Methods of multi-dimensional statistical analysis for assessing the impact of applying technology of paint formulation

Application information of the method of canonical correlations to assess the influence of technological factors on the quality of paint coat of building products and structures are provided below. The algorithm for calculating the method of canonical correlations is considered. It is shown that the substrate porosity is determinative for the paint coat quality. The viscosity of the paint applied by the pneumatic method affects the quality indicators less, especially compare to brush application. The coefficients in canonical variables characterize the strength of the influence of the relevant signs-factors and the efficiency of indicators on the level of communication between them. Various ways of applying paint are considered on substrate with a porosity of 24%, 28%, 32% on the example of oil paints MA-15, of alkyd paint PF-115, of water dispersion paint AK111, it is shown, that the porosity of the substrate is a decisive factor in determining the quality of the paint coating. The viscosity of the paint when applied by the pneumatic method affects the quality indicators less compared to the brush application.


Introduction
Previous studies show that the resistance of paint coat, among other factors, is determined by the quality of the external appearance of coat [1,2]. The quality of the appearance of the coatings is significantly influenced by the technology of applying paint, its rheological properties, and the quality of the painted surface. Meanwhile, the process of creating paint coatings on a porous cement substrate is often unstable and irreproducible [3,4]. In this connection, the assessment of the most significant factors influencing the quality of coating is relevant. Current knowledge of the possibilities of mathematical processing of statistical information and the interpretation of the results obtained allows us to investigate the interrelationships of individual sides of technological processes with the involvement of several effective factors in the analysis process. We consider the possibility of using method of multidimensional statistical analysis which are based on the hypothesis about the possibility of studying the existing relationships between the observed phenomena indirectly, consisting in constructing correlation matrices and recognizing them based on factor estimates to identify the causes of coating quality and defect Let us consider the possibility of using multidimensional statistical analysis methods for identify the causes of coating quality deterioration and the appearance of defects [5] . , where Q is the number of realizations. We try to determine the share contributed by individual technological factors to the overall instability of the process.
The method of canonical correlations make it possible to contemporary analyze the relationship between several output parameters and a large number of determining factors. It does not require a lack of correlation, both in the group of performance indicators and in the group of factor indicators.
The algorithm for calculating the method of canonical correlations is constructed in such a way that the original variables are replaced by their linear combinations, which are linearly independent. At the same time, there is a high degree of connection between linear combinations of factors and linear combinations of output parameters. The coefficients in canonical variables characterize the strength of the influence of the relevant signs-factors and the performance of indicators on the level of communication between them.

Materials and research methods
Briefly give the essence of the method. First of all, the covariance matrix is calculated from the array of measured factor values, which is a characteristic of the interaction and its changes: is the covariance of the specified variables, then the matrix S is: ...  , m eigenvectors of U, and n eigenvectors of V. To analyze the influence of the method of applying the paint composition, its rheological properties and the porosity of the substrate on the surface quality of the coatings, we performed the following experiment. Colorful compositions with different rheological characteristics were applied to the mortar substrate with a porosity of 24%, 28%, 32% in two layers with intermediate drying for 20 minutes. Before applying the paint, the substrate surface was primed. In addition, part of the mortar samples was leveled with spackling compounds. The rheological properties of paints were evaluated in terms of their conditional dynamic viscosity and surface tension. As the paint compositions, alkyd enamel of the PF-115 brand, oil paint of the MA-15 brand, acrylic water-dispersion (front) paint were used. Paint were applied by pneumatic method, brush. The surface quality of the coatings was evaluated by the roughness and adhesion strength of the coatings. The surface roughness of the coating was determined using a TR-100 profilograph device, and the adhesion strength was determined by the method of puck separation.

Research result
Analysis of the data (Table 1) shows that the value of the surface roughness of the coating depends on the method of applying the paint composition, its rheological properties and the porosity of the cement substrate. So, for MA15 oil paint (green color), the minimum roughness value equal to Ra = 3.12 mkm is achieved on a substrate with a porosity of P = 24% with a paint viscosity of 0.00261.103 Pa.s when applied with a brush.
For paint PF-115, the minimum roughness value equal to Ra = 1.3 mkm is achieved on a substrate with a porosity of P = 28% with a paint viscosity of 0.00065.103 Pa.s when applied with a brush. For water dispersion paint, a minimum roughness value equal to Ra = 3.5 mkm is achieved on a substrate with a porosity of P = 32% with a paint viscosity of 0.013.103 Pa. with a porosity of P = 24% with a viscosity of paint 0.0347.103 Pa. s when applied with a brush. The minimum roughness value is characteristic of the surface of the coatings on the putty substrate, regardless of the method of application and the rheological properties of the paint formulations. Since the variances of the factor variables differ significantly from one another and there are disparate units of measurement, it is reasonable to use a correlation matrix (Table  3).