United States Air Force Academy. USAF Academy, CO 80840. Keith M. Boyer, Maj, USAF. Department of Aeronautics. USAF Academy, CO 80840. Kelly Cohen ...
41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, Reno, Nevada
AIAA 2003-89
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AIAA 2003-5738
AIAA 2003-0089 WIND TUNNEL COMPRESSOR OPTIMIZATION AND EFFICIENCY ROLLOFF PREDICTION USING FUZZY LOGIC Roland A. Rosario, 2d Lt, USAF United States Air Force Academy USAF Academy, CO 80840 Keith M. Boyer, Maj, USAF Department of Aeronautics USAF Academy, CO 80840 Kelly Cohen, LtCol, IDF Department of Aeronautics USAF Academy, CO 80840
41st Aerospace Sciences Meeting & Exhibit 6-9 January 2003 Reno, Nevada For permission to copy or to republish, contact the copyright owner named on the first page. For AIAA-held copyright, write to AIAA Permissions Department, 1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
AIAA 2003-0089
WIND TUNNEL COMPRESSOR OPTIMIZATION AND EFFICIENCY ROLL-OFF PREDICTION USING FUZZY LOGIC Roland A. Rosario, 2d Lt, USAF* United States Air Force Academy USAF Academy, CO 80840
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Keith M. Boyer, Maj, USAF Department of Aeronautics USAF Academy, CO 80840 Kelly Cohen, LtCol, IDF Visiting Researcher Department of Aeronautics USAF Academy, CO 80840
Abstract The topic of interest presented herein is the possibility of approximating compressor performance, particularly efficiency roll-off, using Fuzzy Logic. The “data” used to support and validate this research come from a streamline curvature numerical model of a large, three-stage, axial flow compressor, which drives a 16-foot square test section wind tunnel. A basic fuzzy inference system was created by implementing conceptual rules that were determined by several experienced operators of the wind tunnel. The fuzzy approximator was first constructed using 4 inputs with fairly good results. Increasing to 6 inputs provided significant gain in simulation fidelity. Results indicate the ability to model the performance of the compressor near the aerodynamic operating limit, thereby offering the potential for eliminating hard-limit operating boundaries. This study shows that it’s feasible for Fuzzy Logic to successfully act as a decision-maker with its ability to differentiate contours of constant efficiency across the compressor map as well as provide insight into impending compressor operating instabilities such as surge. Nomenclature 16T AEDC’s 16x16 foot test section transonic wind tunnel AEDC Arnold Engineering Development Center,
Arnold AFB, TN C-1 16T wind tunnel compressor CPR Overall compressor total pressure ratio DF Diffusion Factor FIS Fuzzy Interference System FL Fuzzy Logic FLC Fuzzy Logic Control IGV Inlet Guide Vane MF Membership Function OGV Outlet Guide Vane S1 C-1 stage 1 stator vane row S2 C-1 stage 2 stator vane row S3 C-1 stage 3 stator vane row SLC Streamline curvature Introduction Operators of wind tunnels that utilize multi-stage axial flow compressors for creating airflow conditions are interested in optimum performance for reasons of economics and test capability. One such wind tunnel is AEDC’s 16T transonic wind tunnel facility, the power consumption of which is on the order of 100 megawatts at high subsonic test conditions. The C-1 compressor powers the 16T wind tunnel. The C-1 is a three-stage, axial flow compressor with variable restagger inlet guide vanes (IGV), stator vanes (S1, S2, S3) and outlet guide vane (OGV) for control of compressor pressure ratio (CPR) required to obtain desired test section flow conditions. Figure 1 is a schematic diagram of the C1 compressor.
*Research performed while Lt. Rosario was Cadet at USAFA. Now stationed at NAIC/FTAW, Wright-Patterson AFB, OH. 1 American Institute of Aeronautics and Astronautics This paper is declared a work of the US Government and is not subject to copyright protection in the United States.
