CN112798622B - Device and method for detecting moisture content of wood based on microwave transmission principle - Google Patents
Device and method for detecting moisture content of wood based on microwave transmission principle Download PDFInfo
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Abstract
The invention discloses a device and a method for detecting the moisture content of wood based on a microwave transmission principle, which are applied to the field of nondestructive detection and aim at solving the problem that the moisture content of wood is too low in detection precision in the prior art; according to the method, the amplitude and the phase of the microwave transmission coefficient are adopted to jointly represent the moisture content of the wood, and the amplitude and the phase of the microwave transmission coefficient and the moisture content of the wood are expressed as linear equations; determining the coefficients to be determined of two parameters of the amplitude of the microwave transmission coefficient of the linear equation by adopting the minimum sum of errors; by adopting the device and the detection method, the detection precision of the moisture content of the wood is effectively improved.
Description
Technical Field
The invention belongs to the field of nondestructive testing, and particularly relates to a wood water content testing technology.
Background
The wood industry is the basic industry of industrial economy in China, is the only green material which can be regenerated and recycled in four raw materials (steel, cement, wood and plastic) in the world at present, and plays an extremely important role in the development of industrial economy. The development of industries such as building, traffic, light industry, paper making and the like is inseparable from the wood industry. Along with the development of modern industry and scientific technology, the use of wood is more and more extensive, and simultaneously, the social requirement on the quality of wood and wood products is higher and higher. Facing the environmental protection and ecological problems caused by the gradual reduction of forest resources in the world, how to effectively utilize wood resources, reduce energy consumption and improve the processing quality of wood and wood products has attracted the wide attention of governments of various countries. The drying of the wood is an important link for guaranteeing and improving the quality of the wood, reducing the loss of the wood and improving the utilization rate of the wood. The method is one of important indexes in the wood drying process when the moisture content of the wood is higher, and the moisture content value of the wood reaches the drying process requirement, so that the final aim of wood drying is fulfilled, the wood drying quality is improved, the drying period is shortened, and considerable economic benefits are brought to wood drying enterprises. Therefore, it is essential to develop the whole wood industry to grasp the moisture content of the wood products.
The existing detection method for detecting the water content of the wood is divided into a direct method and an indirect method:
1. direct method for measuring water content
In general, standard calculations of water content of a substance generally apply the direct method, i.e. by dry or chemical methods. The formula of the water content is as follows:
in the formula M1The weight of the tested sample before drying; m2Is the weight of the sample to be measured after drying.
(1) Drying method
The method is to heat the tested substance by using an electric oven to evaporate the water in the substance so as to detect the water. The moisture content of the sample to be measured is detected by calculating the change of the weight of the sample before and after heating. Because of its high accuracy, it is generally used as a standard for detecting the moisture content. But drying is time consuming and not possible on-line.
(2) Distillation process
The method is to mix the distillate with the powder of the sample and put the mixture into a distillation flask. The distillate is insoluble in water and the boiling point becomes lower after mixing, and the water in the mixture distills out after heating. The method has the disadvantages of less measurable samples and high reagent cost.
2. Indirect method for measuring water content
(1) Resistance method
In general, the dried material has a large resistance and the water has a relatively small resistance, so that the conductivity of the material will be changed when the water content of the material changes. The water content is characterized by measuring the resistance. The disadvantage of this method is that it cannot measure high water content and dielectrics.
(2) Infrared method
The theoretical basis for this measurement method is beer's law. The principle is as follows: when the moisture is subjected to infrared radiation with a wavelength of 1.64pm or 1.94pm, the moisture has a strong absorption band, and the moisture content of the sample to be measured is measured by measuring the light intensity of the infrared ray passing through the sample to be measured. The method has the disadvantages of complicated structure of the measuring equipment, high price and difficult large-scale industrial application.
(3) Ray method
The principle of this method is that different wavelengths of near infrared light are absorbed by different molecules with different characteristics. The intensity of diffuse reflection is related to the composition of the substance to be measured. The method is simple to operate and rapid in measurement, but the method can only measure the water content of the surface.
