Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
2017
Volume 20
Issue 4
Topic:
Wood Technology
ELECTRONIC
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Pento¶ K. , £uczycka D. , Wysoczański T. 2017. THE USE OF RELATIVE PERMITTIVITY AND LOSS COEFFICIENT AS PARAMETERS FOR WOOD SPECIES DIFFERENTIATION, EJPAU 20(4), #02.
Available Online: http://www.ejpau.media.pl/volume20/issue4/art-02.html

THE USE OF RELATIVE PERMITTIVITY AND LOSS COEFFICIENT AS PARAMETERS FOR WOOD SPECIES DIFFERENTIATION

Katarzyna Pento¶, Deta £uczycka, Tobiasz Wysoczański
Institute of Agricultural Engineering, The Faculty of Life Sciences and Technology, Wroc³aw University of Environmental and Life Sciences, Poland

 

ABSTRACT

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.

INTRODUCTION

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 [26]. 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 [10]. 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 [29], strength characteristics estimation and dendrochronology [21]. Forrer and Funck [11] reported that the dielectric properties of wood may be useful parameters for dielectric-based scanning of wood surfaces [11]. It was reported by Tiitta et al. [33] that complex impedance was sufficient to distinguish between the samples from the brown-rot resistant and susceptible Scots pine trees [33]. 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. [13] to determine the division of the state of Pará (Brasil) into homogenous groups according rainfall data [13], by Lin et al. [24] to characterize the aberrantly hypermethylated regions that are highly associated with breast cancer [24], by Vernone et al. [34] for human protein cluster analysis using amino acid frequencies [34]. 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 [36], for enhancing metrology data-quality evaluation [18] or for clustering of multiple web objects for qualitative web prefetching [16]. 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 [23], for the segmentation of brain tumor [2] and for magnetic resonance image brain segmentation [1].

MATERIAL AND METHODS

Wood samples
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. [15], 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 %).

Table 1. Wood species used for determination of dielectric parameters
Wood species
Botanical name
Moisture content range [%]
Sweet cherry
Prunus avium L.
10.0 – 15.5
Roth birch
Betula pendula Roth
12.5 – 15.5
Oak
Quercus robur L.
13.5 – 18.0
Ash
Fraxinus excelsior L.
14.0 – 16.0
European larch
Larix decidua Mill.
10.5 – 15.5
Scotch Pine
Pinus sylvestris L.
9.5 – 15.0
Norway spruce
Picea abies L.
8.5 – 12.0

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.

Fig. 1. The method of specimen labelling

For each specimen, the complex impedance was measured at a room temperature and at frequency ranging from 1 kHz to 1 MHz. The ATLAS 0441 HIA apparatus with parallel plate electrodes was used for the measurements. A good contact between wood surface and electrode was ensured by smoothing a surface with a sand paper. Based on complex impedance values and electrode dimensions, two parameters that characterize wood material depending only on frequency: a relative permittivity (epsilon’) and a loss coefficient (tg delta) were determined as follows:

(1)

(2)

(3)

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.

Cluster analysis
In this study three cluster analysis methods which are described below were used.

Joining (Tree Clustering, Hierarchical clustering)
In this research the Statistica 10 software was used for Tree Clustering. This algorithm groups data into clusters iteratively in order to build a cluster hierarchy displayed as a tree diagram (dendrogram). At a first step, each object represents a separate cluster. At each next step, the two most similar clusters are joined into a new cluster. The horizontal axis of the dendrogram represent the distance (dissimilarity) between clusters. The vertical axis represent objects. The algorithm requires the definition of two parameters: a way to quantify the similarity of two objects (linkage distance) and linkage rule. The most common metric for calculating distance between two points in Euclidean space is Euclidean distance. As a linkage rules the following can be used:

ART2 Neural Network
The ‘RSNNS’ Package for R software was used for clustering with the use of ART2 neural network [6]. 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.

Fuzzy Analysis Clustering
In this research the ‘cluster’ Package for R software was used for clustering with the use of Fuzzy Analysis Clustering [27]. This technique permits each data point to belong to more than one cluster. A degree of membership to each cluster is specified by a membership coefficient that range from 0 to 1. Therefore, this method yields much more detailed information on the data structure than hard clustering methods. On the other hand, this can also make results interpretation more complicated. During the algorithm the objective function is minimized:

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 [22].

RESULTS AND DISCUSSION

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.

Fig. 2. Effect of frequency on relative permittivity values for samples 1B of all wood species

Fig. 3. Effect of frequency on loss coefficient values for samples 1B of all wood species

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.

