Weighted Principal Component Analysis Research Articles

Optimization of MRR and Surface Roughness in PAC of EN 31 Steel Using Weighted Principal Component Analysis

Abstract In this paper, an attempt has been made to optimize the process parameters for multi-responses (material removal rate, MRR and surface roughness) in plasma arc cutting (PAC) of EN 31 steel using weighted principal component analysis (WPCA). For surface roughness characteristics, five different surface roughness parameters (centre line average roughness: R a , root mean square: R q , skewness: R sk , kurtosis: R ku and mean line peak spacing: R sm ) are considered. Three process parameters viz. gas pressure, arc current and torch height are considered. The experimental plan is based on Taguchi L 27 orthogonal array (OA). To convert the multi-responses problem to a single response optimization problem, WPCA is applied to compute a multi-response performance index (MPI) and then MPI has been optimized using Taguchi method. The optimum combination of process parameters has been found for maximum MRR and minimum surface roughness and verified through a confirmation test. Also, ANOVA is carried out and it is seen that the gas pressure is the most significant factor followed by arc current.

Optimization of Correlated Quality Characteristics in WEDM Process using Taguchi Approach Coupled with Principal Component Analysis

AbstractIn the present work, an attempt has been made to solve the correlated multi-response optimization problem of wire electrical discharge machining (WEDM) of EN-31 steel. The experimental investigation have been carried out to evaluate the best process environment which could simultaneously satisfy multiple quality characteristics such as material removal rate (MRR), surface roughness (Ra) and dimensional deviation (DD). In view of the fact that traditional Taguchi method cannot solve a multi response optimization problem, weighted principal component analysis (WPCA) has been coupled with Taguchi method to overcome this limitation. The multiple responses are converted into a single response using principal component analysis so that influence of correlation among the responses can be eliminated. Values of individual principal components multiplied by their priority weight were added to calculate the composite principal component defined as multi-response performance index (MPI). MPI is used as response for optimization using Taguchi's L27 orthogonal array. From analysis of variance, pulse on time was found to be the most significant parameter. Finally, the optimal result obtained was verified through confirmatory test.

Catheter ablation outcome prediction in persistent atrial fibrillation using weighted principal component analysis

Radiofrequency catheter ablation (CA) is increasingly employed to treat persistent atrial fibrillation (AF), yet selection of patients who would positively respond to this therapy is currently a critical problem. Several parameters of the surface 12-lead electrocardiogram (ECG) have been analyzed in previous works to predict AF termination by CA. Nevertheless, they are affected by some limitations, such as manual computation and the examination of a single ECG lead while neglecting contributions from other electrodes. AF spatio-temporal organization has been described on surface ECG by means of the normalized mean square error (NMSE) between consecutive atrial activity (AA) signal segments and their reduced-rank approximations based on principal component analysis (PCA). However, these features do not show to be correlated with CA outcome. In this study, such descriptors are adequately adapted and applied to CA outcome prediction. An NMSE index is put forward, computed over the set of eight linearly independent ECG leads after AA signal rank-1 approximations determined by weighted principal component analysis (WPCA). The final predictor is able to discriminate between successful (70.76±17.74) and failing CA procedures (37.54±20.01) before performing the ablation (p-value=0.0013, AUC=0.91). The proposed WPCA-based technique emphasizes the most descriptive components of AF electrophysiology by selectively enhancing contributions coming from the most representative ECG leads. Our investigation confirms that ECG spatial diversity exploitation in this WPCA-based framework not only endows the NMSE index with clinical value in the context of CA outcome prediction, but it also improves classification accuracy and increases robustness to ECG lead selection.

Analysis and convergence of weighted dimensionality reduction methods

We propose to use a Fisher type discriminant objective function addressed to weighted principal component analysis (WPCA) and weighted regularized discriminant analysis (WRDA) for dimensionality reduction. Additionally, two different proofs for the convergence of the method are obtained. First one analytically, by using the completeness theorem, and second one algebraically, employing spectral decomposition. The objective function depends on two parameters U matrix being the rotation and D diagonal matrix weight of relevant features, respectively. These parameters are computed iteratively, in order to maximize the reduction. Relevant features were obtained by determining the eigenvector associated to the most weighted eigenvalue onthe maximum value in U. Performance evaluation of the reduction methods was carried out on 70 benchmark databases. Results showed that weighted reduction methods presented the best behavior, PCA and PPCA lower than 17% while WPCA and WRDA higher than 45%. Particularly, WRDA method had the best performance in the 75% of the cases compared with the others studied here.

Chemical processes monitoring based on weighted principal component analysis and its application

Conventional principal component analysis (PCA)-based methods employ the first several principal components (PCs) which indicate the most variances information of normal observations for process monitoring. Nevertheless, fault information has no definite mapping relationship to a certain PC and useful information might be submerged under the retained PCs. A new version of weighted PCA (WPCA) for process monitoring is proposed to deal with the situation of useful information being submerged and reduce missed detection rates of T2 statistic. The main idea of WPCA is building conventional PCA model and then using change rate of T2 statistic along every PC to capture the most useful information in process, and setting different weighting values for PCs to highlight useful information when online monitoring. Case studies on Tennessee Eastman process demonstrate the effectiveness of the proposed scheme and monitoring results are compared with conventional PCA method.

Customized Requirements Driven Multivariate Quality Control for Steelmaking Process

In this paper, a new SPC based quality control process model for steelmaking industry is established, in which a Customer Requirements Weighted-Principal Component Analysis (CRW-PCA) method is proposed, the multivariate control charts based on this method can make special emphasis on the controlling of steelmaking quality characters response to customer’s special requirements. Practices show that compared with the traditional PCA-based multivariate control chart, the multivariate control charts based on CRW-PCA is more adaptive to the needs of today’s process quality control of steelmaking due to the adequate consideration of customers’ requirements.

