced by Dykema(Dykema K J. Multilinear function series and transforms in free probability theory. Adv. Math., 2005, 208(1):351–407) in the study of the unsymmetrized T-transform in free probability theory.Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen et al.(Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. European J. Combin., 2008, 29(6): 1408–1426) de?ned the concept of singly covered minimal elements. Let L(n, k) denote the set of linked partitions of [n] with k singly covered minimal elements and let P(n, k) denote the set of permutations of [n] with k cycles. In this paper, we mainly establish two bijections between L(n, k) and P(n, k). The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in L(n, k) and the cycles in P(n, k).

Chrestenson Spectrum and Auto-Correlation Function of Inverse Permutations of Quick Trickle Permutations

In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.

Watermarking Images in the Frequency Domain by Exploiting Self-Inverting Permutations

In this work we propose efficient codec algorithms for watermarking images that are intended for uploading on the web under intellectual property protection. Headed to this direction, we recently suggested a way in which an integer number w which being transformed into a self-inverting permutation, can be represented in a two dimensional (2D) object and thus, since images are 2D structures, we have proposed a watermarking algorithm that embeds marks on them using the 2D representation of w in the spatial domain. Based on the idea behind this technique, we now expand the usage of this concept by marking the image in the frequency domain. In particular, we propose a watermarking technique that also uses the 2D representation of self-inverting permutations and utilizes marking at specific areas thanks to partial modifications of the image’s Discrete Fourier Transform (DFT). Those modifications are made on the magnitude of specific frequency bands and they are the least possible additive information ensuring robustness and imperceptiveness. We have experimentally evaluated our algorithms using various images of different characteristics under JPEG compression. The experimental results show an improvement in comparison to the previously obtained results and they also depict the validity of our proposed codec algorithms.

Double Derangement Permutations

Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for and for , then where .

Modified 2 Satisfiability Reverse Analysis Method via Logical Permutation Operator

The effectiveness of the logic mining approach is strongly correlated to the quality of the induced logical representation that represent the behaviour of the data.Specifically,the optimum induced logical representation indicates the capability of the logic mining approach in generalizing the real datasets of different variants and dimensions.The main issues with the logic extracted by the standard logic mining techniques are lack of interpretability and the weakness in terms of the structural and arrangement of the 2 Satisfiability logic causing lower accuracy.To address the issues,the logical permutation serves as an alternative mechanism that can enhance the probability of the 2 Satisfiability logical rule becoming true by utilizing the definitive finite arrangement of attributes.This work aims to examine and analyze the significant effect of logical permutation on the performance of data extraction ability of the logic mining approach incorporated with the recurrent discrete Hopfield Neural Network.Based on the theory,the effect of permutation and associate memories in recurrent Hopfield Neural Network will potentially improve the accuracy of the existing logic mining approach.To validate the impact of the logical permutation on the retrieval phase of the logic mining model,the proposed work is experimentally tested on a different class of the benchmark real datasets ranging from the multivariate and timeseries datasets.The experimental results show the significant improvement in the proposed logical permutation-based logic mining according to the domains such as compatibility,accuracy,and competitiveness as opposed to the plethora of standard 2 Satisfiability Reverse Analysis methods.

Short-Term Prediction of Photovoltaic Power Generation Based on LMD Permutation Entropy and Singular Spectrum Analysis

The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.

Cloud Resource Integrated Prediction Model Based on Variational Modal Decomposition-Permutation Entropy and LSTM

Predicting the usage of container cloud resources has always been an important and challenging problem in improving the performance of cloud resource clusters.We proposed an integrated prediction method of stacking container cloud resources based on variational modal decomposition(VMD)-Permutation entropy(PE)and long short-term memory(LSTM)neural network to solve the prediction difficulties caused by the non-stationarity and volatility of resource data.The variational modal decomposition algorithm decomposes the time series data of cloud resources to obtain intrinsic mode function and residual components,which solves the signal decomposition algorithm’s end-effect and modal confusion problems.The permutation entropy is used to evaluate the complexity of the intrinsic mode function,and the reconstruction based on similar entropy and low complexity is used to reduce the difficulty of modeling.Finally,we use the LSTM and stacking fusion models to predict and superimpose;the stacking integration model integrates Gradient boosting regression(GBR),Kernel ridge regression(KRR),and Elastic net regression(ENet)as primary learners,and the secondary learner adopts the kernel ridge regression method with solid generalization ability.The Amazon public data set experiment shows that compared with Holt-winters,LSTM,and Neuralprophet models,we can see that the optimization range of multiple evaluation indicators is 0.338∼1.913,0.057∼0.940,0.000∼0.017 and 1.038∼8.481 in root means square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE)and variance(VAR),showing its stability and better prediction accuracy.

