<p dir="ltr">The industry's interest in electrified powertrain-equipped vehicles has increased due to environmental and economic reasons. Electrified powertrains, in general, produce lower sound and vibration level than those equipped with internal combustion engines, making noise and vibration (N&V) from other non-engine powertrain components more perceptible. One such N&V type that arouses concern to both vehicle manufacturers and passengers is gear growl, but the signal characteristics of gear growl noise and vibration and the threshold of those characteristics that can be used to determine whether a gear growl requires attention are not yet well understood. This study focuses on developing a method to detect gear-growl based on the N\&V measurements and determining thresholds on various severities of gear-growl using supervised machine learning classification. In general, a machine learning classifier requires sufficient high-quality training data with strong information independence to ensure accurate classification performance. In industrial practices, acquiring high-quality vehicle NVH data is expensive in terms of finance, time, and effort. A physically informed data augmentation method is, thus, proposed to generate realistic powertrain NVH signals based on high-quality measurements which not only provides a larger training data set but also enriches the signal feature variations included in the data set. More specifically, this method extracts physical information such as angular speed, tonal amplitudes distribution, and broadband spectrum shape from the measurement data. Then, it recreates a synthetic signal that mimics the measurement data. The measured and simulated (via data augmentation) are transformed into feature matrix representation so that the N\&V signals can be used in the classification model training process. Features describing signal characteristics are studied, extracted, and selected. While the root-mean-square (RMS) of the vibration signal and spectral entropy were sufficient for detecting gear-growl with a test accuracy of 0.9828, the acoustic signal required more features due to background noise, making data linearly inseparable. The minimum Redundancy Maximum Relevance (mRMR) feature scoring method was used to assess the importance of acoustic signal features in classification. The five most important features based on the importance score were the angular acceleration of the driveshaft, the time derivative of RMS, the tone-to-noise ratio (TNR), the time derivative of the spectral spread of the tonal component of the acoustic signal, and the time derivative of the spectral spread of the original acoustic signal (before tonal and broadband separation). A supervised classification model is developed using a support vector machine from the extracted acoustic signal features. Data used in training and testing consists of steady-state vehicle operations of 25, 35, 45, and 55 mph, with two vehicles with two different powertrain specs: axles with 4.56 and 6.14 gear ratios. The dataset includes powertrains with swapped axles (four different configurations). Techniques such as cost weighting, median filter, and hyperparameter tuning are implemented to improve the classification performance where the model classifies if a segment in the signal represents a gear-growl event or no gear-growl event. The average accuracy of test data was 0.918. A multi-class classification model is further implemented to classify different severities based on preliminary subjective listening studies. Data augmentation using signal simulation showed improvement in binary classification applications. In this study, only gear-growl was used as a fault type. Still, data augmentation, feature extraction and selection, and classification methods can be generalized for NVH signal-based fault diagnosis applications. Further listening studies are suggested for improved classification of multi-class classification applications.</p>

No description available.

<p dir="ltr">In the field of noise control engineering, the development of effective low-frequency sound absorption treatments has long been a challenge, since conventional solutions tend to require impractically thick layers of traditional porous materials, such as fibrous materials and foams. In contrast, high surface area particles, such as granular activated carbon (GAC) particles, milled aerogels, and zeolites, have inner-particle pores at micro and nano scales, which improve the low-frequency absorption by slowing the local sound speed. As a result, a 30 mm thick GAC stack can achieve an absorption coefficient of 0.3 at 100 Hz. Hence, these materials have already been used in various low-frequency applications in place of fibrous or foam layers: e.g., MEMS speaker back cavities, Helmholtz resonator liners, micro-perforated panel absorbers, and membrane absorbers. One major practical goal of this research was to determine how best to model and optimize novel treatments consisting in whole or in part of high surface area granular materials. </p><p dir="ltr">The detailed work presented in this thesis starts with a review of acoustical models of various material types, followed by two approaches to modeling and coupling