*2.1. The Subject of Research*

Approaching the soil processing phenomenon using an MCLS-type structure involves the statistical processing of experimental results (descriptive and inferential statistics, random process theory). Descriptive and partial inferential statistics were discussed in a previous article [41]. In this article, the focus will be on approaching the problem within the theory of random processes. In another article [41], all the data strings that are generated by the contact between the ground and the working body have a random character and are comparable to the pseudorandom strings generated by special programmes or to the strings of prime numbers of the same length.

In order to approach it within the theory of random functions, the phenomenon of ground processing by each organ was considered a phenomenon of random vibrations. The main random component is the excitement of the process. Excitation is generated by the interaction of the working body with the ground. In the range of demands considered, the vibrations can be considered linear-elastic.

In this article, the analysis will be made only for the MCLS variant with a working width of 1 m because, in the case of this variant, signals were collected from all the supports of the working bodies throughout the experiment. The analysis carried out on the simple version with a width of 1 m can later be extended to the versions with higher working widths, for which the load on each support cannot yet be measured and other random parameters also appear (for example, the clearances in the truss with a working width of 4 m).

The indexing of the measurement locations and the signal transmission channels from the deformation sensors to the acquisition board are shown in Figure 5. An image of the MCLS variant in experimental work, on the parcelled track of the polygon, with the complete data acquisition equipment, is shown in Figure 6.

**Figure 6.** MCLS variant with a working width of 1 m in operation with a 45 HP tractor.

2.1.1. The Formulation of the Problem in Terms of the Theory of Random Vibrations

According to [42], physical processes that cannot be characterised by deterministic functions, i.e., vibrations whose instantaneous values cannot be predicted as functions of time, are called random. The random nature of the vibrations of the investigated structure was demonstrated in [41], where even the degree of randomness was quantified. A relatively simple criterion for experimental recognition of the randomness of a phenomenon that is experimental is formulated, for example, in [42]: if, in several experiments organised under identical controllable conditions, the measured quantities differ only by quantities of the order of errors of measurement, the phenomenon can be considered deterministic; it is reproducible, so its development after the moment of measurement is predictable. Otherwise, the phenomenon is random. Apparently, the criterion seems simple, but in the case of soil processing and, in addition, using non-conventional and insufficiently verified structure load measurement systems (strain gauge methodology), this criterion is difficult to use. Given the findings from [41], we opted for the random vibration variant to describe the working process of the 1 m working width version of the MCLS complex cultivator.

The main characteristic of a random variable is the distribution function [43,44]. This is defined according to Formula (1).

$$F\mathbf{x}(\mathbf{x}) = P(\mathbf{X} < \mathbf{x}) \text{, } \mathbf{x} \in \mathbb{R} \tag{1}$$

where *FX* is *the distribution function of the random variable x*, *<sup>x</sup>* is a real number, and R is the set of real numbers. In Formula (1), some authors use non-strict inequality.
