The paper presents a procedure for the determination of uncertainties in the modeling of surface roughness in the turning of NiTi alloys. The presented procedure is applicable both to the analysis of the measurement values of the two main roughness factors, as well as to research related to the prediction and optimization of the machining process. Type A and B, total, and expanded uncertainties were considered herein, and the obtained uncertainty values were assessed. A procedure for optimizing machining by applying the Monte Carlo (MC) method is also presented. The solutions presented in this paper are important from the point of view of practical solutions related to the prediction and optimization of the machining process. The considered procedure for determining and assessing uncertainty can be useful for the optimal selection of both machining parameters and measuring tools.

The solutions presented in this paper can be the basis for mutual comparison of different types of accelerometers produced by competing companies. An application of a procedure based on the Monte Carlo method to determine the maximum energy at the output of accelerometers is discussed here. The fixed-point algorithm controlled by the Monte Carlo method is used to determine this energy. This algorithm can only be used for the time-invariant and linear measurement systems. Hence, the accelerometer nonlinearities are not considered here. The mathematical models of the accelerometer and the special filter, represented by the relevant transfer functions, are the basis for the above procedure. Testing results of the voltage-mode accelerometer of type DJB A/1800/V are presented here as an example of an implementation of the solutions proposed. Calculation of the energy was executed in Mathcad 14 program with the built-in Programming Toolbar. The value of the maximum output energy determined for a specified time interval corresponds to the maximum integral-square error of the accelerometer. Such maximum energy can be a comparative ratio just like the accuracy class in the case of instruments used for the static measurements. Hence, the main analytical and technical contributions of this paper concern the development of theoretical procedures and the presentation of their application on the example of a real type of accelerometer.

In this paper, we propose using the radial basis functions (RBF) to determine the upper bound of absolute dynamic error (UAE) at the output of a voltage-mode accelerometer. Such functions can be obtained as a result of approximating the error values determined for the assumed-in-advance parameter variability associated with the mathematical model of an accelerometer. This approximation was carried out using the radial basis function neural network (RBF-NN) procedure for a given number of the radial neurons. The Monte Carlo (MC) method was also applied to determine the related error when considering the uncertainties associated with the parameters of an accelerometer mathematical model. The upper bound of absolute dynamic error can be a quality ratio for comparing the errors produced by different types of voltage-mode accelerometers that have the same operational frequency bandwidth. Determination of the RBFs was performed by applying the Python-related scientific packages, while the calculations related both to the UAE and the MC method were carried out using the MathCad program. Application of the RBFs represent a new approach for determining the UAE. These functions allow for the easy and quick determination of the value of such errors.