Fault Detection Based on Probabilistic Kernel Partial Least Square Regression for Industrial Processes

Xie, Ying; Zhang, Yingwei; Jia, Qiang; Zhai, Liang

doi:10.1252/jcej.17we064

Cited by 5 publications

(10 citation statements)

References 33 publications

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“…In PKPLS, the input sample matrix Φ ( X ) ∈ R D and output sample matrix Y ∈ R s are assumed to be generated from the latent variable t ∈ R k , which is described as follows:

\begin{matrix} lefttrue \\ Φ (boldX) = At + {boldμ}_{Φ (boldX)} + {bolde}_{Φ (boldX)}, \\ Y = Bt + {boldμ}_{boldY} + {bolde}_{boldY}, \end{matrix}

where matrices A ∈ R D × k and B ∈ R s × k denote the loading matrices for input and output, respectively; μ Φ ( X ) and μ Y denote the mean vectors of input and output, respectively; t denotes the latent variable vector subjecting to Gaussian distributions, ie, t ~N(0, I ); I denotes an identity matrix; and e Φ ( X ) and e Y are the noises contained in input and output, respectively, which are subject to Gaussian distributions, ie, e Φ ( X ) ~N(0, Ω Φ ( X ) ), and e Y ~N(0, Ω Y ), with

Ω_{boldΦ ((), X)} = σ_{boldΦ ((), X)}^{2} boldI

and

Ω_{Y} = σ_{Y}^{2} boldI

as the covariance matrices of input noise and output noise, respectively.…”

Section: A Review Of Pkpls Modelmentioning

confidence: 99%

“…From Equation , the joint distribution of Φ ( X ) and Y is as follows:

((), \begin{matrix} center \\ Φ (boldX), & Y \end{matrix} (|, \begin{array}{c} boldt, & boldA, & boldB, & Ω_{normalΦ ((), X)}, & Ω_{Y} \end{array})) bold~ boldN ((), \begin{array}{c} μ_{normalΦ ((), X), boldY (|, t)}, & \sum_{normalΦ ((), X), boldY (|, t)} \end{array}),

where

μ_{boldΦ ((), X), boldY (|, t)} = ((), \begin{array}{c} boldAt + μ_{boldΦ ((), X)} \\ boldBt + μ_{Y} \end{array})

\sum_{boldΦ ((), X), boldY (|, t)} = ((), \begin{array}{c} Ω_{boldΦ ((), X)} & 0 \\ 0 & Ω_{Y} \end{array})

.…”

Section: A Review Of Pkpls Modelmentioning

confidence: 99%

“…In the E step, the distributions of latent variables are constructed with training data and the previously estimated parameters. Sufficient statistics of the latent variables are as follows:

\begin{matrix} left \\ E (boldt) = {boldμ}_{t ∣ Φ (boldX), Y}, \\ E ({tt}^{T}) = {boldμ}_{t ∣ Φ (boldX), Y} {boldμ}_{t ∣ Φ (boldX), Y}^{normalT} + \sum_{t ∣ Φ (boldX), Y} . \end{matrix}

…”

Section: Lwpkpls‐based Monitoring Frameworkmentioning

confidence: 99%

“…Ge et al developed another PPLS for regression modeling and applications to industrial refinery processes . Xie et al proposed a probabilistic kernel PLS (PKPLS)‐based fault detection approach with application to the Tennessee Eastman process …”

Section: Introductionmentioning

confidence: 99%

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Fault monitoring based on locally weighted probabilistic kernel partial least square for nonlinear time‐varying processes

Xie

2019

Journal of Chemometrics

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In this paper, novel data‐driven fault detection and diagnosis approaches are proposed on the basis of a new locally weighted probabilistic kernel partial least squares (LWPKPLS). (a) LWPKPLS can construct an accurate model for a time‐varying process by updating itself using the newly coming samples, thus LWPKPLS can be used to monitor time‐varying processes. (b) By the integration of local weighted regression and kernel tricks, the LWPKPLS can be applied to construct models for processes with much stronger nonlinear data characteristics. (c) Meanwhile, as a probabilistic regression model, LWPKPLS can process data with random noises and missing values. (d) A set of process monitoring approaches including fault detection and fault diagnosis are developed on the basis of LWPKPLS. At last, the experiment results from a numerical example and an ion‐exchange membrane electrolysis process (IEMEP) demonstrate that the proposed process monitoring approaches have satisfactory monitoring performance.