分布式装配置换流水车间调度问题研究综述

近几十年来,现代制造业发展迅速,一种趋势是在分布式生产工厂进行工件的加工,待完成后到装配工厂集中装配成最终产品。该模式在带来诸多好处的同时,对资源调度提出了新的挑战。针对分布式装配置换流水车间调度问题(distributed assembly permutation flowshop scheduling problem,DAPFSP),介绍了DAPFSP的背景和存在的主要困难,进而对以最小化最大完工时间为优化目标的DAPFSP,从数学模型、编解码策略、全局和局部搜索算法角度进行探讨,分别综述了以最小化总流程时间等为优化目标,具有零等待等约束,以及考虑准备时间等因素的DAPFSP研究成果。最后,对有待进一步开展的研究工作进行展望。

基于改进变分模态分解和优化堆叠降噪自编码器的轴承故障诊断

针对滚动轴承在噪声干扰下故障特征难以提取的问题,提出一种改进变分模态分解(VMD)和复合缩放排列熵(CZPE)的特征提取新方法,并利用优化堆叠降噪自编码器(SDAE)进行故障分类。首先,提出由“余弦相似度—峭度—包络熵”新综合评价指标自适应优化分解参数的改进VMD方法,并通过该指标筛选分解后的本征模态函数(IMF)分量;然后,为提取更全面的故障特征,引入新的复合缩放排列熵对各有效IMF的故障特征进行量化;最后,提出一种基于鼠群优化算法(RSO)与麻雀搜索算法(SSA)的混合算法优化SDAE网络超参数,将故障特征输入优化后SDAE网络中得到分类结果。采用美国CWRU轴承数据集进行验证,实验结果表明该方法能全面稳定地提取背景噪声下的故障特征,且与其他方法相比具有更好的抗噪性能和更高的故障诊断准确率。

基于信号图像化和CNN-ResNet的配电网单相接地故障选线方法

配电网发生单相接地故障时,零序电流呈现较强的非线性与非平稳性,故障选线较为困难,针对此问题,提出一种基于信号图像化和卷积神经网络-残差网络的配电网单相接地故障选线方法。首先,利用排列熵优化变分模态分解算法的参数,将零序电流信号分解成一系列固有模态函数;其次,引入新的数据预处理方式,将固有模态函数转成二维图像,获得零序电流信号的时频特征图;最后,利用一维卷积神经网络提取零序电流信号的相关性和特征,利用残差网络提取时频特征图的特征,将两个网络融合,构建混合卷积神经网络结构,实现故障选线。仿真与实验结果表明,该方法能够在高阻接地、采样时间不同步、强噪声等情况下准确地选择出故障线路,可满足配电网对故障选线准确性和可靠性的需求。

基于tSNE多特征融合的JTC轨旁设备故障检测

无绝缘轨道电路(Jointless Track Circuit,JTC)的轨旁设备在室外长期运营过程中,其可靠性会逐渐降低,进而给列车行车安全带来严重威胁。以轨道电路读取器(Track Circuit Reader,TCR)感应电压为基础,针对JTC故障诊断研究中轨旁设备故障类型复杂和故障特征提取不充分等问题,提出一种基于t分布随机邻域嵌入(t-distribution Stochastic Neighbor Embedding,tSNE)多特征融合的JTC轨旁设备故障检测模型。首先,根据不同轨旁设备故障对TCR感应电压信号的影响,分析各轨旁设备的故障特性。其次,提取TCR感应电压信号的方差、有效值、峰值因子等幅值域特征,以及排列熵、散布熵特征构成原始故障特征集。为了去除其中的冗余信息,得到具有较高判别性的融合流形特征,利用tSNE算法进行特征融合。最后输入深度残差网络(Deep Residual Network,DRN)得到故障检测混淆矩阵,实现轨旁设备故障定位。实验结果表明:tSNE算法融合后的特征在异类和同类故障样本之间分别有较大的类间间距和较小的类内间距,相比主成分分析(Principal Component Analysis, PCA)、随机相似性嵌入(Stochastic Proximity Embedding, SPE)、随机邻域嵌入(Stochastic Neighbor Embedding,SNE)算法具有更优的融合特征提取效果。此外,结合DRN可以有效识别多种轨旁设备故障,达到98.28%的故障检测准确率。通过现场信号进行实例验证,结果表明该故障检测模型能满足铁路现场对室外设备进行故障定位的实际需求。