AIAA 2003-5738
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Figure 1: C-1 Compressor Schematic Diagram Currently the three stator vane rows are slaved to the IGV by a schedule1. The demand CPR is achieved by control of the IGV only for operation above synchronous speed (600 RPM) and by control of both the compressor RPM and IGV below synchronous speed. Rosario & Steinle2 address the possibility of increasing the efficiency and performance of the C-1 compressor by improving the current stator vane restagger schedule with the use of a neural network application. It was found that a neural net was in fact capable of approximating all the values of stator vane restagger angle that would allow the compressor to operate more efficiently. The only limitation was encountered at the fringe of the operating envelope, where the techniques used to numerically approximate the compressor operation were not sufficient to model the efficiency roll-off and performance. It is desirable for the wind tunnel operators to maximize the performance and efficiency of the compressor as much as possible by reducing the safety margin without ever endangering the machinery, especially at the extreme operating conditions. Currently, safety measures are installed into the C-1 control system so that the compressor will never operate at such a condition as to damage itself by operating outside safe limits and inducing harmful effects such as surge (compressor stall). These limitations on the compressor operation are often times too conservative, limiting its performance capabilities. One reason for this is that the failsafe limits are mostly hard-limit values. That is, if the compressor exceeds a certain value such as the ratio of fluctuating pressure (rms) to inlet stagnation pressure, then the compressor operation is directed to a safe condition (including emergency shut-down in extreme circumstances). Current methods of preventing surge and other harmful effects are not capable of making “shades of gray” decisions, which results in blocked regions of the operating envelope where the compressor could potentially operate safely. Fuzzy logic is capable of non-linear mapping as well as the blending of linguistic knowledge with numerical data. This paper explores the possibility of using fuzzy logic to approximate the efficiency of the compressor, including regions of the operating
envelope where roll-off is observed. This application could eventually lead to the integration of fuzzy logic into the control scheme of the wind tunnel allowing greater performance and efficiency while maintaining a safe margin (although not as conservative as in the current control system) from harmful effects to the compressor. Since fuzzy logic is capable of dealing with situations where one may not be able to sharply distinguish between the boundaries of application of rules or constraints, it is possible for fuzzy logic to act as a decision-maker in the C-1 control system, safely expanding the operating capability of the 16T wind tunnel. The purpose of the study contained herein is to investigate the possibility and benefits of such an application. Background COMPRESSORS: The C-1 compressor is a “classic” high aspect ratio (blade span to chord) 1960’s design. As such, it is well suited to be represented numerically by a streamline curvature (SLC) throughflow model. The applicability and description of the specific SLC method to the C-1 compressor was presented by Rosario and Steinle2. Compressor performance predictions from the model were essential due to inadequate C-1 experimental data. Multistage axial compressor performance is typically characterized by a compressor map (Figure 2). The map shows isentropic efficiency and CPR plotted against air flow rate for numerous compressor rotor speeds. The compressor operating line is typically scheduled to ensure 20-25% stall margin. Compressor stall can occur locally or globally as the relative air angle of attack gets too large and can be accompanied by flow reversal and excessive unsteady aerodynamic loadings on the blades and vanes. For these reasons, avoidance of the stall line is a must. The isentropic efficiency is a measure of the ideal work of compression versus the actual work of compression. As indicated in Figure 2, for a given rotor speed, efficiencies are low for small blade loadings (low flow turning resulting from small air incidence angles), increase with loading until a peak is reached, and then typically decrease as the stalling air angle of attack is approached. This “efficiency roll-off” is typical of most high aspect ratio compressors and is the focus of the current investigation. As implied in Figure 2, efficiency rolloff can be an important indicator of impending stall. A key aspect of a Fuzzy Logic scheme in the current application is the ability to recognize impending compressor unstable operation.
2 American Institute of Aeronautics and Astronautics
AIAA 2003-5738 Because of the need to ensure adequate stall margin, the nominal compressor operating point is below that for peak efficiency for many compressors (indicated on Figure 1 by vertical line through the design point). Consequently, the compressor is not operating at its maximum efficiency. The ability to “recover” this efficiency by safely operating closer to the stall line is additional motivation for the current work.
membership function. This feature enables the designer to approximate the desired input-output mapping in a particular region without having to affect the approximation in other regions as in the case of a global mapping system. The interpolative nature of the fuzzy approximator results in smoother transitions between rules. This feature avoids the “Boolean if” statement that introduces a discontinuity or sharp edges in the approximation5.
Efficiency roll-off
Isentropic efficiency
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Stall line CPR
Stall margin 20-25%
Operating line Design point
The major mechanisms of the fuzzy logic approximator are: a set of if-then statements called linguistic control rules and a fuzzy inference system that interprets the values in the input vector and, based on the linguistic rules, assigns values to the output vector. The structure of a fuzzy logic approximator is depicted in Fig. 3. The purpose of these principle components, based on Lee6, and the subsequent functional behavior in context to this effort are summarized below.
