Typical Manifold Research Articles

Fault Detection-Based Multiple Local Manifold Learning and Its Application to Blast Furnace Ironmaking Process

Process safety plays a vital role in the modern process industry. To prevent undesired accidents caused by malfunctions or other disturbances in complex industrial processes, considerable attention has been paid to data-driven fault detection techniques. To explore the underlying manifold structure, manifold learning methods including Laplacian eigenmaps, locally linear embedding, and Hessian eigenmaps have been utilized in data-driven fault detection. However, only the partial local structure information is extracted from the aforementioned methods. This paper proposes fused local manifold learning (FLML), which synthesizes the typical manifold learning methods to find the underlying manifold structure from different angles. A more comprehensive local structure is discovered under a unified framework by constructing an objection optimization function for process data dimension reduction. The proposed method takes advantage of different manifold learning methods. Based on the proposed dimension reduction method, a new data-driven fault detection method is developed. Hotelling’s T2 and Q statistics are established for the purpose of fault detection. Experiments on an industrial benchmark Tennessee Eastman process whose average MDR and average FAR of FLML T2 are 7.58% and 0.21% and a real blast furnace ironmaking process whose MDR and FAR of FLML T2 are 2.80% and 0.00% are carried out to demonstrate the superiority and effectiveness of the proposed method.

ISL-GKFDA: An incomplete supervision manifold learning framework based on propagation graph of data

To improve manifold classification results using unlabeled data with high dimensional redundancy, we propose an incomplete supervision manifold learning framework. In this framework, Euclidean distance and Euclidean neighborhood are replaced by manifold distance and manifold neighborhood respectively. The pseudo label of unlabeled data is generated by constructing label propagation network in manifold neighborhood. By adding the local manifold neighborhood structure into KFDA (Kernel Fisherś Discriminant Analysis) as regularization term, the local manifold structure is stressed. Subsequently, we propose the ISL-GKFDA (Incomplete Supervision Learning (ISL) with propagation Graph of data in Kernel Fisher Discriminant Analysis) algorithm. We validate ISL-GKFDA by comparing it with FDA (Fisher's Discrimination Analysis), KFDA (Kernel FDA), ISL-FDA (ISL version FDA), ISL-KFDA (ISL version KFDA), SSDA (semi-supervised discriminant analysis based on manifold distance), and KSSDA (Kernel SSDA). In typical manifold datasets, ISL-GKFDA can more accurately capture the boundaries of binary classification; and visually in handwritten digital dataset, ISL-GKFDA can separate three data types more clearly. Finally, we use the UCI database and compare multiple algorithms. When measured by accuracy, the proposed ISL-GKFDA reaches a maximum in at least three datasets of five when labeling ratio is 5%, 15% and 30%, respectively. When measured by F1, ISL-GKFDA reaches the maximum in all datasets.

Local Linear Embedding with Adaptive Neighbors

Dimensionality reduction is one of the most important techniques in the field of data mining. It embeds high-dimensional data into a low-dimensional vector space while keeping the main information as much as possible. Locally Linear Embedding (LLE) as a typical manifold learning algorithm computes neighborhood preserving embeddings of high-dimensional inputs. Based on the thought of LLE, we propose a novel unsupervised dimensionality reduction model called Local Linear Embedding with Adaptive Neighbors (LLEAN). To achieve a desirable dimensionality reduction result, we impose adaptive neighbor strategy and adopt a projection matrix to project data into an optimal subspace. The relationship between every pair-wise data is investigated to help reveal the data structure. Augmented Lagrangian Multiplier (ALM) is devised in optimization procedure to effectively solve the proposed objective function. Comprehensive experiments on toy data and benchmark datasets have been done and the results show that LLEAN outperforms other state-of-the-art dimensionality reduction methods.

