In the paper, the results of investigations on the properties of acoustic emission signals generated in a tested pressure vessel are presented. The investigations were performed by repeating several times the following procedure: an increase in pressure, maintaining a given pressure level, a further increase in pressure, and then maintaining the pressure at new determined level. During the tests the acoustic emission signals were recorded by the measuring system 8AE-PD with piezoelectric sensors D9241A. The used eight-channel measuring system 8AE-PD enables the monitoring, recording and then basic and advanced analysis of signals. The results of basic analysis carried out in domain of time and the results of advanced analysis carried out in the discrimination threshold domain of the recorded acoustic emission signals are presented in the paper. In the framework of the advanced analysis, results are described by the defined by the author descriptors with acronyms ADC, ADP and ADNC. Such description is based on identifying the properties of amplitude distributions of acoustic emission signals by assigning them the level of advancement. It is shown that for signals including continoues AE or single burst AE signals descriptions of such registered signals by means of ADC, ADP and ADNC descriptors and by Upp and Urms descriptors provide identical ordering of registered acoustic emission signals. For complex signals, the description using ADC, ADP and ADNC descriptors based on the analysis of amplitude distributions of recorded signals gives the order of signals with more accurate connection with deformational processes being sources of acoustic emission signals.
The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear discrete-time systems are established. It is shown that every fractional descriptor linear discrete-time systems is not pointwise complete and it is pointwise degenerated in one step (for i = 1).
The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k₁e ≤ f(e) ≤ k₂e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (–¹/k₁, –¹/k₂).
The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils.
The positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.
The positivity of fractional descriptor linear continuous-time systems is investigated. The solution to the state equation of the systems is derived. Necessary and sufficient conditions for the positivity of fractional descriptor linear continuous-time systems are established. The considerations are illustrated by numerical examples.
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to achieve some additional design requirements. An illustrative example shows the effect of the proposed approach.