Lines of constant rotor speed
RULE Air flow
Figure 2: Schematic of Compressor Map FUZZY LOGIC: Fuzzy logic, which is the logic on which fuzzy control is based, is a convenient way to map an input space into an output space3. The logical system that captures the spirit of our approximate, imprecise world was introduced by Lotfi Zadeh4 as the theory of fuzzy sets, which in time proved to be a very powerful tool for dealing quickly and efficiently with imprecision and non-linearity. The experience of the past decade, with the successful marketing of a wide variety of products based on the FLC2, has shown that for certain applications, use of FLC can lead to lower development costs, superior features, and better end product performance. One of the inherent properties of fuzzy logic systems is that it has the capability of being a universal approximator. This implies that by using adequate inputs, a number of rules and a number of fuzzy sets for each input variable, a fuzzy based system can approximate any real continuous nonlinear function to an arbitrary degree of accuracy2. There are two main attributes of importance that make fuzzy logic approximators attractive for the current application. These include the locality of the approximation and the interpolation among rules. When the input membership functions are coupled together with the antecedent of a fuzzy rule, it specifies a “patch” in the antecedent space of the output. Subsequently, the output rule specifies the local approximation based on the nature of the output
“INFERENCE” COMPUTATIONAL UNIT
“DEFUZZIFICATION” ASSIGNMENT INTERFACE
“FUZZIFICATION” INTERPRETATION INTERFACE
PLANT
Figure 3: Fuzzy Logic Approximator The interpretation interface: a) measures the values of the input variables, b) performs a scale mapping that transfers the range of values of input variable into corresponding universes of discourse, and c) performs the function of fuzzification that converts input data into suitable linguistic values which may be viewed as labels of fuzzy sets. The knowledge base: a) provides necessary definitions, which are used to define linguistic control rules and fuzzy data manipulation in an FLC and b) characterizes the control goals and control policy of the domain experts by means of a set of linguistic control rules.
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AIAA 2003-5738 The decision-making logic: has the capability of simulating decision-making based on fuzzy concepts and of inferring fuzzy control actions employing fuzzy implication and the rules of inference in fuzzy logic. The assignment interface: In order to reach a practical approximator a specific action comprising of a single numerical value is required. Therefore, the space of the antecedent is mapped into a non-fuzzy space (crisp) in a process known as defuzzification.
operating envelope, but others pushed the limits testing FL boundary prediction hypothesis. Figure 4 is a plot illustrating the location of the numerical data points used in this study in relation to one map of empirical data points previously gathered (1994 compressor calibration, constant RPM, stator schedule according to Ref 1). The solid black points in Figure 4 represent the points that the fuzzy system was to approximate.
1.6
Approach 1.4 CPR
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1.5
Due to limited experimental data, compressor “data” were provided by application of a streamline curvature model, discussed in the Background section of this paper. Inputs to the SLC model include compressor flowpath geometry, airfoil section information, blade and vane geometry – inlet and exit metal angles (angle of camber line extension at the trailing edge with the compressor axis), solidity (chord/spacing) maximum thickness, and location of maximum camber – and specification of operating condition to be approximated – speed and flow. Output includes compressor and thermodynamic property data at the leading and trailing edges of each blade/vane row and at each radial streamline location specified by the user. The radial distribution of performance was not important for the current work.
1.3 Full Map
1.2
Region of interest
1.1 1.0 10000
12000
14000 16000 18000 Corrected Mass Flow (lbm/sec)
Figure 4: Compressor map comparison of empirical data points to SLC modeled test points
The data that was created with the numerical method described above was treated as “actual” to which the FL approximation was compared. There are several reasons that the SLC model data can confidently act as the baseline data. First, it has been shown that the SLC method used is a good numerical model and any constraints that the model may experience are negligible in the scope of this study. Second, the compressor in question is a basic design, lending itself very well to the techniques used in the SLC calculations. The final reason and perhaps the most important of all is that the SLC model was used to optimize each of the data points used in this research above the current operating standard. The criteria used to optimize the compressor operation was equal work whereby matching the work, or temperature rise, that each stage produced would result in the most efficient operation. Since the compressor in question has three repeating stages, this is a valid assumption.
