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Timestamp: 2019-04-25 04:12:17+00:00

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Electrical and dielectric wood properties are used in many applications. In this work, the complex impedance of seven wood species was measured for frequency range 1 kHz–1 MHz. The measurements were conducted with parallel and perpendicular orientation of the electrical field with respect to specimen visible grain cut from sapwood and heartwood. Based on the complex impedance, values of relative permittivity and loss coefficient were calculated. These parameters of various wood types differs significantly below 10 kHz for relative permittivity and below 200 kHz for loss coefficient. For wood samples classification, the relative permittivity values measured at frequency 5.1 kHz and the loss coefficient values measured at frequency 110 kHz were used in this work. Three different classification methods were employed for clustering. Results show that relative permittivity looks more promising parameter for wood species differentiation.
Key words: dielectric wood properties, relative permittivity, loss coefficient, clustering, wood classification.
Wood is a natural material widely used for its versatility and strength in construction, for furniture manufacturing and as biomass in combustion process. It is a light material with low thermal conductivity, it can be easily treated, but it has some disadvantages, namely, non-humidity-resistance, and can decay and deform . The main components of wood are cellulose, lignin and hemicellulose. It is porous material with porosities ranging from 50 to 80 %vol. There is significant difference between hardwood and softwood microstructure. The open microstructure of softwoods generally results in its higher volume porosity than hardwoods . Several factors affect electrical and dielectric wood properties: wood species, moisture content, density, temperature, chemical properties, fiber direction and field frequency [3, 4, 7–9, 12, 19, 28]. Therefore, these parameters can be used for nondestructive and accurate measurements of wood features. Depending on frequency, electrical and dielectric wood properties have been used in a variety of applications such as moisture content or thickness measurement [20, 31, 32], defects detection , strength characteristics estimation and dendrochronology . Forrer and Funck  reported that the dielectric properties of wood may be useful parameters for dielectric-based scanning of wood surfaces . It was reported by Tiitta et al.  that complex impedance was sufficient to distinguish between the samples from the brown-rot resistant and susceptible Scots pine trees . According to the literature review, there is still lack of research concerning both, dielectric properties of wood at the frequency below 1 MHz and the possibility of the practical use of these parameters. Therefore, in this research, relative permittivity and loss coefficient of wood measured at low frequency were investigated as parameters for wood species identification. For this purpose, different clustering methods were used.
Clustering methods have been applied to a wide variety of research fields, such as agriculture, medicine, biology and many others. This technique is used to classify objects or samples into relatively homogenous groups called clusters. Wide range of clustering algorithms are presented in scientific reports and employed in real-world applications. Hierarchical clustering was used by Goncalves et al.  to determine the division of the state of Pará (Brasil) into homogenous groups according rainfall data , by Lin et al.  to characterize the aberrantly hypermethylated regions that are highly associated with breast cancer , by Vernone et al.  for human protein cluster analysis using amino acid frequencies . Clustering techniques literature shows that other algorithms, called artificial intelligence methods, are also used by researchers. Adaptive resonance theory neural network models ART2 can surpass the dilemma of plasticity and stability of the existing clustering models. Therefore, this technique has many interesting applications, e.g., for group selection of interim product in shipbuilding , for enhancing metrology data-quality evaluation  or for clustering of multiple web objects for qualitative web prefetching . Fuzzy clustering is an objective function based method which assigns each data point to more than one cluster with the degree of membership. This method was recently used for detection of masses and macro calcification in mammogram images , for the segmentation of brain tumor  and for magnetic resonance image brain segmentation .
Seven native softwoods and hardwoods were included in the tests. Samples parameters are detailed in Table 1. As is presented in Table 1, specimens with relatively narrow range of moisture content were chosen for the measurement because dielectric wood parameters differ according to moisture content. The moisture content was measured by means of Brookhuis Micro-Electronics FME moisture meter. Taking into account the results reported by Goreshnev et al. , it can be stated that the differences in moisture content presented in Table 1 have insignificant influence on both, relative permittivity (several %) and loss coefficient (few %).
