Model-based measurements in the monitoring tasks of high-power plants

The tasks of the measuring information obtaining about the state of the blading section and structural elements of gas turbine engines, as typical representatives of high-power plants, in the process of their experimental research and testing are considered. Such measurements are usually characterized by extreme environmental conditions, complex shapes and multidimensional movements of the monitored surfaces, strict constraints on the number and location of primary transducers, etc. As a result, the required measurement information is obtained under the influence of a large number of interfering factors, which are not always available for direct measurements and consideration in the experimental data processing. The approach based on the modeling the immeasurable components counting the current parameters of the power plant mode and environmental conditions is considered as an alternative to the direct measurements. The use of online models allows (in addition to increasing the reliability of measurements) to evaluate the unique characteristics of the monitored object (e.g., changes in shape) and, in some cases, to predict its critical state. The examples of the practical implementation of the approach in specific measurement systems designed for bench testing of gas turbine engines are also given in the article.


Introduction
Gas turbine engines (GTE) for aviation, marine and terrestrial applications are the typical representatives of high-power plants [1].The extensive use of GTE in various fields of industry and technology demands special requirements on their reliability and resource, simultaneously ensuring high economic and environmental performance.Considering of such contradictory requests and their implementation in a specific product requires the power plants' designers to implement difficult and often extraordinary solutions that need to be confirmed in practice.
It should be noted that the use of modern information technologies in the field of power plants' design, including the creation of engines' "digital twins" [2], can significantly reduce the development time of new GTE samples by replacing the long and expensive product improvement stages during the test benches with virtual experiments carried out with specially developed mathematical models.Nevertheless, the experiment is the only standard that confirms or rejects the correctness of the decisions taken and makes it sure that the declared characteristics of the engine are obtained.In addition to the research tasks, it is important to carry out the current monitoring and diagnostic functions of a power plant's state, which are implemented using appropriate technical means.
It is noted in [3][4][5] that the main GTE energy, strength, economic and environmental indicators are largely determined by the state of its gas-air path elements and by the magnitude of the radial clearances 2 (RC) between the rotor blades' tips and the stator of the compressor and turbine, as well as by the magnitude of the axial gaps between the impeller's and outlet straightener's blades.Among other matters, it is indicated that the decrease of the RC value improves the efficiency and stability of the engine, but its excessive reduction may lead to an accident.The vibro-stressed state and integrity of the working blades of the compressor and turbine (e.g., at stall, surging or when the foreign objects get into the engine's gas-air path) can also be determined by the position monitoring of the working blades' tips relative to a fixed point on the stator of the power plant (blade tip-timing technology) [6][7][8][9].And, finally, the detection of the wear particles in the engines' lubrication systems is one of the reliable methods to assess the state of the machines' moving parts and mechanisms of highly loaded machines [1,[10][11][12].
Despite the existing variety of methods for measuring the state parameters of the power plants, their implementation is limited by very harsh and even extreme conditions in the gas-air path, which are associated with high temperatures in the measurement zone (1000C or more in GTE turbines), high linear speeds of the monitored elements, contamination of the measuring medium, vibrations, etc. [13] The measurement methods based on the eddy current sensors are one of the most promising methods in such extreme conditions [14][15][16][17][18][19][20][21][22][23].In turn, the single coil eddy current sensors (SCECS) for aviation applications with sensing element (SE) in a form of a single current loop or its part (e.g., a segment of a linear conductor) constitute a separate and independent branch among the existing eddy current probes [19,22,23].The simplest design of the SE is highly reliable, is high-tech, and does not require the use of the high temperature winding insulation.Furthermore, the use of the materials with a high melting point for the manufacture of sensor's structural elements provides the required mechanical and thermal resistance of the sensor and its operability under extreme temperatures in GTE gas-air path without additional cooling.
It is noted in [13] that the process of the information obtaining about the state parameters of GTE structural elements and its gas-air path with the help of SCECS occurs under the intense influence of a large number of external and internal factors related to the specifics of the machine design and its operation features.Such an influence is not always possible to measure and take into account when processing primary measurement information.In this case, unaccounted factors become a source of uncertainty [24] and may cast doubt on the reliability of the obtained measurement results due to the appearance of additional errors.
The use of on-line models of the monitored objects and measuring tools that take into account the current object's mode and environment parameters, can smooth out and, as far as possible, eliminate these doubts ("verify" the measurement results [25]).Moreover, these models, in fact, can be considered as the channels of "virtual" correction, ensuring the reduction of additional measurement errors associated with the appearance of initially unaccounted interfering factors.The transducers integrated into SCECS (e.g.thermocouple) as well as standard measuring tools which are a part of power plant or bench equipment (speed transducers, pressure and flow sensors, etc.) may be the sources of the information about object's mode and environment parameters.
It should also be noted that the joint processing of experimental data and online simulation results allows to evaluate the unique parameters of the propulsion systems during the experiments (e.g.deformation of the stator shell [26]).In addition, the models can be used to determine the residual life of GTE critical elements, considering real operating conditions in the transition from routine maintenance to actual maintenance of the propulsion systems [27].
This article is devoted to a review of practical tasks focused on the use of model-based measurements in the conditions monitoring of highly loaded structural elements of blade power plants.The generalized concept of the measurements is considered and the examples of the approach implementation in various systems for monitoring the state of the GTE design elements intended for bench tests of power plants are given.At the same time, it should be noted that in accordance with the classification [28], measurement systems implementing the approach considered in the article are called knowledge-based measurement systems.

