4. Conclusions

The prognostic models considered in this chapter are built on the assumption that each observed signal to a certain extent reflects the internal state of the object being studied. In engineering, in medicine, the observed signal is at least indirectly due to the processes occurring in the mechanisms and bioobjects. The task of a complete set of measured parameters as a whole is hardly solvable; one way or another, when studying any object, a model of the object itself is needed, capable of reflecting not only the instantaneous state but also the evolution of the object over time. The observed signal, as a rule, is not obtained directly from an evolving object, because it is impossible to place an accelerometer or a pressure sensor directly into the boiler of

prognosis model in the works [5, 14]. In the most general formulation, the optimization task is reduced to carrying out the necessary maintenance and variation of the management parameters in order to maximize the stay of the process trajectory

In the field of medical applications (cardiology), we can take as an example the transfer of automaton of the R-R interval to the processor of portable ECG recorder for multi-day monitoring. In addition to this automaton and depending on the general analysis of the evolution of states, automata of a specific purpose are also installed. For example, an automaton for the QT interval, which can autonomously predict a change in the QT interval with an estimate of the time, it takes to reach critical values of a given ECG interval. All of the above is also true for the definition and evolution of such ECG indicators as R-R pause length, QT interval dispersion, and other significant ECG predictors of cardiac events. It should be recalled that the onboard automata can also go offline and manage the computing kernels of the remote cluster. In the above example, such transition is carried out on the basis of the prognosis obtained by the onboard automatic devices. In other cases, an automaton on one of the leads may be sufficient, and a specific cascade corresponding to,

in a given homotopy class. The preventive monitoring cluster architecture described above allows reducing the computation time on a remote cluster by transferring a small part of the automata to the monitored object using onboard

for example, the average value of one of the ECG teeth, is monitored.

using wearable ECG gadgets, bracelets, and mHealth platforms.

computations by the entire set of cluster automata.

The described manipulation with automata allows minimizing the cost of the traffic of all ECG leads, as well as the costs associated with the abundance of

Of course, the described optimization of calculations increases the comfort of

events, taking preventive measures to eliminate them or minimize the consequences. An example should be the procedure for optimizing drug therapy for atrial fibrillation. The well-known fact that antiarrhythmic drugs used in the treatment of arrhythmias can provoke the appearance of life-threatening arrhythmias. Timely adjustment of the dose of the drug, the rejection of the drug, and its replacement with another drug is one of the actual problems during treatment. In this situation, predictive automata solve the problem of optimizing drug therapy, determining the ineffectiveness of prescribed drugs, thereby reducing the time they are taken. On the other hand, automata predict with an estimate of the probability and time to achieve proarrhythmic effects, which allows the doctor to take steps in advance to

However, the general goal in this case is prognosis of the life-threatening cardiac

Consider the field of monitoring engineering for mobile objects, in particular, in transport and directly monitoring for internal combustion engines, hybrid engines. Here, as onboard signaling automata, it offers an automatic device that processes signals from onboard standard sensors, for example, a crankshaft angle sensor or a pressure sensor on common rail systems, etc. With an onboard computer and graphics processors, the number of automata can be increased by covering most of the standard sensors that give an analog or digital signal, for example, the automata processing of the so-called uneven stroke. The evolution of the states of automata that process uneven stroke based on the crankshaft angle sensor reflects the evolution of the cylinder-piston group and, therefore, predicts the development of the most dangerous predictors of failure associated with changes in the combustion mode of the fuel mixture. Adding an accelerometer to the family of standard sensors for analyzing the vibrations of the engine body allows to expand the prediction capabilities for the main friction pairs in the engine mechanics and analyze the status of injectors and high pressure fuel pump (diesel engines). The calculated

computing power.

Fault Detection, Diagnosis and Prognosis

correct the treatment.

40

a nuclear reactor, glue the patient's heart with electrodes and install a pressure sensor in the working part of the aircraft turbine. Thus, in the end, there is a signal from only ten electrodes from the surface of the human body; the sensors of the machinery are installed far enough from the combustion zone in engines and turbines. Everything briefly listed above leads to the appearance of artifacts of various natures in the signal, and these artifacts must be taken into account in order to isolate the useful part of the signal. In addition to all the above, signals from the so-called distributed systems are usually analyzed. Strong heterogeneity, complex geometry, and complex processes supporting the functionality of these systems are not restored and not reproduced by a set of a dozen sensors. Therefore, by virtue of the above, physical models of objects and their evolution are needed, using the so-called concise description, where, often, an infinite set of measured parameters necessary for modeling the system is replaced by a much smaller number of parameters. The simplest example and classical descriptive compression is the equilibrium thermodynamics, when coordinates and momenta of all particles are reduced in thermodynamic approximation to such quantities as temperature, pressure, etc.

