MULTIMEASURE OPTIMIZATION AND MONITORING TECHNOLOGY
FOR THE AIRCRAFT GAS TURBINE ENGINES AND THEIR ELEMENTS
Egorov I.N., Moscow, RUSSIA, 3 Jine 1996.
The current state in the mechanical engineering industry is characterized by the fact that the initial stage of a rapid introduction of a computer tools into designing and development processes is practically over. This has caused a qualitative new leap in a development of science-intensive and complicated objects, relieving designers from a lot of routine job and permitting to sensibly apprehend and effectively use a large volume of information on an object under study. At present, the efforts of many scientists are aimed at developing intellectual systems of a higher level, where within the frames of a computer friendly milieu, not requiring to master a large variety of current achievements and knowledge in the field of mathematics, programming and applied sciences, a designer, for making final decision, is given for an expert examination a set of alternative design versions, which are the best ones by one or other quality indexes.
Nowadays, engine manufacturing companies of the world carry out intensive studies, pertaining to a design and development of engines of a new generation and creation of a scientific back-log for next generations. It is assumed that such studies will allow to improve an efficiency by 10...15%, reduce a specific weight by 20...40% and enhance engine service life by up to 3 times.
Making the requirements to engine characteristics more stringent and expanding spheres of using flying vehicle (FV) have caused a necessity to widely use a flow path mechanization. This, in its turn, has stimulated a development of a HIDEC-type control units of aircraft gas turbine engines (GTE) where high accuracy on-board digital electronic computers of high capacity are used. Apart from this, speaking of the perspective military engines there is expected a high level of nonuniformity of an incoming flow and its change during an engine operation within a wide range. There is also anticipated a significant increase in the part of nonstationary modes during a flying cycle. All this testifies to a necessity to develop and use complicated algorithms of the optimum control and monitoring in real time. This can be realized on the basis of optimization of the programs to control variable elements, which are determined according to the conditions of ensuring maximum efficiency in prescribed flying modes with consideration for the levels of external effects on an engine under provision of a gas dynamic stability and with consideration for the technical state of the main engine elements. Development of powerful on-board digital electronic computers will make it possible to realize complex laws to control a large number of variable elements, which will necessitate a search for optimum laws to control a lot of factors and creation of a scientific potential in this direction.
Analysis of possibilities to improve aircraft GTE characteristics has been practically conducted from the beginning of a wide application of jet engines. Until recently the main part in the increase of aircraft GTE specific parameters belonged to the shaping of cycle parameters, that is an increase in gas temperature in front of the turbine and total pressure ratio. However, in perspective engines the gas temperature is already approaching a stoichiometric one. Therefore experts link possibilities to improve engine characteristics with a search for new design solution, with using perspective materials, improving efficiency of individual elements, assuring their optimum matching as included in GTE, optimum frame/engine matching, developing high-intellectual automatic engine control units using on-board digital computers etc.
Thus, due to a substantial sophistication of GTE, increase of their loading and number of variable elements, there arise very serious difficulties to ensure a high level of their efficiency. Proceeding from the concept of developing perspective engines, this problem becomes particularly urgent and vital. With the current complexity level of the aircraft GTE, large number of design-point parameters and achieved gas dynamic perfection, the search for the means to improve GTE efficiency is directly related to a certain extent with a solution of optimization problems.
Despite an evident effectiveness of using aircraft GTE optimization, at present there is known just a relatively small number of works devoted to this problem [1...9,11,13, 15,16]. We assume that it is due to specific features and difficulties in statement and solving the tasks of optimization of engines and their elements, when modeling at a pre-set level of complexity and hierarchy degree. Into this category fall a large dimensionality of the optimization problems (of the order of a few tens or hundreds variables), topological complexity of a function to be optimized and constraints, a lot of computer time required to investigate the aircraft GTE and their elements with required complexity level (2-D and 3-D models), necessity to olve the tasks in a multicriteria setting, high probability of a multiextremulity of the goal function, the large number of constraints etc.
Note, this problem is a integrated one and results in a need for solving a wide range of the complicated particular problems. It is a development of mathematical models of an object which allow to solve a wide class of scientific problems in the field of aircraft engine manufacturing (designing, control, monitoring etc.). It is also a search, modification or, even, a development of such procedure’s of nonlinear programming which ensure to a certain extent a possibility to solve complicated practical problems of optimization. Besides, not less important is a fundamental unity of an engine mathematical modeling with nonlinear programming. Figuratively speaking, one must "plunge" an aircraft engine into optimization medium. Namely, a complex unity of a high level of GTE mathematical modeling with current optimization procedure’s may permit to define the ways and evaluate possibilities to improve the efficiency of current GTE.
