Orthogonal projection based subspace identification against colored noise

Hou, Jie; Liu, Tao; Chen, Fengwei

doi:10.1007/s11768-017-6003-7

Cited by 9 publications

(5 citation statements)

References 21 publications

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“…The initial input parameters of the proposed algorithm are set as follows: the length of the past horizon is p = 10, the length of the future horizon is f = 10, and the number of total samples is N = 2000. In order to verify the effectiveness of the proposed algorithm further, several existing off-line subspace identification algorithms (MOESP [17], N4SID [18], 2ORT-SIM [19]) and the on-line subspace identification algorithm (OSIMPCA-E [24]) are introduced as the comparison. Here, the 1200 sets of sample data in the identification set are used for the relevant training.…”

Section: Identification Results and Validation Analysismentioning

confidence: 99%

“…Here, the proof of Equation ( 15) can be found in reference [19] and the relevant contents are omitted here for brevity. Then, Equation ( 14) can be transformed into…”

Section: Matrix Definitionmentioning

confidence: 99%

“…Van et al [18] derived the subspace state system identification algorithm for mixed deterministic stochastic systems. A subspace method in which the bias can be eliminated was developed, and high identification precision was acquired for industries with colored noises in [19]. In order to realize multivariate predictive control in a continuous polymerization reactor of methyl methacrylate, Song et al [20] developed a subspace algorithm to recognize the Wiener model of the process and then designed a data-based predictive controller.…”

Section: Introductionmentioning

confidence: 99%

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An Improved On-Line Recursive Subspace Identification Method Based on Principal Component Analysis and Sliding Window for Polymerization

Qian,

Zhang,

Lei

et al. 2024

Processes

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Polymerization products are indispensable for our daily life, and the relevant modeling process plays a vital role in improving product quality. However, the model identification of the related process is a difficult point in industry due multivariate, nonlinear and time-varying characteristics. As for the conventional offline subspace identification methods, the identification accuracy may be not satisfying. To handle such a problem, an enhanced on-line recursive subspace identification method is presented on the basis of principal component analysis and sliding window (RSIMPCA-SW) in this paper to obtain the state space model for polymerization. In the proposed on-line subspace identification approach, the initial L-factor is acquired by the LQ decomposition of the sampled historical data, firstly, and then it is updated recursively through the bona fide method after the new data have been handled by the sliding window rule. Subsequently, principal component analysis (PCA) is introduced to calculate the extended observation matrix, and finally the on-line model parameters are extracted. Compared with the traditional subspace schemes, smaller computation complexity and higher identification precision are anticipated in the proposed method. A case study on the modeling of the ethylene polymerization verifies the effectiveness of the developed approach, in which the related statistical indexes of the obtained identification model are better.

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Section: Identification Results and Validation Analysismentioning

confidence: 99%

“…Here, the proof of Equation ( 15) can be found in reference [19] and the relevant contents are omitted here for brevity. Then, Equation ( 14) can be transformed into…”

Section: Matrix Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Improved On-Line Recursive Subspace Identification Method Based on Principal Component Analysis and Sliding Window for Polymerization

Qian,

Zhang,

Lei

et al. 2024

Processes

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“…Estimate

\overset{false^}{A}

\overset{false^}{B}

, and

\overset{false^}{C}

from (48)–(50). Remark 4 Since

{\hat{θ}}_{1}

and

{\hat{θ}}_{2}

are consistent (see Remark 1 and Theorem 1), the retrieved system matrices (

\overset{false^}{A}, \overset{false^}{B}, \overset{false^}{C}

) are also consistent (see [51, 53]. Remark 5 In the OPM‐like SIMs, the parameters of

B w \in ℜ^{n_{x} \times r}

are obtained before estimating

B \in ℜ^{n_{x} \times 1}

and

w \in ℜ^{1 \times r}

, which will result in a dimension problem (the number of parameters for the former is

r n_{x}

which is much larger than

n_{x} + r

).…”

Section: Proposed Methodsmentioning

confidence: 99%

Fixed point iteration‐based subspace identification of Hammerstein state‐space models

Hou

Chen

et al. 2019

IET Control Theory & Applications

Self Cite

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“…The main proponents of these methods are MOESP (Multivariate Output Error State-space) proposed in [4], N4SID (Numerical algorithms for State-space Sub-Space IDentification) in [5], and CVA (Canonical Variate Analysis) in [6]. The statistical properties of these methods are fairly well established in a series of papers [7][8][9][10]. The above-mentioned methods estimate the extended observability matrix or state from a signal subspace of certain noise-free matrix, then retrieve the system matrices based on the above intermediate results.…”

Section: Introductionmentioning

confidence: 99%

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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Orthogonal projection based subspace identification against colored noise

Cited by 9 publications

References 21 publications

An Improved On-Line Recursive Subspace Identification Method Based on Principal Component Analysis and Sliding Window for Polymerization

An Improved On-Line Recursive Subspace Identification Method Based on Principal Component Analysis and Sliding Window for Polymerization

Fixed point iteration‐based subspace identification of Hammerstein state‐space models

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

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