Automated Model Verification Complexes are an important tool for research, testing, and verification of information and measuring instrument control systems, mechanical engineering, and other branches of technology. The model of the automated verification and simulation complex of the instrument system was developed based on the Model, instrument system, simulation, calibration, signal, measure, error, software-
quantization of the sum of input influences and additive interference are given.
of the obtained values, taking into account the operating conditions.
Therefore, in current conditions, the question of creating highly intelligent instrument systems that AMVC are closer to operational ones.
ICST-2023: Information Control Systems & Technologies, September 21-23, 2023, Odesa, Ukraine
ORCID: 0000-0002-6525-9721 (Volodymyr Kvasnikov); 0000-0003-0727-0508 (Lyudmyla Kuzmych); 0000-0002-3045-3508 (Svitlana Yehorova); 0009-0006-0593-4015 (Andriy Kuzmych); 0009-0003-3614-5228 (Vasyl Guryn).
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2023 Copyright for this paper by its authors.
The connection of the system under study with software in full-scale simulation is carried out using physical models and stands for the implementation of environmental influences and processor modules for generating and processing signals [3]. The combination of various mathematical and physical models, as well as the variety of systems or their components determines the diversity of the content of natural states has the form: ( ) = { ( ), ( ), ( )}, (1) where , - are function vectors; - is the vector of unmeasured perturbations (noise) acting on the system under study; - is the vector of observation and signal processing noise.
After a series of experimental tests, as a result of which an assessment of the state of the system under study is determined, the parameters of the latter can be optimized in accordance with its objective function. In Fig.1. the structure of research objects during testing is presented.
The impact in a complex of immeasurable disturbances and noise leads to measurement errors, the magnitude of which decreases with an increase in the number of experiments, i.e. with an increase in the time interval of research Statistical properties of the state vector ̂( ) of the system are described by a posteriori probability distribution density: 1 ( ) = likelihood function; - distribution density of the observation vector. where 0( ) - is the a priori probability density of the vector ; ( ) - is multidimensional In Fig.2. the model of the verification complex of the instrument system is presented.
In the case of automated verification of measuring devices, the method of calibrated signals is most often used. The highest level of automation of verification using calibrators is achieved when using a software-controlled measure. As shown in Fig. 2, a test signal from a PC-controlled measure is applied to the measuring instrument. The signal observed at the output of the tester is converted into a digital code and compared with the code of the test signal. Based on the comparison of the codes, the error at a certain point of the measurement range is determined. The procedure, according to which the processing of measurement results is carried out according to a certain software algorithm, is repeated at each reliable point of the scale of the measuring instrument.
Verification of the methods of standard instruments consists of the fact that an uncalibrated signal is applied to the verification instrument system, the value of which is automatically set by the measuring device of the instrument system to the verification mark of the scale. This signal value is measured by a reference measuring device. The value of the signal from the measuring device and the sample is processed using a PC in order to calculate the metrological characteristics of the calibration device. while the costs of verification are reduced. the center of gravity ̂ of the function 1 (
Measuring transducers can also be trusted in such an installation. Signals specified in the regulatory documentation are sent to the input of the converter to the trusted converter. The optimal method of verification will be when the quality of verification of measuring instruments will increase The minimization of errors in the evaluation of the vector z is connected with the determination of ) at the obtained value of the vector of observations .
The a posteriori integral estimation error of the state vector I1 (uncertainty of the system state) depends on the hyper volume of the body, calculated at 1 = , the value of which is equal to: component of the vector , - the number of components of the vector. where 1 - the proportionality coefficient; 1 - the mean squared error of measurements of the Considering the fact that there is a priori uncertainty of the system state let's introduce an indicator of the effectiveness of field studies: It is obvious that for an effective set of tests > 1, = 1
When designing AMVC, it is necessary to be guided by a number of basic principles. One of them is the principle of a system approach, which determines the creation of flexible hardware and software tools for automating the control of test technologies in accordance with the criteria for the functioning of the simulation complex. In addition, the principle of adaptability and development is important, which allows adapting the configuration of the AMVC for conducting research on a specific system, which ensures the further development of the complex, which is related to the modernization and updating of test tasks. And, finally, the principle of unification and modularity reduces the nomenclature of the component parts of the AMVC, which provides flexibility in the preparation and testing processes, which as a result reduces the cost of the complex.
The experience of development and experimental operation shows that the main characteristics of the AMVC functioning are five indicators: the adequacy of the signal and impact models, the accuracy of the assessment of the parameters of the state of the system under study, the system research time, the reliability of the complex, the cost of the AMVC.
The adequacy of the models determines the hardware and software complexity of the AMVC, which means that it affects its reliability and cost, and together with the assessment accuracy indicator, characterized by the vector of root mean square errors of the measurement of the state vector of the system, establishes the degree of reliability of semi-natural studies.
The system research time tі includes the full time from preparation to the end of the system research and determines the complexity and thus the cost of AMVC. The components of the indicator are: - time of preparation of the experiment, - time of conducting the experiment, and 0 - time of processing experimental data, i.e. = + + 0 . (3)
The experiment at AMVC is conducted in real-time. Therefore, the parameter tе cannot be unreasonably reduced or increased and is determined by a sufficient amount of statistics about the studied system, necessary for its identification.