different types of layers in a general and stable manner. In particular, in the second approach, a large, complicated system is divided into a series of small systems, hence avoiding the direct inverse solution of large systems. As a result, the second approach is more efficient and enables computationally intensive tasks such as multi-layer material characterization and sound package optimization. In addition to the modeling techniques, different types of granular stacks’ acoustical behavior were also experimentally investigated and summarized: i.e., 1. the edge-constraint effect resulting from the friction at the wall of the impedance tube; 2. level-dependent behavior; 3. time-dependent behavior; and 4. other non-linear behavior. To capture the observed acoustical physics of GAC stacks, a triple-porosity poro-elastic model with a depth-dependent modulus was described, followed by characterization frameworks to model the stacks subject to the edge-constraint effect as well as varying excitation levels. These frameworks were validated by comparing the absorption spectra predicted by using the inferred material properties with impedance tube measurements of GAC stacks with varying depths, diameters, and exposure levels. In the end, a novel sound absorption treatment was presented (a GAC stack supported by a soft, porous layer), which was subsequently optimized to develop broadband absorbers.</p>

Recent experimental achievements in active noise control (ANC) for cooling fans have used near-field error sensors whose locations are determined according to a theoretical condition of minimized sound power. A theoretical point source model, based on the condition previously stated, reveals the location of near-field pressure nulls that may be used to optimize error sensor placement. The actual locations of these near-field pressure nulls for both an axial cooling fan and a monopole loudspeaker were measured over a two-dimensional grid with a linear array of microphones. The achieved global attenuation for each case is measured over a hemisphere located in the acoustic far field of the ANC system. The experimental results are compared to the theoretical pressure null locations in order to determine the efficacy of the point source model. The results closely matched the point source model with a loudspeaker as the primary source, and the sound power reduction was greatly reduced when error sensors were placed in non-ideal locations. A weakness of the current near-field modeling process is that a point monopole source is used to characterize the acoustic noise from an axial cooling fan, which may have multipole characteristics. A more complete characterization of fan noise may be obtained using a procedure based on the work of Martin and Roure [J. Sound Vib. 201 (5), 577--593 (1997)]. Pressure values are obtained over a hemisphere in the far field of a primary source and the contributions from point source distributions up to the second order, centered at the primary source, may be calculated using a multipole expansion. The source information is then used in the aforementioned theoretical near-field calculation of pressure. The error sensors are positioned using the complete fan characterization. The global far-field attenuation for the multipole expansion model of fan noise is compared to that of previous experiments. Results show that the multipole expansion model yields a more accurate representation the near field, but is not successful in achieving greater sound power reductions in the far field.

<p>In many practical multi-channel active sound control (ASC) applications, such as active noise control (ANC), various constraints need to be satisfied, such as the robust stability constraint, noise amplification constraint, controller output power constraints, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over-satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the <em>H</em>₂/<em>H</em>_inf control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In this dissertation, the traditional <em>H</em>₂/<em>H</em>_inf formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming formulation and simplified by exploiting the problem structure in its dual form to obtain a more numerically efficient and stable formulation. A warmstarting strategy is also proposed to further reduce the required iterations. Results show that, compared with the traditional methods, the proposed method is more reliable and the computation time can be reduced from the order of days to seconds. When the acoustic feedback path is not strong enough to cause instability, then only constraints that prevent noise amplification outside the desired noise control band are needed. A singular vector filtering method is proposed to maintain satisfactory noise control performance in the desired noise reduction bands while mitigating noise amplification.</p> <p><br></p> <p>The proposed convex conic formulation can be used for a wide range of ASC applications. For example, the improvement in numerical efficiency and stability makes it possible to apply the proposed method to adaptive ANC filter design. Results also show that compared with the conventional constrained adaptive ANC method (leaky FxLMS), the proposed method can achieve a faster convergence rate and better steady-state noise control performance. The proposed conic method can also be used to design the room equalization filter for sound field reproduction and the hear-through filter design for earphones.