The efficiency was maximized for each data point. All but a scarce few of the data points were matching work produced between stages to within a few percent, resulting in the most efficient operation for a given mass flow and CPR. The higher efficiency was achieved by finding the optimal S1 and S2 restagger angles. These operating conditions are a marked improvement in efficiency produced by the compressor for the same operating conditions (mass flow and CPR) due in large part to the conservative stator vane schedule currently in place1. One of the main reasons for the current stator schedule is compressor safety. Even though the SLC computed data points are showing higher efficiency at the same operating conditions, each data point was checked to ensure that feasible and safe operating conditions were simulated (DF equal to or less than 0.6). Referring back to the objective of the study, the question that this research attempts to answer is whether use of Fuzzy Logic will provide a method robust enough to predict these higher efficiency points and adequately model the safety margin for operation at these higher efficiency conditions.
One characteristic of the SLC model that affected the region of data points tested was that the code was limited to simulating compressor operation at moderate mass flows. It was incapable of producing points at very high or very low mass flow rates where internal flow physics were violated. Most of the points lay within the heart of the compressor
Throughout the course of the research presented, two fuzzy inference systems and rule bases were developed. First, a simple approach with only 4 inputs and a limited number of membership functions and rules showed that a fuzzy system could in fact mimic the trend created by the actual compressor efficiencies. A total of 11 linguistic rules were
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20000
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AIAA 2003-5738 identified by the experienced wind-tunnel operators, or compressor experts as being desirable for monitoring of a safe operating margin7. These rules were simply words describing the very thought process governing the operation and safety of the wind tunnel. The rules included everything from blade stress margins to ratios of RMS fluctuating pressure and CPR. Due to the constraints of the SLC model the available data had to be adapted to the rule base, yet still accurately reflect the behavior of the compressor. One adaptation was the diffusion factor, which, as an output of the SLC code, reflected the rate of change of pressure ratio with guide vane angle. Although it was not a dynamic output, it was a reasonable assumption that a DF over 0.6 indicated that the rate of change of pressure ratio with guide vane angle was closely approaching zero. As the rate of change of pressure ratio with guide vane angle approaches zero, stall is imminent, which, of course necessitates the compressor safety margin. Ultimately, all of the original 4 rules revolved around three concepts delivered among the 11 “expert” rules: rate of change of pressure ratio with guide vane angle, CPR and equal work produced by each stage. The 4 original inputs were as follows: CPR margin, DF margin, stage 1 equal work margin and stage 2 equal work margin. The CPR margin was defined as the normalized CPR ranging from 0 to 1 (Eq 1). It varied from less than 0.1 to greater than 0.6.
CPRm arg in = CPR − 1.0
(1)
The DF margin was 1.0 minus the ratio of the actual diffusion factor to the maximum DF, or 0.6 (Eq 2).
DFm arg in = 1.0 −
DF 0. 6
(2)
As the DF margin increases (caused by the actual DF decreasing), the compressor operation becomes safer. However, DF margin varies inversely with efficiency such that lower DF margins generally yield greater operating efficiency. Other variables notwithstanding, the compressor operation is considered safe if the DF is below 0.6. The last two inputs were essentially the same concept. The first stage equal work margin is 1.0 minus the ratio of the absolute value of the difference between the total temperature rise (work produced) across stage 1 and stage 2 to the preceding stage total temperature rise. Similarly, the second stage equal work margin applies to the difference between the work produced by stage 2 and stage 3 (Eq 3).
Stage1EqWorkM arg in = 1.0 −
∆Tt rise− st1, 2 Stage1Tt rise (3)
The higher the margin is, the greater the efficiency achieved. Lower margins indicated a greater difference in work across the identical stages. As previously described, each input requires membership functions in order to be a fuzzy inference system. In the first trial, with only 4 inputs, only three membership functions were applied to each input. Although the first trial was simple, the results were satisfactory. It was not until more complexity was added with two more inputs and several more rules that the Fuzzy Logic prediction became much more accurate and subtle nonlinearities were more easily resolved. The reason for including both in this paper is to illustrate the improvement in the accuracy of the prediction from one trial to the next. The two inputs that were added to the prior existing ones from the first trial were S1 and S2 restagger angles. Adding membership functions to the existing 4 inputs increased the resolution of the FL prediction function; however, due to the extreme variability of the efficiency function for the conditions mapped, more inputs were needed to improve the accuracy. This should have been obvious from the beginning since the algorithm used to derive the higher efficiency operating points with the SLC directly depended on S1 and S2 as variables. The efficiency was directly optimized by adjusting the two stator vane restagger angles. Without the two added inputs the existing 4 were simply incapable of capturing all the changes in efficiency. In many cases, rules and membership functions that improved the accuracy of the efficiency function in one place had a contradictory effect in another. It was impossible to further resolve the prediction by refining the membership functions because the input values for the two opposing patches would always occupy the same membership functions. Adding S1 and S2 inputs helped resolve some of these instances, but even the 6 inputs were not enough in at least one case. Since there were other variables, in addition to S1 and S2, that directly affected the efficiency (such as IGV angle), the remaining inaccuracies in the prediction are expected. The results confirm that even without a complete input set, the resolution of the fuzzy system still improves. MATLAB® and its accompanying Fuzzy Logic Toolbox were used as the main engine for the FL system development. No adaptive measures were attempted. This is reflected in the recommendations.