(4) Capacitance method
The relative dielectric constant of the substance to be measured is between that of the absolutely dry substance and water when the substance is hydrated. When the distance between the plate area of the capacitor and the trigger is ensured to be unchanged, the relative dielectric constant of the tested sample can be calculated by measuring the changed capacitance value, and then the water content of the tested sample is obtained. The method has the disadvantages that factors influencing the detection result are more, and the electrode is extremely easy to corrode.
(5) Microwave method
The microwave measuring method is a non-contact measuring method, because of the strong penetrating power of the microwave, the microwave measuring method can not only detect the moisture on the surface of the wood, but also detect the moisture content in the wood, meanwhile, the microwave has wide frequency band, and different frequencies can be selected for measurement according to the characteristics of the measured object. And has the obvious advantages of high speed, short time, high efficiency and the like.
The principle of detecting the moisture content of the wood by a microwave method is that the dielectric constant of water is far greater than that of a common material in a microwave frequency range. Therefore, when the microwave penetrates through the material with the water content, the microwave energy loss caused by the water content is far larger than that caused by other dry materials, the dielectric constant of the material is obviously influenced by the water content in the material, and the water content of the wood can be calculated by measuring the attenuation of the microwave energy. In the scanning process, the microwave vertically enters the surface of the tested test, if the water content of the tested test piece is greater than that of an absolutely dry test piece, basic parameters of the transmitted wave, such as amplitude and phase, can be changed obviously, and therefore quantitative detection of the water content of the wood is achieved.
Zhang Gui and Guo Xin propose a method for rapidly detecting the water content of wood (Chinese patent: CN 104390880A). In the patent, the absorbance of a wood sample at a wavelength of 3100nm is collected, and an equation is obtained by using least square linear regression of the absorbance and the water content of the wood sample.
The method mainly has the following problems:
1) the method can only measure the surface water content of the test piece;
2) the method cannot realize large-scale online detection;
3) the detection precision of the method is 5 percent and needs to be improved;
a method for detecting the moisture content of wood based on radar waves is proposed by Gao Lin and civil engineering and the like (Chinese patent: CN 103808624A). The method comprises the steps of transmitting radar waves with the frequency of 900MHz to wood with known thickness by using a radar antenna, collecting the transmitted waves, calculating the travel time of the radar waves in the wood by using a data manager, calculating the relative dielectric constant of the wood, and obtaining the water content of the wood by using a relation model of the relative dielectric constant and the water content of the wood.
The method mainly has the following problems:
1) the whole structure is complex, and large-scale commercial application is difficult;
2) the relation between the dielectric constant and the water content of the wood is a nonlinear relation, and the detection precision of the water content of the wood is inverted by a relation model of the relative dielectric constant and the water content of the wood to be improved;
a grain moisture content detection device and a grain moisture content detection method based on a microwave technology are proposed by Zhangtao and Li Chengxiao and the like (Chinese patent: CN 102721709A). The method utilizes a microwave mixing microwave technology, simultaneously detects the amplitude and phase changes of microwave transmitted waves and reflected waves, and combines an internal algorithm of a single chip microcomputer to realize the detection of the moisture content of the grains.
The method mainly has the following problems:
1) the detection precision of the method needs to be improved;
2) the method is susceptible to grain density;
disclosure of Invention
In order to solve the technical problems, the invention provides a device and a method for detecting the moisture content of wood based on a microwave transmission principle, which are used for quantitatively detecting the moisture content of the wood according to a transmission coefficient phase and an amplitude value.
The technical scheme adopted by the invention is as follows: a wood moisture content detection device based on a microwave transmission principle comprises: the device comprises a vector network analyzer, a tested sample, a mobile platform, a transmitting antenna, a receiving antenna, a signal acquisition and processing module and a moisture content quantitative detection module; the vector network analyzer is connected with the transmitting antenna and used for generating microwave signals in a certain frequency range; the transmitting antenna receives the microwave signal generated by the vector network analyzer and transmits the microwave signal to the receiving antenna;
the tested sample is arranged between the transmitting antenna and the receiving antenna; the mobile platform is respectively connected with the transmitting antenna and the receiving antenna and is used for adjusting the distance between the transmitting antenna and the receiving antenna and the measured sample;
the receiving antenna receives the signal attenuated by the tested sample and transmits the received signal to the signal acquisition and processing module; the signal acquisition and processing module acquires amplitude and phase information of the transmission coefficient according to the received signal, calculates the optimal detection distance and then calculates the optimal detection frequency according to the optimal detection distance; the water content quantitative detection module establishes a mapping relation between the amplitude and the phase of the transmission coefficient and the water content of the wood according to the amplitude and the phase information of the transmission coefficient obtained by the signal acquisition and processing module, and obtains the water content of the wood through inversion of the mapping relation.