It should be noted that there are few specialists, engaged in solution of practical optimization problems at a professional level in the field of mechanical engineering. An existent opinion, that optimization problems of the given object do not require a respective training of engineers and are easily solved by experts-mathematicians, is totally incorrect. It turns out that any mathematician is practically helpless when formulating, solving and, especially, analyzing the most of the applied problems, based on fine and complicated physical processes and specific features of a complicated object under study. Not a single application-oriented expert, without appropriate knowledge in the field of optimization, will be able to formulate and competently set a mathematically intricate problem of a nonlinear programming. To-day, a practical usefulness of engine optimization problems is generally achieved in the cases, when it is required not only to use the latest advances in the field of nonlinear programming, but to solve some new optimization problems, which are just at a theoretical phase of a development.
Therefore, first, at the current level of perfection of aircraft GTE the solution of optimization problems is necessary; second, availability of powerful computers and up-to-date advances in the field of engine mathematical modeling and nonlinear program-ming create a real basis to solve such a problems; and, at last, professional training of specialists in aircraft engine manufacturing is, on the whole, at such a level, that the-ory, methods and specificity of optimization is quite simple and clear to a broad section of specialists. This enables to make a conclusion of an importance and urgency to develop a methodology of optimization for the aircraft GTE and their elements.
In order to solve this problem in the Air Force Engineering Academy were developed the information-calculation technology of optimization studies problematically oriented to the investigations, comparative analysis, search for the ways to improve the efficiency and prediction of elaborating of aircraft engines during their designing, operational development and modification by means of a multimeasure (up to 200 and more variables) optimization of parameters, characteristics and laws to control in both steady and unsteady operating modes. Within the frame of this paper we can point out only the main features of these technologies without some details.
Despite a generality in solving complicated applied tasks of nonlinear programming with consideration for aircraft engines, there is a number of specific features. Experi-ence proves that optimization of such an intricate object, as an aircraft engine, presents in itself not a pure "mechanical" use of a mathematical model and procedure of nonli-near programming. In essence, it is a whole process of optimization studies (OS) of GTE and their elements, and for realization of this process it was necessary to develop of a strategy of search for the most effective technical solution, based on corresponding methodological, algorithmical, program and other means. One of the main problem was that at present the conceptual aspects of aircraft GTE optimization problems are not outlined in full. These aspects include a wide range of questions, for instance: analysis of specific features of the optimization tasks for engines and their elements, their classification; substantiation of the requirements to mathematical models (MM) of an object to be optimized; investigation into possibilities to use MM during an optimization of different levels of complexity and hierarchy degree of modeling; analysis of efficiency and applicability of nonlinear programming methods for a given class of the tasks; determination of possibilities to use them according to a number of variables, level of complexity of modeling; substantiation and selection of a computer type for the studies; assessment of time expenditures to conduct OS; formulating of the requirements to both mathematical models and optimization methods, etc., etc. Not less important aspect is to indicate a structure of an engine optimization strategy, to determine the main phases, their sequence and interconnection.
MM of an object under study is an important means to carry out OS. This MM must be an open in the sense of a possibility to put up and use the modules, evaluating specific features of an object from various standpoints (technological, structural, gas dynamic, strength, costs etc.). This requirement is in a full conformity with an available trend of a multidiscipline approach to the investigations into aircraft GTE and their elements.
However, in GTE optimization problems one must consider not just a "simple" MM but the object's optimization model, which presents in itself a totality of this MM; optimization criterion (criteria), which makes it possible to assess the quality of one or another solution; variables to be varied, which determine through what there is effected an effort to improve an effectiveness of a technical solution; constraints, which determine an area where a search for extremum is allowed; and, also, determination of an area of the GTE operation, that is an area, which determines an engine specificity as a technical system with consideration for peculiarities of engine operating modes.
For the real-life problems of aircraft GTE optimization one should take into account some nonlinear programming aspects that are still at a stage of a theoretical development. They include a multicriteriality and large dimensionally of the problems for multiextremum, nondifferentiated, stochastic and nonconvex goal functions.
For example, during a search for the most effective technical solutions, it is of high priority to have a possibility to solve the problems of a large dimensionality. It is qualitative demonstrated in Fig.1 on the base of the results of number compressor's optimization problems solving. It is evident, that the most increase in a compressor efficiency is achieved with a large dimensionality of an optimization task, that is to say in the area, where intuition and experience of designers is practically feeble. Moreover, one knows great efforts of scientists-mathematicians aimed at solving the multimeasure problem during optimization of nonlinear goal functions. In the opinion of experts, the tasks, having a dimensionality of more than 30 variables, are considered as very complicated, and it is highly problematic to achieve a practical result [12,13]. And this is illustrated by the fact, that only single examples of solution of the tasks of this class are known [1,3,5,11].