Optimization of Multiple Roughness Characteristics of Chemically Deposited Ni-P-W Coating Using Weighted Principal Component Analysis

The present investigation deals with the chemical deposition of Ni-P-W coating on mild steel substrate and optimization of multiple surface roughness characteristics on the basis of different coating process parameters. Three coating parameters which are varied to have the optimum condition are concentration of nickel source, concentration of reducing agent, and concentration of tungsten source. Five different roughness parameters, namely, centre line average (Ra), root mean square roughness (Rq), skewness (Rsk), kurtosis (Rku), and mean peak line spacing (Rsm) are considered. Weighted principal component analysis (WPCA) method is adopted to convert the multiple-response problem into a single performance index and Taguchi L27 orthogonal array is used. ANOVA is performed to find the significance of the each coating process parameters and their interactions. The EDX analysis, XRD analysis, and SEM are performed to study the composition and structural aspects.

Bead Geometry Optimization of Submerged Arc Weld: Exploration of Weighted Principal Component Analysis (WPCA)

The present work attempts to overcome underlying assumptions in traditional Taguchi based optimization techniques highlighted in literature. Taguchi method alone fails to solve multi-response optimization problems. In order to overcome this limitation, exploration of grey relation theory, desirability function approach, utility theory etc. have been found amply applied in literature in combination with Taguchi method. But aforesaid approaches relies on the assumption that individual response features are uncorrelated i.e. independent of each other which are really impossible to happen in practice. The study takes into account this response correlation and proposes an integrated methodology in a case study on optimization of multiple bead geometry parameters of submerged arc weldment. Weighted Principal Component Analysis (WPCA) has been applied to eliminate response correlation and to convert correlated responses into equal or less number of uncorrelated quality indices called principal components. Based on individual principal components a Multi-response Performance Index (MPI) has been introduced to derive an equivalent single objective function which has been optimized (maximized) using Taguchi method. Experiments have been conducted based on Taguchi’s L25 Orthogonal Array design with combinations of process control parameters: voltage, wire feed, welding speed and electrode stick-out. Different bead geometry parameters: bead width, bead height, penetration depth and HAZ dimensions have been optimized. Optimal result has been verified by confirmatory test. The study highlights effectiveness of the proposed method for solving multi-objective optimization of submerged arc weld.

A Weighted Principal Component Analysis and Its Application to Gene Expression Data

In this work, we introduce in the first part new developments in Principal Component Analysis (PCA) and in the second part a new method to select variables (genes in our application). Our focus is on problems where the values taken by each variable do not all have the same importance and where the data may be contaminated with noise and contain outliers, as is the case with microarray data. The usual PCA is not appropriate to deal with this kind of problems. In this context, we propose the use of a new correlation coefficient as an alternative to Pearson's. This leads to a so-called weighted PCA (WPCA). In order to illustrate the features of our WPCA and compare it with the usual PCA, we consider the problem of analyzing gene expression data sets. In the second part of this work, we propose a new PCA-based algorithm to iteratively select the most important genes in a microarray data set. We show that this algorithm produces better results when our WPCA is used instead of the usual PCA. Furthermore, by using Support Vector Machines, we show that it can compete with the Significance Analysis of Microarrays algorithm.

Combined quality loss (CQL) concept in WPCA-based Taguchi philosophy for optimization of multiple surface quality characteristics of UNS C34000 brass in cylindrical grinding

The present study highlights a multi-objective optimization problem by applying Weighted Principal Component Analysis (WPCA) coupled with Taguchi method through a case study in cylindrical grinding of UNS C34000 Medium Leaded Brass. The study aimed at evaluating the best process environment which could simultaneously satisfy multiple requirements of surface quality. In view of the fact that traditional Taguchi method fails to solve a multi-objective optimization problem, to overcome this limitation, WPCA has been coupled with Taguchi method. Furthermore, to follow the basic assumption of Taguchi method, i.e., quality attributes should be uncorrelated or independent; which is not always satisfied in practical situation; the study applied WPCA to eliminate response correlation and to evaluate independent or uncorrelated quality indices called principal components which were aggregated by WPCA to compute overall quality index denoted as Multi-Response Performance Index. A combined quality loss was then estimated which was optimized (minimized) finally. The study combined WPCA and Taguchi method for predicting optimal setting. Optimal result was verified through confirmatory test. This indicates application feasibility of the aforesaid methodology proposed for multi-response optimization and off-line control of correlated multiple surface quality characteristics in cylindrical grinding.

Metabolic Profiling ofEchinaceaGenotypes and a Test of Alternative Taxonomic Treatments

The genus Echinacea is used as an herbal medicine to treat a variety of ailments. To better understand its potential chemical variation, 40 Echinacea accessions encompassing broad geographical and morphological diversity were evaluated under controlled conditions. Metabolites of roots from these accessions were analyzed by HPLC-photo diode array (HPLC-PDA), GC-MS, and multivariate statistical methods. In total, 43 lipophilic metabolites, including 24 unknown compounds, were detected. Weighted principal component analysis (WPCA) and clustering analysis of the levels of these metabolites across Echinacea accessions, based on Canberra distances, allowed us to test two alternative taxonomic treatments of the genus, with the further goal of facilitating accession identification. A widely used system developed by McGregor based primarily on morphological features was more congruent with the dendrogram generated from the lipophilic metabolite data than the system more recently developed by Binns et al. Our data support the hypothesis that Echinacea pallida is a diverse allopolyploid, incorporating the genomes of Echinacea simulata and another taxon, possibly Echinacea sanguinea. Finally, most recognized taxa of Echinacea can be identified by their distinct lipophilic metabolite fingerprints.