The adjustment accuracy of the moving module is 0.1 mm.
The invention also provides a method for detecting the moisture content of the wood based on the microwave transmission principle, which comprises the following steps:
s1, placing the wood sample to be tested in a constant temperature and humidity box;
s2, measuring the amplitude and phase information of the transmission coefficient corresponding to the wood sample with the water content under the optimal lift-off distance and the optimal detection frequency;
s3, calculating the moisture content of the wood to be measured according to the following formula:
wherein, W0Indicates the water content of the wood to be measured, A0Amplitude information, k, representing the transmission coefficient corresponding to the wood sample to be tested1Is represented by A0The coefficient of (a) is determined,
phase information, k, representing the transmission coefficient corresponding to the wood sample to be tested2To represent
The coefficient of (a); coefficient k1、k2And determining by using the error least square sum.
Step S2 specifically includes:
s21, obtaining a plurality of same timbers to be tested, and preparing timber samples under different relative humidities by changing the humidity of the constant temperature and humidity chamber;
s22, measuring the moisture content of the wood sample at each relative humidity after being processed in the step S31 by using a traditional drying method;
s23, obtaining a first optimal lift-off distance corresponding to a first frequency step length by fitting the relationship between the distance between the antenna and the wood sample under each relative humidity and the amplitude of the transmission coefficient;
s24, on the basis of the first optimal lift-off distance and the corresponding first frequency step length, obtaining a first optimal detection frequency by fitting the relation between the amplitude of the transmission coefficient and the water content of the wood sample under the relative humidity;
s25, obtaining a second optimal lift-off distance corresponding to a second frequency step length by fitting the relation between the distance between the antenna and the wood sample under the relative humidity and the phase of the transmission coefficient;
s26, on the basis of the second optimal lift-off distance and the corresponding second frequency step length, obtaining a second optimal detection frequency by fitting the relation between the phase of the transmission coefficient and the water content of the wood sample under the relative humidity;
s27, measuring the amplitude information of the transmission coefficient corresponding to the wood sample to be detected under the condition based on the first optimal lift-off distance and the first optimal detection frequency;
and S28, measuring the phase information of the transmission coefficient corresponding to the wood sample to be detected under the conditions of the second optimal lifting distance and the second optimal detection frequency.
Coefficient k1、k2The specific solving process is as follows:
establishing the following formula according to the transmission coefficient amplitude and the phase information corresponding to the wood samples under different relative humidities, and obtaining a coefficient k by solving the formula1、k2The value of (A) is as follows:
wherein N represents the total number of wood samples prepared in step A1 at different relative humidities, AiAmplitude information indicating the transmission coefficient corresponding to the wood sample at the i-th relative humidity,
phase information indicating the transmission coefficient corresponding to the wood sample at the i-th relative humidity.
The invention has the beneficial effects that: the method detects the moisture content of the wood by using a double-parameter method, namely, the moisture content of the wood is represented by using an amplitude value and a phase together; determining undetermined coefficients of the empirical formula of the two-parameter method by using the error least squares sum (the error least squares sum is a professional term for data processing); compared with the prior art, the method can accurately obtain the moisture content of the wood, the provided detection method is high in detection efficiency and detection precision, and the adopted detection device is simple in structure and low in cost.
Drawings
FIG. 1 is a flow chart of a detection method of the high-precision wood moisture content detection method of the present invention;
FIG. 2 is a detecting device of the high-precision method for detecting the moisture content of wood according to the present invention.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
The traditional method for detecting the moisture content of the wood based on the microwave method generally only considers one parameter, such as microwave power, microwave emission coefficient or transmission coefficient amplitude and the like, and converts a microwave signal of a single parameter into a voltage signal so as to measure the moisture content of the wood. The problem with single parameter measurements is that the accuracy needs to be improved. If the water content of the wood is measured by adopting the combined quantity phase shift and the amplitude value, the measurement accuracy of the measurement system is high.