The concept and typical tasks of model-based measurements
Separate implementations of the model-based measurement approach were published earlier in [24,[29][30][31][32][33].At the same time, the solution of new practical problems, as well as the analysis of the earlier obtained results led to the revision, correction, and generalization of the certain provisions of the approach.Fig. 1 summarizes the functional diagram of the system implementing the concept of modelbased measurements.The "physical" measurement channels are shown as solid lines in the figure, and their "virtual" analogues which provide the calculation of influencing factors and correction of the results, are dotted.The monitored object (power plant, GTE) is characterized by a vector of measured (monitored) parameters PM (blade tips movement, blade vibrations, shaft movement in thrust bearings, the number and size of wear particles of friction pairs in lubrication systems, etc.) and a vector of object's mode and environment parameters PE (temperature in the measuring zone, shafts' rotational speed, etc.).From the point of view of the tasks being solved, the elements of PE vector are the influencing factors that often have an interfering (negative) effect on the measuring tools [13].
It is assumed that SCECS and/or their cluster varieties are used to measure the state parameters of the power plant [19].In turn, the object's mode and environment parameters are usually monitored by standard measuring tools (RPM sensors, thermocouples, etc.), which are a part of power plant or bench equipment.
After the PM and PE conversion, they are transformed into CМ and CE vectors that usually contain digital codes corresponding to the elements of PМ и PE vectors.Separate measurement results of mode and environment parameters in the form of digital codes CE or directly calculated physical values PE * (e.g., angular velocities and accelerations of the rotor, temperatures in the measurement zone, etc.), can be directly used for the algorithmic correction of the monitored parameters conversion results [13].
The online simulation unit is central on the functional scheme on fig.condition is that the calculations must be carried out at the experiment rate for current operation conditions and the environment state.Thus, the main requirement for the models is their performance.It should also be noted that despite the wide use of microprocessor technologies in modern measurement systems, the resources of on-board computers are still significantly inferior to full-scale CAE-systems used, for example, to simulate the GTE operational processes [34].Therefore, the simulation algorithms embedded in the systems should not impose excessive requirements on RAM, CPU time, etc.The solution of these problems may require the use of simplified or unconventional models based on new principles (e.g., fuzzy logic models [32,35]) in the measurement systems.Nevertheless, even with the simplifications, models should generate a plausible set of time-changing output vectors of SNM (nonmeasurable influencing factors), SD (deformations), SR (residual resource).
If, for example, it is not possible for the reasons of constructive or technological nature to install the sensors on the power plant or on the bench to measure the environment and mode conditions that affect the conversion of the monitored parameters (PМ * ), then the results of the physical measurements (PE * ) are replaced by their virtual analogues, obtained by calculating the corresponding behavior models of the object and/or the measuring tools (SNM).The models can also be used successfully to solve the problems related to the study of the deformations of power plant design elements (D * ).For example, it is known that the RC between the working blade tips and the inner surface of the compressor or turbine stator is the closing size.Therefore, the information about the RC contains not only data on radial displacement of the engine's rotor components, but also data on deformations at SCECS location points.At the same time, the separation of information about the coordinates of the displacements and deformations of GTE designed elements gives the important information to GTE developers, the value of which increases if the information is received in real time.If the impeller's beat is absent or negligible, the stator shell deformation is determined by measuring the physical values of the gaps on engine's dry motoring and working regimes, considering RC changes due to the elastic and temperature deformations of the impeller elements calculated using the appropriate models (SD).
The assessment of the residual resource (R * ) of GTE parts and assemblies (e.g., bearings in GTEdriving units) is another area of the models' application in the monitoring tasks of power plants' state parameters (fig.1).It is obvious that the actual operating conditions of the unit may differ from those which are specified in its technical documentation.Therefore, unit's residual resource can vary both in decreasing and increasing.To evaluate the resource the comparison of the current measuring information about unit's operating conditions (PM * ) with the corresponded modeling results of its destruction (SR) is used [36].For example, for forecasting of bearing remaining resource the model (it relies on a common theory of the destruction process of friction pairs) calculates the intensity and size of metal particles washed from the working surfaces by the oil flow depending on the number of working revolutions of the bearing.The results of the model calculation are compared with actual information deriving from metal parts (debris) detection measuring system.If measuring results do not exceed modeling values, then the model is used for calculation of the remaining resource of the bearing unit.When there are significant differences between modeling results and measurement data, especially for increasing the real rate of metal particles (debris) in the oil and their size, the system goes to the mode of forecasting of "critical" time before bearing's emergency destruction on the basis of expert assessments.