Visualization methodology of the health state for wind turbines based on dimensionality reduction techniques

Performance degradation of wind turbines (WT) is inevitable in long-term operation. Therefore, reliable and intuitive visualization of their health state are essential for condition-based maintenance. It is, however, difficult to extract effective information from the SCADA data due to its massive scale, high dimensionality and nonlinearity. Dimensionality reduction (DR) techniques provide an efficient way for structure visualization of complex datasets. In this paper, we use the diffusion map (DM) algorithm for DR and propose a health state visualization methodology, diffusion map-features geodesic distance (DM-FGD). The DM-FGD fulfills online operation by calculating multivariate statistics of the SCADA data and then reducing its dimensionality. The extracted features present the typical manifold and clustering characteristics. Accordingly, we construct a health indicator, confidence value (CV), and analyze the embedding features by clustering. The CV describes the performance degradation process of the WT and the clustering results illustrate its health status. We further propose a centroid sliding technique to extract the monotonicity characteristic of the CV. Case studies confirm the efficiency of the DM-FGD in real-time health state visualization, and justify its effectiveness and reliability by comparing it with other deviation-based methods. We also verify its extendibility through comparison studies with other DR algorithms.

Design optimization of a high-temperature fin-and-tube heat exchanger manifold – A case study

High-temperature fin-and-tube heat exchangers are widely used in many industries such as petrochemical industry, automotive, energy, and many others. The major advantage of those heat exchanger is a large heat transfer area within a compact shape. However, it is necessary to ensure uniform distribution of velocity in all the tubes. Failing that, it leads to large differences in mean temperature in the tubes. Consequently, excessive thermal stress occurs, that may cause the heat exchanger to break down. The small volume of collectors of the heat exchangers implicates possibility of improper flow condition inside the tubes, causing an unsuitable inner distribution of thermal and mechanical loads. This case study presents a design optimization of high temperature fin and tube heat exchanger manifold. The modified design of heat exchanger manifold is proposed. To optimize the manifold shape, the Particle Swarm Optimization and Continuous Genetic Algorithms are used. The design consists of tube used for a typical manifold, welded to the wedge, that enlarges the volume of the fluid and improves the flow distribution to tubular space of heat exchanger. The ANSYS CFX based CFD simulations are performed in order to determine the flow distribution in the tubes of fin-and-tube heat exchanger. The structural analysis is performed with ANSYS to determine the occurring thermal stresses. The new design of heat exchanger manifolds allowed one to reduce the tube wall temperature from 185 °C to 134 °C and compressible stresses in the construction of heat exchanger by nearly five times (from 105 MPa to 23 MPa), compared to the traditional fin-and-tube heat exchanger manifold.

Prediction of design loads for deep water subsea lifting operations based on non-stationary time response

Two methodologies for the prediction of the design loads of deep water subsea lifting operations crossing resonance zones are presented. These methodologies are applicable to models that consider the influence of the payout speed on the dynamics of the operation, leading to a non-stationary time series for the dynamic forces on the system. The first model is based on running several random simulations of the same scenario and using these simulations as a sample in which statistical parameters are inferred. The second model uses a weighted least squares approach to predict a normalizing function that is used to evaluate the statistical parameters of the response. Both models are tested by considering the installation of a typical manifold in the Pre-Salt fields, in Brazil, and are able to predict the general form of the envelope of forces on the cable for various sea states and payout speeds. The models also provided similar results for the availability of the vessel after evaluating the weather window for this operation. Finally, the advantages of using the weighted least squares approach in comparison to the direct method are discussed, since it may considerably reduce the total number of simulations required to perform a real operation assessment, especially during preliminary design phases.

COLLAPSED BUILDING CLASSIFICATION WITH OPTICAL AND SAR DATA BASED ON MANIFOLD LEARNING

Abstract. The collapse of buildings is a major factor in the casualties and economic losses of earthquake disasters, and the degree of building collapse is an important indicator for disaster assessment. In order to improve the classification of collapsed building coverings (CBC), a new fusion technique was proposed to integrate optical data and SAR data at the pixel level based on manifold learning.Three typical manifold learning models, namely, Isometric Mapping(ISOMAP), Local Linear Embedding (LLE) and principle component analysis (PCA), were used, and their results were compared. Feature extraction were employed from SPOT-5 data with RADARSAT-2 data. Experimental results showed that 1) the most useful features of the optical and SAR data were contained in manifolds with low-intrinsic dimensionality, while various CBC classes were distributed differently throughout the low- dimensionality spaces of manifolds derived from different manifold learning models; 2) in some cases, the performance of Isomap is similar to PCA, but PCA generally performed the best in this study, yielding the best accuracy of all CBC classes and requiring the least amount of time to extract features and establish learning; and 3) the LLE-derived manifolds yielded the lowest accuracy, mainly by confusing soil with collapsed building and rock. These results show that the manifold learning can improve the effectiveness of CBC classification by fusing the optical and SAR data features at the pixel level, which can be applied in practice to support the accurate analysis of earthquake damage.