Through research literature and simulation research, the amplitude A of the transmission coefficient S21 is in a linear relation and phase with the water content W of the wood
And the water content of the wood is also in a linear relation with the water content W of the wood. From amplitude A and phase
The empirical equation for determining W is written as a linear equation as shown in equation (2).
k1Is A0Coefficient of (a), k2Is composed of
The coefficient of (a);
and writing the formula (2) into a vector form as shown in the formula (3).
Determination of coefficients of empirical formula
When the moisture content of the wood takes m different values, the true values of the corresponding moisture content are respectively W1、W2、W3...WmRecord WiThe water content is the true value of the water content of the ith wood, namely the water content determined by the formula (1). A. theiThe resulting transmission coefficient magnitude was measured for the ith wood,
the resulting transmission coefficient phase was measured for the ith wood. The coefficients of the empirical formula are determined in such a way that the sum of the squared errors is minimized. The expression for calculating the sum of the squares of the moisture content errors can be expressed as formula (4):
to make the sum of the squared errors H (k)1,k2) At minimum, the target expression may have a partial derivative of 0 for each coefficient, that is, the equation set shown in equation (5) should be satisfied.
The formula (6) can be obtained by bringing the formula (4) into the formula (5).
Equation (6) can be regarded as the unknown coefficient k with respect to empirical formula1And k2Solving the linear equation to obtain k1、k2。
The invention discloses a wood moisture content detection device based on a microwave transmission principle, which comprises a vector network analyzer, an antenna sensor, a signal acquisition module and a display module; the vector network analyzer generates a microwave signal, the microwave signal acts on a tested sample through the transmitting antenna, partial energy is absorbed by the tested sample, and signal energy is attenuated. The microwave signal after the energy attenuation passes through a receiving antenna, is collected by a data acquisition card, and the waveform of the microwave signal is displayed on an upper computer.
As shown in FIG. 1, the high-precision water content measuring method of the invention comprises the following steps:
the first step is as follows: placing a wood sample to be tested in a constant temperature and humidity box to prepare wood samples under different relative humidity, and preparing at least five samples with different water contents;
the second step is that: determining the respective water content ψ of the wood samples treated in step S1 by using a conventional drying method;
the third step: setting the frequency range of the sweep frequency according to the characteristics of the tested sample and the antenna sensor, wherein the starting frequency is f1The maximum frequency is f2；
The fourth step: determining optimal lift-off and optimal detection frequencies
A) Selecting wood with different water contents for experiment, and measuring the transmission coefficient S under different water contents21Amplitude, phase of;
B) changing the lift-off distance d to be in the range of 0 to the full wavelength of the center frequency, i.e.
And c is the speed of light. Selecting a distance step length of t, t is more than or equal to 2mm and less than or equal to 5mm, determining different step lengths t according to detection precision and requirements, and measuring transmission coefficients S under different lifting distances21Amplitude, phase of;
C) selecting center frequency of sweep range
According to the transmission coefficient S21Amplitude, selecting a frequency step a, based onDetermining a value a with smaller value a, higher precision but longer time, the general value range of a is more than or equal to 0.1GHz and less than or equal to 0.5GHz, and the fitting distance and S are21The relation between the amplitudes, then the optimal lift-off d is determined according to the linearity and the optimal sensitivity of the fitted curven；
D) Selecting center frequency of sweep range
According to the transmission coefficient S21The phase curve of (a) is selected as a frequency step length b, a value b is determined according to detection precision and requirements, the smaller the value b is, the higher the precision is, but the longer the required time is, and the general value range of b is more than or equal to 0.1GHz and less than or equal to 0.5 GHz. Fitting distance and S21The relation between phases, and then the optimal lift-off d is determined according to the linearity and the optimal sensitivity of the fitted curvem；
E) At the optimum lift-off dnNext, selecting a frequency step c, fitting S21Determining the optimal detection frequency f according to the linearity and sensitivity of the fitted curve based on the relationship between the amplitude and the water contentn；
