doi: / Dust Concentration Measuring Based on Nonlinear Amended Capacitance Method

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1 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 doi:0.3/ Dust Concentration Measuring Based on Nonlinear Amended Capacitance Method Zemin Wang*, Yongsheng Fu, Bingshan Lei School of Electronic Information Engineering, Xi an Technological University,Xi an 7003, Shaanxi, China *Corresponding author( Abstract The research on dust concentration measurement method has important significance to measure the accuracy and precision of dust concentration. There are some problems such as low accuracy in the traditional capacitance method for dust concentration measurement. This paper presents a nonlinear fitting data correction algorithm based on least squares for capacitance method, and dust concentration measurement system is established. The dust concentration signal frequency characteristic is analyzed, and math relation between the output frequency of capacitance and the dust concentration is given, and the sum of squares of errors is smallest when degree is, and the effective control of dust concentration measurement error small than %. The experiment and simulation results show that the nonlinear correction algorithm can eliminate the errors. Key words: Method of Capacitance, Dust Concentration, Nonlinear Fitting. INTRODUCTION With the industrial development, the dust pollution in the air is getting worse. The dust in the air not only seriously endangers the human health, and it also has the danger of dust explosion when the dust concentration is excessive. It is very important to measure dust concentration. There are two categories methods for the dust concentration measurement(münkel and Eresmaa, 007; Hanesch and Scholger, 003). The first category method is sampling method that the dust is precipitated before measurement, and this method representative samples containing dust particles from the measured area are chose and send the analysis measuring device system to measure dust particle concentration and particle size. The other category is the non-sampling method, and these methods can directly measured with the physical properties of dust particles such as electric, optics and acoustics and without sampling previously in the process of measurement(etyemezian and Kuhns, 003; Hoffmann and Funk, 008). The capacitance method from non-sampling method is widely used because of the simple device and the low price, but the capacitance method will bring the nonlinear measurement error for the influence of measuring environment, the edge effect of the capacitor and the distributed capacitance(douwes and Versloot, 995; Khettabi and Songmene, 007). Lotters designed the active electrical bridge circuit (Lotters and Olthuis, 999), achieving the linear output of capacitance sensor and solving the nonlinear problem to a certain extent, but this method has the low accuracy because of influence of the environment. Li added the balance circuit to compensate the measurement error caused by the characteristic drift of electronic components, and the error is small but the accuracy is relative finite(li and Fan, 007). Fan processed output data use piecewise linear, and this method has the great limitation(fan, 004). In this paper, the nonlinear processing of the capacitance sensor output with the least squares method is proposed to eliminate the influence of the measurement results caused by nonlinear parameters. The nonlinear correction is completed with the computer online data processing. The least squares method is simple and convenient and has the less error with the optimization strategy of gradient criterion. The experiment is verified and the experimental results show that this method can effectively improve the measurement accuracy and the processing is flexible.. DUST CONCENTRATION MEASUREMENT PRINCIPLE OF CAPACITANCE METHOD Capacitance method for measuring dust concentration is to convert the concentrations change of being measured parameters to capacitance changes of capacitors, the capacitance of the capacitor is related to the shape of plates, dielectric materials, the relative position between the plates and other factors, the capacitance value can be represented in the following formula (). C f ( s, l, d, eff ) () It makes s, l, d, ε eff and other parameters change as the measured parameter changes, the capacitance capacity also changes. Fix other parameters, only change one parameter, the dielectric constant ε err can be changed into the corresponding capacitance change volume. Conduct further processing for output signal, we 57

