A New Subspace Identification Approach Based on Principal Component Analysis and Noise Estimation

Wu, Ping; Pan, Heng; Ren, Jia; Yang, Chunjie

doi:10.1021/ie504824a

Cited by 9 publications

(11 citation statements)

References 27 publications

(52 reference statements)

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“…The unbiased estimate of the noise term E can be derived by a least‐squares method through Equation as the sampling number tends to infinity. The noise term estimation

\overset{E}{true}

can be obtained by minimizing the objective J ,

min_{[boldA]} J = {‖β - Aα‖}_{F}^{2},

where

{‖•‖}_{F}^{2}

indicates the Frobenius norm operator . In order to solve Equation , QR factorization is performed to estimate the least‐squares residual

\overset{E}{true}

.…”

Section: Methodology Of Eepcamentioning

confidence: 99%

“…A can be calculated by the following equation:

([], \begin{array}{c} boldI \\ - A^{T} \end{array}) = ([], \begin{array}{c} {\overset{true˜}{boldP}}_{β} \\ {\overset{true˜}{boldP}}_{α} \end{array}) boldΓ,

where Γ is the constant nonsingular matrix and

\overset{P}{true} = {[\begin{matrix} center \\ {\overset{P}{true}}_{boldβ}^{T} & {\overset{P}{true}}_{boldα}^{T} \end{matrix}]}^{T}

. By taking Γ as the identity matrix, the model coefficient matrix A could be estimated from

{\overset{true˜}{boldP}}_{β}

and

{\overset{true˜}{boldP}}_{α}

.…”

Section: Methodology Of Eepcamentioning

confidence: 99%

“…where • k k 2 F indicates the Frobenius norm operator. 35 In order to solve Equation 7, QR factorization is per-…”

Section: Noise Term Estimationmentioning

confidence: 99%

“…By taking Γ as the identity matrix, the model coefficient matrix A could be estimated [35][36][37] from e P β and e P α .…”

Section: Model Establishmentmentioning

confidence: 99%

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Development of energy efficiency principal component analysis model for factor extraction and efficiency evaluation in large-scale chemical processes

Zhu

Chen

2018

Int J Energy Res

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Summary In a large‐scale chemical plant, it is important to evaluate the energy efficiency (EE) of production to improve the production process and make production decisions. Essentially, finding the relationship model is the foundation of EE evaluation. Given the requirements of universality and practicability, the data‐driven model is widely used to describe the variable relationships. However, the variables stored in the data bank may be redundant, and some variables contain disturbances in the large‐scale chemical process, increasing the complexity of the model establishment. In this paper, a new EE factor extraction and EE evaluation method based on principal component analysis (PCA) (EEPCA) is proposed to enhance the accuracy of the EE values. By three stages (noise term estimation, model establishment, and model variable selection) in EEPCA, the accurate relationship models of utilized energy mediums and chemical products are established. On the basis of the built models, the EE of the chemical processes is evaluated and inferred. The effectiveness and practicality of the proposed method are demonstrated via a simulated process and a practical ethylene production.

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“…The unbiased estimate of the noise term E can be derived by a least‐squares method through Equation as the sampling number tends to infinity. The noise term estimation

\overset{E}{true}

can be obtained by minimizing the objective J ,

min_{[boldA]} J = {‖β - Aα‖}_{F}^{2},

where

{‖•‖}_{F}^{2}

indicates the Frobenius norm operator . In order to solve Equation , QR factorization is performed to estimate the least‐squares residual

\overset{E}{true}

.…”

Section: Methodology Of Eepcamentioning

confidence: 99%

“…A can be calculated by the following equation:

([], \begin{array}{c} boldI \\ - A^{T} \end{array}) = ([], \begin{array}{c} {\overset{true˜}{boldP}}_{β} \\ {\overset{true˜}{boldP}}_{α} \end{array}) boldΓ,

where Γ is the constant nonsingular matrix and

\overset{P}{true} = {[\begin{matrix} center \\ {\overset{P}{true}}_{boldβ}^{T} & {\overset{P}{true}}_{boldα}^{T} \end{matrix}]}^{T}

. By taking Γ as the identity matrix, the model coefficient matrix A could be estimated from

{\overset{true˜}{boldP}}_{β}

and

{\overset{true˜}{boldP}}_{α}

.…”

Section: Methodology Of Eepcamentioning

confidence: 99%

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Development of energy efficiency principal component analysis model for factor extraction and efficiency evaluation in large-scale chemical processes

Zhu

Chen

2018

Int J Energy Res

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“…For example, the ARX and ARARX processes have been extended for the case of additive white noise on the input and output observation 23 . Similarly, subspace identification based on principal component analysis has been proposed by estimating the noise term 24 . Under different noise models using closed‐loop operation data, several subspace identification methods (i.e., canonical variate analysis, CVA, N4SID, PLS, ARX) were able to identify correctly the process models 25 .…”

Section: Introductionmentioning

confidence: 99%

Machine learning modeling and predictive control of nonlinear processes using noisy data

Rincón

Liu

et al. 2021

AIChE Journal

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This work focuses on machine learning modeling and predictive control of nonlinear processes using noisy data. We use long short‐term memory (LSTM) networks with training data from sensor measurements corrupted by two types of noise: Gaussian and non‐Gaussian noise, to train the process model that will be used in a model predictive controller (MPC). We first discuss the LSTM training with noisy data following a Gaussian distribution, and demonstrate that the standard LSTM network is capable of capturing the underlying process dynamic behavior by reducing the impact of noise. Subsequently, given that the standard LSTM performs poorly on a noisy data set from industrial operation (i.e., non‐Gaussian noisy data), we propose an LSTM network using Monte Carlo dropout method to reduce the overfitting to noisy data. Furthermore, an LSTM network using co‐teaching training method is proposed to further improve its approximation performance when noise‐free data from a process model capturing the nominal process state evolution is available. A chemical process example is used throughout the manuscript to illustrate the application of the proposed modeling approaches and demonstrate their open‐ and closed‐loop performance under a Lyapunov‐based model predictive controller with state measurements corrupted by industrial noise.

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An Improved Consistent Subspace Identification Method Using Parity Space for State-space Models

Hou

Chen

et al. 2019

Int. J. Control Autom. Syst.

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In this paper, an alternative consistent subspace identification method using parity space is proposed. The future/past input data and the past output data are used to construct the instrument variable to eliminate the noise effect on consistent estimation. The extended observability matrix and the triangular block-Toeplitz matrix are then retrieved from a parity space of the noise-free matrix using a singular value decomposition based method. The system matrices are finally estimated from the above estimated matrices. The consistency of the proposed method for estimation of the extended observability matrix and the triangular block-Toeplitz matrix is established. Compared with the classical SIMs using parity space like SIMPCA and SIMPCA-Wc, the proposed method generally enhances the estimated model efficiency/accuracy thanks to the use of future input data. Two examples are presented to illustrate the effectiveness and merit of the proposed method.

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A New Subspace Identification Approach Based on Principal Component Analysis and Noise Estimation

Cited by 9 publications

References 27 publications

Development of energy efficiency principal component analysis model for factor extraction and efficiency evaluation in large-scale chemical processes

Development of energy efficiency principal component analysis model for factor extraction and efficiency evaluation in large-scale chemical processes

Machine learning modeling and predictive control of nonlinear processes using noisy data

An Improved Consistent Subspace Identification Method Using Parity Space for State-space Models

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