Research into the possibility of applying the electric impedance spectrometry (EIS) method and the dielectric capacitance method (DECM) simultaneously above fibre saturation point (FSP) and in harsh kiln conditions has been relatively scarce. In the framework of this research, tests were carried out on the operational reliability of the measuring capacitor (MEC) prototype used for calibrating the DECM in the harsh internal climate (50°C and 98% RH) of the kiln. Condensation of water vapor on MEC plates, leakage of MEC insulators and the emergence of static electric charges on MEC plates were studied. Quantitative ranges were found for MEC performance-disrupting effects on the parasitic capacities induced by each effect. The DECM was found to be less reliable than the EIS method for application in harsh kiln conditions. Secondly, under the same test conditions and for the same wood species (birch), the possibilities of the DECM method and the EIS method were comparatively modeled with the predetermined Rozema quality criterion of ±1.75% MC for predicting the moisture content (MC) of birch wood above FSP. It was found that, under the same test conditions, the DECM method proved more accurate than the EIS method for predicting birch wood MC above FSP. Based on the tests, it was concluded that DECM can be used in practice by applying a non-destructive method to reliably determine the average moisture content of a wood batch immediately prior to commencing the wood-drying process.

#### Key words

- dielectric capacitance method
- electric impedance spectroscopy
- wood drying

In drying wood, it is necessary to monitor the moisture content of the wood in order to control the drying process. It is particularly important to reliably determine the average moisture content (MC) of freshly sawn wood prior to commencing the wood-drying process in order to use a simulation program to assess the drying time, energy consumption, risk of cracks developing during the drying process and other changes in wood quality (Salin, 1990; Tamme, 2016).

In practice, the direct current (DC) electric resistance method (Stamm, 1927; Tamme

Where _{0}

A flat ring capacitor for measuring wood MC below FSP (e.g., Brookhuis, (2020), FMW moisture indicator, 3.5 MHz operating frequency measured with an oscilloscope) and a flat slit capacitor (9.375 GHz operating frequency) for measuring wood MC both below FSP and above FSP have also been used (Johansson

The objective of our research was to test the MEC prototype developed for the paper in harsh conditions similar to those of a kiln in order to assess risks to the reliability of the MEC. The second objective was to use regression analysis to identify the possibilities of the DECM and EIS methods to establish the predetermined accuracy and to make a reliable determination of wood MC above FSP within the EIS operating frequency range of 1 Mz–10 Hz.

The relationship between electric capacitance, the wood impedance modulus and average moisture content above and below FSP (FSP is agreed at 30% wood moisture content) was explored using a clear birch board with a thickness of 35 mm, width of 150 mm and length of 470 mm.

The moisture content of the birch wood specimen was varied by means of a specially developed laboratory drying schedule (Tamme

The average MC of wood was determined by weighing the specimen at various randomly selected times using a precision weight with a resolution of 0.1 g. After weighing the specimen at the same average MC, other necessary measurements were also carried out as quickly as possible, such as measurements of the wood electric capacitance and wood impedance. In the final stage of the tests, the dry weight of the specimen was determined by drying it at 103°C. The actual moisture content of the specimen (relative to its dry weight) at the moment of weighing was identified according to ISO 3130:1975 (1975) standard.

An improved version of the parallel plate MEC was developed to determine the electric capacitance of wood at different moisture levels above FSP, compared to that used in our previous paper (Tamme

The cubic measure between the MEC plates was chosen at about 10% larger than the cubic measure of the specimen. This difference between the cubic measures ensured the necessary slack (tolerance zone) for the specimen when it was replaced between the plates after each weighing. The MEC allowed for the possibility of separate and combined heating of the insulators and plates in the form of a film of water vapor in the climate chamber to study condensation on MEC structural elements and to remove static electric charges of triboelectric origin (Tamme

According to literature (Moschler, 2004), the microwave measuring capacitor prototype with parallel plates was tested at room temperature and at temperatures of 40°C and 60°C. Moschler (2004) contains no data on the relative humidity in the chamber during the tests, which is an important climate parameter. The measurements of electric capacitance presented in this paper were carried out using the LCR55 (Wavetek Meterman, 2021) capacitance meter (CAM). The LCR55 capacitance meter has an operating frequency of 1,000 Hz as measured with an oscilloscope.

