Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

Feature Extraction of Kernel Regress Reconstruction for Fault Diagnosis Based on Self-organizing Manifold Learning

The feature space extracted from vibration signals with various faults is often nonlinear and of high dimension.Currently,nonlinear dimensionality reduction methods are available for extracting low-dimensional embeddings,such as manifold learning.However,these methods are all based on manual intervention,which have some shortages in stability,and suppressing the disturbance noise.To extract features automatically,a manifold learning method with self-organization mapping is introduced for the first time.Under the non-uniform sample distribution reconstructed by the phase space,the expectation maximization(EM) iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention.After that,the local tangent space alignment(LTSA) algorithm is adopted to compress the high-dimensional phase space into a more truthful low-dimensional representation.Finally,the signal is reconstructed by the kernel regression.Several typical states include the Lorenz system,engine fault with piston pin defect,and bearing fault with outer-race defect are analyzed.Compared with the LTSA and continuous wavelet transform,the results show that the background noise can be fully restrained and the entire periodic repetition of impact components is well separated and identified.A new way to automatically and precisely extract the impulsive components from mechanical signals is proposed.

Research on fault diagnosis method of piston rod based on harmonic wavelet and manifold learning

As the core part of reciprocating compressor,piston rod is easy to cause a serious accident when abrasion and breakage fault occur to it. Therefore,it is very important to monitor its running state. At present,a small number of reciprocating compressors have been installed on-line monitoring and diagnosis system,most of which can only monitor a single vertical subsidence of piston rod and it can't fully represent the running state of piston rod. Therefore,a method of monitoring the vertical and horizontal displacement of piston rod axis orbit is simultaneously used. In view of the characteristics that the piston rod axis orbit is disordered and difficult to extract features,purification of the axis orbit is carried out based on harmonic wavelet and then features are extracted such as vibration energy,natural frequency and the axis orbit envelope area. After that,a nonlinear local tangent space manifold learning algorithm is used to reduce the dimension of the features and obtain sensitive features. By analyzing the practical cases,the effectiveness of the method for fault monitoring and diagnosis of reciprocating compressor piston rod assembly has been verified. Finally,as BP neural network has the characteristics of solving complex nonlinear problems,the validity of the fault diagnosis method of reciprocating compressor piston rod based on harmonic wavelet and manifold learning is proved by actual case data analysis based on BP neural network.

Face recognition based on manifold learning and Rényi entropy

Though manifold learning has been success-fully applied in wide areas, such as data visu-alization, dimension reduction and speech rec-ognition;few researches have been done with the combination of the information theory and the geometrical learning. In this paper, we carry out a bold exploration in this field, raise a new approach on face recognition, the intrinsic α-Rényi entropy of the face image attained from manifold learning is used as the characteristic measure during recognition. The new algorithm is tested on ORL face database, and the ex-periments obtain the satisfying results.

Fault diagnosis model based on multi-manifold learning and PSO-SVM for machinery

Fault diagnosis technology plays an important role in the industries due to the emergency fault of a machine could bring the heavy lost for the people and the company. A fault diagnosis model based on multi-manifold learning and particle swarm optimization support vector machine(PSO-SVM) is studied. This fault diagnosis model is used for a rolling bearing experimental of three kinds faults. The results are verified that this model based on multi-manifold learning and PSO-SVM is good at the fault sensitive features acquisition with effective accuracy.

Semi-Supervised Learning Based on Manifold in BCI

A Laplacian support vector machine （LapSVM） algorithm, a semi-supervised learning based on manifold, is introduced to brain-computer interface （BCI） to raise the classification precision and reduce the subjects＇ training complexity. The data are collected from three subjects in a three-task mental imagery experiment. LapSVM and transductive SVM （TSVM） are trained with a few labeled samples and a large number of unlabeled samples. The results confirm that LapSVM has a much better classification than TSVM.

