On wavelet-based statistical process monitoring

Cohen, Achraf; Atoui, Mohamed Amine

doi:10.1177/0142331220935708

Cited by 16 publications

(13 citation statements)

References 110 publications

(116 reference statements)

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“…Let 𝜏 be a fixed number, then according to Equation ( 13), one may substitutes 𝜃 1 𝑖𝑗 by θ1 𝑖𝑗 to estimate 𝛾 2 . The estimator θ1 𝑖𝑗 is the sample mean of the estimated wavelet coefficients of images which are taken after time 𝜏 and is defined as Equation (21). 𝑖𝑗 in Equation ( 13) leads to the following estimator:…”

Section: The Proposed Methodsmentioning

confidence: 99%

Two‐dimensional wavelet based statistical monitoring of image data

Koosha

Noorossana

Ahmadi

2022

Quality & Reliability Eng

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Statistical process monitoring techniques are widely used to monitor process stability. In high volume and highly automated processes, effective methods are required to monitor several quality characteristics of interest. Advances in imaging technology have paved the grounds to capture and analyze product images from different perspectives in real time. Advantages of considering images have led to their increasing role in process monitoring. When images are used for process monitoring, complicated data structures should be analyzed. Various methods including data transformation and dimension reduction have been proposed in the literature to cope with these complexities. In this paper, a two‐dimensional (2D) wavelet based method is proposed to monitor image data. A likelihood ratio test (LRT) is developed to monitor the expected values of wavelet coefficient, and the derived likelihood ratio based statistic is monitored over time to detect out‐of‐control conditions as well as change point estimation. This information can help practitioners to diagnose the process, find the potential assignable cause(s) and return the process to the in‐control state. One of the advantages of the proposed method compared to other competing methods is that the performance of the proposed method does not depend on the fault location. Simulation studies indicate satisfactory performance for the proposed method in detecting out‐of‐control conditions and estimating change points. Moreover, the performance of the proposed method is also compared to two existing approaches. The results reveal that the proposed approach performs superior in detecting either diagonal or square defects.

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Section: The Proposed Methodsmentioning

confidence: 99%

Two‐dimensional wavelet based statistical monitoring of image data

Koosha

Noorossana

Ahmadi

2022

Quality & Reliability Eng

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“…According to the above-mentioned two properties, the non-parametric regression approach is used to model the profile created by the image. Recently, the non-parametric regression approach using wavelet transformation has become more popular than other non-parametric methods for modeling profiles [15,16]. Using wavelets profiles could be modelled efficiently without losing important features of the data.…”

Section: Large-scale Monitoringmentioning

confidence: 99%

“…Therefore, non-parametric regression methods are more streamlined because of their ability in approximating complicated functions. Many of non-parametric regression methods have been suggested for profile monitoring, some of these include the use of spline estimators, component analysis, wavelet transformation, and simple data-driven metrics [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Statistical modeling and monitoring of image data in the presence of temporal and spatial correlations

et al. 2022

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Owing to the increasing sensitivity of the processes and the inadequacy of the methods based on human inspection, use of product images in statistical process control has been considered by some researchers. In this paper, the regression-based approach was developed to monitor image data under two-scale analysis, large-scale and small-scale. Because geometric profiles created from images have complex and non-linear behaviour, wavelet transformation was used to extract the main features (regression coefficients) under large-scale analysis. Observations in mentioned profiles could be temporally or spatially correlated as well. To monitor the small-scale components which could be expressed by correlation in error terms, one parametric and one nonparametric methods were developed. After extracting features for both scales, some appropriate test statistics were computed. Then, monitoring the process was performed by plotting these test statistics on corresponding control charts. Performance of the proposed method was evaluated in terms of run-length and change-point measures. Simulation and industrial case studies were also performed to evaluate the proposed method's performance in detecting different shifts. The results indicated the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identify the source of variability.

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“…( 15) is described based on continuous wavelet transform (CWT) which gives redundant information since the parameters e and d are continuously changing. In most practical applications, multi-scale decomposition is performed using discrete wavelet transform (DWT) which also provides an additional benefit of computational efficiency [24]. In wavelet-based data-representation, an input signal can be decomposed into two parts, namely: the scaled or approximation coefficients that captures lowfrequency components of the signal and detailed coefficients that captures high-frequency components of the signal.…”

Section: Multi-scale Ica Modeling Using Waveletsmentioning

confidence: 99%

“…The noise masks important features in the data, thus reducing the task of extracting information from process data. The industrial data acquired from a process consists of information (features) occupying different regions on a time-frequency scale [23,24]. The measured data is termed multi-scale since it is a blend of infectious noise as well rich data that is concentrated in the time and frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Improved Process Monitoring Scheme Using Multi-Scale Independent Component Analysis

Kini

Madakyaru

2021

Arab J Sci Eng

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The task of fault detection is crucial in modern chemical industries for improved product quality and process safety. In this regard, data-driven fault detection (FD) strategy based on independent component analysis (ICA) has gained attention since it improves monitoring by capturing non-gaussian features in the process data. However, presence of measurement noise in the process data degrades performance of the FD strategy since the noise masks important information. To enhance the monitoring under noisy environment, wavelet-based multi-scale filtering is integrated with the ICA model to yield a novel multi-scale Independent component analysis (MSICA) FD strategy. One of the challenges in multi-scale ICA modeling is to choose the optimum decomposition depth. A novel scheme based on ICA model parameter estimation at each depth is proposed in this paper to achieve this. The effectiveness of the proposed MSICA-based FD strategy is illustrated through three case studies, namely: dynamic multi-variate process, quadruple tank process and distillation column process. In each case study, the performance of the MSICA FD strategy is assessed for different noise levels by comparing it with the conventional FD strategies. The results indicate that the proposed MSICA FD strategy can enhance performance for higher levels of noise in the data since multi-scale wavelet-based filtering is able to de-noise and capture efficient information from noisy process data.

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On wavelet-based statistical process monitoring

Cited by 16 publications

References 110 publications

Two‐dimensional wavelet based statistical monitoring of image data

Two‐dimensional wavelet based statistical monitoring of image data

Statistical modeling and monitoring of image data in the presence of temporal and spatial correlations

Improved Process Monitoring Scheme Using Multi-Scale Independent Component Analysis

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