﻿ 基于改进自适应遗传算法的多波长测温计算
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 应用科技  2018, Vol. 45 Issue (3): 28-34  DOI: 10.11991/yykj.201705007 0

### 引用本文

FENG Chi, WANG Li, GAO Shan. Multi-wavelength temperature calculation based on the improved adaptive genetic algorithm[J]. Applied Science and Technology, 2018, 45(3), 28-34. DOI: 10.11991/yykj.201705007.

### 文章历史

Multi-wavelength temperature calculation based on the improved adaptive genetic algorithm
FENG Chi, WANG Li, GAO Shan
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: Multiple wavelength thermometry is an important way of radiation temperature measurement. In this paper, the error function model of the multiple wavelength and the adaptive genetic algorithm are improved, and the least square method and the improved adaptive genetic algorithm are combined to improve the precision and stability of the calculative results. Applied the spectrum areas of the near-infrared multi-wavelength pyrometer are 1 000~1 100 nm, 1 260~1 450 nm, 1 500~1 750 and 1 850~2 000 nm respectively, the range of the temperature measurement is 500~1 000 ℃, through spectrum regions divided, error function model established and the crossover probability and mutation probability adjusted adaptively can effectively remove the environmental reflection and the influences of the unknown emissivity, and then calculative temperature value is higher accurate and stability.
Key words: multiple wavelength thermometry    error function    temperature    emission rate    the least square method    the improved adaptive genetic algorithm    accuration    stability

1 多波长辐射测温原理

 ${I_{{\lambda _i}}} = \varepsilon \left( {{\lambda _i},T} \right){I_b}\left( {{\lambda _i},T} \right)$ (1)

 ${I_b} = {C_1}{\lambda ^{ - 5}}{\left( {{{\rm e}^{{C_2}/\lambda T}} - 1} \right)^{ - 1}}$

 ${\varepsilon _i}\left( \lambda \right) = {a_{i,0}} + {a_{i,1}}\lambda , \; \lambda \in \left( {{\lambda _{i,\min }},{\lambda _{i,\max }}} \right)$ (3)

 $F = {\sum\limits_{i = 1,j = 1}^N {\sum\limits_{{\lambda _j} \in \left( {{\lambda _{i,\min }},{\lambda _{i,\max }}} \right)}^M {\left[ {\left( {{I_{{\lambda _j}, {\rm meas}}} - {\varepsilon _i}\left( {{\lambda _j}} \right){I_{{\lambda _j},b}}} \right)/{I_{{\lambda _j}, {\rm meas}}}} \right]^2} } }$

 ${I_{\lambda , {\rm eff}}} = \varepsilon {I_{\lambda ,b}} + \rho {I_{\rm envir}}$ (5)

 $\begin{split}F = & \sum\limits_{i = 1,j = 1}^N {\sum\limits_{{\lambda _j} \in \left( {{\lambda _{i,\min }},{\lambda _{i,\max }}} \right)}^M {\left[ {\left( {{I_{{\lambda _j}, {\rm eff}. {\rm meas}}} - {\varepsilon _i}\left( {{\lambda _j}} \right){I_{{\lambda _j},b}} - } \right.} \right.} } \\& {\left. {\left. {\left( {1 - {\varepsilon _i}\left( {{\lambda _j}} \right)} \right){I_{\rm envir}}} \right)/{I_{{\lambda _j}, {\rm eff}. {\rm meas}}}} \right]^2}\end{split}$ (6)

2 改进自适应遗传算法原理 2.1 最小二乘法

2.1.1 算法概述

$y = f\left( x \right)$ ，在实际问题要求构造近似函数 $\varphi \left( x \right)$ 在包含全部基点 ${x_i}$ 的区间上最好地逼近 $f\left( x \right)$ ，而不必满足插值原则，这就是曲线拟合问题。称函数 $y = f\left( x \right)$ 为经验公式或拟合曲线。具体做法是先根据观测数据得到各点 $\left( {{x_i},\;{y_i}} \right),\;\;i = 1\;,\;2\;, \cdots, n$ ，再选择函数 $\varphi \left( x \right)$ 的类型，

 $\varphi \left( x \right) = {c_1}{\varphi _1}\left( x \right) + {c_2}{\varphi _2}\left( x \right) + \cdots + {c_m}{\varphi _m}\left( x \right)\;\;\left( {m < n} \right)$