A multiextremum problem in optimization is well known. In spite of great efforts of experts, there are no, even up to now, methods, which permit to determine a global extremum with a probability 1.0. This problem is so serious, that at present there are no even universally recognized multiextremum test function, using which it could be possible to assess an efficiency of one or another multiextremum algorithm. Actually, today we can only speak of a development of such a method, which makes it possible to determine a global extremum with high probability. At the same time the multiextremum problem in the field of aviation occurs more often than one can expect. As an example Fig.2 demonstrates a change in compressor efficiency depending on the 2 structural parameters of blade rows. Initially, it was very difficult to assume an availability of several extreme, and not only of this but even of such topological complexity of the goal function and constraints as well.
Another not less important problem is a problem of multicriteria optimization. On the one hand, it is of great interest for any designer to look through a whole set of optimal design-point solutions according to the different criteria, analyzing which one selects the most acceptable compromise solution on the basis of permissible concessions by one or another particular criterion. On the other hand, it is important to develop a design of an engine, which has a high efficiency over the whole range of operating modes. For instance, an article [1] demonstrates that an optimum compressor, designed with consideration for a single, the so called "design-point" operating mode, may have a low efficiency in other modes. Therefore, to optimize design-point parameters in this very operating mode, as it is suggested in papers [11,13,16], is probably of low effectiveness for practical needs. And, at last, a requirement is possible to ensure an extremity of not one but several engine parameters over a wide range of operating modes. All this inevitably results in the problems of a multicriteria optimization, whose solution require to develop the special algorithms [8,10].
Development of a "technique" to obtain an extremum value and, especially, its analysis as such is a problem, which is no less important during GTE optimization. And the latter is of great significance for practical needs, since experts are, probably, more interested in a behavior of a criterion of optimization and constraints in the extremum area and not an optimum solution in itself. Besides, an urgency of the developed optimization technology may consist in a fact, that there is a rather wide range of problems when optimization is used indirectly. This can be exemplified by identification, diagnostics, processing of experimental data, the tasks of nonlinear and interval assessment etc.
When solving the problems of increasing GTE efficiency it is necessary to use the mathematical models that are of a very high significance. On the one hand, a requirement to in-depth and detailed studies of GTE in order to investigate into new phenomena and processes, which can make it possible to determine new technical solution, results inevitably in a necessity to develop intricate algorithms of calculation. When modeling such complex objects as aircraft engine, using a computer, the time required for studies on powerful computers may amount to tens and hundreds of hours [2]. On the other hand, a more detailed study of an object results generally in an increase of a possible number of parameters to be varied, whose optimum matching must be ensured. And this brings forth a set of problems, such as, for instance, a large dimensionality, complicated topology of a function to be optimized and constraints etc. Under these conditions, an availability of a high-speed super computer to successfully solve a given class of tasks is a necessary although insufficient condition. For these purposes there is required a development of new high effective structural-parametrical procedure’s of op-timization which are practically invariant to a topology of a function to be optimized and permit to recognize a situation during a search for extremum, adaptively change the parameters of an algorithm and strategy of a search. These procedure’s permit to carry out an adaptive setup of an algorithm to a particular practical problem of optimization directly during a search for extremum. One of the possible versions of a such kind algorithms is the Indirect Optimization method on the basis of Self-Organization (IOSO) [2], which forms the basis of the optimization technology.
A necessity for close integration of design-theoretical studies with direct manufacturing process can be regarded as a peculiarity of a current level of developing mathematical modeling in the field of engine manufacturing. It can be exemplified by the technology of aircraft engine production at the Rolls-Royce company known as "Simultaneous Engineering" (SE) [14]. Experience of the R-R company has proved that SE makes it possible to directly introduce into production the most effective design-theoretical results, obtained with consideration for the latest achievements in the field of production technology. And this both ensures a high level of production and encourages development of such theoretical studies, which have a real practical result. Synthesis of CAD and CAM allows to introduce into a project advanced scientific-technical developments and improve simultaneously a quality of mathematical modeling. Other leading engine manufacturing companies of the world also use their own technologies, which reflect their specificity and their own concept of GTE designing. Note, that practically in any of such technologies a problem of search for optimum design solution (more or less perfect judging by a degree of a design) occupies a prominent place.
However, all the known technologies use the so called "deterministic" approach, based on the assumption that the final (obtained) project will be realized in actual practice with absolute accuracy. But, as it is known, not a single, even the highest production technology can ensure this. The fact, that one considers at best a level of production technology only in a mathematical model of an object under study without regard for a real deviation of design-point parameters directly during a search for optimum solution, results in a low probability of realizing a design solution in actual practice. Thus, the absence of consideration for a level of production technology of an object during a search for the most effective technical solutions may result in an unjustified risk when ensuring indexes set at a designing stage. Such a design solution doesn't correspond in full measure to the notion "optimum", because it doesn't take into consideration a probability of realizing a project.
