ON THE DATA ACQUISITON FOR AEROELASTIC ANALYSIS USING PZT (LEAD ZIRCONATE TITANATE) EXCITATION AND TEST PARAMETERS DEFINITION

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1 ON THE DATA ACQUISITON FOR AEROELASTIC ANALYSIS USING PZT (LEAD ZIRCONATE TITANATE) EXCITATION AND TEST PARAMETERS DEFINITION Éder L. Oliveira 1, Roberto G. A. da Silva 2, Nuno M. M Maia 3, Adolfo G. Marto 4, Frederico J. Afonso 1, Afzal Suleman 1 1 CCTAE, IDMEC, Instituto Superior Técnico, Universidade de Lisboa Avenida Rovisco Pais, , Lisboa, Portugal eder.oliveira@tecnico.ulisboa.pt, frederico.afonso@ist.utl.pt, suleman@tecnico.ulisboa.pt 2 Instituto Tecnológico de Aeronáutica, Divisão de Engenharia Aeronáutica Praça Marechal Eduardo Gomes, 50 - Vila das Acácias, , São José dos Campos -SP, Brazil gil@ita.br 3 LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa Avenida Rovisco Pais, , Lisboa, Portugal nmaia@dem.ist.utl.pt 4 Instituto de Aeronáutica e Espaço, Divisão de Aerodinâmica Praça Marechal Eduardo Gomes, 50 - Vila das Acácias, , São José dos Campos -SP, Brazil agmarto@iae.cta.br Keywords: data acquisition, noise, experimental modal analysis, piezoelectric materials. Abstract: This paper aims to improve the data acquisition in experimental aeroelastic analyses using PZT (Lead Zirconate Titanate) excitation and appropriate test parameters definition. High noise levels are usually associated to data acquisition in experimental aeroelastic analyses, leading to spurious roots in the stabilization diagram. Some procedures can be applied to improve the acquisition, for instance by working with the average number of a set of acquisitions. When working with the average number of a set of acquisitions, the noncorrelated inputs (such as noise) tend to disappear. Nevertheless, even when using a broader acquisition set from which to compute an average, it is not possible to obtain a good structural response, due to the poor relationship between signal and noise. Therefore, with the signal/noise relationship enhancement in mind an excitation can be used since it also helps to excite vibration modes that cannot be naturally excited by aerodynamic/turbulence forces. This study has four main investigation fields: (a) to choose the most appropriate type of signal excitation from the available ones; (b) to identify the average number, which improves the structural response when high speeds are the main focus of the wind tunnel test; (c) to define the test parameters aiming to improve the quality of the acquisition data, such as, estimator and window function; and (d) to identify the excitation level, which allows working in the linear structural response. Besides investigating the usage of PZT excitation to improve the data acquisition and showing the importance of an appropriate selection of the test parameters, this work also aims to encourage the development of investigative procedures to enhance data acquisition. 1

