Recursive transformed component statistical analysis for incipient fault detection

Shang, Jun; Chen, Maoyin; Ji, Hongquan; Zhou, Donghua

doi:10.1016/j.automatica.2017.02.028

Cited by 124 publications

(46 citation statements)

References 42 publications

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“…Suppose that in a stationary process there are

m

correlated variables

x = {[x_{1}, x_{2}, \dots, x_{m}]}^{normalT}

, which follow a multivariate Gaussian distribution as follows:

boldx \sim 풩 (μ, Σ)

The fault type considered in this work is the sensor precision degradation fault. That is, if the jth sensor is faulty, its reading becomes:

x_{j}^{f} = x_{j} + e_{j}, j = 1,2, \dots, m

where

x_{j}

denotes the normal part and

e_{j}

, independent of

x_{j}

, is zero‐mean noise representing precision degradation, i.e.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Hence, the following fault detection logic is adopted in practice:

true{\begin{matrix} left \\ center K L D (t_{i}, t_{i}^{f}) \leq η_{i}, \forall i \in {1,2, \dots, l} fault‐free \\ center K L D (t_{i}, t_{i}^{f}) > η_{i}, \exists i \in {1,2, \dots, l} faulty \end{matrix}

where

η_{i}

is the control limit or threshold, reflecting the allowed fluctuation in the divergence caused by stochastic noise and parameter estimation errors. We determine

η_{i}

based on the historical data collected under normal conditions, which is known as the empirical method . Specifically, normal samples are divided into two parts with equal length.…”

Section: Proposed Methodsmentioning

confidence: 99%

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Diagnosis of sensor precision degradation using Kullback‐Leibler divergence

Zhou

2017

Can J Chem Eng

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For practical industrial processes, detection and isolation of a sensor precision degradation fault is of vital importance. In comparison with other sensor fault types such as complete failure and mean shift, the precision degradation fault is usually more difficult to detect and further to isolate. This paper proposes a new fault detection algorithm for sensor precision degradation using Kullback-Leibler divergence (KLD). The KLD is employed to quantify the dissimilarity between probability densities of each reference score and the actual one within the principal component analysis (PCA) framework. Under the assumption of Gaussian-distributed data, KLD for each score reduces to a measure of the variance difference, which is proven effective in detecting sensor precision degradation. Control limit of the KLD is established based on historical data, and online fault detection is implemented by adopting a sliding window. The fault isolation issue is also discussed, which aims to determine the faulty sensor with precision degradation. This task may be achieved by checking the PCA loading matrix and matching the fault detection result. Case studies on a synthetic numerical example and the continuous stirred tank reactor (CSTR) process are carried out to demonstrate the effectiveness of the proposed method, in comparison with conventional approaches.

show abstract

“…Suppose that in a stationary process there are

m

correlated variables

x = {[x_{1}, x_{2}, \dots, x_{m}]}^{normalT}

, which follow a multivariate Gaussian distribution as follows:

boldx \sim 풩 (μ, Σ)

The fault type considered in this work is the sensor precision degradation fault. That is, if the jth sensor is faulty, its reading becomes:

x_{j}^{f} = x_{j} + e_{j}, j = 1,2, \dots, m

where

x_{j}

denotes the normal part and

e_{j}

, independent of

x_{j}

, is zero‐mean noise representing precision degradation, i.e.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Hence, the following fault detection logic is adopted in practice:

true{\begin{matrix} left \\ center K L D (t_{i}, t_{i}^{f}) \leq η_{i}, \forall i \in {1,2, \dots, l} fault‐free \\ center K L D (t_{i}, t_{i}^{f}) > η_{i}, \exists i \in {1,2, \dots, l} faulty \end{matrix}

where

η_{i}

is the control limit or threshold, reflecting the allowed fluctuation in the divergence caused by stochastic noise and parameter estimation errors. We determine

η_{i}

based on the historical data collected under normal conditions, which is known as the empirical method . Specifically, normal samples are divided into two parts with equal length.…”

Section: Proposed Methodsmentioning

confidence: 99%

Diagnosis of sensor precision degradation using Kullback‐Leibler divergence

Zhou

2017

Can J Chem Eng

Self Cite

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show abstract

“…Without detailed assumption of data distribution, we use the empirical method to determine the control limit. With presetting a significance level, the control limit

δ_{α}

can be determined from the validation dataset to control the false alarm rate.…”

Section: Methodsmentioning

confidence: 99%

Covariance eigenpairs neighbour distance for fault detection in chemical processes

2017

Self Cite

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This paper presents a new data-driven fault detection method called covariance eigenpairs neighbour distance (CEND) for monitoring chemical processes. It processes measured data in one-step sliding windows to estimate covariance, and the eigenpairs of each sample covariance matrix are recursively calculated using rank-one modification. The eigenvalues and selected elements of eigenvectors are stacked into reference vectors. For each window data containing the latest measurement vector, the neighbour distance of eigenpairs from the reference matrix can be effectively calculated by virtue of k-d tree. The neighbour distance serves as the detection index, whose control limit can be determined by validation dataset with assigning a significance level. A high neighbour distance exceeding the control limit implies the occurrence of fault. Simulations on the continuous stirred tank reactor (CSTR) and the Tennessee Eastman process (TEP) both indicate the superior fault detectability of the proposed method, compared with conventional multivariate statistical process monitoring (MSPM) methods such as principal component analysis (PCA) and independent component analysis (ICA).

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“…Zhao et al proposed a dynamic distributed monitoring strategy for large‐scale nonstationary processes under closed‐loop control, which can separate the dynamic variations from the steady states and monitor concurrently them. Shang et al proposed a new method to monitor the incipient fault by monitoring the statistical characteristics (mean, variance, skewness, kurtosis, etc) of the transformed component. Zeng et al proposed using recursive mutual information‐based variable selection and dissimilarity analysis with no prior information to monitor online process.…”

Section: Introductionmentioning

confidence: 99%

A new incipient fault monitoring method based on modified principal component analysis

Yang

Wang

Liu

2019

Journal of Chemometrics

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A novel multivariate statistical process monitoring (MSPM) method based on modified principal component analysis (PCA) is proposed to solve the low detection rate problem of incipient fault. In this modified PCA, on the basis of normal PCA model, the columns of loading matrix are reordered by mutual information between different statistic component matrices and training data. Then, instead of cumulative percent variance criterion, the principal component subspace is selected according to the largest mutual information. The selected PC subspace can maximally reflect fault characteristics into a new statistical index. Besides, a detection index based on the sliding average control chart statistic is proposed, which eliminates the effect of noise by proper averaging of the most recent samples, greatly improving the ability and accuracy of fault detection. The case study of a numerical simulation and Tennessee Eastman process shows that the proposed method can effectively detect incipient fault.

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Recursive transformed component statistical analysis for incipient fault detection

Cited by 124 publications

References 42 publications

Diagnosis of sensor precision degradation using Kullback‐Leibler divergence

Diagnosis of sensor precision degradation using Kullback‐Leibler divergence

Covariance eigenpairs neighbour distance for fault detection in chemical processes

A new incipient fault monitoring method based on modified principal component analysis

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