ISMA23 - International Conference on Noise and Vibration Engineering HELSINKI UNIVERSITY OF TECHNOLOGY Sept. 16-18, 1998, Leuven, Belgium Adaptive Design of a Unidirectional Adaptive Design of a Unidirectional Source in a Duct Source in a Duct Vesa Välimäki 1 and Seppo Uosukainen 2 1 Helsinki University of Technology Laboratory of Acoustics and Audio Signal Processing (Espoo, Finland) 2 VTT Building Technology, Acoustics (Espoo, Finland) Vesa Välimäki & Seppo Uosukainen 1998 1
HELSINKI UNIVERSITY OF TECHNOLOGY Adaptive Design of a Unidirectional Adaptive Design of a Unidirectional Source in a Duct Source in a Duct Outline ➤ Introduction ➤ Principal unidirectional two-element constructions ➤ Adaptive design of a unidirectional two-element source ➤ Simulation examples ➤ Conclusions and future work Vesa Välimäki & Seppo Uosukainen 1998 2
HELSINKI UNIVERSITY OF TECHNOLOGY Introduction Introduction A unidirectional acoustic source in a narrow duct ➤ multiple actuators (see Refs. [1-7] of the paper) ➤ the input of each actuator must be processed (filtered) Motivation ➤ to be used in feedforward broadband ANC systems ➤ anti-noise must to radiate downstream but not upstream In this paper, we present structures and an adaptive design method for unidirectional two-element sources Vesa Välimäki & Seppo Uosukainen 1998 3
HELSINKI UNIVERSITY OF TECHNOLOGY Advantages of unidirectional sources Advantages of unidirectional sources ➤ the acoustic feedback is eliminated ➤ feedback neutralization filter is not needed ➤ SPL does not increase in the upstream direction due to the secondary source ➤ the sound pressure level may be attenuated in the upstream direction, since further reflections from duct terminations are eliminated Vesa Välimäki & Seppo Uosukainen 1998 4
HELSINKI UNIVERSITY OF TECHNOLOGY Disadvantages of unidirectional sources advantages of unidirectional sources Dis ➤ limited frequency band of about 2 to 4 octaves: not unidirectional at low frequencies (close to 0 Hz) and above an upper frequency limit ➤ need for several actuators ➤ in practice, both disadvantages are tolerable ➤ also other ANC systems also suffer from these defects Vesa Välimäki & Seppo Uosukainen 1998 5
HELSINKI UNIVERSITY OF TECHNOLOGY Why adaptive design? Why adaptive design? ➤ deviations in the actuator responses degrade the obtainable attenuation of unidirectional ANC systems – mutual difference ➤ also, measurement error in the distance between the actuator elements causes degradation ➤ to automatically overcome both problems, we propose an adaptive design method that learns how to equalize the loudspeakers and account for the propagation delay between them ➤ related earlier work: Elliott, 1993 Vesa Välimäki & Seppo Uosukainen 1998 6
HELSINKI UNIVERSITY OF TECHNOLOGY Principal unidirectional Principal unidirectional 2-element constructions 2-element constructions ➤ 4 different unidirectional two-element structures have been proposed: – two-element Swinbanks source (Swinbanks, 1973) – three versions of the JMC-based two-element source (Uosukainen & Välimäki, 1998) ➤ these will be reviewed in the following Vesa Välimäki & Seppo Uosukainen 1998 7
HELSINKI UNIVERSITY OF TECHNOLOGY Two-element Swinbanks source Two-element Swinbanks source ➤ ideal 2-element unidirectional source by Swinbanks: – delay the 1st actuator by delay between the sources, τ – feed the actuators in oppposite phases τ q 1 τ L - τ /2 q L c 0 / d ∫ d t 1/2 A q 2 -1 ➤ the amplification factor is A = kd / sin( kd ) Vesa Välimäki & Seppo Uosukainen 1998 8
HELSINKI UNIVERSITY OF TECHNOLOGY JMC-based solutions JMC-based solutions ➤ the JMC method (Jessel, Mangiante & Canévet) is suitable for formulating the ANC problem with the general system theory ➤ three types of secondary sources are needed: monopoles, dipoles, and quadripoles ➤ in the case of plane waves (such as in a narrow duct), quadripoles vanish ➤ ideal JMC actuators in a duct consist of monopole and dipole sources only Vesa Välimäki & Seppo Uosukainen 1998 9
HELSINKI UNIVERSITY OF TECHNOLOGY JMC-based two-element sources JMC-based two-element sources ➤ inter-channel delay can be optimized in 3 different ways 1. downstream 2. upstream 3. no delay at all ➤ the control structures for the 3 cases are illustrated next Vesa Välimäki & Seppo Uosukainen 1998 10