Experimental and numerical investigation of hydrodynamic coefficients of subsea manifolds

ABSTRACT Hydrodynamic coefficients of subsea manifolds are significant parameters in predicting dynamic responses during deep-water installation. To calculate these coefficients, a series of model tests of the drag coefficients of a typical subsea manifold with eight slots were carried out at Zhejiang University. A numerical simulation was performed using the computational fluid dynamics (CFD) method, and the Navier–Stokes equations were solved to obtain the drag and added mass coefficients. On the prediction of drag coefficient, a similar tendency was found for both the numerical and experimental results, proving the accuracy and reliability of the proposed CFD method. The effects of variables such as the Keulegan-Carpenter (KC) number and frequency of forced oscillation on the added mass coefficients were analysed. The added mass coefficients increase nearly linearly as the KC number increases, but the oscillation frequency has little influence on the added mass coefficients.

Semi-supervised hyperspectral image classification algorithm based on graph embedding and discriminative spatial information

Image classification is one of the important techniques in computer vision. Due to the limited access of labeled samples in hyperspectral images, semi-supervised learning (SSL) methods have been widely applied in hyperspectral image classification. Graph based semi-supervised learning provides an effective solution to model data in classification problems, of which graph construction is the critical step. In this paper we employ the graphs constructed with a typical manifold learning method-locally linear embedding (LLE), based on which semi-supervised classification is then conducted. To exploit the valuable spatial information contained in hyperspectral images, discriminative spatial information (DSI) is then extracted. The proposed classification method is evaluated using three real hyperspectral data sets, revealing state-of-art performance when compared with different classification methods.

Fault diagnosis for industrial robots based on a combined approach of manifold learning, treelet transform and Naive Bayes

This research introduces a novel fault diagnosis method for an industrial robot based on manifold learning algorithms, Treelet Transform (TT) and Naive Bayes. The vibration signals of an industrial robot working under three working conditions are acquired as the raw data. Three typical manifold learning algorithms, Principal Component Analysis (PCA), Locality Preserving Projections (LPPs), and Isometric Feature Mapping (ISOMAP), are utilized to extract three-dimensional features from the vibration signals. Then, these features were combined into nine-dimensional features and, these nine-dimensional features were reduced to three-dimensional feature vectors by TT. Finally, a Naive Bayes model is trained with these three-dimensional feature vectors. Experimental results show that compared with the three methods, PCA, LPP, and ISOMAP, the accuracy of the proposed combined method is higher than the single method. The fault diagnosis method presented in this paper is easy to implement and can effectively identify the fault types.

Flow measurement and parameter optimization of right-angled flow passage in hydraulic manifold block

This study was conducted to investigate the flow field characteristics of right-angled flow passage with various cavities in the typical hydraulic manifold block. A low-speed visualization test rig was developed and the flow field of the right-angled flow passage with different cavity structures was measured using 2D-PIV technique. Numerical model was established to simulate the three-dimensional flow field. Seven eddy viscosity turbulence models were investigated in predicting the flow field by comparing against the particle image relocimetry (PIV) measurement results. By defining the weight error function K, the S-A model was selected as the appropriate turbulence model. Then, a three-factor, three-level response surface numerical test was conducted to investigate the influence of flow passage connection type, cavity diameter and cavity length-diameter ratio on pressure loss. The results show that the Box-Benhnken Design (BBD) model can predict the total pressure loss accurately. The optimal factor level appeared in flow passage connection type II, 14.64 mm diameter and 67.53% cavity length-diameter ratio. The total pressure loss decreased by 11.15% relative to the worst factor level, and total pressure loss can be reduced by 64.75% when using an arc transition right-angled flow passage, which indicates a new direction for the optimization design of flow passage in hydraulic manifold blocks.