2 1 INTRODUCTION Aeroelasticity (dynamic) is the study of the interaction between aerodynamic, elastic and inertia forces [1]. This term aeroelasticity was introduced in 1932 by Roxbee Cox & Pugsley [2] report. There are several aeroelastic phenomena, of which flutter is considered the most important [3] and the most difficult to predict [4] among these. The first ever recorded flutter occurred in 1916 on a Handley Page O/400 twin engine biplane bomber [5], caused by a problem related to the elevator, which right and left parts were independently actuated [6]. The importance of predicting flutter is justified since it is closely related to flight safety. It is crucial and mandatory in any certification process of a new aircraft to conduct flight flutter tests to assess the safety conditions in the entire flight envelope, also for expanding the envelope of an existing aircraft this process is required [7]. Several aspects in the flutter prediction make it a difficult process, but probably the high presence of noise on the acquired data from flight and wind tunnel tests is the most influential. The experimental identification of the flutter boundary by employing flight or wind tunnel tests is always based on modal parameters extraction. The accurate estimation of the flutter boundary is an important issue in aircraft certification [8]. The flutter prediction involves the identification of close modes, which in itself is a difficult task as claimed by Ewins [9]. By using any 1 of the Frequency Response Function (FRF) measurements of the testing structure [10] the modal parameters, natural frequencies and damping factors can be estimated through modal analysis. Modal analysis can be defined as the study of structure s dynamics behaviour in terms of its vibration modes. A vibration mode is characterized by its modal parameters: natural frequency, damping factor and mode shape. The structure s dynamic behaviour description in terms of its vibration modes was first used over a century ago [11] by Rayleigh. The employment of modal analysis to study the aircraft s dynamic behaviour is not recent, in fact, it was first used as an engineering tool for this purpose around 1940 [12]. The vibration tests technology evolved due to improvements in digital signal processing, modal identification methods, finite element methods, piezoelectric materials, etc. However, advances in aviation led to lighter and faster aircraft, thereby increasing the danger for severe aeroelastic behavior [13]. Despite the successful application of numerical linear models in providing estimates of an aircraft s response to gust, turbulence and external excitations, the aircraft s behavior can not be accurately predicted for high subsonic or transonic Mach numbers [14]. According to [15], one of the most intriguing challenges of modern times is the development of reliable and computationally efficient analysis capabilities for aeroelasticity. The majority of nonlinear aeroelastic models still need to be validated or checked, thus justifying the prime importance of experimental data, although is uncommon to find significant nonlinear aeroelastic data available [13]. As aforementioned, flight flutter testing is extreme important in any aircraft development program, although it is very expensive and time consuming [16]. Several improvements on experimental aeroelastic analysis were reached, nevertheless, the basic procedure has remained the same [17]. Nonetheless, despite the testing methodology remained the same, the achieved improvements had a direct positive impact on the experimental aeroelastic investigations. One of the reached advances was the development of different excitation methodologies including a wide range of excitation devices, such as Control Surface Pulses, 1 Except those for which the excitation or response Degree of Freedom (DOF) is in a nodal position, i.e., where the mode shape is zero. 2

3 Oscillating Control Surfaces, Thrusters, Inertial Exciters, Aerodynamic Vanes, Dynamic Engineering Incorporated (DEI), Rotating Cylinder Exciters and Random Atmospheric Turbulence [18]. Another possibility is the employment of piezoelectric actuator, which in the recent past aroused the interest of reputed researching centers. Aiming to advance the state of the art in the application of piezoelectric actuators to aeroelastic systems, NASA Langley Research Center and the Massachusetts Institute of Technology worked together in the last decades [19]. The employment of piezoelectric elements as sensors and/or actuators as active elements integrated on structure (smart structures) is wide, including general aeronautic applications such as flutter suppression [20 23], buffet alleviation [24 27], gust response alleviation [28], flight control [29], morphing aircraft and adaptive control [30 33]. The accuracy level of the results in any experimental test depends on several aspects. Beyond being related to the methodology itself, an appropriate definition of the testing parameters for the data acquisition procedure is of crucial importance. Nevertheless, it is very important to have a good knowledge of the employed instrumentation. Improvements on the data acquisition can be reached when a good signal-to-noise ratio is obtained. In experimental aeroelastic analysis is very difficult to achieve a good signal/noise ratio because the testing environment is always noisy, whether performed in wind tunnel or flight testing. One of the ways to enhance the signal/noise ratio is to excite the structure by using a PZT (Lead Zirconate Titanate) element and use the signal which is supplied to the PZT in the FRF calculation. For the FRF calculation, it must be adopted a suffice average number of set acquisitions (auto-correlation function). 2 INVESTIGATION ABOUT POSSIBLE NOISE SOURCES Before embarking on any modal test, a very important step is to define clearly the objectives of the test [12]. A good test planning added to a right experimental setup preparation is necessary to achieve good results. The test setup preparation must be done by looking for possible noise sources which can be eliminated (or minimized at least). A good practice before beginning a wind tunnel test or a flight test is to check up if a good response can be obtained (especially in terms of noise) in a testing environment without wind. 2.1 Preparing the Test Structure For the testing structure preparation, a noise source which usually can be avoided is the poorly fixed cables. However, other more improbable noise sources also must be investigated. The adhesive has influence on the elastic and inertial properties of the testing structure, the adhesive layer itself changes as well the actuation capability and also the required voltage [34]. The piezoelectric actuation can lead the adhesive to early collapse, which not means necessarily that the piezoelectric element will unstuck completely. If the piezoelectric element not has an appropriate contact with the testing structure, the excitation will produce a knocking between the piezoelectric and structure. Beyond loosing the most actuation capability, in this case, the excitation mechanism will introduce much noise in the system. In Fig. 1 (a), it can be seen the FRFs for a case where a cyanoacrylate adhesive was used to embed a PZT in the testing structure. This structure is a composite flat plate and a PZT element (used as actuator) was embedded using cyanoacrylate near the root. Laser Doppler Vibrometry was used to compute the FRFs by using four different excitation intensities. The amplitude differences shown in Fig. 1 (a) are due to the adjusted sensitivity. The achieved 3