 $\begin{split}R = & \sum\limits_{i = 1}^n {{{\left( {\varphi \left( {{x_i}} \right) - {y_i}} \right)}^2}} = \\& {\sum\limits_{i = 1}^n {{{\left( {{c_1}{\varphi _1}\left( {{x_i}} \right) + {c_2}{\varphi _2}\left( {{x_i}} \right) + \cdots + {c_m}{\varphi _m}\left( {{x_i}} \right) - {y_i}} \right)}^2}} } \end{split}$

2.1.2 超定方程最小二乘解

 $\left\{ \begin{array}{l}{a_{11}}{c_1} + {a_{12}}{c_2} + \cdots + {a_{1m}}{c_m} = {y_1}\\\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \left( {n > m} \right)\\{a_{n1}}{c_1} + {a_{n2}}{c_2} + \cdots + {a_{nm}}{c_m} = {y_n}\end{array} \right.$ (9)

 $\left\| {{ A { c} - { y}}} \right\|_2^2 = \sum\limits_{i = 1}^n {{{\left( {{a_{i1}}{c_1} + {a_{i2}}{c_2} + \cdots + {a_{im}}{c_m} - {y_i}} \right)}^2}}$ (10)

 $\left\{ \begin{array}{l}{c_1}{\varphi _1}\left( {{x_1}} \right) + {c_2}{\varphi _2}\left( {{x_1}} \right) + \cdots + {c_m}{\varphi _m}\left( {{x_1}} \right) = {y_1}\\{c_1}{\varphi _1}\left( {{x_2}} \right) + {c_2}{\varphi _2}\left( {{x_2}} \right) + \cdots + {c_m}{\varphi _m}\left( {{x_2}} \right) = {y_2}\\ \quad \quad \quad \quad \quad \quad \cdots \cdots \\{c_1}{\varphi _1}\left( {{x_n}} \right) + {c_2}{\varphi _2}\left( {{x_n}} \right) + \cdots + {c_m}{\varphi _m}\left( {{x_n}} \right) = {y_n}\end{array} \right.$

 $\varphi \left( {{x_i}} \right) = {y_i},\;\;i = 1\;,\;2\;, \cdots ,\;n.$
2.2 遗传算法

2.3 自适应遗传算法

 {P_c} = \left\{ \begin{aligned}& \frac{{{k_1}\left( {{f_{\max }} - {f'}} \right)}}{{{f_{\max }} - {f_{\rm avg}}}}, \;\;\;{f'} \geqslant {f_{\rm avg}}\\& {k_2}, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{f'} < {f_{\rm avg}}\end{aligned} \right. (7)
 {P_m} = \left\{ \begin{aligned}& \frac{{{k_3}\left( {{f_{\max }} - {f'}} \right)}}{{{f_{\max }} - {f_{\rm avg}}}},\;\;{f'} \geqslant {f_{\rm avg}}\\& {k_4},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{f'} < {f_{\rm avg}}\end{aligned} \right. (8)

2.4 改进自适应遗传算法

 {P_c} = \left\{ \begin{aligned}& {P_{c_{_1}}} - \frac{{\left( {{P_{{c_{_1}}}} - {P_{{c_{_2}}}}} \right)\left( {{f'} - {f_{\rm avg}}} \right)}}{{{f_{\max }} - {f_{\rm avg}}}},\;\;\;\;\;{f'} \geqslant {f_{\rm avg}}\\& {P_{{c_{_1}}}},\quad \quad \;\;\;\; \quad \quad \quad \quad \quad \quad \quad {f'} < {f_{\rm avg}}\end{aligned} \right. (14)
 {P_m} = \left\{ \begin{aligned}& {P_{{m_{_1}}}} - \frac{{\left( {{P_{{m_{_1}}}} - {P_{{m_{_2}}}}} \right)\left( {{f_{\max }} - f} \right)}}{{{f_{\max }} - {f_{\rm avg}}}},\;\;\;f \geqslant {f_{\rm avg}}\\& {P_{{m_{_1}}\;}},\quad \quad \;\; \quad \quad \quad \quad \quad \quad \quad f < {f_{\rm avg}}\end{aligned} \right. (15)

3 仿真过程

3.1 自适应遗传算法仿真结果

3.2 改进的自适应遗传算法仿真结果

3.3 结果分析