2 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 can turn changes into more easily observation parameters like voltage, current or frequency, that is to say, it is achievable to change non-power to power. Because dust and gas are two-phase fluid with different concentration proportions, which makes sea collection fluid has different dielectric constants. As concentration portion changes, it will cause mixed body equivalent dielectric constant changes, then makes capacitor value c changes. So according to the change of capacitor value, on can get solid dust concentration, air (continuous phase) dielectric constant is ε, and dust (discrete phase) dielectric constant is ε. Assume the equivalent dielectric constant is ε eff when dust and air have mixed. Assume dust distribution is uniform in the air, then ε eff is determined by the volume ratio of the two phases. V V () V V In equation (), V and V are each for the volume of dust and air, V= V +V is the total volume, then it can be changed into the following equation. Then, V V V V V V V (3) K f ( V, V ) K f ( ) (4) In equation (4), K is characteristic constant, it is determined by structure size of capacitor sensor. So in theory, if structural parameters of capacitors are fixed, the output capacitance c is only associated with phase concentration of dust and air a. In reality, dust is generally not evenly distributed in the continuous gas phase, so the relationship between the equivalent dielectric constant ε eff and concentration portion is relatively complex. Under normal circumstances, this relationship is not absolutely linear. For multiphase mixing dielectric constant ε eff, and different models and expressions have been proposed. This paper uses the Maxwell-Garnett model, the calculation formulas of dielectric constants are common models to calculate the dielectric constant with twophase mixture. Expression formula of this model is shown. eff 3 (5) ( ) The equation (5) is a dominant formula to calculate two-phase mixture dielectric constant, parameter representative meaning is as follows: ε and ε are each for dielectric constant of continuous and discrete phase. The model regards dust particles as discrete ball particles, and it is suitable for smaller diameter dust particles, and these dust particles are uniform in continuous gas phase. It is high precision with the model to calculate mixed dielectric constant, so this model is the application of a wide range in dust concentration measurement field. When the discrete phase fraction is small, and the equation (5) can be approximated. Convert the (6) into equation (7). eff 3 (6) eff eff Equation (7) is called Wagner, it is an transformation of (6), thus, this formula is equivalent to the Maxwell-Garnett model with the same type. Conduct deformation on (7), we can get the following calculation of the explicit formula of dust particle phase. eff - eff (7) (8) 3. NONLINEAR CORRECTION ALGORITHM OF CAPACITANCE METHOD According to the above analysis, dust concentration is theoretically proportional to the output value of measurement, but in actual measurement, a lot of reasons lead to nonlinear output of capacitors. These factors include: Capacitor plates is not ideal parallel plate capacitor, and the edge effect of the plate is very large. Since 58

3 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 the impact of the manufacturing process and structure, position of the capacitor plates can not be completely symmetrical, which makes the distribution of electric field between the capacitor plates is more complex. On the other hand, nonlinear effects result is caused by parasitic capacitance and contact resistance and residual magnetic of metal materials of leading-out line, therefore, the output capacitor is often presented non-linear. Curve fitting method can be used to compensate the nonlinear effect, and it used n-order polynomial to approach non-linear curve. ) Static test calibration capacitor and measuring circuit. The corresponding output frequency values were obtained by measuring the concentration with m mixture solution of known concentration, and get a set of data d, f, d, f,..., d, f. m m ) The input nonlinear function is determined, assume that anti nonlinear characteristics fitting equation is d( f ) a a f a f a f (9) i 0 i i n i In equation: a0, a, a,, a n is coefficients undetermined value of fitting functions, the value of n depends on the nonlinear degree of discrete points, the greater the degree of nonlinearity, n value should be taken to a larger value, the fitting results will be improved accuracy. 3) The basic idea of solving undetermined constants and determining undetermined constant is that determine the values of each d( f i ) and calibration value of each d point of the mean variance should be i minimal, that is minimum value of a function F( a, a,, a n ). m F( a, a,, a ) d( f ) f (0) n i i i 4) In order to obtain the constant of the minimum value of F( a, a,, a n ) in the function formula (6),respectively, variable ( a, a,, a n ) of F( a, a,, a n ) derivative, and make the first derivative is 0, ( a, a,, a ) can be solved as n F( a, a,, a n ) 0 () ai In order to get the measured dust concentration value when output frequency is f,the concentration value d can be obtained by bringing the measured value of f into the fitting equation at each time. 4. DUST CONCENTRATION MEASUREMENT SYSTEM BASED CAPACITANCE METHOD The dust concentration measurement system based capacitance method is shown in Fig.. Capacitance Frequency Measurement Circuit ( CFMC ) is designed by the multi-vibrator, and the multivibrator is composed by timer IC and the measured capacitance, and the output of multi-vibrator is counted by micro-controller unit(mcu) to get the relationship between capacitance value and output square wave frequency of oscillator, thereby square wave frequency is obtained by the measured capacitance value. The measurement process is as follows: dust concentration is tested by capacitor, the probes of capacitor are connected the timer IC. With the dust concentration continuous changes, the capacitance value produces some changes, the timer IC generates different frequency square wave signal, then the MCU detect square wave frequency value by the internal counter, and the data is transmitted to PC by the RS-3. A set of input concentration values and output frequency values are processed by nonlinear fitting method in PC, and the mathematical relationship between the dust concentration and the output frequency is shown in PC. In order to reduce the influence of the line-line capacitance in the measurement, the distance between the measurement circuit and the capacitance should be as far as possible to decrease. Figure. The diagram of dust concentration measurement system 4.DUST CONCENTRATION MEASUREMENT EXPERIMENTAL AND ANALYSIS Lithopone is chosen to the dust for the diameter from 5um to 0um, and the lithopone dispersed uniformly by a fan in an enclosed space with a known volume. The actual dust concentration can be obtained 59