4 FRFs presents a high noise level, despite the low improvement due to the higher excitation, it still remains very noisy considering that the testing was conducted with no wind condition. (a) PZT Embedded with Cyanoacrylate Adhesive (b) PZT Embedded with Epoxy Adhesive Figure 1: Adhesives - Effect on the Noise The PZT and all the adhesive were removed from the structure and an identical PZT was embedded by using epoxy adhesive (3M Scotch-weld Structural Adhesive DP460 Off- White ([35])). Another test was conducted considering the lower excitation used in the previously one and all the same conditions were maintained (see Fig. 1 (b)). The simple adhesive changing was able to clean up the FRF, showing very significant quality 4

5 enhancement in terms of noise. Beyond this, the response amplitude was increased around 25 db. 2.2 Environment Usually, wind tunnels for aeroelastic investigations have open sections or alternatively sometimes the testing model is mounted immediately after the test section (without walls interference). Laser Doppler Vibrometry is a non contact technique which can be applied in a test of this nature. A hypothetical situation was devised and simulated to show that a simple fixation of the laser sensor head at the tripod can become a noise source, if it not well performed. Movement of laser sensor head can be induced by wind flow, specially at high speeds. One accelerometer was attached in the laser sensor head to measure the acceleration response for 30 mmh2o of dynamic pressure. Two cases were tested: firstly using inadequate fixation (slack screw) of sensor head in a tripod; and after was tested using a fully tight screw. Figure 2: Wind Tunnel Testing - Structure Fixation Comparing the response of these different conditions, it was observed that for the slack screw case, the sensor head had a significant acceleration, thus rendering in a noise source which could be easily avoided (see Fig. 2). Using a correct tightening of the screw, the amplitude response was decreased up to 4 times (Fig. 2, black curve). 3 DATA ACQUISITION FOR AEROELASTIC ANALYSIS Several testing parameters must be defined to perform the data acquisition. Some of these 5

6 parameters can potentially improve the quality of the acquisition, for example, choosing the most appropriate FRF estimator able to minimize the noise in the specific test condition. One can find in the literature [36] useful information which can help defining the test parameters, and preliminary investigations can verify/confirm the best one. 3.1 Support Investigations to Help Defining the Test Parameters A piezoelectric element, as for example a single PZT, can be used to excite the structure in wind or flight testing. In a previous work [37], a single PZT was able to excite all the vibration modes (bending and torsion) for the frequency range of interest, until 256 Hz. (a) Hz (b) 0-50 Hz Figure 3: Auto-Correlation Function - Average Number 6

7 A random excitation signal and a suitable average number of a set of acquisitions (autocorrelation function) were used to minimize the noise for wind tunnel testing. The effect in the noise minimization can be seen in the Fig. 3, where 20, 40 and 200 averages were used to calculate the FRFs due a laser vibrometer. All the FRFs were achieved for 7mmH2o of dynamic pressure in a wind tunnel testing. The signal supplied to the PZT was used to compute the FRFs. The noise minimization is especially evident by analyzing the computed FRFs for the frequency ranging from 0 to 50 Hz, Fig. 3 (b) Excitation Intensity Commonly, the use of a piezoelectric excitation devices for flutter investigations in wind tunnel and flight testing has as main targets the excitation of the vibration modes which are not properly excited with other devices, or still as an alternative for it. Consequentially, a better structural response is achieved (in terms of signal-to-noise ratio), thus improving the data acquisition, as showed in the previous work [38]. The concept/idea uses basically the same framing of other excitation apparatus, for example, where the vanes and aileron rotations yield large responses [39], allowing large response-to-noise ratios during flight tests. Figure 4: Damping Factor vs Excitation Intensity Nevertheless, regardless of the used excitation system, careful must be taken to avoid nonlinear problems. Maybe, one of the most usual committed mistakes is to increase the excitation intensity aiming to improve the excitation. Sometimes, this easy and practical solution can lead to incoherent results. An alternative can be the usage of other excitation points. The boundary of the structural linear response can be estimated by identifying the modal parameters as a function of the excitation intensity. Although, it can be done considering all the modal parameters, the damping factor is in general more susceptible to this influence. An investigation example using this methodology is presented in the Fig. 4, where one can observe that up to a specific excitation level the damping factors remain the same for the vibrations modes of interest. This study was performed on a composite flat plate model (carbon/epoxy) with 3 carbon plies oriented in the same direction, 0 ⁰. 7