It seems, that the given problem can be successfully solved by means of GTE and its element optimization in stochastic setting, when under insignificant impairment of efficiency, as compared with a deterministic solution, one succeeds to provide a probability of realizing a project close to 1.0 [6]. The papers [4...8] present some aspects of the developed technology usage for the problem of stochastic optimization of GTE and its elements. Fig.3 presents one of the examples. One may see that a probability of realizing a project obtained in deterministic setting doesn't exceed 0.6. Unlike this a project obtained in stochastic setting ensures a probability close to 1.0. Thus, a project designed and developed at a high professional level may remain just a good project if one doesn't consider a probability of its practical realization during a design and development stage.
Considering a process of designing an engine and its elements from this standpoint, one may see a possibility to solve a wide class of problems, which are very important for the actual practice. This approach makes possible the following: to effect designing for a particular level of production technology; to determine a probability to obtain design-point indexes under impairment of a technology level at separate sections of production assessing at the same time economic return; to substantiate a required level of an object production technology and predict its requirements when designing a new sample; to carry out a search for the most "narrow" spots both in a project itself and in a production cycle; at a stage of designing an object to prescribe in an object project particular properties (e.g., small changes in characteristics of a turbomachine during an exhaustion of service life in a dusty area under respective change in geometrical parameters of rows). This list of problems can be expanded. It should be noted, that deterministic setting of an optimization problem, traditionally used when designing a project, is merely a particular case of stochastic optimization of an object.
The developed technology allowed us to solve a number of optimization problems for the real gas turbine engines and their elements, that now have been developing in a leading Russian scientific-industrial organization, and also in some gas-turbine firms all round the world. The technology is invariant to the object under study and can be adapted for practical problems in various fields of science and engineering. In particular, this technology have been successfully used not only in the field of aircraft gas turbine engines, but in the fields of power plants, automotive engines and optics.
Application of the developed technology for the decision of optimum control problems for the power plants of flying vehicles it is impossible without availability of the authentic information about a state and main parameters of functional elements of a engine. While in service change of such parameters occurs, that it is necessary to take into account at the decision of optimization problems. For the decision of a given problem the technology of the monitoring and diagnostics of complex technical systems can be used. This technology have been developed in the scientific-production company "Techno-Pulsar" on the basis of long-term researches in the area of processing the on-board parametrical information and behavior of air systems in real flight conditions.
The essence of given technology consists of multistep mathematical processing of the parametrical information for the steady-state flight modes on the basis of the results of:
- study of the control laws and principles of work of controllable systems from the point of view them observability through registered parameters;
- research of the parameters which are the most correlated with an output signal:
- definition of the most characteristic for particular device sites of the control.
Pre-filtrated and the sorted out parametrical information is subjected to the dispersion, regression and factor analysis with the purpose of reception of the most exact mathematical models of observable systems, on the basis of Fisher, Student, Tiku and other works. The received mathematical model presents from self the n-measure area, a center of which is a design target parameter. The essence of the monitoring is reduced to valuation of a rule of true measurement in relation to the n-measure area. Normal a rule is that the true measurement is inside the n-measure area. Is otherwise evaluated dispersion, trend and character of the true measurements exit from the individual n-measure areas with the essential or dangerous change of target parameter definition. The valuation of a projection of astable measurement on a axis of the n-measure area and duration in a time permit to define the source parameter, negatively influencing on tar-get parameter. The valuation of diagnostic attributes of controllable devices and their stability in a time permits to predict a state of a system on long term (up to several tens of hours of flight ).
Important principle of the technology reliability is a principle of constant self-training of mathematical models of controllable devices at occurrence of operations modes unknown for system or new combination of source parameters. Important advantage of technology is tolerance to errors of measuring systems, as the controllable system is studied such, which it is at date of statement under the control and its further behavior is further analyzed. The given technology is realized for the vibration state control of engines D-30KP, PS-90, as well as control of a lot of systems of a plane MiG-29 and systems of automatic control and vibration state of the engine RD-33.
The authors are deeply convinced that a development of a such technologies, easily understood by a wide circle of experts, will permit to significantly extend our insight into engines, improve a general level of qualification of experts, considerably decrease time and costs to develop these objects. Undoubtedly, there will be obtained fundamentally new technical solutions, which will enable to significantly improve the efficiency of our engines and reliably cope with complicated and versatile problems of the aviation of tomorrow.
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