Wood impedance was measured using stainless steel insulated pin electrodes made by the company Gann (Gann 2021), which were nailed into the wood across the grain at a spacing of 30 mm (Brookhuis Micro-Electronics, 2009). The nails were driven to a depth of 1/3 of the thickness of the wooden material (Welling, 2010), which is about 12 mm from the board surface for a 35 mm board thickness. After each impedance measurement, the electrodes were nailed into the next randomly selected location on the board and at the same depth from the surface of the board. The impedance modulus of the measured AC complex electric resistance was calculated on the basis of impedance spectrometry (EIS) measurement data using EIS standard formulas (Krause, 2003; Tamme

Interference with the reliability of the measuring capacitor in conditions similar to harsh kiln climate (that is, imitated in a laboratory climate chamber) was also recorded using impedance spectra and processed with the NOVA 1.8 software using the circle-fit analysis tool. To do so, frequency scanning between 1 MHz and 10 Hz and the electric sine wave amplitude of 50 mV were applied.

The possible effect of static electricity on the measurements taken by the measuring capacitor was first investigated indirectly using Keithley’s model 6517B with an electrometer (Keithley, 2004) and then directly for potentials safe for the instrument (up to 0.9 V) using LCR55 (Tamme

Statistical processing of the test results was based on the principles of a metrology standard ISO 3534-1:1993 (1993) and carried out with software R (R Core Team, 2010), MS Excel and NOVA 1.8. In the case of Student t-distribution and linear regression for the single measurement, the upper and lower tolerance lines (confidence limits) of the regression line are presented in MS Excel at 95% confidence level as follows (Kiviste, 1999):

Where _{b0} and _{b1} are the standard errors of the regression line intercept and slope (Kiviste, 1999).

The following formulas were used to estimate the standard error (SE) and the average root-mean-square error (RMSE) of the regression model:

Where _{i}

The non-parametric Kolmogorov-Smirnov test and the Shapiro-Wilk test (Tamme

Changes in electric parameters caused by water vapor condensation were measured using the LCR55 and the EIS method.

The parasitic capacitance of condensation observed on MEC plates (indicated as C_{parasite} in Table 1) and the useful capacitance are shown on the same axis in Figure 2, depending on the average moisture content of wood. The EIS method allowed the development dynamics of the condensation process to be monitored (Figure 4, a) and b)) and the quantitative parameters for the electric capacitance C_{parasite} to be calculated.

The main physical reliability characteristics of the dielectric capacitance method (DECM) in kiln climate and the corresponding capacitance meter (CAM) response.

Effect, parameter, figure no. | Effect range | CAM response |

Condensation of water vapor on MEC plates, Fig. 2, 3 | C_{parasite} = 340 to 845 pF_{parasite} = 681 pF, determined using EIS method |
CAM reading recorded ca. 5× and moderately increasing** |

Leakage of MEC insulators, Fig. 4 | C_{parasite} = 163 to 681 p^{F}_{parallel} = 61 to 0.778 kOhm |
Floating of CAM reading |

Triboelectric charges on MEC plates, Fig. 5 | U_{static} = -10.5 to 4.29 V |
Floating of CAM reading, CAM spoilage risk |

Useful MEC capacitance,* below FSP (0.% to 30%) |
C_{useful} = 121 to 205 pF_{useful} = 205 to 231 pF |
CAM reading stable and reliable |

Useful MEC capacitance depends on the moisture content of wood and the thickness of the wood material according to the MEC, formula 1. Wood moisture content is related to the dielectric constant ε in formula 1.

“Moderately increasing” means that it is possible to manually retrieve a CAM numerical reading, but it slowly increases as the water vapor condensation progresses (see Figure 3).

Figure 3 shows the relative time increments of the parasitic capacitance of condensation on the MEC plates at different wood average moisture levels recorded using the capacitance meter (CAM) LCR55. Both the EIS method and the LCR55 show a similar magnitude for the parasitic capacitance on the MEC plates (C_{parasite} = 660 pF and C_{parasite} = 800 pF, respectively). Based on Figure 3, it may be concluded that the higher the average MC of wood, the greater the value of parasitic capacitance due to water vapor condensation. Parasitic capacitance of approximately 5 times the useful capacitance may completely obscure the correct useful capacitance measurements under conditions favourable for water vapor condensation.