8 For other models with different carbon fiber orientations, this excitation level was sufficient to change considerably the identified damping factors. To improve the accuracy level, other excitation points must be taken. The recent state of art for nonlinear aeroelastic analysis is addressed in [40] Frequency Response Function Estimator The employment of piezoelectric elements as sensors for aeroelastic studies can be done by constructing the FRF such as in a common Experimental Modal Analysis (EMA). The PVDF can be used to measure strain in a similar way to the one of the conventional strain gauges, as long as the strain signal is dynamic [41]. Some works were performed which compares PVDF and strain gauge, e.g., [42]. (a) Laser Doppler Vibrometry (a) PVDF Figure 5: FRF Estimators 8

9 Directly using the PVDF signal response (amplified) together with the excitation signal supplied to PZT, the FRF can be computed, so the FRF will be dimensionless (Volt/Volt). A study to help defining the FRF estimator can be conducted aiming to choose the estimator which better minimizes the noise in a wind tunnel test. This can be done already considering the adopted window function. One example is shown in the Fig. 5, where the FRFs were computed using Laser Doppler Vibrometry (Fig. 5 (a)) and PVDF (Fig. 5 (b)). The data were acquired for 12mmH2o of dynamic pressure and using only 20 average number. The classical FRF estimators (H 1 (ω), H 2 (ω), H V (ω)) were compared between each other. Besides the noise, the ordinary coherence for each FRF also was evaluated. Clearly, the estimator which shown a better ordinary coherence was the H V (ω), for both PVDF and laser estimations. In term of noise and coherence, similar results were achieved by using H 1 (ω) and H 2 (ω) for both PVDF and Laser. 4 CONCLUSIONS The PZT employment as actuator for aerolastic investigation was discussed. Some experimental aspects which have possibility to improve the data acquisition procedure were investigated. FRFs were computed using different average number of a set acquisitions and the noise minimization capability was evaluated together with the ordinary coherence for wind tunnel testing. The use of PZT excitation and calculation of the FRF considering the excitation signal as reference signal to compute the FRF shown good capability to eliminate exogenous inputs. Examples of brief investigations which can be performed to help defining the testing parameters aiming to improve the data acquisition for aeroelastic investigation were shown. The most appropriate FRF estimator to be used in the modal parameters identification for wind tunnel testing was identified. For the simulated case, the H V (ω) presented a better noise minimization capability, producing a much better ordinary coherence. The damping factors of the first four vibration modes (frequency range until 256 Hz) were calculated considering different excitation intensities. By comparing the achieved results the excitation level which allows working in the linear structural response was identified. Investigation about noise sources were performed, showing which precautions must be taken. The hypothetical simulated situation shown that a simple fixation of the laser sensor head at the tripod can render in a noise source, if not well performed. The degradation effect of cyanoacrylate adhesive due to PZT excitation was shown. It was also shown that by using an inadequate adhesive, a lot of noise can be introduced into the system, besides losing a good part of actuation capability. Besides investigating the usage of PZT excitation to improve the data acquisition and showing the importance of an appropriate selection of the test parameters, this work also aims to encourage the development of investigative procedures to enhance data acquisition. ACKNOWLEDGEMETS The authors acknowledge the support received from the Brazilian Research Agency CNPQ 9