Adaptive Neighboring Selection Algorithm Based on Curvature Prediction in Manifold Learning

Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear,global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring region selection. However,so far for the references we know,few of which propose a generally accepted algorithm to well select the neighboring region. So in this paper,we propose an adaptive neighboring selection algorithm,which successfully applies the LLE and ISOMAP algorithms in the test. It is an algorithm that can find the optimal K nearest neighbors of the data points on the manifold. And the theoretical basis of the algorithm is the approximated curvature of the data point on the manifold. Based on Riemann Geometry,Jacob matrix is a proper mathematical concept to predict the approximated curvature. By verifying the proposed algorithm on embedding Swiss roll from R3 to R2 based on LLE and ISOMAP algorithm,the simulation results show that the proposed adaptive neighboring selection algorithm is feasible and able to find the optimal value of K,making the residual variance relatively small and better visualization of the results. By quantitative analysis,the embedding quality measured by residual variance is increased 45. 45% after using the proposed algorithm in LLE.

Software Defect Prediction Based on Non-Linear Manifold Learning and Hybrid Deep Learning Techniques

Software defect prediction plays a very important role in software quality assurance,which aims to inspect as many potentially defect-prone software modules as possible.However,the performance of the prediction model is susceptible to high dimensionality of the dataset that contains irrelevant and redundant features.In addition,software metrics for software defect prediction are almost entirely traditional features compared to the deep semantic feature representation from deep learning techniques.To address these two issues,we propose the following two solutions in this paper:(1)We leverage a novel non-linear manifold learning method-SOINN Landmark Isomap(SL-Isomap)to extract the representative features by selecting automatically the reasonable number and position of landmarks,which can reveal the complex intrinsic structure hidden behind the defect data.(2)We propose a novel defect prediction model named DLDD based on hybrid deep learning techniques,which leverages denoising autoencoder to learn true input features that are not contaminated by noise,and utilizes deep neural network to learn the abstract deep semantic features.We combine the squared error loss function of denoising autoencoder with the cross entropy loss function of deep neural network to achieve the best prediction performance by adjusting a hyperparameter.We compare the SL-Isomap with seven state-of-the-art feature extraction methods and compare the DLDD model with six baseline models across 20 open source software projects.The experimental results verify that the superiority of SL-Isomap and DLDD on four evaluation indicators.

Semi-Supervised Dimensionality Reduction of Hyperspectral Image Based on Sparse Multi-Manifold Learning

In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturally gives relative importance to the labeled ones through a graph-based methodology. Then it tries to extract discriminative features on each manifold such that the data points in the same manifold become closer. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated and compared through experiments on a real hyperspectral images.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.

Dynamic Analogical Association Algorithm Based on Manifold Matching for Few-Shot Learning

At present,deep learning has been well applied in many fields.However,due to the high complexity of hypothesis space,numerous training samples are usually required to ensure the reliability of minimizing experience risk.Therefore,training a classifier with a small number of training examples is a challenging task.From a biological point of view,based on the assumption that rich prior knowledge and analogical association should enable human beings to quickly distinguish novel things from a few or even one example,we proposed a dynamic analogical association algorithm to make the model use only a few labeled samples for classification.To be specific,the algorithm search for knowledge structures similar to existing tasks in prior knowledge based on manifold matching,and combine sampling distributions to generate offsets instead of two sample points,thereby ensuring high confidence and significant contribution to the classification.The comparative results on two common benchmark datasets substantiate the superiority of the proposed method compared to existing data generation approaches for few-shot learning,and the effectiveness of the algorithm has been proved through ablation experiments.

Clustering Analysis of Stocks of CSI 300 Index Based on Manifold Learning

As an effective way in finding the underlying parameters of a high-dimension space, manifold learning is popular in nonlinear dimensionality reduction which makes high-dimensional data easily to be observed and analyzed. In this paper, Isomap, one of the most famous manifold learning algorithms, is applied to process closing prices of stocks of CSI 300 index from September 2009 to October 2011. Results indicate that Isomap algorithm not only reduces dimensionality of stock data successfully, but also classifies most stocks according to their trends efficiently.