</p> <p><br></p> <p>Besides efficient filter design methods, efficient filter implementation methods are also developed to reduce real-time computations in implementing designed control filters. A polyphase-structure-based filter design and implementation method is developed for ANC systems that can reduce the computation load for high sampling rate real-time filter implementation but does not introduce an additional time delay. Results show that, compared with various traditional low sampling rate implementations, the proposed method can significantly improve the noise control performance. Compared with the non-polyphase high-sampling rate method, the real-time computations that increase with the sampling rate are improved from quadratically to linearly. Another efficient filter implementation method is to use the infinite impulse response (IIR) filter structure instead of the finite impulse response (FIR) filter structure. A stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in the ANC applications. The result demonstrated that the proposed method can achieve better fitting accuracy and noise control performance in high-order applications.</p>

In the last decade acoustic noise has become more and more regarded as a problem. In cars, boats, trains and aircraft, low-frequency noise reduces comfort. Lightweight materials and more powerful engines are used in high-speed vehicles, resulting in a general increase in interior noise levels. Low-frequency noise is annoying and during periods of long exposure it causes fatigue and discomfort. The masking effect which low-frequency noise has on speech reduces speech intelligibility. Low-frequency noise is sought to be attenuated in a wide range of applications in order to improve comfort and speech intelligibility. The use of conventional passive methods to attenuate low-frequency noise is often impractical since considerable bulk and weight are required; in transportation large weight is associated with high fuel consumption. In order to overcome the problems of ineffective passive suppression of low-frequency noise, the technique of active noise control has become of considerable interest. The fundamental principle of active noise control is based on secondary sources producing ``anti-noise.'' Destructive interference between the generated and the primary sound fields results in noise attenuation. Active noise control systems significantly increase the capacity for attenuating low-frequency noise without major increase in volume and weight. This doctoral dissertation deals with the topic of active noise control within the passenger cabin in aircraft, and within headsets. The work focuses on methods, controller structures and adaptive algorithms for attenuating tonal low-frequency noise produced by synchronized or moderately synchronized propellers generating beating sound fields. The control algorithm is a central part of an active noise control system. A multiple-reference feedforward controller based on the novel actuator-individual normalized Filtered-X Least-Mean-Squares algorithm is introduced, yielding significant attenuation of such period noise. This algorithm is of the LMS-type, and owing to the novel normalization it can also be regarded as a Newton-type algorithm. The new algorithm combines low computational complexity with high performance. For that reason the algorithm is suitable for use in systems with a large number of control sources and control sensors in order to reduce the computional power required by the control system. The computational power of the DSP hardware is limited, and therefore algorithms with high computational complexity allow fewer control sources and sensors to be used, often with reduced noise attenuation as a result. In applications, such as controlling aircraft cabin noise, where a large multiple-channel system is needed to control the relative complex interior sound field, it is of great importance to keep down the computational complexity of the algorithm so that a large number of loudspeakers and microphones can be used. The dissertation presents theoretical work, off-line computer experiments and practical real-time experiments using the actuator-individual normalized algorithm. The computer experiments are principally based on real-life cabin noise data recorded during flight in a twin-engine propeller aircraft and in a helicopter. The practical experiments were carried out in a full-scale fuselage section from a propeller aircraft. / Buller i vår dagliga miljö kan ha en negativ inverkan på vår hälsa. I många sammanhang, i tex bilar, båtar och flygplan, förekommer lågfrekvent buller. Lågfrekvent buller är oftast inte skadligt för hörseln, men kan vara tröttande och försvåra konversationen mellan personer som vistas i en utsatt miljö. En dämpning av bullernivån medför en förbättrad taluppfattbarhet samt en komfortökning. Att dämpa lågfrekvent buller med traditionella passiva metoder, tex absorbenter och reflektorer, är oftast