For each wood species, four rectangular specimens (60 mm width × 60 mm length × 15 mm thickness) were cut from sapwood and heartwood, with the thickness either in the tangential or longitudinal direction of wood fiber. The surfaces of specimens adjacent to electrodes were oriented parallel or perpendicular with respect to visible grain. Depending on electrical field orientation with respect to the visible grain and specimen origin, specimens were labeled as 1A, 1B, 2A and 2B what is shown in Figure 1.
where C is capacitance of capacitor with wood sample (F), epsilon0 is permittivity of vacuum (F·m-1), S is upper electrode surface area (m2), h is distance between electrodes (m), omega is angular frequency of electromagnetic field (Hz) and R is resistance of wood sample (Ohm). Values of C and R were calculated based on real and imaginary part of impedance.
In this study three cluster analysis methods which are described below were used.
Single linkage (nearest neighbor) where the distance between two clusters is calculated as the distance of the two closest objects from these clusters.
Complete linkage (furthest neighbor) where the distance between two clusters is determined using the greatest distance between any two objects in these clusters.
Centroid linkage where the distance between two clusters is calculated as the distance between the centroids of these clusters. The centroid of a cluster is the average point in the multidimensional space defined by the dimensions.
Average linkage where the distance between two clusters is determined by the use of average distance between all pairs of objects in the two separate clusters .
The ‘RSNNS’ Package for R software was used for clustering with the use of ART2 neural network . ART2 (Adaptive Resonance Theory) network is a kind of non-supervised neural network. The network is composed of two fully connected layers (in both directions), the input/comparison layer F1 and the recognition layer F2. The nodes of F2 layer compete with each other to produce a winning unit. The winning unit returns the signal to the F1 layer. Then, the similarity between activation in F1 and input signal is calculated and compared with the vigilance value. Based on this comparison, weights in the network can be updated or a new node in F2 layer can be produced. ART2 networks offer rapidly learning, adaptation to a nonstable environment, stability and plasticity. The number of clusters is determined exactly and automatically.
where n is the number of observations, k is the number of clusters, r is the membership exponent and d(i, j) is the dissimilarity between observations i and j.
The algorithm is described in details by Kaufman and Rousseeuw .
A relative permittivity and a loss coefficient of the samples were measured for frequency range from 1 kHz to 1MHz. In Figures 2 and 3 the dependence of relative permittivityand loss coefficient on frequency is presented for samples 1B of all wood species. In plots concerning relative permittivity, the frequency range was reduced for greater readability of the Figure. For higher frequencies, the parameters presented in plots are constant.
The differences in both, relative permittivity and loss coefficient between wood species are observed over the entire frequency range. However, the most significant differences appear for lower frequencies (below 10 kHz for relative permittivity and below 200 kHz for loss coefficient). Therefore, for wood samples classification, the relative permittivity values measured at frequency 5.1 kHz and the loss coefficient values measured at frequency 110 kHz were used in this work. Classification was performed separately for relative permittivity and for loss coefficient. Each sample was described by four parameters measured for specimens labeled as 1A, 1B, 2A and 2B.
Three different classification methods were used for clustering because different methods and even different parameters of these methods can cause results dissimilarities.
The typical result of this method is a dendrogram. In Figures 4 and 5 the horizontal dendrograms describing clustering results are presented.
The results presented in Figure 4 show that, according to relative permittivity, samples of ash, larch and Norway spruce are assigned to separate clusters with a low Euclidian distance (not exceeding 0.1). Higher distance is observed for oak samples (0.33) which are also joined together in one cluster and are different from other wood species. The samples of birch and Scotch pine are assigned to the separate clusters, however, single sweet cherry samples are linked to these groups. Only sweet cherry samples are not linked together into separate cluster. The graph shows a high similarity between birch and ash samples (the distance not exceeding 0.22) as well as between Scotch pine, larch and Norway spruce (the distance not exceeding 0.17).
The results shown in Figure 5 suggest that, according to loss coefficient, only samples of larch and Norway spruce are assigned to the separate clusters representing single wood species. Samples of ash and oak are linked into separate cluster, however, they are joined with other wood species.
The results of clustering by ART2 for both, relative permittivity and loss coefficient are presented in Table 2. One of ART2 parameters is a number of clusters. In this research, it was set as eight.
