With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the perfor...With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.展开更多
The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid（FSLS） model was presented by substituting the Abel dashpot for N...The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid（FSLS） model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid（SLS） model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.展开更多
基金supported by Science and Technology Commission of Shanghai Municipality (No.14142201400)
文摘With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.
文摘The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid（FSLS） model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid（SLS） model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.
