Wavelets for scrutinizing multivariate exploratory models? interpreting models through multiresolution analysis

An SPC monitoring system for cycle-based waveform signals using haar transform

“…The multiscale principal component analysis (MSPCA) method is proposed for the monitoring of continuous chemical processes [8], [9]. In MSPCA, PCA is conducted on the wavelet coefficients of each scale of a windowed sample of continuous processes.…”

“…Since the dimension of is often much smaller than the dimension of , the statistic for the Haar coefficients instead of the signal itself is used to monitor the process. Thus, we use (9) To set up multivariate control charts on the individual observations, two phases are needed. The production is monitored in Phase II.…”

An SPC monitoring system for cycle-based waveform signals using haar transform

“…The multiscale principal component analysis (MSPCA) method is proposed for the monitoring of continuous chemical processes [8], [9]. In MSPCA, PCA is conducted on the wavelet coefficients of each scale of a windowed sample of continuous processes.…”

“…Since the dimension of is often much smaller than the dimension of , the statistic for the Haar coefficients instead of the signal itself is used to monitor the process. Thus, we use (9) To set up multivariate control charts on the individual observations, two phases are needed. The production is monitored in Phase II.…”

Spectra of wavelet scale coefficients from process acoustic measurements as input for PLS modelling of pulp quality

“…The usefulness of multiscale analysis in combination with multivariate models for solving process industry problems is well shown by Bakshi [20]. From analysing PLS models for process data covering a large time span, Teppola and Minkkinen [21] showed that MRA on scores can reveal different types of process variation, such as process trends and faults. However, for time series with high sampling rates and with signals distributed over the entire frequency range, the interpretation may be hard or even impossible.…”

Statistical quality control using image intelligence: A sparse learning approach

“…Their method selects important wavelet coefficients and applies a nonparametric procedure for detecting process faults based on the selected wavelet coefficients. Bakshi (1998) and Teppola and Minkkinen (2001) used multiscale principal component analysis for monitoring continuous chemical processes. Ganesan et al (2004) provided a comprehensive review wavelet‐based multiscale statistical process monitoring.…”

An SPC monitoring system for cycle-based waveform signals using haar transform

“…The multiscale principal component analysis (MSPCA) method is proposed for the monitoring of continuous chemical processes [8], [9]. In MSPCA, PCA is conducted on the wavelet coefficients of each scale of a windowed sample of continuous processes.…”

“…Since the dimension of is often much smaller than the dimension of , the statistic for the Haar coefficients instead of the signal itself is used to monitor the process. Thus, we use (9) To set up multivariate control charts on the individual observations, two phases are needed. The production is monitored in Phase II.…”

Spectra of wavelet scale coefficients from process acoustic measurements as input for PLS modelling of pulp quality

“…The usefulness of multiscale analysis in combination with multivariate models for solving process industry problems is well shown by Bakshi [20]. From analysing PLS models for process data covering a large time span, Teppola and Minkkinen [21] showed that MRA on scores can reveal different types of process variation, such as process trends and faults. However, for time series with high sampling rates and with signals distributed over the entire frequency range, the interpretation may be hard or even impossible.…”

Statistical quality control using image intelligence: A sparse learning approach

“…Their method selects important wavelet coefficients and applies a nonparametric procedure for detecting process faults based on the selected wavelet coefficients. Bakshi (1998) and Teppola and Minkkinen (2001) used multiscale principal component analysis for monitoring continuous chemical processes. Ganesan et al (2004) provided a comprehensive review wavelet‐based multiscale statistical process monitoring.…”

An SPC monitoring system for cycle-based waveform signals using haar transform

“…The multiscale principal component analysis (MSPCA) method is proposed for the monitoring of continuous chemical processes [8], [9]. In MSPCA, PCA is conducted on the wavelet coefficients of each scale of a windowed sample of continuous processes.…”

“…Since the dimension of is often much smaller than the dimension of , the statistic for the Haar coefficients instead of the signal itself is used to monitor the process. Thus, we use (9) To set up multivariate control charts on the individual observations, two phases are needed. The production is monitored in Phase II.…”

Spectra of wavelet scale coefficients from process acoustic measurements as input for PLS modelling of pulp quality

“…The usefulness of multiscale analysis in combination with multivariate models for solving process industry problems is well shown by Bakshi [20]. From analysing PLS models for process data covering a large time span, Teppola and Minkkinen [21] showed that MRA on scores can reveal different types of process variation, such as process trends and faults. However, for time series with high sampling rates and with signals distributed over the entire frequency range, the interpretation may be hard or even impossible.…”

Statistical quality control using image intelligence: A sparse learning approach

“…Their method selects important wavelet coefficients and applies a nonparametric procedure for detecting process faults based on the selected wavelet coefficients. Bakshi (1998) and Teppola and Minkkinen (2001) used multiscale principal component analysis for monitoring continuous chemical processes. Ganesan et al (2004) provided a comprehensive review wavelet‐based multiscale statistical process monitoring.…”