Actor-Critic Reinforcement Learning and Application in Developing Computer-Vision-Based Interface Tracking

This paper synchronizes control theory with computer vision by formalizing object tracking as a sequential decision-making process.A reinforcement learning(RL)agent successfully tracks an interface between two liquids,which is often a critical variable to track in many chemical,petrochemical,metallurgical,and oil industries.This method utilizes less than 100 images for creating an environment,from which the agent generates its own data without the need for expert knowledge.Unlike supervised learning(SL)methods that rely on a huge number of parameters,this approach requires far fewer parameters,which naturally reduces its maintenance cost.Besides its frugal nature,the agent is robust to environmental uncertainties such as occlusion,intensity changes,and excessive noise.From a closed-loop control context,an interface location-based deviation is chosen as the optimization goal during training.The methodology showcases RL for real-time object-tracking applications in the oil sands industry.Along with a presentation of the interface tracking problem,this paper provides a detailed review of one of the most effective RL methodologies:actor–critic policy.

Extended DMPs Framework for Position and Decoupled Quaternion Learning and Generalization

Dynamic movement primitives(DMPs)as a robust and efcient framework has been studied widely for robot learning from demonstration.Classical DMPs framework mainly focuses on the movement learning in Cartesian or joint space,and can’t properly represent end-efector orientation.In this paper,we present an extended DMPs framework(EDMPs)both in Cartesian space and 2-Dimensional(2D)sphere manifold for Quaternion-based orientation learning and generalization.Gaussian mixture model and Gaussian mixture regression(GMM-GMR)are adopted as the initialization phase of EDMPs to handle multi-demonstrations and obtain their mean and covariance.Additionally,some evaluation indicators including reachability and similarity are defned to characterize the learning and generalization abilities of EDMPs.Finally,a real-world experiment was conducted with human demonstrations,the endpoint poses of human arm were recorded and successfully transferred from human to the robot.The experimental results show that the absolute errors of the Cartesian and Riemannian space skills are less than 3.5 mm and 1.0°,respectively.The Pearson’s correlation coefcients of the Cartesian and Riemannian space skills are mostly greater than 0.9.The developed EDMPs exhibits superior reachability and similarity for the multi-space skills’learning and generalization.This research proposes a fused framework with EDMPs and GMM-GMR which has sufcient capability to handle the multi-space skills in multi-demonstrations.

Personalized movie recommendation method based on ensemble learning

Aiming at the personalized movie recommendation problem,a recommendation algorithm in-tegrating manifold learning and ensemble learning is studied.In this work,manifold learning is used to reduce the dimension of data so that both time and space complexities of the model are mitigated.Meanwhile,gradient boosting decision tree(GBDT)is used to train the target user profile prediction model.Based on the recommendation results,Bayesian optimization algorithm is applied to optimize the recommendation model,which can effectively improve the prediction accuracy.The experimental results show that the proposed algorithm can improve the accuracy of movie recommendation.

Learning neural operators on Riemannian manifolds

Learning mappings between functions(operators)defined on complex computational domains is a common theoretical challenge in machine learning.Existing operator learning methods mainly focus on regular computational domains,and have many components that rely on Euclidean structural data.However,many real-life operator learning problems involve complex computational domains such as surfaces and solids,which are non-Euclidean and widely referred to as Riemannian manifolds.Here,we report a new concept,neural operator on Riemannian manifolds(NORM),which generalises neural operator from Euclidean spaces to Riemannian manifolds,and can learn the operators defined on complex geometries while preserving the discretisation-independent model structure.NORM shifts the function-to-function mapping to finite-dimensional mapping in the Laplacian eigenfunctions’subspace of geometry,and holds universal approximation property even with only one fundamental block.The theoretical and experimental analyses prove the significant performance of NORM in operator learning and show its potential for many scientific discoveries and engineering applications.