Ultimately, the predicting set of automata will have the ability to adapt, i.e., restructuring of its entire structure with changes in the properties of the observed signal, adding signals from new sensors, and changing the operating conditions of

Predicting Sets of Automata: Architecture, Evolution, Examples of Prognosis, and Applications

Thus, the family of automata is capable of analyzing a multitude of signals from various sensors, which makes it possible to use them in all types of engineering and medicine. In the initial stage of operation of the automata, one should limit ourselves to standard onboard diagnostic sensors, which allows one to obtain the necessary data on the need for additional sensors, which, in turn, provides further calculation of the ROI for construction of optimizing maintenance strategies, cal-

engineering.

Author details

Sergey Kirillov<sup>1</sup>

43

and Yuri Kaganovich<sup>3</sup>

\*, Aleksandr Kirillov<sup>1</sup>

\*Address all correspondence to: skirillovru@gmail.com

1 SmartSys Prognosis Center, Moscow, Russia

provided the original work is properly cited.

, Vitalii Iakimkin<sup>1</sup>

2 Center for Advanced Life Cycle Engineering, University of Maryland, MD, USA

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

3 Department of Cardiology, Assuta Medical Center, Tel Aviv, Israel

, Michael Pecht<sup>2</sup>

culating optimal operating conditions, etc.

DOI: http://dx.doi.org/10.5772/intechopen.83807

In the cases under consideration, the main emphasis in constructing the prognostic model for evolving distributed systems is to take into account the internal symmetry of the observed signal, without discussing the relationship between the internal signal symmetry and the symmetry inherent in the state of the object and the processes in it.

So, internal symmetry allows representing a signal as a product of slowly varying amplitude and a rapidly oscillating phase cofactor. The phase cofactor has symmetry groups, which acts transitively in pseudo-phase space. Ultimately, the state of the system is described as a vector in multidimensional space, and when taking into account the space of degeneration of a point in the space of degeneration, the evolution of the system is a trajectory of states in the space of degeneration or a multiple space of loops. Further analogies with the theory of topological defects of condensed media make it possible to formalize the evolution of the prediction problem in the form of the evolution of the set of trajectories, their transformations, and a change in the types of trajectories with various kinds of lifting degenerations. The transition to symbolic space, and in fact to the space of probability measures, offers different interpretations of the evolution of a measure in time, in particular, in the form of a complex-arranged walk of the point in a multidimensional simplex. This, in turn, allows to construct families of predictive automata, the evolution of which internal states takes into account the topological nontriviality of the space of degeneracy. Considering the topological nontriviality and, as a result, the topological nontriviality of the set of trajectories determines the complex topological dynamics of the trajectories and the dynamics of the interaction of topological singularities and, most importantly, provides an opportunity for algorithmic construction of the search and definition of predictors of various events associated with changes in the characteristics of the trajectory. Finally, it becomes clear that any change in the characteristic features of the trajectory is associated with the violation of the corresponding symmetry, the removal of the degeneracy in groups or subgroups of the isotropy of the space of degeneracy.

The resulting set of automata has a number of properties that must be mentioned in the context of their further development:


### Predicting Sets of Automata: Architecture, Evolution, Examples of Prognosis, and Applications DOI: http://dx.doi.org/10.5772/intechopen.83807

Ultimately, the predicting set of automata will have the ability to adapt, i.e., restructuring of its entire structure with changes in the properties of the observed signal, adding signals from new sensors, and changing the operating conditions of engineering.

Thus, the family of automata is capable of analyzing a multitude of signals from various sensors, which makes it possible to use them in all types of engineering and medicine. In the initial stage of operation of the automata, one should limit ourselves to standard onboard diagnostic sensors, which allows one to obtain the necessary data on the need for additional sensors, which, in turn, provides further calculation of the ROI for construction of optimizing maintenance strategies, calculating optimal operating conditions, etc.
