A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

Liu, Kai; Chen, YangQuan; Domański, Paweł D.; Zhang, Xi

doi:10.3390/a11070090

Cited by 14 publications

(9 citation statements)

References 35 publications

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“…A short literature survey provides several of examples of current real applications that require the proposed method. Thus, in signal processing, non-stationary, non-Gaussian, spiky signals are usually regarded as outliers and thus discarded (see [35][36][37][38] as typical cases). In this context, it should be noted that Mood's median test is preferred to the Kruskal-Wallis test when outliers are present [39].…”

Section: Further Discussionmentioning

confidence: 99%

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Jäntschi

2019

Symmetry

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One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution.

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Section: Further Discussionmentioning

confidence: 99%

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Jäntschi

2019

Symmetry

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“…• integral time measures, e.g., Mean Square Error (MSE), Integral Absolute Error (IAE) [86], Integral Time Absolute Value (ITAE) [87], Integral of Square Time derivative of the Control input (ISTC) [88], Total Squared Variation (TSV) [89], and Amplitude Index (AMP) [71]; • correlation measures, such as oscillation detection index [90] or relative damping index [91]; • statistical factors utilizing different probabilistic distribution function (standard deviation, variance, skewness, kurtosis, scale, shape, etc.) [92], variance band index [93], or the factors of other probabilistic distributions [94][95][96]; • benchmarking methods [97]; and • alternative indexes using wavelets [98], orthogonal Laguerre [99] and other functions [65], Hurst exponent [100], persistence measures [101,102], entropy [103][104][105], multifractal approaches [106], or fractional-order [107,108].…”

Section: Data-driven Methodsmentioning

confidence: 99%

“…Furthermore, fractional-order dynamics increases possible set of robust and non-Gaussian indicators [107,108]. Xu et al [161,162] proposed to evaluate MPC performance and capture the fluctuation of the process variables with a performance index based on Mahalanobis distance.…”

Section: Data-driven Approachesmentioning

confidence: 99%

Performance Assessment of Predictive Control—A Survey

Domański

2020

Algorithms

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Model Predictive Control constitutes an important element of any modern control system. There is growing interest in this technology. More and more advanced predictive structures have been implemented. The first applications were in chemical engineering, and now Model Predictive Control can be found in almost all kinds of applications, from the process industry to embedded control systems or for autonomous objects. Currently, each implementation of a control system requires strict financial justification. Application engineers need tools to measure and quantify the quality of the control and the potential for improvement that may be achieved by retrofitting control systems. Furthermore, a successful implementation of predictive control must conform to prior estimations not only during commissioning, but also during regular daily operations. The system must sustain the quality of control performance. The assessment of Model Predictive Control requires a suitable, often specific, methodology and comparative indicators. These demands establish the rationale of this survey. Therefore, the paper collects and summarizes control performance assessment methods specifically designed for and utilized in predictive control. These observations present the picture of the assessment technology. Further generalization leads to the formulation of a control assessment procedure to support control application engineers.

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“…In other words, the statistical properties of this kind of data cannot be described by the robust covariance matrix estimation. Furthermore, outliers may contain very important information, so the outliers cannot be simply deleted or replaced (Liu et al 2018). The data also have some nondominant local structure features besides the outliers.…”

Section: Motivation Of Robust L 1 -Plsmentioning

confidence: 99%

New Robust Projection to Latent Structure

Jing

Zhou

Chen

2022

Intelligent Control and Learning Systems

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In many actual nonlinear systems, especially near the equilibrium point, linearity is the primary feature and nonlinearity is the secondary feature. For the system that deviates from the equilibrium point, the secondary nonlinearity or local structure feature can also be regarded as the small uncertainty part, just as the nonlinearity can be used to represent the uncertainty of a system (Wang et al. 2019). So this chapter also focuses on how to deal with the nonlinearity in PLS series method, but starts from an different view, i.e., robust PLS. Here the system nonlinearity is considered as uncertainty and a new robust $$\mathrm{L}_1$$ L 1 -PLS is proposed.

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A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

Cited by 14 publications

References 35 publications

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

Performance Assessment of Predictive Control—A Survey

New Robust Projection to Latent Structure

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