A Method to Measure Humidity Based on Dry-Bulb and Wet-Bulb Temperatures

This study tries to analyze the theory of measuring humidity based on dry-bulb and wet-bulb temperatures. And a theoretical formula is deduced for the calculation of relative humidity from dry-bulb and wetbulb temperatures. Through analysis of the theoretical formula, a two-dimensional conversion table is produced to transform dry-bulb and wet-bulb temperatures into relative humidity. A method is proposed to obtain humidity by combining searching table and linear smoothing algorithm, which is suitable for rapid control. Error analysis and experimental data indicate that the relative error is less than 4%. The proposed method has certain value for humidity control in industrial control process.


INTRODUCTION
The air Relative Humidity (Hr) is an important control parameter in the wood drying process.There are several different methods to measure the relative humidity, such as electronic humidity sensor hygrometry, paper hygrometry and psychrometric hygrometry.The maintenance of psychrometric hygrometry is simple.In practical use, we just periodically add water to wet bulb and replace the gauze of wet bulb.Compared with electronic humidity sensor hygrometry and paper hygrometry, psychrometric hygrometry will not produce the problems of aging and decline in accuracy.Therefore, psychrometric hygrometry is more suitable for measuring humidity in the harsh environment (Zelin et al., 2010).
Traditional psychrometric hygrometry requires searching the saturation vapor pressure table.There are hundreds of thousands of data in the table.It is a huge workload to store the table in the microcontroller and the memory capacity is also not allowed.Therefore the table is not suitable for embedded applications (Xiaoyin and Liangen, 2003).A more efficient method of searching table and smooth transformation to calculate the air relative humidity is proposed based on the theoretical dry-and-wet bulb equation.And the proposed method is suitable for humidity control in industrial control process.

CALCULATION OF RELATIVE HUMIDITY FROM DRY-BULB AND WET-BULB TEMPERATURES
The principle of psychrometric hygrometry is that the humidity is calculated by the dry-and-wet bulb equation according to dry-bulb and wet-bulb temperatures (Zelin et al., 2010).The dry-and-wet bulb equation (Jun, 2008) where, Hr = The relative humidity ew = The saturation vapor pressure in the wet-bulb temperature ed = The saturation vapor pressure in the dry-bulb temperature A = The measuring humidity coefficient P = The mean atmospheric pressure Δt = The difference between the dry-bulb temperature and the wet-bulb temperature (assumed to be Td -Tw) According to formula (1), we can note that: The keys to getting relative humidity are ew, ed and A.
In this study, we use the Buck formula (Buck, 1981) to calculate ew and ed.Compared with the  As shown in formula (6), we note that: the Relative Humidity (Hr) depends on both the dry-bulb and wetbulb temperatures (Td and Tw).However, formula ( 6) is so complex to calculate humidity that isn't suitable for embedded applications which are limited in resources.
According to formula (6), we get a twodimensional table which transforms dry-bulb and wet- bulb temperatures into relative humidity while the drybulb temperature (Td) is assumed to be 20, 25, 30…95, 100 and the difference between the dry-bulb temperature and wet-bulb temperature (Δt) is assumed to be 1, 2, 3 …39, 40.Parts of data are shown in Table 1 and the row of Table 1 is Td and the column of Table 1 is Δt.
Figure 1 is the surface chart generated by Table 1.As shown in Fig. 1, we note that the surface has a smooth trend.

SEARCHING TABLE AND SMOOTH TRANSFORMATION
In Table 1, for the dry-bulb temperatures (Td) in the data table, such as 20, 25, 30 and so on, we can obtain their humidity data directly.
However, for Td not in the data table, their humidity can be obtained by linear smoothing.The first thing is to find the upper and lower limits of the neighboring segment of Td.Then, we look up the table to find the humidity values of the upper and lower limits.At last, we linearly smooth the two humidity values to get the humidity value of Td.
Based on the above ideas, the flow chart of searching table and smooth transformation is shown in Fig. 2.

COMPARISON OF THEORETICAL VALUES AND LINEAR SMOOTH VALUES
The essence of the calculation method is that, when the conversion table obtained from the theoretical formula is as reference data, we search the reference data to find two humidity values according to the drybulb and wet-bulb temperatures and linearly smooth the two values to obtain the humidity value of Td.As shown in   ----------------------------------- According to Table 2, we note that, the maximum relative error between the linear smooth values and the theoretical values is 3.6%.For the error analysis theory, we know that, the absolute error of total synthesis function is equal to the algebraic sum of the product of the absolute error of each part and the partial derivative of each part.The absolute error of Td and Tw is assumed to be ΔTd and ΔTw.The relative error of Hr is assumed to be ΔHr/Hr, so we have: (9) Calculated by formula (9), the relative error of Hr is less than 4%.The method is suitable for engineering calculations with high accuracy.
In point of computing speed, searching table is faster than theoretical formula.And the linear smoothing algorithm is also fast and the algorithm time complexity is only  (n).In this study, we use a combination of searching table and linear smoothing algorithms, which is very suitable for embedded applications with limited resources.
Through of analysis of error and computing speed, the proposed method has certain value for humidity control in industrial control process.

CONCLUSION
This study tries to analyze the theory of measuring humidity based on dry-bulb and wet-bulb temperatures.And a theoretical formula is deduced for the calculation of relative humidity from dry-bulb and wet-bulb temperatures on the basis of accurately determining the empirical formulas of measuring humidity coefficient and saturation vapor pressure.A conversion table is produced according to the theoretical formula.A method is proposed to obtain humidity by combining searching table and linear smoothing algorithm, which is suitable for rapid control.Experimental data shows that, compared with the traditional manual searching table, the proposed method is not only simple and fast but also has high veracity.And its relative error is less than 4%.Therefore, the proposed method has certain value for humidity control in industrial control process.

Table 1 :
Conversion table of dry-bulb and wet-bulb temperatures to relative humidity (Xihua et al., 2003;ssure formula which is proposed by Coff in 1965(Xihua et al., 2003; Smithsonian, 1984), the Buck formula is simpler and easier.The Buck formula is as follows: (2)According to formula (2), we can get ew and ed.
Flow chart of searching table and smooth transformationFor example, when Td is 53 and Tw is 41, we find: Tdl is 50 and Tdh is 55.Because the difference between Td and Tw is 12, we note: Hrl is 47, Hrh is 49.Then we have: Table 2, we randomly calculate ten values of Hr and compare with theoretical values obtained from manual look-up table (Environmental Standards Committee Working Group, 1986).

Table 2 :
Comparison of theoretical values and linear smooth values