In the software-hardware verification complex of full-scale simulation, the time for preparing the experiment is calculated as [6, 7, 8, 9, 10]: =1 = ∑( where - the time of creating the file and signal values; - the time of attestation of the signal signals that are used for system testing. parameters, - the time of loading the file into the signal generator, - the total number of simultaneously generated signals, - the time of entering the output data for modeling.
The file generation time is proportional to the number of counts in the file. The time of attestation of signal parameters i depend on the parameter estimation method. In the general case, for random signals, it is necessary to use correlation-spectral analysis [8, 11, 12, 13, 14]. Then the certification time is proportional to the square of the number of readings in the file and is the most capacious value in the expression for the time to prepare the experiment . The reduction is due to the full hardware implementation of the signal shaper. At the same time, the process of generation of readings, as well as attestation of parameters proceeds in parallel in the real-time scale of the experiment, therefore
= . Another reduction solution is to create a library of typical certified
The time of experimental data 0 processing to is determined by the time of calculation of diagnosed system
parameters and output (documentation) of information. The calculation of diagnosed parameters with the high performance of a specialized processing processor can proceed in parallel with the experiment, then = 0. Otherwise, the calculation is performed after the end of the experiment and the value of are proportional to the time of the experiment .
When developing AMVC, there is a natural desire to achieve the best values of each of the indicators of the complex. However, the improvement of one of the indicators can cause the deterioration of a number of other indicators due to countervailing relationships. The AMVC optimization criterion [15, 16, 17, 18, 19] deserves attention when two main indicators are distinguished: technical one, which determines the usefulness of the system; economic one or utility fee (cost of AMVC).
Optimization of the system is carried out by choosing the most acceptable option according to these two indicators while limiting other indicators of the complex.
Of the five named indicators of AMVC, the concept of usefulness is most satisfied by such an indicator as system research time. The simulation complex is designed to replace the time- and material-intensive full-scale tests with semi-full-scale tests. Therefore, the smaller the , is the higher the utility of AMVC. However, as decreases, the cost of achieving its value and the cost of the complex increase. The latter depends not only on the main parameter , but also on the adequacy parameters, as well as on the errors of estimating the parameters of the studied system. Optimization of the complex is related to the best combination of software and hardware within the framework of
The complex implemented in accordance with Fig. 2 solves the following main tasks of testing and the described optimization criterion [20-24]. checking the instrument system: different levels of simulation; simulation of sensor dynamics with an arbitrary position of the measurement object with formation of an adequate electromagnetic environment (signals and disturbances); modeling of the signal propagation environment; operational change of initial data, dynamic management of the testing process in real-time; collection and processing of current values of system sensor parameters and display in realspectral correlation analysis and documentation of research results.
The complex includes an IBM PC for modeling dynamic parameters of the environment and influences, an IBM PC for fixing and processing the states of the system under test, a specialized electronic block for forming electromagnetic influences and collecting information about the system state, and software. The electronic unit contains digital elements, including signal processors, analog nodes for system operation as part of the instrument system, information converters, and connections. The software is open, allows expansion, and is built according to the modular principle, with the possibility of software reconfiguration of the complex for the study of a specific system [25, 26, 27, 28, 29].
The basics of using simulation modeling to determine the values of error characteristics stem from the structure of the measurement procedure and the methods of determining errors and their characteristics.
When developing the principles of the application of simulation modeling in metrology, the experience accumulated in related fields of technology, in particular in automatic control, measuring technology, radio technology, etc., was used.
According to [20, 25], simulation modeling should be understood as "a method of mathematical modeling in which direct substitution of numbers simulating external influences, parameters and variables of processes into mathematical models of processes and equipment is used", that is, a method based on reproducing the procedure measurements in numerical form using a PC. Thus, for simulation modeling of the measurement process, it is necessary to have a software system, which includes programs for reproducing input effects, analog measurement transformations, analog-todigital transformations, processor-based measurement transformations, as well as programs for processing simulation results.
Calculation of the mathematical methodical error and the mean square deviation of the methodical error when quantizing the sum of input influences and additive interference.
Let and be the input influence and interference in the - th measurement experiment, respectively. The amount + . is received at the input of the Analog-Digital Converter (ADC). Then the adopted algorithm (measurement equation) will look like this:
Since the true value of is determined by the equation: ∗ = [[ + ]∆н [ ]0]
0 then the methodological error will be: where ∆м ∗ = [[ + ]∆н
0 [ ]0] − [[ ]0[ ]0] = ∆ ∗ + ∆к ∗,
м м 0
The first component is equal to and its characteristics correspond to the characteristics of the disturbance, i.e.: [∆м ∗] = [ ]; [∆ ∗] = [ ].
м
The second component is due to the quantization of the sum of two random variables: = + . Accordingly, to determine the characteristics of ∆км ∗, it is necessary to establish the type of density of the probability distribution ( ). In the general case, the density of the probability distribution of the sum of two random variables will be determined as follows:
The expediency of a new refined mathematical model, algorithms, and programs for calculating metrological characteristics during metrological certification of a new measured system was confirmed by Automated Model Verification Complexes (AMVC).
All the main conclusions made as a result of analytical studies were experimentally confirmed during the metrological certification of the system.
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