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AIAA 2003-5738
Figures 5 and 6 are a straight comparison of the efficiency by both the SLC model and the FL prediction as a function of the operating point number. The operating point number arbitrarily identifies the data points used here and roughly corresponds to increasing CPR and mass flow as the operating point increases. Table 1 is a listing of various parameters for each of the operating point numbers. Referring back to Figure 4, each of the black, solid points are represented in Table 1. The approximate pattern that the points follow, increasing in operating point number, is a walk through of several mass flow rates varying by 500 lbm/s for each of several values of CPR from 1.1 to 1.6 varying by 0.05. This relationship is apparent in the table. The table also sheds light on the formation of the variations in efficiency as a function of each of the inputs. 100 90 80
Efficiency (%)
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70 60
SLC Model FL
50 40 30 20 10 0 0
20
40
60
Compressor Operating Point
Figure 5: Efficiency comparison by compressor operating point number between SLC model and FL prediction for first trial (4 inputs)
100 90 80 Efficiency (%)
All refining of the fuzzy inference system was an iterative process with manual tuning of the rule base and the membership functions. Up to 9 and as little as 5 membership functions per input were used in the final, and more accurate, trial. A variety of membership functions were employed including triangular, trapezoidal, Gaussian and Gaussian squared functions. The MFs were generally broad and not too localized. One distinct advantage that fuzzy logic demonstrated over other, traditional predictive methods was its ease of use for FIS refinement. Results
70 60
SLC Model FL
50 40 30 20 10 0 0
20
40
60
Compressor Operating Point
Figure 6: Efficiency comparison by compressor operating point number between SLC model and FL prediction for second trial (6 inputs) Table 1: Compressor operating point table Operating Point 1
CPR 1.1056
Corr mdot (lbm/s) 14000
2
1.1017
14500
4.5
1.81
3
1.1005
15000
2.38
-0.22
4
1.0946
15500
0.25
-2.51
5
1.0995
16000
-2.06
-4.06
6
1.1546
13500
8.09
6.19
7
1.1555
14000
6
4.08
8
1.1567
14500
3.84
1.9 -0.16
S1 (deg) 6.6
S2 (deg) 4.09
9
1.1465
15000
1.87
10
1.1401
15500
-0.31
-2
11
1.1555
16000
-2.68
-3.97
12
1.2011
13500
7.45
5.89
13
1.2082
14000
5.24
3.79
14
1.1983
14500
3.32
1.72
15
1.2092
15000
1.03
-0.39
16
1.2001
15500
-1
-1.85
17
1.2099
16000
-3.4
-4.06
18
1.258
13000
8.44
8.04
19
1.257
13500
6.54
5.48
20
1.2581
14000
4.43
3.45
21
1.2556
14500
2.38
1.33
22
1.257
15000
0.25
-0.76
23
1.2541
15500
-1.95
-2.17
24
1.2495
16000
-4.07
-4.36
25
1.3092
13000
7.4
7.39
26
1.3035
13500
5.65
4.87
27
1.3098
14000
3.44
2.81
28
1.2954
14500
1.67
1.03
29
1.3027
15000
-0.5
-0.5
30
1.3048
15500
-2.88
-2.67
31
1.3017
16000
-5.02
-4.8
32
1.3557
13000
6.45
6.02
33
1.3483
13500
4.65
4.19
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AIAA 2003-5738 34
1.3472
14000
2.65
2.23
35
1.355
14500
0.39
-0.03
36
1.3545
15000
-1.79
-1.27
37
1.3555
15500
-3.93
-3.48
38
1.4082
13000
5.05
4.55
39
1.4071
13500
3.08
2.72
40
1.3998
14000
1.3
1.01
41
1.3955
14500
-0.6
0
42
1.399
15000
-2.83
-2.15
43
1.4033
15500
-5.13
-4.44
44
1.4568
13000
3.43
2.81
45
1.4512
13500
1.7
1.25
46
1.4592
14000
-0.42
0
47
1.4548
14500
-2.47
-1.79
48
1.46
15000
-4.69
-4.04
49
1.4487
15500
-6.45
-5.77
50
1.5063
13000
1.3
-0.16
51
1.5059
13500
-0.5
-0.5
52
1.5007
14000
-2.29
-1.93
