Comparison of microwave moisture evaluation quality in time and frequency domain

The article presents the comparison of two methods of microwave data analysis for evaluation of moisture content in porous materials. The content of the paper covers the short description of microwave technique for moisture evaluation and the description of the two methods of microwave data analysis – the time domain and frequency domain. In the second part, the dependences between red brick moisture and apparent permittivity are presented. Apparent permittivity values are determined by microwave antenna and calculated in time and frequency domain. With the calculated values, regression models were estimated and quality of both evaluated. Using the analyzed data, the advantages and disadvantages of both techniques were defined and the measuring potential evaluated.


Introduction
Microwave technique of moisture detection enables non-invasive estimation of the masonries moisture.It is an indirect technique that measures parameters different from moisture but dependent on it.Among these parameters relative permittivity plays significant role.It is a measure of the matter particles behaviour in external alternating electric field and differs depending on material chemical compound and molecule charge distribution [1].That's why apparent permittivity of water equals 80, which is the consequence of the asymmetric charge distribution of the water molecule.On the other hand apparent permittivity of air equals 1 and solid phase between 1 and 15 depending on material chemical composition [2].
Application of microwave measurement techniques allows obtaining non-invasive and noncontact solution for evaluation of complex permittivity of a building material, which may be in the form of a sample (e.g. a brick) or for full masonry wall.The especially convenient solution is the measurement of microwave reflection coefficient with the use of one antenna, usually wideband, and an one-port vector network analyser (VNA).Then the measurement may be performed from a distance (without contact) and with access to only one side of a material.
Apparent permittivity can be evaluated by microwave measurements using two types of signal analysis methods: time domain (TD) and frequency domain (FD) [3].
Evaluation of the apparent permittivity value using time domain analysis method focusses on the measurement of the time of microwave propagation across the investigated material sample or building barrier.The readouts are based on searching for the reflections on the sample discontinuities which could be the front surface, back surface or internal disturbances such as joints or other materials in the wall.The time intervals between the particular reflections can be measured and recalculated into the relative permittivity value using to the equation [4]: where c -light velocity in vacuum [m/s], tp -time of signal propagation along the sensor [s], Ldistance between the TDR sensor markers [m].
The second approach to define the apparent permittivity is to use frequency domain signal in the form of complex reflection coefficient values measured for a range of frequencies.The reflection coefficient is determined from ratio of received reflected signal complex amplitude to emitted signal complex amplitude.It has direct relation to material complex impedance.
The aim of the article is to present the potential of applying the microwave technique to evaluate building materials moisture using two types of signal: time domain and frequency domain.Together with the presented results, the advantages and disadvantages of both types of signals will be presented together with the analysis of the microwave technique measuring uncertainty evaluated as residual standard error (RSE) and root mean square error (RMSE).

Materials
Samples for the research were made of red ceramic brick.A set of samples was delivered from one producer to minimize the influence of production technology on the readouts.Average bulk density of the samples was 1790±10 kg/m 3 and maximum water absorptivity equal 25 vol.%.The samples were dried and moistened to several intermediate values between 0 vol.% and 25.2 vol.%.

Methods
Measurements were conducted in the area surrounded with microwave absorbing materials to provide a reflection-free environment.The measuring setup consisted of two major elements: VNA analyzer model Agilent N5224A and a double ridge pyramidal horn antenna.During measurement the antenna was set 8 cm in front of the brick surface.Figure 1 presents measurement setup during investigations.The measurements were conducted in constant temperature equal 20 ±1° C and air humidity equal 50 ±5%.All samples were investigated by VNA analyzer and microwave antenna.VNA analyzer has been calibrated for measurements of reflection coefficient S11.The frequency range was set between 1 GHz and 11 GHz.The results were achieved as the complex S11 values (magnitude and angle).Those data was utilized for frequency analysis.In parallel, the S11 values were automatically converted by the VNA analyser into time domain to visualize a broadband signal as a short pulse, further reflected from material discontinuities along the direction of wave propagation.
The complex values of reflection coefficient measured at frequency points within the specified range carries information about intrinsic impedance of measured material.This allows to evaluate frequency dependance of the material impedance.The measured values are referred to VNA input port i.e. contains the influence of antenna parameters and free-space propagation at the distance from antenna to material.Proper calibration allows excluding these effects.The corrected values of reflection coefficient converted to impedance of the material allow calculating the material relative permittivity.
Time domain analysis is based on signal reflections detection and evaluation of time between the discontinuities.The first reflection peak comes from the impedance difference between the air and the surface of the brick.The second peak utilized in measurement comes from the reflection of the signal returning from the brick surface on the opposite side.The distance between those two peaks measured in time gives information about material relative permittivity according to the formula (1) and thus moisture.
Microwave readouts transformed into relative permittivity values both in frequency and time domain were then compared to the volumetric water content values measured in laboratory by gravimetric method and the calibration formulas were established together with the valuation of fit quality and standard uncertainty of both sensors expressed as relative standard error RSE and root mean squared error RMSE [5][6][7][8].

