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.

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.

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.

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.

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.

两个一维总体分布相等性的permutation检验

检验两个一维总体分布的相等性,采用理论证明和数值模拟的方法,在Prastgaard提出的Kolmogorov-Smirnov统计量T1及相应的permutation统计量T 1基础上,提出了基于K-S统计量的新统计量T2及相应的permutation统计量T 2,研究了在一维的情形下T2与T 2的分布,并进行了数值模拟.结果表明:新统计量在原假设下有相同的极限分布,数值模拟结果优于原统计量.该方法对检验两总体分布的相等性有一定的参考价值.

REVERSIBLE LOGIC GATE NETWORK CASCADE BASED ON PERMUTATION GROUP

The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation Sn is proved to be generated by a n-cycle 9 and a permutation τ= （ij,ik） together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit. Based on the above theory, a cascade algorithm for reversible logic gate networks is proposed. A reversible example of logic gate network cascade is given to show the correctness of the algorithm.

Bootstrap和Permutation方法在样本率多重比较中的应用

目的介绍Bootstrap和Permutation方法在样本率多重比较中的应用。方法调用SAS中的MULTTEST过程,编写程序实现样本率的两两比较和与控制组比较,并通过实例说明效果。结果运用Bootstrap和Permutation方法能较好解决样本率的多重比较问题。结论使用Bootstrap和Permutation方法的SAS程序,简单明了,结果准确,使用方便。

Fractal sorting vector-based least significant bit chaotic permutation for image encryption

The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security.

Matching spatial relation graphs using a constrained partial permutation strategy

A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.

On the Representations of Γ1-Nonderanged Permutation Group gp

Representation theory is concerned with the ways of explaining or visualizing a group as a group of matrices. In this paper, we extend the permutation pattern of to a two-line notation. We consider the representations of this non-deranged permutation group(p ≥ 5 and p a prime). Also we reveal some interesting properties and results of the character of where .

Microseismic signal denoising by combining variational mode decomposition with permutation entropy

Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.

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.

Decryption of pure-position permutation algorithms

Pure position permutation image encryption algorithms, commonly used as image encryption investigated in this work are unfortunately frail under known-text attack. In view of the weakness of pure position permutation algorithm,we put forward an effective decryption algorithm for all pure-position permutation algorithms. First, a summary of the pure position permutation image encryption algorithms is given by introducing the concept of ergodic matrices. Then, by using probability theory and algebraic principles, the decryption probability of pure-position permutation algorithms is verified theoretically; and then, by defining the operation system of fuzzy ergodic matrices, we improve a specific decryption al-gorithm. Finally, some simulation results are shown.

Anomalies in Special Permutation Flow Shop Scheduling Problems

Recent researches show that there are some anomalies,which are not satisfied with common sense,appearing in some special permutation flow shop scheduling problems(PFSPs).These anomalies can be divided into three different types,such as changing the processing time of some operations,changing the number of total jobs and changing the number of total machines.This paper summarizes these three types of anomalies showing in the special PFSPs and gives some examples to make them better understood.The extended critical path is proposed and the reason why these anomalies happen in special PFSPs is given:anomalies will occur in these special PFSPs when the time of the operations on the reverse critical path changes.After that,the further reason for these anomalies is presented that when any one of these three types of anomalies happens,the original constraint in the special PFSPs is destroyed,which makes the anomalies appear.Finally,the application of these anomalies in production practice is given through examples and also with the possible research directions.The main contribution of this research is analyzing the intial reason why the anomalies appear in special PFSPs and pointing out the application and the possible research directions of all these three types of anomalies.

A WATERMARKING ALGORITHM BASED ON PERMUTATION AND 2-D BARCODE

This letter presents a method for digital image watermarking for copyright protection. This technique produces a watermarked image that closely retains the quality of the original host image while concurrently surviving various image processing operations such as lowpass/highpass filtering, lossy JPEG compression, and cropping. This image watermarking algorithm takes full advantage of permutation and 2-D barcode (PDF417). The actual watermark embedding in spatial domain is followed using permutated image for improving the resistance to image cropping. Much higher watermark robustness is obtainable via a simple forward error correction technique, which is the main feature of PDF417 codes. Additional features of this technique include the easy determination of the existence of the watermark and that the watermark verification procedure does not need the original host image. The experimental results demonstrate its effectiveness.

NEW CONSTRUCTIONS OF LDPC CODES BASED ON CIRCULANT PERMUTATION MATRICES FOR AWGN CHANNEL

Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.

Morphology Similarity Distance for Bearing Fault Diagnosis Based on Multi-Scale Permutation Entropy

Bearings are crucial components in rotating machines,which have direct effects on industrial productivity and safety.To fast and accurately identify the operating condition of bearings,a novel method based on multi⁃scale permutation entropy(MPE)and morphology similarity distance(MSD)is proposed in this paper.Firstly,the MPE values of the original signals were calculated to characterize the complexity in different scales and they constructed feature vectors after normalization.Then,the MSD was employed to measure the distance among test samples from different fault types and the reference samples,and achieved classification with the minimum MSD.Finally,the proposed method was verified with two experiments concerning artificially seeded damage bearings and run⁃to⁃failure bearings,respectively.Different categories were considered for the two experiments and high classification accuracies were obtained.The experimental results indicate that the proposed method is effective and feasible in bearing fault diagnosis.

Hybrid artificial immune system and extremal optimization algorithm for permutation flowshop scheduling problem

The permutation flowshop scheduling problem （PFSP） is one of the most well-known and well-studied production scheduling problems with strong industrial background. This paper presents a new hybrid optimization algorithm which combines the strong global search ability of artificial immune system （AIS） with a strong local search ability of extremal optimization （EO） algorithm. The proposed algorithm is applied to a set of benchmark problems with a makespan criterion. Performance of the algorithm is evaluated. Comparison results indicate that this new method is an effective and competitive approach to the PFSP.

Frame-indifference of cross products,rotations,and the permutation tensor

Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.