Flow Mixing Optimisation inside a Manifold using Computational Fluid Dynamics

This paper presents an analysis of fluid flow in a typical manifold. A commerciallyavailable Computational Fluid Dynamics (CFD) package has been used to analyze the flow pattern inside the manifold. Temperatureand velocity in whole fluid domain and mass flow rate in all the outlets in the manifold have been computed. Based on the preliminary results, a simple modification to inside of the main pipe of the manifold has been incorporated. The performance of the modified design has been compared with the original design from the point of view of average temperature and mass flow rate at the outlets. This simple modification has been shown to improve the uniformity of temperature and mass flow at the outlets, thus enhancing the efficiency of the mixing manifold.

Fault Diagnosis Method for Hydraulic Pump Based on Fuzzy Entropy of Wavelet Packet and LLTSA

As the vibration signal characteristics of hydraulic pump present non-stationary and the fault features is difficult to extract, a new feature extraction method was proposed .This approach combines wavelet packet analysis techniques, fuzzy entropy and LLTSA (liner local tangent space alignment) which is one of typical manifold learning methods to extracting fault feature. Firstly, the vibration signals were decomposed into eight signals in different scales, then the fuzzy entropies of signals were calculated to constitute eight dimensions feature vector. Secondly, LLTSA method was applied to compress the high-dimension features into low-dimension features which have a better classification performance. Finally, the SVM (support vector machine) was employed to distinguish different fault features. Experiment results of hydraulic pump feature extraction show that the proposed method can exactly classify different fault type of hydraulic pump and this method has a significant advantage compared with other feature extraction means mentioned in this paper.

A manifold learning approach to urban land cover classification with optical and radar data

Urban land covers (ULC) are essential data for numerous studies of urban landscape ecology performed on various scales. Nevertheless, it remains difficult to obtain accurate and timely ULC information. This study presents a methodological framework for fusing optical and synthetic aperture radar (SAR) data at the pixel level with manifolds to improve ULC classification. Three typical manifold learning models, namely, ISOMAP, Local Linear Embedding (LLE) and principle component analysis (PCA), were employed, and their results were compared. SPOT-5 data were used as optical data to be fused with three different SAR datasets. Experimental results showed that 1) the most useful information of the optical and SAR data were included in the manifolds with intrinsic dimensionality, while various ULC classes were distributed differently throughout the feature spaces of manifolds derived from different learning methods; 2) in certain cases, ISOMAP performed comparably to PCA, but PCA generally performed the best out of all the study cases, yielding the best producer's and user's accuracy of all ULC classes and requiring the least amount of time to build the machine learning models; and 3) the LLE-derived manifolds yielded the lowest accuracy, primarily by confusing bare soils with dark impervious surfaces and vegetation. These results indicate the effectiveness of the new manifold technology to fuse optical and SAR data at the pixel level for improving ULC classification, which can be applied in practice to support the accurate analysis of urban landscape.

Exponential elastic preserving projections for facial expression recognition

Abstract As a typical manifold learning method, elastic preserving projections (EPP) can well preserve the local geometry and the global information of the training set. However, EPP generally suffers from two issues: (1) the algorithm encounters the well known small sample size (SSS) problem; (2) the algorithm is based on the adjacent graph such that it is sensitive to the size of neighbors. To address these problems, we propose a novel method called exponential elastic preserving projections (EEPP), principally for facial expression recognition. By utilizing the properties of matrix exponential, EEPP is not only able to exploit the manifold structure of data, but also can get rid of the issues mentioned above. Experiments conducted on the synthesized data and several benchmark databases illustrate the effectiveness of our proposed algorithm.

Assessment of Thermo-Mechanical Fatigue Performance of an Exhaust Manifold through Simulation

Exhaust manifold of an IC engine typically experiences cyclic thermal and mechanical loading and are prone to TMF failure. Thermo-mechanical fatigue resistance needs to be ensured for exhaust manifold to meet the requirement of durability in order to meet the demanding needs of recent trends in IC engine design. Considering reduced product development cycle time, more accurate design procedure for exhaust manifold through simulation route is preferred. The present work is an attempt in this direction, where methodology to carry out TMF analysis of exhaust manifold through simulation is formulated and successfully implemented. The complete simulation process involved four important stages, namely simplified 1-D simulation of engine, thermal analysis of exhaust manifold, and structural analysis of exhaust manifold and TMF life evaluation of exhaust manifold. The developed methodology has been successfully implemented considering a typical exhaust manifold. Thermal inputs obtained through simplified engine simulation using 1-D gas dynamics and engine simulation software required for thermal analysis of exhaust manifold are found to be satisfactory and has eliminated the need for complex 3-D CFD simulations. TMF life valuated at critical locations indicate that except one location all other locations have life exceeding the LCF limit.

