Azizov A.M. Single-channel principle of invariance in the dynamics of measuring systems

Monograph. — SPb.: Naukoemkie technologii, 2020. — 112 p. — ISBN 978-5-6044429-4-4.The physical single-channel principle of invariance based on the statement and solution of the extended problem of dynamic measurements is considered. In this formulation of the problem, both the signal to be measured and the parameters characterizing dynamic properties of the linear measuring system are considered unknown.
This principle of invariance allows us to solve a number of complex tasks of dynamic measurements, including the most important problem of elimination of the influence of parametric phenomena on measurement accuracy.
The main applied focus of the monograph is the field of measurement of non-electrical parameters of technological processes. The above mentioned methods and results can also be used to solve the general problem of determining the reaction of the input action object for linear non-stationary dynamic objects of any nature.
For scientists and technical engineers.Introduction.
Mathematical models of typical subsystems that are sources of parametric phenomena.
Subsystems with lumped parameters.
Subsystems with distributed parameters.
Sources of parametric phenomena.
Manifestation and analytical accounting of parametric effects.
Invariance in the dynamics of measuring systems.
On the formulation of the problem of dynamic measurements.
Physically single-channel principle of invariance.
Invariance algorithms for linear measuring systems with lumped parameters.
Invariance algorithm for one class of nonlinear measuring systems.
Model implementation of single-channel invariance principle.
Methods of construction of basic SLAE (simultaneous linear algebraic equations) for recovery of measured signals.
Direct and indirect criteria for the accuracy of signal recovery.
Modeling of recovery processes of measured signals.
The first scheme of invariance algorithm implementation.
The second scheme of invariance algorithm implementation.
Modeling of recovery processes of typical deterministic signals.
Special issues related to the application of the invariance principle.
On the stability of invariance algorithms.
Invariance algorithm for linear measuring systems with lumped unstructured parameters.
Single-channel invariance principle for measuring systems with distributed parameters.
Parametric phenomena in statistical dynamics of measuring systems.
Elements of the theory of Markov random processes.
Statistical methods of moment equations.
Parametric effects in the dynamics of measuring systems.
The principle of invariance in statistical dynamics of measuring systems.
Conclusion.
References.