ineffektivt. Det krävs stora, skrymmande absorbenter för att dämpa denna typ av buller samt tunga skiljeväggar för att förhindra att bullret transmitteras vidare från ett utrymme till ett annat. Metoder som är mera lämpade vid dämpning av lågfrekvent buller är de aktiva. De aktiva metoderna baseras på att en vågrörelse som ligger i motfas med en annan överlagras och de släcker ut varandra. Bullerdämpningen erhålls genom att ett ljudfält genereras som är lika starkt som bullret men i motfas med detta. De aktiva bullerdämpningsmetoderna medför en effektiv dämpning av lågfrekvent buller samtidigt som volymen, tex hos bilkupen eller båt/flygplanskabinen ej påverkas nämnvärt. Dessutom kan fordonets/farkostens vikt reduceras vilket är tacksamt för bränsleförbrukningen. I de flesta tillämpningar varierar bullrets karaktär, dvs styrka och frekvensinnehåll. För att följa dessa variationer krävs ett adaptivt (självinställande) reglersystem som styr genereringen av motljudet. I propellerflygplan är de dominerande frekvenserna i kabinbullret relaterat till propellrarnas varvtal, man känner alltså till frekvenserna som skall dämpas. Man utnyttjar en varvtalssignal för att generera signaler, så kallade referenssignaler, med de frekvenser som skall dämpas. Dessa bearbetas av ett reglersystem som generar signaler till högtalarna som i sin tur generar motljudet. För att ställa in högtalarsignalerna så att en effektiv dämpning erhålls, används mikrofoner utplacerade i kabinen som mäter bullret. För att åstadkomma en effektiv bullerdämpning i ett rum, tex i en flygplanskabin, behövs flera högtalare och mikrofoner, vilket kräver ett avancerat reglersystem. I doktorsavhandlingen ''Active Control of Propeller-Induced Noise in Aircraft'' behandlas olika metoder för att reducera kabinbuller härrörande från propellrarna. Här presenteras olika strukturer på reglersystem samt beräkningsalgoritmer för att ställa in systemet. För stora system där många högtalare och mikrofoner används, samt flera frekvenser skall dämpas, är det viktigt att systemet inte behöver för stor beräkningskapacitet för att generera motljudet. Metoderna som behandlas ger en effektiv dämpning till låg beräkningskostnad. Delar av materialet som presenteras i avhandlingen har ingått i ett EU-projekt med inriktning mot bullerundertryckning i propellerflygplan. I projektet har flera europeiska flygplanstillverkare deltagit. Avhandlingen behandlar även aktiv bullerdämpning i headset, som används av helikopterpiloter. I denna tillämpning har aktiv bullerdämpning används för att öka taluppfattbarheten.

Cette thèse s'inscrit dans le cadre de la recherche des moyens de réduction du bruit. Le but est d’analyser et de créer par une méthode passive, le confinement d’énergie acoustique dans les irrégularités géométriques via le phénomène de localisation pour ensuite la dissiper. En prélude à l'atténuation du bruit par les géométries irrégulières, les mécanismes de la dissipation acoustique sont rappelés et illustrés par quelques exemples de réseaux de résonateurs quart-d'onde. Le phénomène de localisation est ensuite étudié par une analyse modale. Le caractère localisé d'un mode est quantifié par son volume d'existence relatif (VER) qui donne, en fraction du volume total du domaine, le volume effectif concerné par l'énergie du mode. Il ressort de cette étude que seules les cavités irrégulières ayant des irrégularités en forme de sous-cavités couplées à une cavité principale sont « localisantes ». La fréquence d'un mode localisé est liée aux dimensions de la zone irrégulière de localisation. Le lien entre les irrégularités géométriques et la dissipation acoustique est ensuite analysé au moyen des indicateurs tels que le facteur de qualité, le coefficient d'absorption ou le taux d'amortissement de l'énergie. Cette étude montre que les cavités irrégulières amortissement mieux une onde acoustique comparativement aux cavités à géométrie régulière. Toutefois, la dissipation de l'énergie acoustique des cavités irrégulières n'est pas uniquement liée à la localisation. Elle dépend également d'autres paramètres (porosité, résistivité, etc.). Lorsque les irrégularités des parois rigides ne permettent pas de réaliser une dissipation suffisante, elles peuvent être réalisées dans les matériaux poroélastiques à performance acoustique moyenne pour augmenter leur capacité dissipative. Enfin, des études expérimentales menées ont permis de valider l'existence du phénomène de localisation et de confirmer la tendance plus dissipative des géométries irrégulières par rapport aux géométries régulières. De même, des mesures du coefficient d'absorption d'un échantillon de forme préfractale d'un béton de chanvre (matériau ayant une performance acoustique moyenne) montrent une augmentation de la dissipation de plus de 40% induite par la forme irrégulière. La contribution majeure de cette thèse est d’avoir répondu à un défi technologique important consistant à effectuer une mise en évidence expérimentale du phénomène de localisation jusque-là difficile à réaliser avec des microphones. Pour y parvenir, un outil optique peu conventionnel dans la métrologie acoustique est adopté; il s'agit de la réfracto-vibrométrie qui consiste à utiliser, sous certaines conditions, le