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“…In PKPLS, the input sample matrix Φ ( X ) ∈ R D and output sample matrix Y ∈ R s are assumed to be generated from the latent variable t ∈ R k , which is described as follows:

\begin{matrix} lefttrue \\ Φ (boldX) = At + {boldμ}_{Φ (boldX)} + {bolde}_{Φ (boldX)}, \\ Y = Bt + {boldμ}_{boldY} + {bolde}_{boldY}, \end{matrix}

Ω_{boldΦ ((), X)} = σ_{boldΦ ((), X)}^{2} boldI

and

Ω_{Y} = σ_{Y}^{2} boldI

as the covariance matrices of input noise and output noise, respectively.…”

Section: A Review Of Pkpls Modelmentioning

confidence: 99%

“…From Equation , the joint distribution of Φ ( X ) and Y is as follows:

((), \begin{matrix} center \\ Φ (boldX), & Y \end{matrix} (|, \begin{array}{c} boldt, & boldA, & boldB, & Ω_{normalΦ ((), X)}, & Ω_{Y} \end{array})) bold~ boldN ((), \begin{array}{c} μ_{normalΦ ((), X), boldY (|, t)}, & \sum_{normalΦ ((), X), boldY (|, t)} \end{array}),

where

μ_{boldΦ ((), X), boldY (|, t)} = ((), \begin{array}{c} boldAt + μ_{boldΦ ((), X)} \\ boldBt + μ_{Y} \end{array})

\sum_{boldΦ ((), X), boldY (|, t)} = ((), \begin{array}{c} Ω_{boldΦ ((), X)} & 0 \\ 0 & Ω_{Y} \end{array})

.…”

Section: A Review Of Pkpls Modelmentioning

confidence: 99%

“…In the E step, the distributions of latent variables are constructed with training data and the previously estimated parameters. Sufficient statistics of the latent variables are as follows:

\begin{matrix} left \\ E (boldt) = {boldμ}_{t ∣ Φ (boldX), Y}, \\ E ({tt}^{T}) = {boldμ}_{t ∣ Φ (boldX), Y} {boldμ}_{t ∣ Φ (boldX), Y}^{normalT} + \sum_{t ∣ Φ (boldX), Y} . \end{matrix}

…”

Section: Lwpkpls‐based Monitoring Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fault monitoring based on locally weighted probabilistic kernel partial least square for nonlinear time‐varying processes

Xie

2019

Journal of Chemometrics

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“…The last decade has witnessed the development and usages of the nonlinear variant of projection based MSPM strategies to primarily address the Fault Detection and Diagnosis of complex process industries displaying nonlinear profiles amongst the associated Process and Feedstock characteristics. The nonlinear counterparts of the linear based MSPM techniques can be broadly classified as those based on linear approximation techniques [5,6], Kernel Function based techniques [7][8][9][10] and Artificial Intelligence (AI) [11] based techniques. In linear approximation based technique the entire data space is approximated by several linear subspaces and separate monitoring strategy is developed for each subspace which are further amalgamated using Bayesian Inferences, while in Kernel Function based technique the nonlinear data matrix or the measurement space is mapped to higher dimensional feature space using Kernel Function such as Gaussian Kernel function where data behaves linearly and PCA is implemented over the feature space for components extraction.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear process monitoring strategy with a 2-phase fault diagnosis approach

Das

2022

Eng. Res. Express

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The article delves into the development of Statistical Fault Detection and Diagnosis Strategies for an Integrated Steel Plant (ISP) taking into account the nonlinear relationship amongst the monitored Process and Feedstock Characteristics. The strategies being devised are based on Neural Network Fitting model cum Principal Component Analysis based technique (NNF-PCA) and Kernel Principal Component Analysis (KPCA) based technique. For detection of fault(s) Hotelling T2chart based on PCA and KPCA scores were employed. The article also proposes a 2-phase Fault Diagnosis approach christened as Preliminary Diagnosis phase and Specific Diagnosis phase. The Preliminary Diagnosis phase is based on Pattern Analysis of the control chart monitoring statistic observations and the Specific Diagnosis phase is based on the employment of appropriate Fault Diagnostic Statistic. The Preliminary Diagnosis reveals the broader source of assignable cause for the onset of the fault(s) and the Specific Diagnosis reveals the relative contribution of the individual Process and Feedstock characteristics. An in-depth comparative analysis between the NNF-PCA based strategy and KPCA based strategy w.r.t. three comparative aspects and four comparative parameters were carried out with their findings being duly highlighted which revealed the slight effectiveness of the KPCA based strategy with respect to the NNF-PCA based counterpart.

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