Joining
The typical result of this method is a dendrogram. In Figures 4 and 5 the horizontal dendrograms describing clustering results are presented.

Fig. 4. Cluster dendrogram generated for relative permittivity

Fig. 5. Cluster dendrogram generated for loss coefficient

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.

ART2 Neural Network
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.

Table 2. The results of clustering by ART2
Sample
Relative permittivity
Loss coefficient
Cluster number
Cluster number
birch1
1
1
birch2
2
2
birch3
2
5
birch4
2
2
sweet cherry1
1
2
sweet cherry2
3
3
sweet cherry3
1
2
sweet cherry4
4
2
oak1
5
4
oak2
5
4
oak3
5
4
oak4
5
4
ash1
6
5
ash2
6
5
ash3
6
5
ash4
6
5
larch1
7
6
larch2
7
6
larch3
7
6
larch4
7
6
scotch pine1
1
4
scotch pine2
6
4
scotch pine3
1
4
scotch pine4
1
4
norway spruce1
2
5
norway spruce2
2
5
norway spruce3
2
5
norway spruce4
2
5

Fuzzy Analysis Clustering
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).

Table 3. Fuzzy Analysis Clustering results for relative permittivity
Sample
Membership coefficient for each cluster
Cluster of the sample
1
2
3
4
5
6
7
8
birch1
44
15
5
4
4
11
9
7
1
birch2
66
8
3
2
2
8
7
4
1
birch3
28
11
7
7
6
22
12
8
1
birch4
69
7
3
2
2
8
6
4
1
sweet cherry1
12
35
4
3
3
8
14
21
2
sweet cherry2
0
0
99
0
0
0
0
0
3
sweet cherry3
26
20
7
5
5
14
12
10
1
sweet cherry4
24
16
11
5
5
15
13
12
1
oak1
0
0
0
95
3
0
0
0
4
oak2
13
9
6
22
23
12
8
7
5
oak3
8
7
6
25
32
9
7
6
5
oak4
1
1
0
4
92
1
1
0
5
ash1
13
10
4
4
4
49
11
6
6
ash2
8
5
2
2
2
72
5
3
6
ash3
10
6
3
3
3
63
8
4
6
ash4
5
3
1
2
2
82
4
2
6
larch1
7
10
2
2
2
7
62
7
7
larch2
9
14
3
3
3
8
48
12
7
larch3
9
10
3
3
3
9
55
8
7
larch4
4
5
1
1
1
3
81
4
7
scotch pine1
4
80
1
1
1
3
5
5
2
scotch pine2
10
46
3
2
2
7
15
14
2
scotch pine3
17
39
4
4
4
11
13
10
2
scotch pine4
5
81
1
1
1
3
5
4
2
norway spruce1
4
7
2
1
1
3
6
77
8
norway spruce2
1
2
1
0
0
1
2
92
8
norway spruce3
2
4
1
1
1
2
3
88
8
norway spruce4
1
2
0
0
0
1
2
93
8

Table 4. Fuzzy Analysis Clustering results for loss coefficient
Sample
Membership coefficient for each cluster
Cluster of the sample
1
2
3
4
5
6
7
8
birch1
18
14
13
9
11
13
10
12
1
birch2
8
74
5
2
2
3
2
5
2
birch3
22
15
29
4
7
9
5
9
3
birch4
27
19
13
6
8
10
7
11
1
sweet cherry1
12
13
10
20
6
7
16
17
4
sweet cherry2
0
0
0
0
98
0
0
0
5
sweet cherry3
16
46
9
4
5
6
5
10
2
sweet cherry4
17
26
15
7
10
7
7
12
2
oak1
8
4
5
2
2
72
3
4
6
oak2
35
13
11
4
4
17
5
11
1
oak3
16
11
12
6
7
30
8
11
6
oak4
6
3
3
1
2
79
2
3
6
ash1
18
12
39
4
5
8
5
10
3
ash2
10
7
63
3
4
5
3
5
3
ash3
7
5
75
2
2
3
2
4
3
ash4
6
4
79
1
2
3
2
3
3
larch1
4
3
3
6
2
2
75
5
7
larch2
5
4
4
10
2
3
66
6
7
larch3
6
5
5
9
3
4
61
8
7
larch4
2
2
2
3
1
1
86
3
7
scotch pine1
6
6
4
3
2
3
4
71
8
scotch pine2
12
10
10
9
4
7
17
30
8
scotch pine3
24
14
10
5
5
15
7
19
1
scotch pine4
9
7
5
3
2
4
5
65
8
norway spruce1
4
4
3
71
2
3
8
5
4
norway spruce2
1
1
1
92
1
1
3
1
4
norway spruce3
2
2
2
85
1
1
4
2
4
norway spruce4
1
1
1
92
1
1
2
1
4

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 [17], the differences in the actual pore size distribution existing among woods with the same volume porosity may cause slight differences in relative permittivity [17]. 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 [5]. 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 [25] 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 [30], 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 [14] pointed out that the resistivity differs among species and growth forms without respect to regional origin of wood. Pentoś et al. [30] reported that complex impedance can be used as a parameter for wood species differentiation.