53
1.5076
14500
-4.58
-4.12
54
1.5002
15000
-6.25
-5.73
55
1.4917
15500
-7.98
-7.64
56
1.5593
12500
-0.86
-2.5
57
1.5433
13000
-1
-1.67
58
1.5515
13500
-3.23
-4.09
59
1.5474
14000
-4.69
-5.03
60
1.5429
14500
-6.37
-6.31
61
1.5492
15000
-8.66
-8.87
62
1.5595
15500
-12.06
-8.94
63
1.5921
12000
2
2
64
1.5907
12500
-0.06
8
65
1.5939
13000
-5.59
-7.98
66
1.5975
13500
-6.94
-10.53
67
1.5978
14000
-8.41
-11.25
68
1.5969
14500
-10.06
-12.42
69
1.6011
15000
-13.73
-9.25
CPR at a fixed RPM is achieved by setting IGV, S1, S2 and S3 angles. The result of these settings is the diffusion factor, equal work margins and the efficiency. Figure 5 is an attempt to model the efficiency using the CPR, DF and equal work margins. Comparison of Figures 5 and 6 plainly shows that an increase in complexity, or taking into account more “knowledge” (6 inputs instead of 4), corresponds to improved predictive accuracy. Both plots also illustrate the feasibility of fuzzy logic as a predictor of compressor performance. As a feasibility study, this research is successful in demonstrating the non-linear robustness of fuzzy logic as a predictive method. Figure 6 is the best example of this. Even with limited potential for rules and inputs, fuzzy logic still shows outstanding robustness.
The most time consuming factor in developing an accurate fuzzy system is the refining of the fuzzy inference system to close the margin of error between the prediction and actual data, and more accurately represent the actual data thereby increasing the accuracy. However, this is the most essential step if this method is to be employed in a control system, particularly one where safety is paramount. Figure 6 shows a generally very good degree of accuracy given the simplicity of the system and the complex non-linearities of the efficiency function. The substantial difference amongst the compressor operating points that number just greater than 20 is one example where it was impossible to further resolve the function, given the lack of distinctive inputs that described this unusual behavior. Modifying the FIS to increase the accuracy in this patch would have an adverse effect on other portions. The reason for this is that the values for the inputs into the FIS were virtually the same for this patch as other patches. Thus, this example necessitates other unique inputs. Ultimately this was close to the best overall solution resulting in the least mean error. Figures 7 and 8 provide some appreciation for the complexity of the efficiency function. Items to note in each of the figures are the lines of constant mass flow descending in efficiency as the guide vane angles and DF margin increase. The step-change nature greatly increases the complexity of the function as well as the difficulty for any approximator to model the behavior. Even though this difficulty exists, the fuzzy system was able to transition between step-functions remarkably well (refer back to Figure 6). DF margin and S1 restagger angle are just two examples of the non-linear variation of efficiency as a function of other variables. All this must not only be embedded within the fuzzy inference system, but must also be exploited to predict the eventual scalar value for efficiency. Although the FIS requires some degree of complexity in order to accurately produce its predictions, it is fairly easy to accomplish and should compare very well among conventional methods. This is simply another good example of the advantage of fuzzy logic in this application.