A supervised multimanifold method with locality preserving for face recognition using single sample per person

Although real-world experiences show that preparing one image per person is more convenient, most of the appearance-based face recognition methods degrade or fail to work if there is only a single sample per person(SSPP). In this work, we introduce a novel supervised learning method called supervised locality preserving multimanifold(SLPMM) for face recognition with SSPP. In SLPMM, two graphs: within-manifold graph and between-manifold graph are made to represent the information inside every manifold and the information among different manifolds, respectively. SLPMM simultaneously maximizes the between-manifold scatter and minimizes the within-manifold scatter which leads to discriminant space by adopting locality preserving projection(LPP) concept. Experimental results on two widely used face databases FERET and AR face database are presented to prove the efficacy of the proposed approach.

Improved Multi-Bandwidth Mode Manifold for Enhanced Bearing Fault Diagnosis

Variational mode decomposition(VMD) has been proved to be useful for extraction of fault-induced transients of rolling bearings. Multi-bandwidth mode manifold(Triple M, TM) is one variation of the VMD, which units multiple fault-related modes with different bandwidths by a nonlinear manifold learning algorithm named local tangent space alignment(LTSA). The merit of the TM method is that the bearing fault-induced transients extracted contain low level of in-band noise without optimization of the VMD parameters. However, the determination of the neighborhood size of the LTSA is time-consuming, and the extracted fault-induced transients may have the problem of asymmetry in the up-and-down direction. This paper aims to improve the efficiency and waveform symmetry of the TM method.Specifically, the multi-bandwidth modes consisting of the fault-related modes with different bandwidths are first obtained by repeating the recycling VMD(RVMD) method with different bandwidth balance parameters. Then, the LTSA algorithm is performed on the multi-bandwidth modes to extract their inherent manifold structure, in which the natural nearest neighbor(Triple N, TN) algorithm is adopted to efficiently and reasonably select the neighbors of each data point in the multi-bandwidth modes. Finally, a weight-based feature compensation strategy is designed to synthesize the low-dimensional manifold features to alleviate the asymmetry problem, resulting in a symmetric TM feature that can represent the real fault transient components. The major contribution of the improved TM method for bearing fault diagnosis is that the pure fault-induced transients are extracted efficiently and are symmetrical as the real. One simulation analysis and two experimental applications in bearing fault diagnosis validate the enhanced performance of the improved TM method over the traditional methods. This research proposes a bearing fault diagnosis method which has the advantages of high efficiency, good waveform symmetry and enhanced in-band noise removal capability.

基于包络学习和分级结构一致性机制的不平衡集成算法

集成方法是不平衡学习方法的重要分支,然而,现有不平衡集成方法均作用于原样本而没考虑样本的结构信息,因此其效能仍然有限.样本的结构信息包括局部和全局结构信息.为了解决上述问题,本文提出了一种基于深度样本包络网络(Deep Instance Envelope Network,DIEN)和分级结构一致性机制(Hierarchical Structure Consistency Mechanism,HSCM)的不平衡集成学习算法.该算法在考虑局部流形和全局结构信息的情况下,通过多层样本聚类,生成高质量的多层包络样本,从而实现类平衡化.首先,算法基于样本近邻拼接和模糊C均值聚类算法,设计DIEN来挖掘样本的结构信息,得到深度包络样本.然后,设计局部流形结构度量和全局结构分布度量来构建HSCM用于增强层间样本的分布一致性.接着,将DIEN和HSCM结合起来,构建出优化后的深度样本包络网络——DH(DIEN with HSCM).之后,将基分类器应用于包络样本.最后,设计bagging集成学习机制来融合基分类器的预测结果.文末组织了多组实验,采用了十多个公共数据集和有代表性的相关算法进行验证比较.实验结果表明,本文算法在AUC(Area Under Curve),F-measure等四个性能指标上显著最优.