CONCLUSIONS

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.

REFERENCES

  1. Altameem T., Zanaty E.A., Tolba A., 2015. A new fuzzy C-means method for magnetic resonance image brain segmentation. Connection Sci., 27, 305–321.
  2. Ananthi V.P., Balasubramaniam P., Kalaiselvi T., 2016. A new fuzzy clustering algorithm for the segmentation of brain tumor. Soft Comput., 20, 4859–4879.
  3. Avramidis S., 2016. Dielectric properties of four softwood species at low-level radio frequencies for optimized heating and drying. Drying Tech., 34, 753–760.
  4. Avramidis S., Iliadis L., Mansfield S.D., 2006. Wood dielectric loss factor prediction with artificial neural networks. Wood Sci. Technol., 40, 563–574.
  5. Ay N., Sahin H., 2004. Dielectric constant of Turkish timbers in the longitudinal direction at a 9.8-GHz frequency. Forest Prod. J., 54, 65–68.
  6. Bergmeir C., Benítez J.M., 2012. Neural Networks in R Using the Stuttgart Neural Network Simulator: RSNNS. J Stat. Softw., 46, 1–26.
  7. Bossou O.V., Mosig J.R., Zurcher J.F., 2010. Dielectric measurements of tropical wood. Measurement, 43, 400–405.
  8. Brischke C., Lampen S.C., 2014. Resistance based moisture content measurements on native, modified and preservative treated wood. Eur. J. Wood Wood Prod., 72, 289–292.
  9. Brischke C., Sachse K.A., Welzbacher C.R., 2014. Modeling the influence of thermal modification on the electrical conductivity of wood. Holzforschung, 68, 185–193.
  10. Duchow K.J., Gerhardt R.A., 1996. Dielectric characterization of wood and wood infiltrated with ceramic precursors. Mat. Sci. Eng. C-Biomim, 4, 125–131.
  11. Forrer J.B., Funck J.W., 1998. Dielectric properties of defects on wood surfaces. Holz Als Roh-Und Werkstoff, 56, 25–29.
  12. Fredriksson M., Wadso L., Johansson P., 2013. Small resistive wood moisture sensors: a method for moisture content determination in wood structures. Eur. J. Wood Wood Prod., 71, 515–524.
  13. Goncalves M.F., Blanco C.J.C., dos Santos V.C., Oliveira L.L.D., Pessoa F.C.L., 2016. Identification of Rainfall Homogenous Regions taking into account El Nino and La Nina and Rainfall Decrease in the state of Para, Brazilian Amazon. Acta Scientiarum-Technol., 38, 209–216.
  14. Gora E.M., Yanoviak S.P., 2015. Electrical properties of temperate forest trees: a review and quantitative comparison with vines. Can. J. Forest Res., 45, 236–245.
  15. Goreshnev M.A., Litvishko E.S., Lopatin V.V., 2016. Dielectric Properties of Birch Wood in the High-Frequency Range. Russ. Phys. J., 58, 1297–1300.
  16. Gracia C.D., Sudha S., 2016. ART2 Clustering of Multiple Web Objects for Qualitative Web Prefetching. App. Artif. Intell., 30, 475–493.
  17. Hilfer R., 1991. Geometric and dielectric characterization of porous media. Phys. Rev. B, 44, 60.
  18. Huang Y.T., Cheng F.T., Shih Y.H., Chen Y.L., 2014. Advanced ART2 scheme for enhancing metrology-data-quality evaluation. J. Chin. Inst. Eng., 37, 1064–1079.
  19. Husein I., Sadiyo S., Nugroho N., Wahyudi I., Agustina A., Komariah R.N., Khabibi J., Purba C.Y.C., Ali D., Iftor M., Kahar T.P., Wijayanto A., Jamilah M., 2014. Electrical properties of Indonesian hardwood. Case study: Acacia Mangium, Swietenia Macrophylla and Maesopsis Eminii. Wood Res., 59, 695–703.
  20. Inagaki T., Ahmed B., Hartley I.D., Tsuchikawa S., Reid M., 2014. Simultaneous prediction of density and moisture content of wood by terahertz time domain spectroscopy. J. Infrared Millim. Te., 35, 949–961.
