High-dimensional Linear Space Research Articles

A novel global modelling strategy integrated dynamic kernel canonical variate analysis for the air handling unit fault detection via considering the two-directional dynamics

As an indispensable component of air-conditioning system, the air handling unit (AHU) always exhibits strong nonlinearity and two-directional dynamics (time-wise and batch-wise dynamics). However, existing monitoring strategies cannot adequately figure out the AHU's two-directional dynamics from the nonlinear data. To boost the AHU's fault detection performance, a novel global modelling scheme integrated dynamic kernel canonical variate analysis (GDKCVA) is developed in this paper. The first contribution is to collect datasets from various days to develop a three-way training dataset and then normalize it along the batch-wise to suppress the batch-wise dynamics and variables' correlations. The second contribution is to establish the dynamic kernel CVA by integrating autoregressive moving average exogenous framework to more effectively confront the time-wise dynamics and variables' nonlinear relationships. The kernel matrices of augmented batch dataset are determined utilizing the kernel trick that transforms nonlinear data into high-dimensional linear space by leveraging kernel function. The third contribution is to propose a novel global modelling strategy to further eliminate the batch-wise dynamics by computing the total average kernel matrices from all the normal batch datasets. Finally, experiments and comparisons on the ASHRAE RP-1312 datasets are carried out to assess the suggested GDKCVA's fault detection capability. Compared with the kernel CVA (KCVA), the three-way training dataset based CVA (TCVA) and the three-way training dataset based KCVA (TKCVA), the proposed GDKCVA has the highest fault detection rates and its average fault detection rates of three monitoring statistics for eleven fault patterns reach 99.38 %, 99.15 % and 100 %, respectively.

A novel industrial process fault monitoring method based on kernel robust non-negative matrix factorization

Industrial processes are characterized by large amounts of nonlinear and noisy data, which pose a critical challenge to the accuracy and rapidity of fault detection. In this paper, an industrial process fault monitoring method based on kernel robust non-negative matrix factorization is proposed. This method uses the kernel technique to map the nonlinear data to high-dimensional linear space, where the local features of the sample will be extracted by the non-negative matrix factorization (NMF) method. However, noise signals will inevitably be mixed. Therefore, a sparse error matrix is introduced to isolate fault and noise information. Finally, a new monitoring statistics and a fault detection framework are constructed. On the TE platform, the algorithm proposed in this paper is compared with kernel principal component analysis and kernel NMF methods in nonlinear experiments and robustness experiments through two performance indicators: fault detection rate and fault delay. The results prove the effectiveness of the algorithm in this paper.

The Code for Facial Identity in the Primate Brain

Primates recognize complex objects such as faces with remarkable speed and reliability. Here, we reveal the brain's code for facial identity. Experiments in macaques demonstrate an extraordinarily simple transformation between faces and responses of cells in face patches. By formatting faces as points in a high-dimensional linear space, we discovered that each face cell's firing rate is proportional to the projection of an incoming face stimulus onto a single axis in this space, allowing a face cell ensemble to encode the location of any face in the space. Using this code, we could precisely decode faces from neural population responses and predict neural firing rates to faces. Furthermore, this code disavows the long-standing assumption that face cells encode specific facial identities, confirmed by engineering faces with drastically different appearance that elicited identical responses in single face cells. Our work suggests that other objects could be encoded by analogous metric coordinate systems. PAPERCLIP.

Synchronization of Kuramoto model in a high-dimensional linear space

Abstract In this Letter, Kuramoto model in a high-dimensional linear space is investigated. Some results on the equilibria and synchronization of the classical Kuramoto model are generalized to the high-dimensional Kuramoto model. It is proved that, if the interconnection graph is connected and all the initial states lie in a half part of the state space, the synchronization can be achieved. Finally, numerical simulations are given to validate the obtained theoretical results.

Fault Diagnosis of Rolling Bearings Based on LLE_KFDA

Locally linear embedding (LLE) algorithm is an unsupervised technique recently proposed for nonlinear dimension reduction. In this paper,LLE manifold learning algorithm is introduced into the field of equipment fault diagnosis firstly, a method of the fault diagnosis based on LLE_KFDA is proposed. By LLE algorithm, original sample data is directly mapped to its’ intrinsical dimension space,which data still keep primary nonlinear form. then via kernel fisher discriminant analysis(KFDA), the characteristics data in intrinsical dimension space are mapped into knernel high-dimensional linear space,and then different fault data are discriminated based on a criterion of between-class and insid-class deviatione ratio maximum. LLE_KFDA algorithm is based on original data, avoided from fall of pattern recognition ability which caused by inappropriate or blind choice of the feature parameters in the traditional fault diagnosis method.The experiment to fault diagnosis of rolling bearing shows this method can effectively identify the equipment fault pattern, diagnostic result is good.

Multiway kernel independent component analysis based on feature samples for batch process monitoring

Most batch processes generally exhibit the characteristics of nonlinear variation. In this paper, a nonlinear monitoring technique is proposed using a multiway kernel independent component analysis based on feature samples (FS-MKICA). This approach first unfolds the three-way dataset of a batch process into the two-way one and then chooses representative feature samples from the large two-way input training dataset. The nonlinear feature space abstracted from the unfolded two-way data space is then transformed into a high-dimensional linear space via kernel function and an independent component analysis (ICA) model is established in the mapped linear space. The proposed FS-MKICA method can significantly reduce the computational cost in extracting the kernel ICA model since it is based on the small subset of feature samples rather than on the entire input sample set. We supply two statistics, the I 2 statistic of process variation and the squared prediction error statistic of residual, for on-line monitoring of batch processes. The proposed method is applied to detecting faults in the fed-batch penicillin fermentation process. The standard linear ICA method for batch process monitoring, known as the multiway independent component analysis (MICA), is also applied to the same benchmark batch process. The simulation results obtained in this nonlinear batch process application clearly demonstrate the power and superiority of the new nonlinear monitoring method over the linear one. The FS-MKICA approach can extract the nonlinear features of the batch process while the MICA method cannot.

A novel classification method based on hypersurface

The main idea of the support vector machine (SVM) classification approach is mapping the data into higher-dimensional linear space where the data can be separated by hyperplane. Based on the Jordan curve theory, a general nonlinear classification method by the use of hypersurface is proposed in this paper. The separating hypersurface is directly used to classify the data according to whether the number of intersections with the radial is odd or even. In contrast to the SVM approach, the proposed approach has no need for mapping from lower-dimensional space to higher-dimensional space. Furthermore, the approach does not use kernel functions and it can directly solve the nonlinear classification problem via the hypersurface. Numerical experiments showed that the proposed approach can efficiently and accurately solve the classification problems with a large amount of data.