Optimal design of fractional order linear system with stochastic inputs/parametric uncertainties by hybrid spectral method

Duong, Pham Luu Trung; Lee, Moonyong

doi:10.1016/j.jprocont.2014.08.009

Cited by 3 publications

(5 citation statements)

References 28 publications

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“…Fractional derivative (FD) is a novel branch of derivative calculus, which is widely applied in the control systems, signal smoothing, biological engineering, and image processing [36][37][38]. Since integer-order derivative models may insufficiently represent the fractional order-based systems, the FD can better represent such issues [39].…”

Section: Introductionmentioning

confidence: 99%

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

et al. 2020

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Leaf chlorophyll concentration (LCC) is an important indicator of plant health, vigor, physiological status, productivity, and nutrient deficiencies. Hyperspectral spectroscopy at leaf level has been widely used to estimate LCC accurately and non-destructively. This study utilized leaf-level hyperspectral data with derivative calculus and machine learning to estimate LCC of sorghum. We calculated fractional derivative (FD) orders starting from 0.2 to 2.0 with 0.2 order increments. Additionally, 43 common vegetation indices (VIs) were calculated from leaf spectral reflectance factor to make comparisons with reflectance-based data. Within the modeling pipeline, three feature selection methods were assessed: Pearson’s correlation coefficient (PCC), partial least squares based variable importance in the projection (VIP), and random forest-based mean decrease impurity (MDI). Finally, we used partial least squares regression (PLSR), random forest regression (RFR), support vector regression (SVR), and extreme learning regression (ELR) to estimate the LCC of sorghum. Results showed that: (1) increasing derivative order can show improved model performance until certain order for reflectance-based analysis; however, it is inconclusive to state that a particular order is optimal for estimating LCC of sorghum; (2) VI-based modeling outperformed derivative augmented reflectance factor-based modeling; (3) mean decrease impurity was found effective in selecting sensitive features from large feature space (reflectance-based analysis), whereas simple Pearson’s correlation coefficient worked better with smaller feature space (VI-based analysis); and (4) SVR outperformed all other models within reflectance-based analysis; alternatively, ELR with VIs from original reflectance yielded slightly better results compared to all other models.

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Section: Introductionmentioning

confidence: 99%

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

et al. 2020

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“…This closed loop OP can be used to obtain the first-and second-order moment of the random output from (24). The parameters of the PI D controller can be obtained by optimizing the cost function defined as [37] min , , , ,…”

Section: Optimal Pi D Controller Designmentioning

confidence: 99%

“…The set point ( ) is a random process with a unit mean and covariance function ( ) = 0.01 ( ). This input ( ) can be viewed as a combination of the deterministic set point and zero mean measurement noise [37]. The control objective is to track the deterministic unit step input.…”

Section: (C) Example 2(c)mentioning

confidence: 99%

“…This can be achieved by minimizing objective function defined in Section 4. The search space for the optimal parameters of the controller was limited to 0 ≤ ≤ 5; 0 ≤ ≤ 5; 0 ≤ ≤ 5; 0.1 ≤ ≤ 1.9; 0.1 ≤ ≤ 1.9 for simplicity, as in other studies on the probabilistic approach [29,37]. The resulting controller can be expressed as 1 ( ) = 0.2805 + 1.1458/ 0.6422 .…”

Section: (C) Example 2(c)mentioning

confidence: 99%

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Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method

Duong

Kwok²,

Lee³

2015

Mathematical Problems in Engineering

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The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem.

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“…Studies showed that first-and second-order derivatives have greater discrepancy from the raw data and are prone to missing data that impacts model precision. Meanwhile, fractional-order derivative as the derived concept of integer-order derivative is widely applied in the control system, signal smoothening, biological engineering, and image processing [17][18][19][20][21]. Its wide applicability is due to the fact that integer-order derivative models lack the precision when presenting the fractional order-based systems in real life.…”

Section: Introductionmentioning

confidence: 99%

Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region

Xiong

Tian

2019

Journal of Spectroscopy

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Discussion on the application of fractional derivative algorithm in monitoring organic matter content in field soil is scarce. This study is aimed at improving the accuracy of soil organic matter (SOM) content estimation in arid region, and the undesirable model precision caused by the missing information associated with the larger discrepancy between conventional integer-order, i.e., first order and second order, derivative, and raw spectral data. We utilized fractional derivative (of zeroth order to second order in 0.2-order interval) processing on the field spectral reflectance (R) of the salinized soil sample from Fukang, Xinjiang, and its square root-transformed (R), log-transformed (lgR), inverse-transformed (1/R), and inverse log-transformed (1/lgR) values. The correlation coefficient of each fractional derivative of transformed value with SOM content was calculated. The simulation showed the derivative reflectance value approximates zero. When increasing from zeroth order to first order, the derivative curve gradually aligns to the first-order curve, and the destination alignment was also seen while increasing from first order to second order. The significance test of 0.05 showed initial increase and later decay of bands in the five spectral transformations as the order increases. For specific bands, the derivative algorithm clearly justifies the correlation between soil spectra and organic matter content, and all of the absolute highest correlation coefficient values were obtained at fractional orders. When compared with integer-order derivative, fractional derivative is significantly better in improving correlation, showing overall superiority. The result supports the application of fractional derivative in the hyperspectral remote monitor of SOM in arid zone, which may in turn realize the timely and accurate SOM monitor in arid zone, and provides the basis for ecological restoration.

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Optimal design of fractional order linear system with stochastic inputs/parametric uncertainties by hybrid spectral method

Cited by 3 publications

References 28 publications

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

Quantifying Leaf Chlorophyll Concentration of Sorghum from Hyperspectral Data Using Derivative Calculus and Machine Learning

Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method

Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region

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