10 through the INCT-EIE, the support provided by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES, as well as the support received from Instituto Tecnológico de Aeronáutica, ITA. The authors also acknowledge the Portuguese Science Foundation FCT, through CCTAE / IDMEC, under LAETA. 5 REFERENCES [1] C. Panda and S. R. P. Venkatasubramani. Aeroelasticity - in general and flutter phenomenon. In Emerging Trends in Engineering and Technology (ICETET), nd International Conference on, pages 81 85, Dec [2] H. Roxbee Cox and A.G. Pugsley. Theory of loss of lateral control due to wing twisting. Technical report, London: HMSO, Aeronautical Research Committee R&M No 1506, [3] Virgil Stanciu, Gabriela Stroe, and Irina Carmen Andrei. Linear models and calculation of aeroelastic flutter. U.P.B. Sci. Bull., Series D, 74:29 38, [4] A. R. Collar. The first fifty years of aeroelasticity. Aerospace, 5:12 20, [5] Michael W. Kehoe. A historical overview of flight flutter testing. NASA Technical Memorandum 4720, [6] F.W. Lancaster. Torsional vibrations of the tail of an aeroplane, reports and memoranda, no. 276, july AIAA Selected Reprint Series, Aerodynamic Flutter, V:12 15, [7] R. V. Vaidyanathan and E. Hemalatha. Flight flutter testing and clearance of the baseline configuration of a developmental combat aircraft. In Proceedings of ISMA2010 Including USD2010, [8] H. Haddad Khodaparast, S. Marques, K. J. Badcock, and J. E. Mottershead. Estimation of flutter boundaries in the presence of structural uncertainty by probabilistic and fuzzy methods. In International Conference on Structural Engineering Dynamics, 2009, Ericeira, Portugal, June, [9] D.J. Ewins. Modal Testing: Theory, Practice and Application. Research Studies Press LTD, [10] H. herlufsen and br uel&kjær, modal analysis using multi-reference and multiple-input multiple-output techniques, Application Note. [11] Nick A. J. Lieven and D. J. Ewins. The context of experimental modal analysis. Philosophical Transactions of the Royal Society of London Series A - Mathematical Physical and Engineering Sciinces, 359:5 10, [12] Maia, Silva, He, Lieven, Lin, Skingle, To, and Urgueira. Theoretical and Experimental Modal Analysis. John Wiley and Sons, Inc., New York, Chichester, Toronto, Brisbane, Singapore,

11 [13] Flávio D. Marques, Eduardo M. Belo, Vilma A. Oliveira, José R. Rosolen, and Andréia R. Simoni. On the investigation of state space reconstruction of nonlinear aeroelastic response time series. Shock and Vibration, 13: , [14] Sunil L. Kukreja. Non-linear system identification for aeroelastic systems with application to experimental data. NASA TM , [15] F. Picardi, N. Paletta, M. Belardo, and M. Pecora. Fast automatic procedure for flutterclearance assessment when in the presence of significant structural damage. Journal of Aerospace Engineering, 27(6):14 23, [16] J. E. Cooper. Towards faster and safer flight flutter testing. In RTO AVT Symposium on Reduction of Military Vehicle Acquisition Time and Cost through Advanced Modelling and Virtual Simulation, Paris, France, April [17] R. B. Ramsay. Flutter certification and qualification of combat aircraft. In IFASD 1995, International Forum on Aeroelasticity and Structural Dynamics, Paper 92. [18] Xie Jiang Yang Fei. Aeroelastic response simulation for di_erent excitation techniques in flight flutter test of modern civil. In ICAS Proceedings of the 29th Congress of the International Council of the Aeronautical Sciences, [19] Jennifer Heeg, Anna-Maria R. McGowan, Edward F. Crawley, and Charrissa Lin. Piezoelectric aeroelastic response tailoring investigation: a status report. Proc. SPIE 2447, Smart Structures and Materials 1995: Industrial and Commercial Applications of Smart Structures Technologies, 2 (May 12, 1995), pages 2 13, [20] Naoki Kawai. Flutter control of wind tunnel model using a single element of piezoceramic actuator. In ICAS TH International Congress of the Aeronautical Sciences, [21] Seong Hwan Moon and Joon Seok Hwang. Panel flutter suppression with an optimal controller based on the nonlinear model using piezoelectric materials. Composite Structures, 68: , [22] Jennifer Heeg. Analytical and experimental investigation of flutter suppression by piezoelectric actuation. NASA Technical Paper, (3241), [23] C. Nam and Y. Kim. Active flutter suppression of composite plate with piezoelectric actuators. AIAA Paper, ( CP), [24] S. Hanagud, M. Bayon de Noyer, H. Luo, D. Henderson, and K. S. Nagaraja. Tail buffet alleviation of high performance twin tail aircraft using piezo-stack actuators. AIAA Journal, 40(4): , [25] USAF Joseph S. Browning, Captain. F-16 Ventral Fin Bu_et Alleviation Using Piezoelectric Actuators. PhD thesis, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio,