vibromètre laser pour mesurer un champ acoustique (pression acoustique). Bien que contraignante, cette technique présente l'avantage d'être non intrusive et donc moins encombrante même pour de petites cavités comparativement aux microphones. / In this thesis, the acoustical behavior of irregular cavities leading to localization phenomenon is investigated for noise reduction applications. The aim of this work is to study and create by means of passive method, an accumulation of acoustical energy and dissipate it. Before addressing geometrical irregularities effects on the sound field, viscothermal dissipation mechanisms of sound are recalled and illustrated through few networks of quarter-wave resonators. In a second part, a study of the localization phenomenon is carried out by a modal analysis approach. The localization is quantified by the relative existence volume (VER), an indicator which gives a measure of the volume of the region in which a mode is localized as a fraction of the total cavity volume. The localization analysis is conducted using both regular and irregular cavities. It has been shown that only cavities with irregular geometry, such that sub-cavities are formed, can localize some acoustical modes. Moreover, the frequency of a localized mode is related to the dimensions of the localization region. Following the investigation of the localization phenomenon, the relation between cavities geometry and sound energy dissipation has been studied by the estimation of damping indicators, such as the quality factor, the sound absorption coefficient or the energy damping rate. According to this study, irregular cavities have higher capability to damp sound waves compared to regular cavities. However, for the case of irregular cavities only, the induced dissipation is not proportional to the localization. Nevertheless, when irregularities of rigid walls are not able to achieve sufficient dissipation, this can be obtained with slightly absorptive porous materials of irregular geometry. In fact, the dissipative properties of some porous materials can be optimized by giving them irregular interface. Finally, an experimental set-up has been designed to validate the localization phenomenon and to confirm the damping tendency of irregular geometries in comparison to regular ones. Moreover, measurements of the sound absorption coefficient of a hemp concrete reveal that the sample of irregular geometry achieves sound dissipation more than 40% higher than the one achieved by a regular plane sample. Finally, this thesis has addressed a technological challenge consisting of experimentally validating the localization phenomenon which is so far very difficult to obtain by the use of conventional pressure microphones. In the framework of this thesis, an optical non-conventional sound pressure measurement technique has been used. The used technique is the laser refracto-vibrometry which consists of using a laser vibrometer in some specific conditions to measure the acoustical field (sound pressure). This technique is difficult to conduct but it has the advantage of being contactless, thus less cumbersome for even very small cavities as compared to pressure microphones.

Ce projet de doctorat consiste en la proposition d'une solution technologique d'un résonateur de Helmholtz adaptatif à volume variable, permettant ainsi de s'affranchir du caractère mono-fréquentiel des résonateurs de Helmholtz passifs. Le réglage de volume s'effectue grâce à l'utilisation d'une membrane en polymère électroactif (EAP), permettant ainsi d'accorder les résonances du résonateur de Helmholtz. Le comportement mécanique de ces matériaux est modifié lorsqu'ils sont stimulés par un champ électrique. Des améliorations significatives en perte par transmission acoustique sont obtenues en basses fréquences par deux effets: la variation de raideur de la membrane et l'augmentation de volume due à la déformation de la membrane. Des études numériques, analytiques et expérimentales sont réalisées pour déterminer le potentiel des concepts proposés. Enfin, une structure périodique contenant 9 résonateurs adaptatifs à membranes électroactives est étudiée en champs diffus permettant d'évaluer les performances acoustiques du concept distribué. / This main goal of the project consists in proposing a technological solution of an adaptive Helmholtz resonator with variable volume, which allows to overcome the mono-frequency character of passive Helmholtz resonators. The volume control is achieved by the use of an electroactive polymer membrane (EAP), allowing the resonances of the Helmholtz resonator to be tuned. The mechanical behavior of these materials changes when they are stimulated by an electric field. Significant improvements in acoustic transmission loss are obtained at low frequencies by two effects: the variation of stiffness of the membrane and the increase of volume due to the deformation of the membrane. Numerical, analytical and experimental studies are carried out to determine the potential of the proposed concepts. Finally, a periodic structure containing 9 adaptive resonators with electroactive membranes is studied in diffuse fields to evaluate the acoustic performances of the distributed concept.