The examples of practical applications
The section describes some model-based measurement systems that implement certain provisions of the concept discussed above.The systems are focused on bench tests of GTE and their components.However, the possibilities of the approach are not limited only to the practical tasks considered in the article and can be successfully expanded to other applications characterized by similar conditions for information obtaining about the state of monitored objects.

System for radial clearances' measuring in GTE seals
The system (fig.2) was developed for monitoring the shafts' radial displacements during the testing of the brush seals of aviation GTE on a specialized bench.The technical equipment of the system consisted of two pairs of SCECS with elongated current conductors, a device-matching unit and two PC, equipped with standard analog and discrete data acquisition facilities (PCL-712 boards) [19,29].In each sensors' pair one SCECS performs working functions and directly interacts with the monitored object.The second SCECS (SCECS-witness) performs compensatory functions and provides the reducing of additional temperature error.The PC functions of the system are also different.One is used for operation monitoring and the other -for continuous recording of measurement information.Initially, it was supposed that overall dimension of the monitored object guaranteed SCECS placing when the axial displacements of the rotor were minimal and did not affect the measuring result and could be neglected.However, the first system launches on the test bench produced the results that could not always be interpreted correctly in terms of the monitored object functioning.The attempt to assess the reliability of the RC measurements was the impetus to a kind of "intellectualization" of the system by supplementing its software with rapid simulation tools of RC changes in SCECS installation areas.The simplified fuzzy logical models of temperature and elastic deformations of the structural elements of the monitored object (fig.3) were used.These models with acceptable accuracy (discrepancies in fuzzy model results with numerical models did not exceed 4%) provided the performance of 1-4 orders higher than traditional approaches.The temperature conversion results in the SCECS location areas, obtained by the built-in thermocouples, and rotor speed measuring results, obtained by RPM sensor (DCHV-2500), which is a part of bench equipment, were used as the initial data for simulation.
The comparison of the empirical and model data at the pace of the experiment supported the verification process ("validation") of the measurement information and made it possible to identify some operation features of both the specialized bench and the measuring system [37].In particular, axial movements of the shaft in the radial thrust bearing affected the measuring results were detected and subsequently considered.