  21. Jackson J.B., Mourou M., Labaune J., Whitaker J.F., Duling I.N., Williamson S.L., Lavier C., Menu M., Mourou G.A., 2009. Terahertz pulse imaging for tree-ring analysis: a preliminary study for dendrochronology applications. Meas. Sci. Technol., 20, 075502.
  22. Kaufman L., Rousseeuw P.J., 1990. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
  23. Kowsalya S., Priyaa D.S., 2016. An integrated approach for detection of Masses and Macro Calcification in Mammogram Images using Dexterous Variant Median Fuzzy C-means Algorithm. Proceedings of the 10th International Conference on Intelligent Systems and Control (Isco'16).
  24. Lin I.H., Chen D.T., Chang Y.F., Lee Y.L., Su C.H., Cheng C., Tsai Y.C., Ng S.C., Chen H.T., Lee M.C., Chen H.W., Suen S.H., Chen Y.C., Liu T.T., Chang C.H., Hsu M.T., 2015. Hierarchical Clustering of Breast Cancer Methylomes Revealed Differentially Methylated and Expressed Breast Cancer Genes. PLoS ONE 10(2): e0118453.
  25. Lis Z., Rapp P., 2005. Drewno i materiały drewnopochodne [Wood and wood-based materials]. In: Budownictwo ogólne, t.1, materiały i wyroby budowlane [General construction, t.1, materials and construction products]. Arkady Warszawa. [In Polish].
  26. Mirski R., 2010. The effect of variable environmental conditions on dimensional changes in thin wood-based materials part II. Desorption changes. EJPAU, 13(3), #13.
  27. Maechler M., Rousseeuw P., Struyf A., Hubert M., Hornik K., 2016. Cluster: ClusterAnalysis Basics and Extensions. R package version 2.0.5.
  28. Olmi R., Bini M., Ignesti A., Riminesi C., 2000. Dielectric properties of wood from 2 to 3 GHz. J. Microwave Power EE., 35, 135–143.
  29. Oyama Y., Zhen L., Tanabe T., Kagaya M., 2009. Sub-terahertz imaging of defects in building blocks. Ndt & E Int., 42, 28–33.
  30. Pentoś K., Łuczycka D., Wysoczański T., 2016. The use of complex impedance as a parameter for wood differentiation. Wood Res., 61, 13–24.
  31. Sahin H., Ay N., 2004. Dielectric properties of hardwood species at microwave frequencies. J. Wood Sci., 50, 375–380.
  32. Teti A.J., Rodriguez D.E., Federici J.F., Brisson C., 2011. Non-Destructive Measurement of Water Diffusion in Natural Cork Enclosures Using Terahertz Spectroscopy and Imaging. J. Infrared Millim. Te., 32, 513–527.
  33. Tiitta M., Kainulainen P., Harju A.M., Venalainen M., Manninen A.M., Vuorinen M., Viitanen H., 2003. Comparing the effect of chemical and physical properties on complex electrical impedance of Scots pine wood. Holzforschung 57, 433–439.
  34. Vernone A., Berchialla P., Pescarmona G., 2013. Human Protein Cluster Analysis Using Amino Acid Frequencies. PLoS ONE 8(4): e60220. 
  35. www.statsoft.com.
  36. Zhong Y.G., Xue K., Shi D.Y., 2014. Clustering and group selection of interim product in shipbuilding. J. Intell. Manuf., 25, 1393–1401.

Accepted for print: 13.10.2017


Katarzyna Pento¶
Institute of Agricultural Engineering, The Faculty of Life Sciences and Technology, Wroc³aw University of Environmental and Life Sciences, Poland
ul. J. Che³mońskiego 37/41
51-630 Wroc³aw
Poland
email: katarzyna.pentos@upwr.edu.pl

Deta £uczycka
Institute of Agricultural Engineering, The Faculty of Life Sciences and Technology, Wroc³aw University of Environmental and Life Sciences, Poland
ul. J. Che³mońskiego 37/41
51-630 Wroc³aw
Poland
email: deta.luczycka@upwr.edu.pl

Tobiasz Wysoczański
Institute of Agricultural Engineering, The Faculty of Life Sciences and Technology, Wroc³aw University of Environmental and Life Sciences, Poland
ul. J. Che³mońskiego 37/41
51-630 Wroc³aw
Poland

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.