12 [26] Patrick J. Roberts. An Experimental Study of Concurrent Methods for Adaptively Controlling Vertical Tail Bu_et in High Performance Aincraft. PhD thesis, School of Aerospace Engineering, Georgia Institute of Technology, [27] N. Ashokpandiyan, A. Mythiliraj, and P. Rajkumar. Reducing the vibration on wing by using piezoelectric actuator. Journal of Aeronautical and Automotive Engineering (JAAE), 1(1):13 16, [28] A. Suleman and A. P. Costa. Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators. Elsevier Science - Computers and Structures, 82: , [29] R. Barret. Adaptive Fight Control Actuators and Mechanisms for Missiles, Munitions and Uninhabited Aerial Vehicles (UAVs), Advances in Flight Control Systems. InTech, [30] T. D. Usher, K. R. Ulibarri Jr, and G. S. Camargo. Piezoelectric microfiber composite actuators for morphing wings. ISRN Materials Science, 2013:8pp, [31] O. Bilgen, K.B. Kochersberger, A.J. Diggs, E.C.and Kurdila, and D.J. Inman. Morphing wing micro-air-vehicles via macro-fiber-composite actuators. Structural Dynamics and Materials Conference, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 15th, 26 April [32] D. K. Kim and J. H. Han. Smart flapping wing using macro-fiber composite actuators. Smart Structures and Materials 2006: Smart Structures and Integrated Systems, 6173, [33] D. K. Kim, J. H. Han, and K. J. Kwon. Wind tunnel tests for a flapping wing model with a changeable camber using macro-fiber composite actuators. J. Smart Mater. Struct., 18, [34] A. Baz and S. Poh. Performance of an active control system with piezoelectric actuators. Journal of Sound and Vibration, 126(2): , [35] 3M Scotch-Weld Epoxy Adhesives DP460 O_-White, Technical Data, Mach, [36] LMS International. The LMS Theory and Background Book, [37] É. L. Oliveira, Roberto G. A. da Silva, Adolfo G. Marto, Frederico J. Afonso, Nuno M. M. Maia, and Afzal Suleman. Experimental aeroelastic investigation using piezoelectric transducers for modal parameters identification. In SMART 2015, 7th ECCOMAS Thematic Conference on Smart Structures and Materials, [38] Éder L. Oliveira. Application of piezoelectric materials as sensor and actuator for aeroelastic investigation. Master s thesis, Aeronautics Institute of Technology, São José dos Campos, São Paulo, Brazil, [39] E. Nissim. The effectiveness of vane-aileron excitation in the experimental determination of flutter speed by parameter identification. Technical report, NASA Ames Research Center, Dryden Flight Research Facility, Edwards, CA, NASA TP-2971,

13 [40] Xiang Jinwu, Yan Yongju, and Li Daochum. Recent advance in nonlinear aeroelastic analysis and control of the aircraft. Chinese Journal of Aeronautics, 27(1):12 22, [41] R. H. Brown. Comparison between piezo film sensor, strain gauge, and accelerometer on bending beam. Technical report, Sensor Products Division (Europe), RB 33/02, [42] Singiresu S. Rao. Vibrações Mecânicas. Pearson Prentice Hall, Person Education do Brasil, COPYRIGHT STATEMENT The authors confirm that they, and/or their company or organization, hold copyright on all of the original material included in this paper. The authors also confirm that they have obtained permission, from the copyright holder of any third party material included in this paper, to publish it as part of their paper. The authors confirm that they give permission, or have obtained permission from the copyright holder of this paper, for the publication and distribution of this paper as part of the IFASD 2015 proceedings or as individual off-prints from the proceedings. 13