<div> <div> <div> <p>Speech quality is a demand in voice commanded systems and in telephony. The voice communication system in real time often suffers from audible echoes. In order to cancel echoes, an acoustic echo cancellation system is designed and applied to increase speech quality both subjectively and objectively. </p> <p>In this research we develop various nonlinear adaptive filters wielding the new channel sparsity-aware recursive least squares (RLS) algorithms using a sequential update. The developed nonlinear adaptive filters using the sparse sequential RLS (S-SEQ-RLS) algorithm apply a discard function to disregard the coefficients which are not significant or close to zero in the weight vector for each channel in order to reduce the computational load and improve the algorithm convergence rate. The channel sparsity-aware algorithm is first derived for nonlinear system modeling or system identification, and then modified for application of echo cancellation. Simulation results demonstrate that by selecting a proper threshold value in the discard function, the proposed nonlinear adaptive filters using the RLS (S-SEQ-RLS) algorithm can achieve the similar performance as the nonlinear filters using the sequential RLS (SEQ-RLS) algorithm in which the channel weight vectors are sequentially updated. Furthermore, the proposed channel sparsity-aware RLS algorithms require a lower computational load in comparison with the non-sequential and non-sparsity algorithms. The computational load for the sparse algorithms can further be reduced by using data-selective strategies. </p> </div> </div> </div>

Helicopters suffer from severe vibration levels compared to fixed-wing aircraft. The main source of vibration in a helicopter is the main rotor which operates in a highly unsteady aerodynamic environment. Active vibration control methods are effective in helicopter vibration suppression since they can adapt to various flight conditions and often involve low weight penalty. One such method is the actively controlled flap (ACF) approach. In the ACF approach, a trailing-edge flap (TEF) located in each rotor blade is deflected at higher harmonics of rotor frequency to reduce vibratory loads at the rotor hub. The ACF approach is attractive because of its simplicity in practical implementation, low actuation power and enhanced airworthiness, since the flap control is independent of the primary control system. Multiple-flaps are better suited to modify the aerodynamic loading over the rotor blade and hence offer more flexibility compared to a single flap. They also provide the advantage of redundancy over single-flap configuration. However, issues like the number, location and size of these individual flaps need to be addressed based on logic and a suitable performance criteria. Preliminary studies on a 4-bladed hingeless rotor using simple aerodynamic and wake models predict that multiple-flaps are capable of 70-75 percent reduction in hub vibration levels. Numerical studies confirm that multiple-flaps require significantly less control effort as compared to single-flap configuration for obtaining similar reductions in hub vibration levels. Detailed studies include more accurate aerodynamic and wake models for the rotor with TEF’s. A simple and efficient flap control algorithm is chosen from literature and modified for use in multiple-flap configuration to actuate every flap near complete authority. The flap algorithm is computationally efficient and performs creditably at both high and low forward speeds. This algorithm works reasonably well in the presence of zero-mean Gaussian noise in hub load data. It is also fairly insensitive to small changes in plant parameters, such as, blade mass and stiffness properties. The optimal locations of multiple TEF’s for maximum reduction in hub vibration are determined using Response Surface methodology. Piezoelectric stack actuators are the most promising candidates for actuation of full-scale TEF’s on helicopter rotors. A major limitation of piezoelectric actuators is their lack of accuracy due to nonlinearity and hysteresis. The hysteresis in the actuators is modeled using the classical Preisach model (CPM). Experimental data from literature is used to estimate the Preisach distribution function. The hub vibration in this case is reduced by about 81-86 percent from baseline conditions. The performance of the ACF mechanism can be further improved by using an accurate hysteresis compensation scheme. However, using a linear model for the piezoelectric actuator or an inaccurate compensation scheme can lead to deterioration in ACF performance. Finally, bench-top experiments are conducted on a commercially available piezostack actuator (APA500L from CEDRAT Technologies) to study its dynamic hysteresis characteristics. A rate-dependent dynamic hysteresis model based on CPM is used to model the actuator. The unknown coefficients in the model are identified using experiments and validated. Numerical simulations show the importance of modeling actuator hysteresis in helicopter vibration control using TEF’s. A final configuration of multiple flaps is then proposed by including the effects of actuator hysteresis and using the response surface approach to determine the optimal flap locations. It is found that dynamic hysteresis not only affects the vibration reduction levels but also the optimal location of the TEF's.