HELSINKI UNIVERSITY OF TECHNOLOGY Inter-channel delay optimized downstream downstream Inter-channel delay optimized + Σ q 1 -1/2 b + τ L - τ /2 τ q L 1/2 + τ /2 c 0 / d ∫ d t Σ q 2 a _ ➤ filters a and b are given in Table 1 Vesa Välimäki & Seppo Uosukainen 1998 11
HELSINKI UNIVERSITY OF TECHNOLOGY Inter-channel delay optimized upstream upstream Inter-channel delay optimized τ + Σ q 1 -1/2 b + τ L - τ /2 q L 1/2 + τ /2 c 0 / d ∫ d t Σ q 2 a _ Vesa Välimäki & Seppo Uosukainen 1998 12
HELSINKI UNIVERSITY OF TECHNOLOGY No Inter-channel delay No Inter-channel delay + Σ q 1 b -1/2 + τ L q L 1/2 + c 0 / d ∫ d t Σ q 2 a _ ➤ in the non-adaptive case, the delayless version has been found to be easiest to design (Uosukainen & Välimäki, 1998) Vesa Välimäki & Seppo Uosukainen 1998 13
HELSINKI UNIVERSITY OF TECHNOLOGY Adaptive design of a unidirectional Adaptive design of a unidirectional two-element source two-element source Mic 1 Act 1 Act 2 Mic 2 Mic 1 Act 1 Act 2 Mic 2 Ventilation system S 11 ( z ) S 12 ( z ) Open end S 21 ( z ) S 22 ( z ) y 1 ( n ) y 2 ( n ) y m1 ( n ) H 1 ( z ) H 2 ( z ) y m2 ( n ) - e 1 ( n ) e 2 ( n ) – ⊕ M-LMS + Ref. signal Ref. signal z - ∆ NOISE Delay Delay Vesa Välimäki & Seppo Uosukainen 1998 14
HELSINKI UNIVERSITY OF TECHNOLOGY Different phases of the adaptive design Different phases of the adaptive design ➤ adaptive design contains 3 phases 1. calibrate transfer functions S ij ( z ) from both actuators to both microphones 2. calibrate the unidirectionality (using the above system) 3. calibrate the error path from the unidirectional source to the error detector ➤ after these phases, the ANC operation may start using a single-channel adaptive system (one more adaptive filter!) Vesa Välimäki & Seppo Uosukainen 1998 15
HELSINKI UNIVERSITY OF TECHNOLOGY Adaptive Swinbanks configuration Adaptive Swinbanks configuration ➤ the proposed adaptive structure can in principle design any of the four unidirectional two-element structures ➤ here we show examples of designing the Swinbanks source ➤ the adaptive structures for the JMC-based structures are shown in our paper Vesa Välimäki & Seppo Uosukainen 1998 16
HELSINKI UNIVERSITY OF TECHNOLOGY Example 1 Example 1 ➤ the delay between the two actuators has been chosen to be T = 1/ f s , that is, one sampling interval ➤ the impulse responses of 0.5 filters H 1 ( z ) and H 2 ( z ) are 0 shown here (20 coefficients) −0.5 0 5 10 15 20 Sample index 0.5 0 −0.5 0 5 10 15 20 Sample index Vesa Välimäki & Seppo Uosukainen 1998 17
HELSINKI UNIVERSITY OF TECHNOLOGY ➤ magnitude responses upstream (upper) and downstream (lower) in Example 1 Magnitude (dB) 0 −20 −40 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency 2 Magnitude (dB) 0 −2 −4 −6 −8 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency Vesa Välimäki & Seppo Uosukainen 1998 18
HELSINKI UNIVERSITY OF TECHNOLOGY ➤ back-to-front ratio (La Fontaine & Shepherd, 1985) 1 Back−to−front ratio 0.5 0 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency ➤ obtainable sound radiation downstream (w/ideal anti-noise) 0 Magnitude (dB) −20 −40 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency Vesa Välimäki & Seppo Uosukainen 1998 19
HELSINKI UNIVERSITY OF TECHNOLOGY ➤ magnitude responses upstream (upper) and downstream (lower) in Example 2 (delay between actuators = 2 samples) Magnitude (dB) 0 −20 −40 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency 2 Magnitude (dB) 0 −2 −4 −6 −8 0 0.1 0.2 0.3 0.4 0.5 Normalized frequency Vesa Välimäki & Seppo Uosukainen 1998 20
HELSINKI UNIVERSITY OF TECHNOLOGY Conclusions and future work Conclusions and future work ➤ automatic design of a unidirectional two-element system was described ➤ further work is needed to implement and evaluate the adaptive design of JMC-based unidirectional structures ➤ a more advanced adaptive system could be designed that adapts all transfer functions online: H 1 ( z ), H 2 ( z ), S ij ( z ), and the error path model ➤ finally, adaptive unidirectional systems should be tested in actual real-time situations Vesa Välimäki & Seppo Uosukainen 1998 21
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