基于余弦相似度列置换的Q矩阵修正方法

国内外研究者已开发出多种有效的Q矩阵修正方法,但当Q矩阵错误率较高时,仍存在修正效果不佳的问题.该文将基于塔克一致性系数和余弦相似度的列置换方法融入4种Q矩阵修正方法(GDI、Hull、MLR-B和stepwise)中,并借助Q矩阵向量和元素正确率等指标来评价新方法的修正效果.蒙特卡罗(Monte Carlo)模拟研究结果表明:在各种条件组合下,4种Q矩阵修正方法经过列置换后的修正效果得到明显提升,特别是当Q矩阵错误率较高时效果更加显著.

基于新混合乌鸦搜索算法的置换流水车间调度

为了更加有效地求解以最大完工时间最小化为目标的置换流水车间调度问题,提出一种新混合乌鸦搜索算法(NHCSA)。首先,对一种基于NEH的启发式算法进行了改进,在此基础上提出新的方法以改善初始种群的质量和多样性;其次,采用SPV(Smallest-Position-Value)规则进行编码,使算法能够处理离散的调度问题;最后,针对迭代贪婪算法,提出了自动调整重插入工件范围的方法、引入了TB机制,并采用改进的迭代贪婪算法对最佳工件排序进行局部搜索,以提升算法收敛的精度。基于典型测试集进行了仿真测试,结果验证了所提算法的寻优能力和稳定性。尤其是在针对Rec19和Rec25算例的比较中,仅NHCSA取得了当前最优解,进一步证明了其优越性。

基于PE-HMM的渡槽结构运行状态评价

随着远距离、高流量、大跨度渡槽工程的不断发展,渡槽运行状态监测与评价日益重要。以广东省罗定市长岗坡渡槽工程为例,基于渡槽泄流振动位移数据,提出一种基于排列熵算法(PE)和隐马尔可夫模型(HMM)的渡槽运行状态评价方法。首先,运用排列熵算法和K-means法提取振动位移数据基本特征,形成HMM模型的观测状态序列。其次,运用HMM算法训练模型参数,以平均误差百分比为指标,筛选出最佳模型参数,并以该参数为初值再次训练得到渡槽运行期隐状态的概率分布。最后,结合渡槽运行期隐状态对应的分值等级及概率值,求得渡槽运行状态期望值,从而量化评价渡槽运行状态。结果表明,基于PE-HMM法的渡槽运行状态评价结果与实地勘察结论一致,可见PE-HMM法能够从渡槽振动位移数据角度出发,真实反映渡槽结构运行状态,具有较高的评判精度与工程指导意义。

基于小波散射变换和MFCC的双特征语音情感识别融合算法

为了充分挖掘语音信号频谱包含的情感信息以提高语音情感识别的准确性,提出了一种基于小波散射变换和梅尔频率倒谱系数(Mel-frequency cepstral coefficient,MFCC)的排列熵加权和偏差调整规则的语音情感识别融合算法(PEW-BAR)。算法首先获取语音信号的小波散射特征和梅尔频率倒谱系数的相关特征;然后按尺度维度扩展小波散射特征,利用支持向量机得到情感识别的后验概率并获得排列熵,并使用排列熵对后验概率进行加权;最后采用一种偏差调整规则进一步融合MFCC的相关特征的识别结果。实验结果表明,在EMODB、RAVDESS和eNTERFACE05数据集上,与传统的基于小波散射系数的语音情感识别方法相比,该算法将ACC分别提高了2.82%、2.85%和5.92%,将UAR分别提升了3.40%、2.87%和5.80%,IEMOCAP上提高了6.89%。