Performance Improvement of a Typical Manifold using Computational Fluid Dynamics

This paper presents an analysis of fluid flow in a typical manifold. A commercially available Computational Fluid Dynamics (CFD) package has been used to analyze the flow pattern inside the manifold. Pressure drop in whole fluid domain and mass flow rate in all the outlets in the manifold have been computed. Based on the preliminary results, a modification to inside of the main pipe of the manifold has been incorporated. The performance of the modified design has been compared with the original design from the point of view of average temperature and mass flow rate at the outlets. A simple modification has been shown to improve the uniformity of temperature and mass flow at the outlets.

MANIFOLD LEARNING AND VISUALIZATION BASED ON DYNAMIC SELF-ORGANIZING MAP

For the data sampled from a low-dimensional nonlinear manifold embedded in a high-dimensional space, such as Swiss roll and S-curve, Self-Organizing Map (SOM) tends to get stuck in local minima and then yield topological defects in the final map. To avoid this problem and obtain more faithful visualization results, a variant of SOM, i.e. Dynamic Self-Organizing Map (DSOM), was presented in this paper. DSOM can dynamically increase the map size, as the training data set is expanded according to its intrinsic neighborhood structure, starting from a small neighborhood in which the data points can lie on or close to a linear patch. According to the locally Euclidean nature of the manifold, the map can be guided onto the manifold surface and then the global faithful visualization results can be achieved step by step. Experimental results show that DSOM can discover the intrinsic manifold structure of the data more faithfully than SOM. In addition, as a new manifold learning method, DSOM can obtain more concise visualization results and be less sensitive to the neighborhood size and the noise than typical manifold learning methods, such as Isometric Mapping (ISOMAP) and Locally Linear Embedding (LLE), which can also be verified by experimental results.

A manifold learning method to detect respiratory signal from liver ultrasound images

Respiratory gating has been widely applied for respiratory correction or compensation in image acquisition and image-guided interventions. A novel image-based method is proposed to extract respiratory signal directly from 2D ultrasound liver images. The proposed method utilizes a typical manifold learning method, based on local tangent space alignment based technique, to detect principal respiratory motion from a sequence of ultrasound images. This technique assumes all the images lying on a low-dimensional manifold embedding into the high-dimensional image space, constructs an approximate tangent space of each point to represent its local geometry on the manifold, and then aligns the local tangent spaces to form the global coordinate system, where the respiratory signal is extracted. The experimental results show that the proposed method can detect relatively accurate respiratory signal with high correlation coefficient (0.9775) with respect to the ground-truth signal by tracking external markers, and achieve satisfactory computing performance (2.3s for an image sequence of 256 frames). The proposed method is also used to create breathing-corrected 3D ultrasound images to demonstrate its potential application values.

Image clustering based on sparse patch alignment framework

Image clustering methods are efficient tools for applications such as content-based image retrieval and image annotation. Recently, graph based manifold learning methods have shown promising performance in extracting features for image clustering. Typical manifold learning methods adopt appropriate neighborhood size to construct the neighborhood graph, which captures local geometry of data distribution. Because the density of data points’ distribution may be different in different regions of the manifold, a fixed neighborhood size may be inappropriate in building the manifold. In this paper, we propose a novel algorithm, named sparse patch alignment framework, for the embedding of data lying in multiple manifolds. Specifically, we assume that for each data point there exists a small neighborhood in which only the points that come from the same manifold lie approximately in a low-dimensional affine subspace. Based on the patch alignment framework, we propose an optimization strategy for constructing local patches, which adopt sparse representation to select a few neighbors of each data point that span a low-dimensional affine subspace passing near that point. After that, the whole alignment strategy is utilized to build the manifold. Experiments are conducted on four real-world datasets, and the results demonstrate the effectiveness of the proposed method.