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

Teppola, Pekka; Minkkinen, Pentti

doi:10.1002/1099-128x(200101)15:1<1::aid-cem595>3.0.co;2-n

Cited by 9 publications

(7 citation statements)

References 29 publications

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“…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.…”

Section: B Multivariate Control Chart Designmentioning

confidence: 99%

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

Zhou

Sun

Shi

2006

IEEE Trans. Automat. Sci. Eng.

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Abstract-Due to the rapid development of computer and sensing technology, many measurements of process variables are readily available in manufacturing processes. These measurements carry a large amount of information about process conditions. It is highly desirable to develop a process monitoring and diagnosis methodology that can utilize this information. In this paper, a statistical process control monitoring system is developed for a class of commonly available process measurements-cycle-based waveform signals. This system integrates the statistical process control technology and the Haar wavelet transform. With it, one can not only detect a process change, but also identify the location and estimate the magnitude of the process mean shift within the signal. A case study involving a stamping process demonstrates the effectiveness of the proposed methodology on the monitoring of the profile-type data.Note to Practitioners-Cycle-based signal refers to an analog or digital signal that is obtained through automatic sensing during each operation cycle of a manufacturing process. The cycle-based signal is very common in various manufacturing processes (e.g., forming force in stamping processes, the holding force, and the current signals in spot welding processes, the insertion force in the engine assembly process). In general, cycle-based signals contain rich process information. In this paper, cycle-based signal monitoring will be accomplished by monitoring the wavelet transformation of the signal, instead of monitoring the raw observations themselves. Further, a decision-making technique is developed using the SPC monitoring system to locate where the mean shift occurred and to estimate magnitudes of mean shifts. Thus, this paper presents a generic framework for the enhanced statistical process control technique of cycle-based signals.

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Section: B Multivariate Control Chart Designmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

Zhou

Sun

Shi

2006

IEEE Trans. Automat. Sci. Eng.

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“…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.…”

Section: Wavelets and Fftmentioning

confidence: 99%

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

Björk

Danielsson

2002

Journal of Chemometrics

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Acoustic and vibration signals are captured by simple standard accelerometers. These can often be mounted directly on operative process equipment, creating a completely non-invasive measurement system. The signals from the accelerometer are then amplified, digitized by an analogue-to-digital converter and stored in some suitable format in a PC. The method most often used for signal processing of acoustic data has been to apply variants of fast Fourier transform (FFT) on sampled data to produce a frequency domain representation. An alternative way tried here is to use the fast wavelet transform (FWT) in combination with FFT. The FWT has the advantage that it produces timeresolved representations and, on each time scale, different features can be extracted. However, in this case, time resolution has no meaning, since the starting points for data acquisitions were not fixed. The wavelet step can be seen as a series of pre-filters and it is here followed by FFT on coefficients at each wavelet scale. The results are compared to those obtained after FFT on the complete time series. We have used spectra of wavelet scale coefficients in an attempt to model pulp quality with PLS. In this case the number of points in the resulting wavelet multiresolution spectrum (WT-MRS) can be limited to a low number, e.g. 255 compared to 1025 with direct FFT on the time series. In the PLS modelling step the advantage is that the first two components describe Y much better than when using the conventional approach, e.g. 72% explained Y variance compared to 40%. A second advantage is that the model requires fewer coefficients.

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“…It has been used in removing baselines, denoising, constructing regression models, rectifying signals, modeling time series, extracting process trends and compressing data (Nason et al 1999;Teppola and Minkkinen 2001). Recently, applications of WT in biomedical research and molecular biology are also booming rapidly (Unser and Aldroubi 1996;Liò 2003).…”

Section: Introductionmentioning

confidence: 99%

Integration of wavelet transform with PCA and ANN for metabolomics data-mining

Xia

Yang

2007

Metabolomics

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PCA (principal components analysis) and ANN (artificial neural network) are two broadly used pattern recognition methods in metabolomics data-mining. Yet their limitations sometimes are great obstacles for researchers. In this paper the wavelet transform (WT) method was used to integrate with PCA and ANN to improve their performance in manipulating metabolomics data. A dataset was decomposed by wavelets and then reconstructed. The ''hard thresholding'' algorithm was used, through which the detail information was discarded, and the entire ''metabolomics image'' reconstructed on the significant information. It was supposed that the most relevant information was captured after this process. It was found that, thanks to its ability in denoising data, the WT method could significantly improve the performance of the non-linear essence-extracting method ANN in classifying samples; further integration of WT with PCA showed that WT could greatly enhance the ability of PCA in distinguishing one group of samples from another and also its ability in identifying potential biomarkers. The results highlighted WT as a promising resolution in bridging the gap between huge bytes of data and the instructive biological information.

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

Cited by 9 publications

References 29 publications

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

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

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

Integration of wavelet transform with PCA and ANN for metabolomics data-mining

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