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AIAA 2003-5738 Conclusion
Efficiency
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
Figure 7: Function of efficiency vs diffusion factor margin
Efficiency
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -15
-10
-5 0 S1 Restagger Angle (deg)
5
10
Figure 8: Function of efficiency vs S1 stator vane restagger angle margin Figure 9 presents a perhaps more intuitive comparison of the actual and predicted efficiency. Efficiency is plotted as a function of corrected mass flow. As the initial efficiency comparison also illustrated, the FL prediction diverges from the actual efficiency at certain points, but generally there is a low margin of error. 1 0.9 0.8 0.7 Efficiency
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DF Margin
0.6 0.5 0.4
COCODEC FL
0.3 0.2 0.1 0 11000
12000
13000 14000 15000 Corrected Mass Flow (lbm/sec)
16000
Figure 9: Compressor Efficiency vs Corrected Mass Flow, actual and FL comparison
17000
As a feasibility study, this research is successful in demonstrating the strengths of fuzzy logic as a universal approximator particularly for the application of large-scale wind-tunnel compressors. Furthermore this research reveals fuzzy logic’s versatility in adapting to subtle or localized nonlinearities. In addition to the current study’s approach, a fuzzy set could also be developed using some of the same inputs as above in addition to others such as IGV position and S3 angle in order to predict the actual safety margin, namely diffusion factor, or the rate of change of pressure ratio with guide vane angle. This essentially is the safety criteria. It has been well established that there is essentially no limit to the resolution and complexity that fuzzy logic can achieve. This study shows that a fuzzy logic application could serve as a decision maker, approximating compressor efficiency roll-off and imminent harmful effects (e.g. surge), provided that the condition can be defined. Results do not necessarily prove that this particular FIS could be implemented in a wind tunnel control system. It does, however, open a world of possibilities for fuzzy logic applications to this problem. The obvious advantage of implementing this type of control system would be safely increased compressor performance and efficiency without the overly-conservative control schedule currently in place. Naturally, increased performance would lead to various opportunities requiring higher pressure ratio. The increased efficiency translates into reduced operating costs. Recommendations Three recommendations accompany the findings presented above. First, in order to really delve into the possibility of instating this predictive technique into a wind tunnel compressor’s control system it is necessary to acquire empirical data. Examples include blade stress, fluctuating pressure, temperatures, etc… This data could be used to tailor a fuzzy system to a specific wind-tunnel/compressor combination. Accompanying this, it would be necessary to develop more inputs, each of which would offer a unique look at the efficiency relationship. In addition, the possibility of using fuzzy logic to directly predict safety criteria (i.e. diffusion factor) as well as efficiency should be investigated. The final recommendations stem from the need and frankly exciting prospect of doing follow-on work. In this work, no adaptive methods were attempted such as ANFIS, an adaptive technique for refining fuzzy systems. It is possible that ANFIS could identify and
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AIAA 2003-5738 resolve certain non-linearities that are difficult in human, open-loop iterations. Also the investigation of Neuro-fuzzy systems could reveal yet other opportunities and methods for improvement. One way that this research could be improved using the same tools is to try separate fuzzy systems for each line of constant mass flow thus making the approximation more accurate locally, as well as globally provided some method was developed to generate smooth transitions and interpolations between the fuzzy systems.
Downloaded by UNIVERSITY OF CINCINNATI on December 7, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.2003-89
Acknowledgements The authors gratefully acknowledge the many professionals at Arnold Engineering Development Center, Arnold AFB, TN, and in particular, Dr Frank Steinle for his invaluable advice and assistance.
References 1
AEDC-TMR-81-P2 Rosario, Roland A. and Steinle, Frank W. Jr. Neural Network Application for Optimizing Multi-Stage Wind Tunnel Compressor Efficiency. AIAA 20020308, 40th AIAA Aerospace Sciences Meeting and Exhibit. 14-17 January. Reno, 2002. 3 Kosko, B., 1997, Fuzzy Engineering, Prentice Hall International, Inc., New Jersey, pp.89-94. 4 Zadeh L.A., 1965, "Fuzzy Sets", Informat. Control, 8, pp. 339-353. 5 Thomas D.E. and Armstrong-Hélouvry B., 1995, "Fuzzy Logic Control - A Taxonomy of Demonstrated Benefits", Proceedings of the IEEE, 83(3), pp. 407-421. 6 Lee, C.C., 1990, "Fuzzy Logic in Control Systems: Fuzzy Logic Controller", IEEE Transactions on Systems, Man, and Cybernetics, 20(2), 404-435. 7 Private Communication: William E. Milam, Frank W. Steinle, and Alan A. Hale: JacobsSverdrup/AEDC Division, Arnold AFB, TN, March 11, 2002. 2
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