Results and discussion
In figure 2 there are presented readouts of apparent permittivity achieved by microwave signal time domain (a) and frequency (b) analysis.The results are compared with gravimetric water evaluation and second order polynomial regression models have been evaluated.Data presented in figure 2 prove the dependence between microwave readouts and gravimetric measurement.It is visible that in case of Time Domain analysis the dependence is more linear and the 95% confidence intervals (shaded areas) are wider compared to the Frequency Domain analysis.With the data achieved regression formulas have been evaluated and presented in table 1 Both models are polynomial.It must be emphasised that for Time Domain the dependence is more linear which is confirmed by the value of the first estimator close to zero.In the case of FD analysis, the relationship is clearly polynomial and the values of the estimators for all independent variables are different from zero.Both techniques of signal analysis describe the examined dependence in good quality what is confirmed by high values of R 2 which are close to 1. Better value is achieved for FD technique (0.959), but the difference between R 2 for FD is not significant (0.931).Together with the polynomial dependences RSE and RMSE were estimated for both data analysis methods.In case of the Time Domain method the RSE value equals 2.28 vol.% and RMSE 2.04 vol.% while for the Frequency Domain analysis those values are 1.76 vol.% and 1.58 respectively.This short comparison confirms that using the Frequency Domain method of microwave antenna data analysis it is possible to achieve better accuracy of measurement comparing to the Time Domain method.Additionally it is worth emphasising that all values of RSE and RMSE achieved within presented evaluation are close to the corresponding data in the world literature on indirect moisture detection techniques.The achieved standard error values are comparable or lower than the values given by the reported sources (4-5 vol.% [9], 1-6.6 vol.% [5] or 0.8-3.7 vol.% [6]), but most of the reported studies were performed using other techniques (mainly TDR), which utilise invasive probes that can be inserted into the test medium and which can provide better readings accuracy.
Figure 3 represents the dependences between the relative permittivity readouts and volumetric water content values estimated using both techniques of microwave data interpretation.Black dots visible in figure 3a represent the relative permittivity readouts in the same samples, that have the same value of moisture.Blue line is the linear fit of the measurement results obtained with both sensing methods.Slope estimator value is greater than 0.9 which means that there is a clear linear dependence between data achieved using both techniques.Only one of the FD readouts is showing a decreased value of the relative permittivity.Similar observations can be noted for moisture values (figure 3b) estimated using both techniques of data analysis.It only must be noticed that FD technique is slightly overestimating moisture comparing to the TD method, because y-intercept value is higher from zero.

Conclusions
According to the analysis of data achieved for two techniques of microwave signal interpretation to evaluate red brick relative permittivity, the following conclusions may be formulated: • Both techniques of signal analysis provide satisfactory quality of moisture evaluation of porous materials.

•
Polynomial regression models achieved within the research give satisfactory description of the measured dependencies, which is confirmed by values of the of coefficients of determination R 2 between 0.93-0.96.

•
The quality of microwave antenna signal interpretation is slightly better for Frequency Domain analysis compared to the Time Domain.This observation is confirmed by more favourable values of R 2 coefficients and RSE and RMSE standard errors.

Figure 1 .
Figure 1.Measurement setup used in experiment

Figure 2 .
Figure 2. Relation between volumetric water content and relative permittivity estimated using (a) Time Domain analysis method, (b) Frequency Domain method

Figure 3 .
Figure 3. Dependences between signal interpretation using TD and FD method; (a) evaluation of relative permittivity, (b) evaluation of volumetric water content

Table 1 .
. Regression models showing dependences between material moisture and relative permittivity achieved using TD and FD analysis method