The results presented in Table 2 differ slightly from these obtained by joining method. According to relative permittivity, samples of oak, ash and larch are assigned to the separate clusters. The samples of birch and Norway spruce are linked together. One sample of birch, two samples of sweet cherry and three samples of Scotch pine are connected into one group. In the case of loss coefficient as a clustering parameter, oak samples are connected with Scotch pine and ash samples are connected with Norway spruce. Scotch pine samples are joined together into separate cluster. Birch and sweet cherry samples are assigned to different groups.
This method, in addition to the information about cluster number set for certain sample, gives also a degree of membership to this cluster. In Table 3 and 4, the results for relative permittivity and loss coefficient as a clustering parameter are presented. Since the number of groups is the parameter of Fuzzy Analysis Clustering method, in this work it was set as eight. As results of the method, the membership coefficients (in %, rounded) for each of eight clusters is presented, as well as the number of group with the highest degree of membership (“Cluster of the sample” column).
According to the data presented in Table 3, when relative permittivity is a clustering parameter, results are similar to these obtained with the use of other methods. Samples of ash, larch, Scotch pine and Norway spruce are grouped into separate clusters with quite high membership coefficients (49–82% for ash, 48–81% for larch, 39–81% for Scotch pine and 77–93% for Norway spruce). Birch samples are connected with two samples of sweet cherry, and in the case of oak, only three samples are joined together in separate cluster.
In the case of loss coefficient as a clustering parameter, ash, larch and Norway spruce samples are joined together into separate clusters according to wood species, with quite high membership coefficients (39–79% for ash, 61–86% for larch and 71–92% for Norway spruce). Groups of oak and Scotch pine are composed of only three samples of these wood species. Samples of birch and sweet cherry are assigned to different groups. Similar results were obtained with the use of other methods.
The loss coefficient represents the ability of material to convert electromagnetic energy into heat at a certain temperature and frequency. The relative permittivity shows the ability of molecule to become polarized under the electric field and the differences in relative permittivity between wood species are a result of a different volume porosity. However, according to Hilfer , the differences in the actual pore size distribution existing among woods with the same volume porosity may cause slight differences in relative permittivity . A lower relative permittivity is produced by higher porosity. Taking into account that volume porosity is correlated with density, at constant moisture content, wood species with higher density have higher relative permittivity . The density is the characteristic parameter for wood species, therefore in the result of clustering, samples of certain wood species (or wood species with the similar density) should be joined together. In the case of relative permittivity, wood samples were generally grouped according to wood species by all clustering algorithms. Additionally, combining the density values reported by Lis and Rapp  with clustering results shown in the dendrogram, it can be seen that there is similarity between birch and ash (the density equals 650 kg/m3 and 750 kg/m3 respectively) as well as between Scotch pine (the density equals 520 kg/m3), larch (the density equals 690 kg/m3) and Norway spruce (the density equals 470 kg/m3). This is in agreement with our previous results , where we reported that wood samples classified as similar according to complex impedance are different according to density.
When a loss coefficient was a clustering parameter, less wood species form separate groups (only ash, larch and Norway spruce). These results can lead to assumption that some other physical or chemical parameters which differentiate wood species influence significantly on relative permittivity and loss coefficient.
Other scientific reports prove the potential applicability of electrical wood parameters for wood species differentiation. Gora and Yanoviak  pointed out that the resistivity differs among species and growth forms without respect to regional origin of wood. Pentoś et al.  reported that complex impedance can be used as a parameter for wood species differentiation.
Two dielectric wood parameters were used for species separation, namely, relative permittivity and loss coefficient. Three methods of clustering were employed and generally, they produced similar results. Relative permittivity seems to be a better species differentiation parameter because only cherry samples were not joined together into separate clusters according to this parameter. The Tree Clustering method showed similarities between certain wood species. Different similarities between wood species are observed depending on dielectric parameter. In the case of relative permittivity similarity between birch and ash as well as between Scotch pine, larch, and Norway spruce are observed. In the case of loss coefficient larch is similar to Scotch pine. Dielectric wood parameters are correlated with density. Therefore, similarities between wood species of different density can lead to assumption that some other parameters influence significantly on dielectric parameters.
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