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    Journals >Infrared and Laser Engineering >Volume 50 >Issue 8 >Page 20200471 > Article
    • Infrared and Laser Engineering
    • Vol. 50, Issue 8, 20200471 (2021)
    Hybrid PSO-AMLS-based method for data fitting in the calibration of the infrared radiometer
    Sen Yang
    Author Affiliations
  • College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150000, China
    • show less
    DOI: 10.3788/IRLA20200471 Cite this Article
    Sen Yang. Hybrid PSO-AMLS-based method for data fitting in the calibration of the infrared radiometer[J]. Infrared and Laser Engineering, 2021, 50(8): 20200471 Copy Citation Text show less

    Abstract

    A hybrid PSO-AMLS-based method for data fitting in the calibration of the infrared radiometer was described. The proposed method was based on Particle Swarm Optimization (PSO) in combination with Adaptive Moving Least Squares (AMLS). The optimization technique involved parameters setting in the AMLS fitting, which significantly influenced the fitting accuracy. However, its use in the calibration of the infrared radiometer has not been yet widely explored. Bearing this in mind, the PSO-AMLS-based method, which was based on the local approximation scheme, was successfully used here to get the relationship between the radiation of the standard source and the output voltage of the infrared radiometer. The main advantages of this method were the flexible adjustment mechanism in data processing and the ability in reducing the adverse effect resulting from the non-uniform distribution of fitting data. Numerical examples and experiments are performed to verify the superior performance of the PSO-AMLS-based method compared to the conventional data fitting method.

    Keywords

    $ f(x) = \sum\limits_{i = 1}^m {{p_i}} (x){a_i}(x) = {P^{\rm T}}(x)a(x) $(1)

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    $ J = \sum\limits_{I = 1}^N {{w_I}} (x){[P({x_I})a(x) - f({x_I})]^2} $(2)

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    $ w(r) = \left\{ {\begin{array}{*{20}{c}} {\dfrac{{{\rm exp}( - {r^2}{\beta ^2}) - {\rm exp}( - {\beta ^2})}}{{1 - {\rm exp}( - {\beta ^2})}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} r \leqslant 1} \\ {{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} r > 1} \end{array}} \right. $(3)

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    $ J = {[Pa(x) - f]^{\rm T}}W[Pa(x) - f] $(4)

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    $ P = {\left[ {\begin{array}{*{20}{c}} {{P^{\rm T}}({x_1})} \\ {{P^{\rm T}}({x_2})} \\ \vdots \\ {{P^{\rm T}}({x_N})} \end{array}} \right]_{N \times m}} $(5)

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    $ W = \left[ {\begin{array}{*{20}{c}} {\omega (x - {x_1})}&0& \cdots &0 \\ 0&{\omega (x - {x_2})}& \cdots &0 \\ \vdots & \vdots & \ddots & \vdots \\ 0&0& \cdots &{\omega (x - {x_N})} \end{array}} \right] $(6)

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    $ \frac{{\partial J}}{{\partial a(x)}} = [{P^{\rm T}}WP]a(x) - [{P^{\rm T}}W]f = 0 $(7)

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    $ a(x) = {[{P^{\rm T}}WP]^{{\rm{ - }}1}}[{P^{\rm T}}WP]f $(8)

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    $ f(x) = {P^{\rm T}}(x){[{P^{\rm T}}WP]^{{\rm{ - }}1}}[{P^{\rm T}}WP]f $(9)

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    $ \begin{split} {v_i}\left( {k + 1} \right) =& \omega \cdot {v_i}\left( k \right) + {c_1} \cdot {r_1} \cdot \left( {{p_{ibest}} - {x_i}\left( k \right)} \right) + {c_2} \cdot \\ & {r_2} \cdot \left( {{g_{best}} - {x_i}\left( k \right)} \right) \\ \end{split} $(10)

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    $ {x_i}\left( {k + 1} \right) = {x_i}\left( k \right) + {v_i}\left( {k + 1} \right) $(11)

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    $ {R^2} = \sum\limits_{i = 1}^n {{{\left( {{y_i} - {y_{if}}} \right)}^2}} $(12)

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    $ f(x) = 1 + \sqrt x $(13)

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    $ \delta = {y_i} - {y_{if}} $(14)

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    $ {\delta ^*} = {T_t} - {T_m} $(15)

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    Sen Yang. Hybrid PSO-AMLS-based method for data fitting in the calibration of the infrared radiometer[J]. Infrared and Laser Engineering, 2021, 50(8): 20200471
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