General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method

Gorry, P.A.

doi:10.1021/ac00205a007

Cited by 581 publications

(249 citation statements)

References 10 publications

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“…A procedure to compute the convolution weights h j is given by Gorry (1990), the method allows considering also the end points of the data set. In the present case, the smoothing was performed using 7 points (m = 3).…”

Section: Numerical Validationmentioning

confidence: 99%

Application of the virtual fields method to large strain anisotropic plasticity

Rossi

Pierron

Štamborská

2016

International Journal of Solids and Structures

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The identification of the plastic behaviour of sheet metals at severe deformation is extremely important for many industrial application such as metal forming, crashworthiness, automotive, aerospace, piping, etc. In this paper, the virtual fields method (VFM) was employed to identify the constitutive parameters of anisotropic plasticity models. The method was applied using the finite deformation theory in order to account for large strains. First the theoretical principles to implement the method are described in details, especially how to derive the stress field from the strain field. Afterwards a numerical validation was performed using the Hill48 model. Several aspects were studied with the numerical model: the effect of the used virtual fields, the minimum number of specimens required to identify the parameters, the stress distribution obtained from the specimen and its influence in the identification performance. A brief analysis on the influence of noise is also conducted. Finally a series of experiments was conducted on notched specimens of stainless steel, cut along different anisotropic directions. The displacement and strain fields were obtained by digital image correlation. Afterwards, the VFM was used to identify the parameters of the Hill48 model and the Yld2000-2D model. In this case, the Hill48 model was not able to correctly describe the material behaviour, while a rather good agreement was found with the Yld2000-2D model. The potential and the limitation of the proposed method are finally discussed.

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Section: Numerical Validationmentioning

confidence: 99%

Application of the virtual fields method to large strain anisotropic plasticity

Rossi

Pierron

Štamborská

2016

International Journal of Solids and Structures

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“…In this study, in order to reduce the spectral noise, baseline drift, and the interference from other backgrounds as well as distinguish overlapping peaks, five preprocessing methods were applied to improve spectral resolution, sensitivity, and the signal-to-noise ratio of the spectra [25]. Among them, the Savitzky-Golay (S-G) smoothing algorithm uses a weighted average method to quantize the data in the moving window by polynomial least squares fitting as well as emphasizes the central role of the center point [26].…”

Section: Spectral Preprocessing Methodsmentioning

confidence: 99%

The Effects of Drying Temperature on Nitrogen Concentration Detection in Calcium Soil Studied by NIR Spectroscopy

Nie

Dong

et al. 2018

Applied Sciences

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Soil nitrogen is one of the crucial components for plant growth. An accurate diagnosis based on soil nitrogen information is the premise of scientific fertilization in precision agriculture. Soil nitrogen content acquisition based on near-infrared (NIR) spectroscopy shows the significant advantages of high accuracy, real-time analysis, and convenience. However, soil texture, soil moisture content, and drying temperature all affect soil nitrogen detection by NIR spectroscopy. In order to investigate the effects of drying temperature on calcium soil nitrogen detection and its characteristic bands, soil samples were detected at a 25 • C placement (ambient temperature) after 40 • C drying (medium temperature), 60 • C drying (medium-high temperature), 80 • C drying (high temperature), and 105 • C drying (extreme high temperature), respectively. Besides that, the original spectra were pretreated with five preprocessing methods, and the characteristic variables were selected by competitive adaptive reweighted squares (CARS) and backward interval partial least squares (BIPLS). The partial least squares (PLS) method was used for modeling and analysis. The predictive abilities were assessed using the coefficients of determination (R 2 ), the root mean squared error (RMSE), and the residual predictive deviation (RPD). As a result, the characteristic bands focus on 928-960 nm and 1638-1680 nm when soil was detected after 40 • C, 60 • C, and 80 • C drying. Calcium soil obtained the best prediction accuracy (R 2 p = 0.966, RMSE p = 0.128 g kg , RPD = 5.03) after 40 • C drying by the method of CARS-BIPLS-PLS. Meanwhile, the prediction model also performed well when soil was detected after 60 • C drying (R 2 p = 0.946, RMSE p = 0.172 g/kg, RPD = 4.53) and 80 • C drying (R 2 p = 0.961, RMSE p = 0.143 g kg , RPD = 4.98). However, the calcium soil obtained the worst detection result when soil was placed at 25 • C. In conclusion, a low or extremely high drying temperature had an adverse influence on the soil nitrogen detection, and the 40 • C drying temperature as well as the CARS-BIPLS-PLS method were optimal to enhance the soil nitrogen detection accuracy.

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“…In general, filters based on least squares minimization are known as Savitzky-Golay filters, cf. [12,13]. It is not only the stability, but also robustness and accuracy of the meshless method is then affected by the WLSQ filter.…”

Section: Numerical Filteringmentioning

confidence: 99%

“…[12,13]. The WLSQ filtration technique serves primarily for the stabilization of the numerical scheme and can be utilized under the assumption that the governing equations are linear and the solution is smooth enough.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the acoustic wave propagation using a meshless method

et al. 2017

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Abstract. This paper presents numerical simulations of the acoustic wave propagation phenomenon modelled via Linearized Euler equations. A meshless method based on collocation of the strong form of the equation system is adopted. Moreover, the Weighted least squares method is used for local approximation of derivatives as well as stabilization technique in a form of spatial filtering. The accuracy and robustness of the method is examined on several benchmark problems.

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General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method

Cited by 581 publications

References 10 publications

Application of the virtual fields method to large strain anisotropic plasticity

Application of the virtual fields method to large strain anisotropic plasticity

The Effects of Drying Temperature on Nitrogen Concentration Detection in Calcium Soil Studied by NIR Spectroscopy

Simulation of the acoustic wave propagation using a meshless method

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