In the study, 28 bread wheat varieties, 11 durum wheat varieties, 8 barley varieties, 6 oat varieties and 4 triticale varieties were used as material (

Table 1). The varieties used were obtained from the Bahri Dagdas International Agricultural Research Institute (Konya, Turkey, 2015). The physical properties belonging to the varieties were determined in the study. Thousand kernel weight, geometric mean diameter, sphericity, kernel volume, surface area, bulk density, true density, porosity and colour were the parameters used. Kernels belonging to the varieties used in the study were cleaned from all sorts of foreign materials such as dust, stones, hays, immature and damaged kernels. Measurements were made at the moisture content of 8.9%.

#### 2.1. Physical Properties

In order to determine the physical sizes of kernels, 100 kernels were randomly divided into groups of 10 each. Lengths, widths and thicknesses of the 10 kernels from each group defined were measured and their averages were taken. In the measurements, a digital Vernier calliper with a sensitivity of 0.1 mm was used [

25,

26].

Geometric mean diameters, sphericities, kernel volumes and kernel surface areas were calculated by the following formulas [

23,

25].

Thousand kernel weight was determined by weighing 400 kernels counted with 4 replications and taking their average [

27,

28].

Bulk density was measured according to the method of Association of Official Analytical Chemists. In this method, kernels were filled into a cylinder of 500 mL from the height of 15 cm. The kernels in the cylinder were weighed by flattening and sweeping them without any pressure applied. Bulk density was calculated by proportioning the weight of the kernels to the cylinder volume [

25,

29,

30].

True density was measured by using the water displacement method. In this method, first, 500 mL water was filled into a cylinder of 1000 mL. Then, 30 g of kernels were put into the water in this cylinder. The rise in the water level was immediately measured. True density was calculated by proportioning the weight of the kernels to the displaced liquid volume [

29,

31].

To calculate the porosity, the following equation was used [

23].

Colour parameters (

L,

a,

b) were measured by using the Hunter Lab Mini Scan XEplus Colourimeter (Hunter Associates Laboratory Inc., Reston, VA, USA). In the Hunter scale,

L value of 100 means white while zero means black; when the value of

a is positive, it means redness; when negative, greenness; and the value of

b is positive, it means yellowness; when negative, blueness [

32,

33].

#### 2.2. Artificial Neural Networks

The ANN model was developed by using the Matlab NN Toolbox (The Mathworks Inc., Natick, MA, USA). In the model, 539 data in total were used. In the ANN model, thousand kernel weight, geometric mean diameter, sphericity, kernel volume, surface area, bulk density, true density, porosity and colour parameters (L, a, b) were used as input parameters; and species and varieties as output parameters.

While establishing the ANN model, all the data were normalized between 0 and 1 [

34].

For normalization, the following equation was used:

To obtain real values from the normalized values, “y” value was calculated using the same formula.

To develop the ANN model, normalized data were divided into two data sets of training and test. In the training set, 502 data were used, whereas 37 data in the test set. The numbers of the most fit neurons in the hidden layers were found to be in the range of 2–25 by the trial and error method. In the ANN model, to obtain the most fit epoch number, epoch numbers from 1 to 10,000 were tried. As a result of trials, the most fit epoch number for the model was determined.

In the ANN model, Feed Forward Back Propagation, Multilayer Perceptron network structure was used. The back-propagation algorithm in this network is the most popular and commonly used algorithm. It minimizes the total error by varying the weights in order to enhance the network performance [

35,

36]. The training algorithm used is the Levenberg-Marquart algorithm [

37,

38].

Training of the network was continued until the test error reaches the determined tolerance value. After training of the network ended successfully, the network was tested by test data [

9].

In order to determine the performances of the results,

RMSE and

R^{2} values that are considered to be principal accuracy measures and that are based on the concept of mean error and commonly used were calculated using the following formulas [

39].

Here RMSE, Root Mean Square Error, R^{2}, coefficient of determination, m, number of data, x, real value and x_{1}, estimated value.

The error between real values and estimated ones was calculated by means of the following equation [

40].

Here ε, relative error, m, data number, x, real value and x_{1}, estimated value.

Data concerning the physical parameters obtained were evaluated by conducting a factorial experiment in a randomized complete block design, using the JMP statistical program (SAS Institute Inc., Cary, NC, USA) [

41].