System Identification in Presence of Outliers

Abstract

The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low rank and sparse matrices, and further recast as a semidefinite programming problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low-rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers, and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered "clean" data from the proposed method can give much better parameter estimation compared with that based on the raw data.

Data-Driven Method for Missing Harmonic Data Completion

“…2) Run the merging K-means clustering algorithm to cluster prior information from the power quality monitor which has data loss, and establish the signal threshold vector (10) and a prior information model (11). 3) Reconstructed unknown graph signals using (13). 4) Determine the duration of a certain harmonic data state.…”

“…Matrix completion is defined as completing the original matrix with only a portion of the data recorded. Low-rank matrix completion has been applied in several fields, such as computer vision [10], collaborative filtering [11], image analysis [12], and system identification [13]. The low-rank property plays an important role in data matrix completion techniques.…”

Recursive identification for Wiener non‐linear systems with non‐stationary disturbances

“…On the basis of the adaptive variable FF matrix scheme, a robust method is presented for linear output error models with load disturbance [33]. A fast algorithm is proposed to solve an outlier detection problem and recover ‘clean’ data to give better parameter estimation for linear systems [34]. For identification of a system with bounded noise, a membership set algorithm is used and its convergence is also analysed with a proof [35].…”

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

“…In the literature, a large number of models have been utilized for representing outliers, some of which are non‐Gaussian distributions such as α ‐stable noise, t‐distribution, and amplitude‐modulated binary‐state sequence such as Bernoulli‐Gaussian . Furthermore, for the purpose of outlier detection, outlying measurements has been represented deterministically . It is almost universal in the literature of the Hammerstein modeling that the estimation algorithms are based on either minimizing the sum of squares of prediction errors, ie, least squares (LS), or quadratic Lyapunov function.…”

“…34,35 Furthermore, for the purpose of outlier detection, outlying measurements has been represented deterministically. 36,37 It is almost universal in the literature of the Hammerstein modeling that the estimation algorithms are based on either minimizing the sum of squares of prediction errors, ie, least squares (LS), or quadratic Lyapunov function. These identification methods are proved efficient under the assumption that the measurement noises are Gaussian.…”