PrefaceThe development and use of models of various objects is becoming a more common practice in recent days. This is due to the ease with which models can be developed and examined through the use of computers and appropriate software. Of those two, the former -high-speed computers -are easily accessible nowadays, and the latter -existing programs -are being updated almost continuously, and at the same time new powerful software is being developed.Usually a model represents correlations between some processes and their interactions, with better or worse quality of representation. It details and characterizes a part of the real world taking into account a structure of phenomena, as well as quantitative and qualitative relations. There are a great variety of models. Modelling is carried out in many diverse fields. All types of natural phenomena in the area of biology, ecology and medicine are possible subjects for modelling. Models stand for and represent technical objects in physics, chemistry, engineering, social events and behaviours in sociology, financial matters, investments and stock markets in economy, strategy and tactics, defence, security and safety in military fields. There is one common point for all models. We expect them to fulfil the validity of prediction. It means that through the analysis of models it is possible to predict phenomena, which may occur in a fragment of the real world represented by a given model. We also expect to be able to predict future reactions to signals from the outside world.There are many ways of the describing a system or its events, which means many ways of constructing a model. We may use words, drawings, graphs, charts, tables, physical models, computer programs, equations and mathematical formulae. In other words, for modelling we can use various methods applying them individually or in parallel. If models are developed by the use of words and descriptions, then the link between cause-and-effect is usually of qualitative character only. Such models are not fully satisfying as the quantitative part of the analysis is missing. A necessary supplement of modelling is the identification of parameters and methods of their measurement. A comprehensive model that includes all these parameters in a numerical form will help us explain the reactions and the behaviours of the objects that are of interest. The model must also enable us to predict the progression of events in the future. Obviously, all those features are linked directly to the accuracy of the model, which in turn depends on the construction of the model and its verifications. Preface VIThe most common and basic approach to modelling is the identification approach. When using it, we observe actual inputs and outputs and try to fit a model to the observations. In other words, models and their parameters are identified through experiments.Two methods of identification can be distinguished, namely the active and passive, the latter usually less accurateThe identification experiment lasts a certain period of time. Th...
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.
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