F) At the optimum lift-off dmNext, selecting a frequency step e, and fitting S21Determining the optimal detection frequency f according to the linearity and sensitivity of the fitted curve based on the relationship between the phase and the water contentm；
G) Extracted at the optimum lift-off dnOptimum detection frequency fnExtracting the amplitude information of the lower part to obtain the optimum lift-off dmOptimum detection frequency fmPhase information of (a);
the fifth step: selecting a test piece with unknown water content, and testing the amplitude A under the optimal frequency and the optimal lift-off of the second step0And phase
And a sixth step: calculating W0；
A) Determining k1And k2
Selecting m test pieces with unknown water content at optimal frequencyfnOptimum lift-off dnMeasure the amplitude Aj(j ═ 1, 2, …, m); at the optimum detection frequency fmOptimum lift-off dmLower measure out
A is to bej，
Bringing formula (6) to give formula (7);
solving the linear equation set of the formula (7) to obtain k1、k2；
B) The empirical equation at this time is
The seventh step: inverting the water content of the wood through the amplitude phase;
A) establishing the moisture content psi and W of the woodjThe forward relationship of (c). By the method of the sixth step, W is obtained1、W2...WjEstablishing WjThe relation with the water content psi of the wood is shown in the formula (8)
Wj＝f(ψ) (8)
B) An inverse relation formula (9) is obtained by the formula (8), and the water content is obtained from the inverse relation. Measured at the optimum lift-off dnOptimum detection frequency fnAmplitude of lower, measured at optimum lift-off dmOptimum detection frequency fmThe phase of (d); bringing reverse relation into, solving to obtain inversion water content
ψ＝h(Wj) (9)
In this embodiment, the content of the present invention is further described by taking the experimental wood as larch as an example:
the first step is as follows: placing a larch sample to be detected in a constant temperature and humidity box to prepare samples under different relative humidities;
the second step is that: the water content psi of the wood sample with different relative humidity is measured by using a traditional drying method, and the water content psi is respectively 2.7%, 5.02%, 7.53% and 13.68%;
the third step: the frequency of the sweep frequency of the antenna sensor designed according to the invention is 8GHz-12GHz, and the starting frequency is f18GHz with maximum frequency f2＝12GHz；
The fourth step: determining optimal lift-off and optimal detection frequency
A) The range of the distance d between the antenna and the larch is more than or equal to 0mm and less than or equal to 30mm, the lift-off step length is 5mm, and the amplitude and the phase of the same water content under different lift-off distances are measured
B) Changing the water content of the wood, and measuring amplitude and phase information of different water contents;
C) selecting the center frequency of 10GHz according to the transmission coefficient S21The amplitude curve of (2) is obtained by selecting the frequency step length of 0.25GHz, the fitting distance and the S21The relation between the amplitudes is best according to the linearity of the fitted curve, and the optimal detection distance d is obtained at the momentn＝15mm。
D) Selecting the center frequency of 10GHz according to the transmission coefficient S21The selected frequency step length is 0.25GHz, and the fitting distance and the S are21The relation between the phases, according to the fitted curve, has the best linearity, and the optimal detection distance dm＝15mm。
E) At the optimum lift-off dnUnder 15mm, the frequency step length c is selected to be 0.25GHz, and S is fitted21Determining the optimal detection frequency f according to the optimal linearity of the fitted curve based on the relationship between the amplitude and the water contentn＝8GHz。
F) At the optimum lift-off dmUnder 15mm, the frequency step e is selected to be 0.025GHz, and S is fitted21Determining the optimal detection frequency f according to the linearity and sensitivity of the fitted curve based on the relationship between the phase and the water contentm＝11.195GHz；
G) Extracted at the optimum lift-off dn15mm, optimum detection frequency fnExtracting the amplitude information under 8GHz to obtain the optimum lift-off dm15mm, best testFrequency fm11.195 phase information;
the fifth step: selecting a test piece with unknown water content, and testing the amplitude A under the optimal frequency and the optimal lift-off of the second step0And phase
And a sixth step: calculating W0；
A) Determining k1And k2
Selecting 6 test pieces with unknown water content at optimal frequency fnOptimum lift-off dnMeasure the amplitude Aj(j ═ 1, 2, …, m); at the optimum detection frequency fmOptimum lift-off dmLower measure out
A is to bej，
(iii) bringing into formula (6) to obtain formula (10);
solving the linear equation set of the formula (10) to obtain k1、k2；
B) The empirical equation at this time is
The seventh step: inversion of wood moisture content by amplitude and phase
The final results of the two parameter method are shown in table 1.