System for RC measuring and deformation monitoring of the ducted propfan stator
The RC measurement system [26,38] was designed for bench and on-board tests of the ducted propfan installation with gear-driven shrouded contra-rotating front fans (Kuznetsov NK-93 engine) [48].The main objective of the experimental studies was associated with the monitoring of the dangerous RC between the propeller blade tips and the stator internal surface on a running engine.The hardware of the system (fig.4) included four SCECS with individual converters of sensors' informative parameters, an embedded input/output board for analog and discrete signals (ADC board of L-Card company) and PC.The sensors were placed in one cross section regularly along the generating line of the stator.In addition to RC measuring, the system also allowed to estimate the deformation of the engine stator shell in real time, which was of particular interest to the developers of the power plant.The operating modes of the propfan engines are characterized by significant loads on its structural elements, which are 2.5-4 times higher compared to a conventional propeller [39].Under the influence of aerodynamic loads, the blades have significant bending deformations, and therefore their tips perform multidimensional movement in SCECS sensitivity zone.
Measuring the displacements of power plants' structural elements along several coordinates is traditionally provided by the cluster methods based on using the groups of identical SCECS which sensitive elements are oriented in a certain way toward the monitored surface and the number of sensors in the cluster corresponds to the number of measured coordinates [13,26].In the case under consideration, it was impossible to place more than one SCECS at each control point.Therefore the "unmeasured" coordinates of the tips' displacements were calculated using specially developed models of the blade's bending under aerodynamic loads [26].The fan speed measuring results and the angle of the blades' rotation were used as the initial data for the simulation (corresponding sensors belong to the engine control system).Moreover, the extension of the system's software with models of elastic and thermal extensions of rotor structural elements provided the calculation of the propfan's stator shell deformations in real time (fig.5).

System for diagnostics and estimation of remaining resource of GTE bearings
In contrast to previously considered model-based measurement tools (see sections 3.1, 3.2), the system for diagnosing hazardous conditions of GTE bearing assemblies and assessing their residual life is in the initial stage of the development.Currently, only some of its components have been implemented, primarily in the terms of technical means for collecting and processing measurement information about the friction pairs' state.The description of SCECS-based hardware and software of the system for the determination of axial loads of radial thrust bearings and the detection of metal wear particles in GTE lubrication system is given in [20,23,40].The actual development of the bearings' destruction models, as well as the models for assessment of their residual life has not yet been conducted and is the subject of the further research.Nevertheless, the approach to the construction of such a diagnostic system is formulated in [27].It involves the combined use of the results of continuous monitoring of influencing parameters on rotors bearings, the results of detection of metal particles in the GTE lubrication system, modeling of bearings wear and expert verification of its remaining resource.According to the authors opinion, the models will allow to connect the real operation conditions of the bearing with its operating time and to calculate more accurately the bearing remaining resource.In this case the expert system will predict the time before bearing active destruction and will help to take action to prevent the emergency situation.

Conclusion
The specifics of most modern tasks of measuring and monitoring the conditions of complex technical objects (e.g., GTE), their components and assemblies, is that they are often accompanied by a difficult information situation, which is characterized by significant a priori uncertainty about the properties of the monitored object and its environment, impossibility to directly observe many of the influencing factors, inaccuracy, and incomplete experimental information about them.The use of classical methodology in such a situation often makes the solution ineffective due to the poor quality of the result and the uncontrolled level of residual uncertainty.The incorporation of the models, which reflect our knowledge and understanding of the processes taking place in the monitored object and appropriate measuring tools, into the measuring procedures will increase the measuring systems' possibilities and expand the limits of their applicability.One possible concept of the approach, as well as the examples of implemented or planned measurement systems, has been presented in the article.At the same time, it should be particularly noted that the of modern electronics and microprocessor technology removes certain limitations related to the performance and complexity of the models used in the systems.It gives hope for a wider application of the proposed approach.

Figure 1 .
Figure 1.Functional diagram of the system implementing the concept of model-based measurements.
1.The CE(PE * ) vectors are the input parameters for the behavior models of the monitored object and measurement tools.The models set is determined by the specific test task and can vary from experiment to experiment.An indispensable

Figure 2 .
Figure 2. System for radial clearances' measuring in GTE seals: Technical equipment.

Figure 3 .
Figure 3. System for radial clearances' measuring in GTE seals: Fuzzy modelling software.

Figure 4 .
Figure 4. Hardware of the system for RC measuring and deformation monitoring of the ducted propfan.

Figure 5 .
Figure 5. Working screen with the results of RC measuring and determining the deformations of propfan's stator shell.