4 error sum of squares deviate/% Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 according to value the adding dust, after the conversion of measuring circuit, the corresponding capacitance frequency. 30 sets of data practical concentration and the corresponding frequency are shown in Table. Table. Experimental data N mg/m 3 f/khz N mg/m 3 f/khz N mg/m 3 f/khz According to Table, there is a significant correlation between the practical dust concentration and the output frequency. In order to derive the corresponding model, and the linear relation between the dust concentration and the frequency value through the linear regression method is assumed as linear relation model is D=af+b, a and b are the coefficients of linear relation, and a=0.046, b=4.030, and the sum of squares of errors is 0.055, then the relative error curve between the theoretical value and the practical value by this relation model is shown in Figure concentrations/mg/m 3 Figure. One liner error By comparison, it can be found that the error of the linear model is larger, so we consider the use of nonlinear method for error correction, get different sum of squares of errors when the number of fitting polynomial degree is different. The simulation of sum of squares of errors when fitting degree respectively equals to ~0 as shown in Figure degree of polynomial/degree Figure 3. Error sum of square for different degree vaule 60

5 deviate/% Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 Analyzing Figure 3, the sum of squares of errors is smallest when degree=, therefore we regard this fitting curve as the relational model of input and output, the corresponding relative error curve between the theoretical value and the practical value is shown in Figure 4. It can be seen that error e =3.956, and calculated by simple linear regression method is 0.055, by comparison, we find that the error is obviously reduce, the deviation between the theoretical value and the average error <%, the error is small concentrations/mg/m 3 Figure 4. Deviation of each point when degree= In order to verify the nonlinear model, we select 0 sets of the dust for measurement in the same way and same concentration range, the result are shown in Table. Using above fitting formula to theoretically calculate the dust concentration, and then making comparison with the practical concentration of mixtures, calculating them error value, getting the relative errors are below %. By analyzing Table, the result shows that compared with simple linear regression model, the output error by the nonlinear data fitting is smaller. Table. 0 Sets value of measurements Measured Concentrations (mg/m 3 ) Theory Concentrations (mg/m 3 ) Relative Error(%) CONCLUSIONS In this paper a capacitance sensor nonlinear fitting data processing algorithm is proposed based on the optimization strategy of least squares method and the principle of gradient, and the mathematical model of the dust concentration changes with measurement circuit output frequency is got. In order to effectively reduce the measurement error, we can reduce the high order polynomial features and improve the effect of artificial operations and environmental factors on the measurement value. It can be eliminated that the effect of capacitance sensor nonlinear factors on the measurement results using this algorithm, and the dust concentration relative errors can be effectively control below %. Acknowledgements This work was supported by Key Industrial Science and Technology Project of Shaanxi Province (No.05GY08) This work was supported by scientific research innovation team building plan of Xi an Technological University. 6

6 Rev. Téc. Ing. Univ. Zulia. Vol. 39, Nº 7, 57-6, 06 REFERENCES Douwes, J., Versloot, P., Hollander, A., Heederik, D., and Doekes, G. (995). Influence of various dust sampling and extraction methods on the measurement of airborne endotoxin, Applied and environmental microbiology, 6(5), pp Etyemezian, V., Kuhns, H., Gillies, J., Green, M., Pitchford, M., and Watson, J. (003). Vehicle-based road dust emission measurement: I-methods and calibration, Atmospheric Environment, 37(3), pp Fan, S., Liang, H. (004). Mathematical Model of Capacitive-Type Moisture Sensor, Chinese Journal of Scientific Instrument, 5(S4), 0. Hanesch, M., Scholger, R., and Rey, D. (003). Mapping dust distribution around an industrial site by measuring magnetic parameters of tree leaves, Atmospheric Environment, 37(36), pp Hoffmann, C., Funk, R., Wieland, R., Li, Y., and Sommer, M. (008). Effects of grazing and topography on dust flux and deposition in the Xilingele grassland, Inner Mongolia, Journal of Arid Environments, 7(5), pp Khettabi, R., Songmene, V., and Masounave, J. (007). Effect of tool lead angle and chip formation mode on dust emission in dry cutting, Journal of Materials Processing Technology, 94(), pp Lotters, J. C., Olthuis, W., Veltink, P. H., and Bergveld, P. (999). A sensitive differential capacitance to voltage converter for sensor applications, IEEE Transactions on Instrumentation and Measurement, 48(), pp Li, X., Fan, Y. (007). Research on High-Precision Capacitive Level Sensor In strumentation, Automation, and Advanced integration Technic Conference Proceedings, Beijing: Scientific Instrument Magazine, 5. Münkel, C., Eresmaa, N., Räsänen, J., and Karppinen, A. (007). Retrieval of mixing height and dust concentration with lidar ceilometer, Boundary-layer meteorology, 4(), pp

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