The leakage effect of the insulators is characterized by the occurrence of parallel resistance of the condensed water film on the insulators in addition to parasitic capacitance, which shunts the resistance of the insulators. The MEC insulator resistance in normal operation is approximately 10 giga-ohms or greater. The circle-fit analysis found that in the initial phase of leakage, the parallel resistance of a leaking insulator is

Figure 5 shows the dynamics of electrostatic charge formation when placing the birch wood specimen between and removing it from the MEC plates. This procedure was repeated 15 times. A measurement interval of 0.1 seconds was used. In Figure 5, one maximum of impulse voltage generated by static charge corresponds to each cycle of placement and removal of the specimen between the MEC plates. Maximum values (or peaks) with negative potential were predominantly recorded. Because the potential was measured from the electrostatic charge removal system (see Figure 1), the wood itself was oppositely charged; that is, predominantly positive. The potential of electrostatic charges generally decreases when the movement of the specimen in relation to the MEC ceases. However, this is not always the case, as Figure 5 shows an exceptional peak where the potential remains high (ca. 10 V) for a considerable time (ca. 30 seconds). The triboelectric potential peak may exceed the CAM LCR55 safe input voltage (up to 0.9V) by about 10 times.

In previous research (Moschler, 2004), the electric capacitance of the measured wood was found to increase slightly with the increase in wood temperature. The same tendency was confirmed in our previous paper (Tamme

In addition, an important trend that emerged during testing must be pointed out: namely, condensation effects that obscure the useful capacitance of MEC predominate when the air RH in the climate chamber is higher than 60%, but electrostatic charges occur often on the MEC when the air RH in the climate chamber is lower than 60%.

To summarize, the various physical characteristics and effects influencing the electric capacitance of the MEC are presented in Table 1. Based on the data in the bottom row of Table 1 (useful capacitance), it can be concluded that the DECM in the range below FSP (0–30% MC) is about 8 times more sensitive per percent of MC compared to the range above FSP (30%–105% MC).

Useful capacitance is defined as the measured capacitance of MEC with wood, which excludes interfering effects, such as condensation on MEC plates, leakage of MEC insulators and the presence of static charges on MEC plates. Our previous paper (Tamme

For useful capacitance only, it would be reasonable to establish a statistically reliable correlation (generally a linear regression model) between the actual (i.e., determined by weighing) average moisture content of wood and the moisture content predicted by the capacitance method or, in other words, to statistically model the capacitance method. The methodology for modelling the EIS method does not differ from modelling the capacitance method.

Comparatively, the results of modelling the capacitance method and the EIS method are presented in Table 2 and Figures 6, 7, 8, 9, 10, 11.

Modelling results of the dielectric capacitance method (DECM) and electric impedance spectrometry (EIS) method. In regression models, the independent _{upper} and _{lower}, are calculated using formulas 2, 3, 4 and 5. The SE is calculated according to formula 6. The tolerance interval (TI) is calculated using the formula TI = _{upper} - _{lower}.

Method type, Fig. no. | Equations for predicting single measurement tolerance bands and TI | R^{2} |
p-value and tests* | SE | |
---|---|---|---|---|---|

DECM (above FSP), Fig. 6 | _{upper} = 1.0131x + 5.9063_{lower} = 0.9406x +0.8399 |
0.97 | <0.01 |
4.88 | |

DECM (below FSP), Fig. 7 | _{upper} = 1.0135x + 0.2792_{lower} = 0.9788x – 0.1954 |
0.99 | <0.01 |
0.61 | |

DECM (above FSP) (multiple), Fig. 8 | _{upper} = 1.006x + 0.44_{lower} = 0.9929x – 0.4163 |
0.99 | <0.01 |
0.46 | |

EIS (above FSP), Fig. 9 | _{upper} = 0.9448x + 11.196_{lower} = 0.787x + 2.41 |
0.87 | <0.01 |
5.01 | |

EIS (above FSP) (multiple), Fig. 10 | _{upper} = 1.0134x +1.728_{lower} = 0.968x – 0.84 |
0.99 | <0.01 |
0.867 |

Kolmogorov-Smirnov (K-S) test and Shapiro-Wilk normality (S-W) test

Formulas in Table 2 and Figure 11, which connect various methods, are presented according to the needs of the wood drying practice. The model RMSE or SE, the p-value and the coefficient of determination ^{2}

In Moschler’s paper (2004) it was found that the actual MC point of 28.60% of the high frequency capacitance method (4.5 to 6.0 GHz) is estimated to have a predicted expanded uncertainty of ±3.62%; thus, the corresponding tolerance interval for this point is 7.24% MC. In comparison, a tolerance interval of 7.26% MC calculated for the same actual MC point of 28.60% was found in this study for the low-frequency capacitance method (see Table 2, second row), using the relevant formulas. Therefore, the consistency of repeated (reproduced) measurements in different laboratories and under different test conditions is surprisingly good. In another paper (Johansson

