Fault Detection and Diagnosis for Nonlinear and Non-Gaussian Processes Based on Copula Subspace Division

A novel copula subspace division strategy is proposed for fault detection and diagnosis. High-dimensional industrial data are analyzed in two elemental subspaces: margin distribution subspace (MDS) modeled by joint margin distribution, and dependence structure subspace (DSS) modeled by copula. The highest density regions of two submodels are introduced and quantified using probability indices. To improve the robustness of the monitoring index, a hyperrectangular control boundary in MDS is designed, and the equivalent univariate control limits are estimated. Two associated contribution indices are also constructed for fault diagnosis. The interactive relationships among the root-cause variables are investigated via a proposed state chart. The effectiveness and superiority of the proposed approaches (double-subspace and multisubspace) are validated using a numerical example and the Tennessee Eastman chemical process. Better monitoring performance is achieved compared with some conventional approaches such as principal component analysis, independent component analysis, kernel principal component analysis and vine copula-based dependence description. The proposed multisubspace approach fully utilizes univariate-based alarm data with a dependence restriction modulus, which is promising for industrial application

Mean tone recognition scores and SDs at different SNRs in each group.

<p>Mean tone recognition scores and SDs at different SNRs in each group.</p

Mean audiogram based on the mean thresholds and SDs at all frequencies, for participants in each group.

<p>A. Mean audiogram of children with NH. B. Mean audiogram of children in the OME-A group. C. Mean audiogram of children in the OME-B group.</p

Results of four repeated-measure ANCOVAs.

<p>Results of four repeated-measure ANCOVAs.</p

Mean PTA and tone recognition threshold in each group.

<p>Mean PTA and tone recognition threshold in each group.</p

Boxplot of tone recognition thresholds in children with NH and in children with OME.

<p>Boxplot of tone recognition thresholds in children with NH and in children with OME.</p

Tone recognition confusion matrices of three child groups under -12 dB SNR to -21 dB SNR.

<p>Data were pooled from all participants in each group. For each panel of 4 × 6 cells, the rows indicate the stimuli and the columns indicate the response tone types. The grey scale in each cell and the value in it represent percentage of responses. NR: no response.</p

Results from the mixed-design repeated-measure ANCOVA.

<p>Results from the mixed-design repeated-measure ANCOVA.</p

Polymorphism of Nifedipine: Crystal Structure and Reversible Transition of the Metastable β Polymorph

We report the first structural determination of the metastable β polymorph of nifedipine (NIF) by single-crystal X-ray diffraction. Stable, high-quality crystals were grown from the melt in the presence of a polymer dopant. Our β NIF structure is characterized by a unit cell similar to that of the structure recently proposed from powder diffraction, but significantly different molecular conformations. Unlike the stable α polymorph, β NIF undergoes a reversible solid-state transformation near 60 °C. The now available β NIF structure clarifies some confusion concerning NIF polymorphs and enables inquiries into the structural basis for the selective crystallization of β NIF from glasses. We report that another polymorph crystallizes concomitantly with β NIF from the supercooled melt and transforms to β NIF at room temperature; this polymorph also undergoes reversible solid-state transformation

Fault Detection and Diagnosis for Nonlinear and Non-Gaussian Processes Based on Copula Subspace Division

A novel copula subspace division strategy is proposed for fault detection and diagnosis. High-dimensional industrial data are analyzed in two elemental subspaces: margin distribution subspace (MDS) modeled by joint margin distribution, and dependence structure subspace (DSS) modeled by copula. The highest density regions of two submodels are introduced and quantified using probability indices. To improve the robustness of the monitoring index, a hyperrectangular control boundary in MDS is designed, and the equivalent univariate control limits are estimated. Two associated contribution indices are also constructed for fault diagnosis. The interactive relationships among the root-cause variables are investigated via a proposed state chart. The effectiveness and superiority of the proposed approaches (double-subspace and multisubspace) are validated using a numerical example and the Tennessee Eastman chemical process. Better monitoring performance is achieved compared with some conventional approaches such as principal component analysis, independent component analysis, kernel principal component analysis and vine copula-based dependence description. The proposed multisubspace approach fully utilizes univariate-based alarm data with a dependence restriction modulus, which is promising for industrial application