TABLE 1 analysis of the results of the double parameter method
According to the table 1, the inversion is carried out by using a double-parameter method, the absolute error of the water content is within 1%, and the detection precision is greatly improved compared with the traditional amplitude detection or phase detection.
The invention discloses a detection device scheme for detecting and amplifying the water content of high-precision wood, which is shown in figure 2.
The main hardware is as follows: vector network analyzer, two-dimensional mobile platform, transmitting antenna, receiving antenna etc.. The vector network analyzer is responsible for generating microwave signals in a certain frequency range; the transmitting antenna receives the microwave signal generated by the vector network analyzer and transmits the microwave signal to the receiving antenna; the receiving antenna is used for receiving the signal attenuated by the tested sample.
The invention has three modules, and each module has the following functions;
the method comprises the following steps: the device specifically comprises a moving module, a signal processing module and a signal processing module, wherein the moving module is used for adjusting the distance between a transmitting antenna, a receiving antenna and a tested sample, and the precision of the moving module is 0.1 mm;
a module II: the method specifically comprises a signal processing module, and the optimal detection frequency is calculated according to the optimal detection distance by firstly calculating the optimal detection distance through amplitude and phase information acquired by an upper computer.
Module III: specifically comprises a water content quantitative detection module, an establishment module and a transmission coefficient S21And (4) obtaining the water content of the wood through inversion of the mapping relation of the amplitude, the phase and the water content of the wood.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (2)
1. A method for detecting the moisture content of wood based on a microwave transmission principle is characterized by comprising the following steps:
s1, placing the wood sample to be tested in a constant temperature and humidity box;
s2, measuring amplitude and phase information of the transmission coefficient corresponding to the wood sample with the water content; step S2 specifically includes:
s21, obtaining a plurality of same timbers to be tested, and preparing timber samples under different relative humidities by changing the humidity of the constant temperature and humidity chamber;
s22, measuring the moisture content of the wood sample at each relative humidity after being processed in the step S21 by using a traditional drying method;
s23, determining a first optimal lift-off distance according to the linearity and the optimal sensitivity of a fitting curve by fitting the relationship between the distance between the antenna and the wood sample under each relative humidity and the amplitude of the transmission coefficient;
s24, on the basis of the first optimal lift-off distance and the corresponding first frequency step length, obtaining a first optimal detection frequency by fitting the relation between the amplitude of the transmission coefficient and the water content of the wood sample under the relative humidity;
s25, determining a second optimal lift-off distance according to the linearity and the optimal sensitivity of a fitting curve by fitting the relation between the distance between the antenna and the wood sample under the relative humidity and the phase of the transmission coefficient;
s26, on the basis of the second optimal lift-off distance and the corresponding second frequency step length, obtaining a second optimal detection frequency by fitting the relation between the phase of the transmission coefficient and the water content of the wood sample under the relative humidity;
s27, measuring the amplitude information of the transmission coefficient corresponding to the wood sample to be detected under the condition based on the first optimal lift-off distance and the first optimal detection frequency;
s28, measuring the phase information of the transmission coefficient corresponding to the wood sample to be detected under the conditions based on the second optimal lift-off distance and the second optimal detection frequency;
s3, calculating the moisture content of the wood to be measured according to the following formula:
wherein, W0Indicates the water content of the wood to be measured, A0Amplitude information, k, representing the transmission coefficient corresponding to the wood sample to be tested1Is shown as A0The coefficient of (a) is determined,
phase information, k, representing the transmission coefficient corresponding to the wood sample to be tested2To represent
The coefficient of (a); coefficient k1、k2And determining by using the error least square sum.
2. The method for detecting moisture content in wood based on microwave transmission principle as claimed in claim 1, wherein the coefficient k is1、k2The specific solving process is as follows:
establishing the following formula according to the transmission coefficient amplitude and the phase information corresponding to the wood samples under different relative humidities, and obtaining a coefficient k by solving the formula1、k2The value of (A) is as follows:
wherein N represents the total number of wood samples prepared in step A1 at different relative humidities, AiAmplitude information indicating the transmission coefficient corresponding to the wood sample at the i-th relative humidity,
phase information indicating the transmission coefficient corresponding to the wood sample at the i-th relative humidity.
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