In our research, comparable experiments for the dielectric capacitance and EIS method were conducted under the same test conditions and for the same tree species (birch). In addition, 16 arithmetic averages in a single series of measurements were modelled in the MC range above FSP. The compared results are presented in Figures 6, 7, 8, 9 and 10 and in Table 2. Figure 11 shows that there is a tendency for the tolerance interval (TI) of a single measurement to increase in proportion to the increase of the actual MC, though the increment is different for each model. The results of the modelling summarized in Figure 11 also show that in the actual MC range (30–150%), the Rozema quality criterion cannot be met either by a single measurement performed with the capacitance method or by a single measurement performed with the EIS method. Using a series of 16 measurements, only the capacitance method can meet the Rozema quality criterion in the actual MC range above FSP (30–150%), whereas the EIS method fails to do so. However, according to Table 2 (row 5), the SE of the EIS method is lower than the Rozema quality criterion (SE = 0.867). Consequently, by increasing the number of measurements (

The reliability of the regression models in Table 2 was verified by the Kolmogorov-Smirnov and Shapiro-Wilk non-parametric test of regression residuals in the program R environment, in accordance with the methodology used in a previous paper (Tamme

The DECM was found to be less reliable than the EIS method for use in harsh kiln climate. The dielectric capacitance method will require more development in the future so that it can be reliably (i.e., without the risk of parasitic capacitance and static charges) used in harsh kiln conditions. However, testing of the DECM and the EIS method under the same test conditions and comparing the modelled test results according to the Rozema quality criterion showed that the dielectric capacitance method exhibits higher accuracy in the MC range above FSP. The DECM of low sensitivity to temperature may prove promising in practice, if the purpose is to quickly and reliably determine prior to the start of the drying process the average moisture content of a wood batch for the wood drying simulation program using a non-destructive method.

#### The main physical reliability characteristics of the dielectric capacitance method (DECM) in kiln climate and the corresponding capacitance meter (CAM) response.

Effect, parameter, figure no. | Effect range | CAM response |

Condensation of water vapor on MEC plates, |
C_{parasite} = 340 to 845 pF_{parasite} = 681 pF, determined using EIS method |
CAM reading recorded ca. 5× and moderately increasing |

Leakage of MEC insulators, |
C_{parasite} = 163 to 681 p^{F}_{parallel} = 61 to 0.778 kOhm |
Floating of CAM reading |

Triboelectric charges on MEC plates, |
U_{static} = -10.5 to 4.29 V |
Floating of CAM reading, CAM spoilage risk |

Useful MEC capacitance, |
C_{useful} = 121 to 205 pF_{useful} = 205 to 231 pF |
CAM reading stable and reliable |

#### Modelling results of the dielectric capacitance method (DECM) and electric impedance spectrometry (EIS) method. In regression models, the independent x-variable is the actual MC (%), and the dependent y-variable is the predicted MC (%). The predicted single measurement tolerance bands on the 95% confidence level, yupper and ylower, are calculated using formulas 2, 3, 4 and 5. The SE is calculated according to formula 6. The tolerance interval (TI) is calculated using the formula TI = yupper - ylower. N is the number of measurements repeated under the same test conditions and k is the number of measurements averaged per series of measurements (i.e., the averaging period). For models with a series of measurements (k), the identification type shall be “multiple”.

Method type, Fig. no. | Equations for predicting single measurement tolerance bands and TI | R^{2} |
p-value and tests |
SE | |
---|---|---|---|---|---|

DECM (above FSP), |
_{upper} = 1.0131x + 5.9063_{lower} = 0.9406x +0.8399 |
0.97 | <0.01 |
4.88 | |

DECM (below FSP), |
_{upper} = 1.0135x + 0.2792_{lower} = 0.9788x – 0.1954 |
0.99 | <0.01 |
0.61 | |

DECM (above FSP) (multiple), |
_{upper} = 1.006x + 0.44_{lower} = 0.9929x – 0.4163 |
0.99 | <0.01 |
0.46 | |

EIS (above FSP), |
_{upper} = 0.9448x + 11.196_{lower} = 0.787x + 2.41 |
0.87 | <0.01 |
5.01 | |

EIS (above FSP) (multiple), |
_{upper} = 1.0134x +1.728_{lower} = 0.968x – 0.84 |
0.99 | <0.01 |
0.867 |

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