New developments in Modal Analysis. Advanced Modal Seminar Brasil, Februari 2017

Transcription

1 New developments in Modal Analysis Advanced Modal Seminar Brasil, Februari 2017 Unrestricted Siemens AG 2016 Realize innovation.

2 Agenda Order Based Modal Analysis (OBMA) Strain Based Modal Analysis Acoustic Modal Analysis Page 2

3 Order Based Modal Analysis (OBMA)

4 Still talking about Modal Analysis!!! Seat Vibration Engine Wheel & Tire Steering Wheel Shake Noise at Driver s & Passenger s Ears Road Turbomachinery Rearview mirror vibration Rotor Gearbox and Transmission Environmental sources Cockpit vibration & noise Structural Integrity Cabin comfort Accessories Source X System Transfer = Receiver Page 4

5 Modal Analysis in Operating conditions Input System Output U H Y Majority of applications: use of output-only data Objective: Identification of modal parameters from output- only data measured on a structure during standard operation. Eigenfrequency Damping Mode shape Output-only operational modal analysis = identifying H Based on Y Without knowing U Desired (but unknown) ambient sources: white spectrum Page 5

6 Operational Modal Analysis Rotational Excitation?? Page 6

7 Operational Modal Analysis End-of-order effect Tacho1 (T1) rpm Hz Frequency g 2 db db g F AutoPow er BODY:1001:+Y Hz End-of-order effect sharp peaks in the spectrum due to orders that end Page 7

8 Order Based Modal Analysis OBMA What? Order-based Modal Analysis: Derive modal parameters In operating conditions During transient (run up/down) operations With dominant rotating source Accurate tacho measurement Angle tracked responses Modal analysis on orders Page 8

9 OBMA Theoretical background output y(t) 2 (correlated) inputs r 0 m Unrestricted Siemens AG 2016 Page 9 XX.XX.20XX

10 OBMA Theoretical background output y(t) (t) f y r 0 m f x (t) 2 f x ( t) rm 0 cos( 0t ) 2 t) rm sin( t ) f y ( 0 0 Unrestricted Siemens AG 2016 Page 10 XX.XX.20XX

11 OBMA Theoretical background output y(t) (t) f y r 0 m f x (t) 2 f x ( t) rm 0 cos( 0t ) 2 t) rm sin( t ) f y ( 0 0 Y( ) H(:, fx) ( ) Fx ( ) H(:, fy) ( ) Fy ( ) Unrestricted Siemens AG 2016 Page 11 XX.XX.20XX H ( ) jh ( ) ( ) 2 Y( ) 0 (:, fx) (:, fy) 0 Measured output: Proportional to squared rotation speed Complex combination of 2 structural FRFs related to x and y excitation

12 OBMA: theoretical background Modal decomposition H ( ) jh ( ) ( ) 2 Y( ) 0 (:, fx) (:, fy) 0 H 1 s 1 1 (:, fx) ( ) V ( si ) Lx LRx UR 2 x H(:, fy) ( ) V ( si ) Ly LRy UR 2 y 1 s H ( ) jh ( ) s V ( si ) ( L jl ) ( LR jlr ) ( UR jur ) 2 Y ( ) s (:, fx) (:, fy) x y 2 s For displacement orders, response is proportional to the squared rotational speed Combined complex participation factors Complex lower and upper residual x y x y Unrestricted Siemens AG 2016 Page 12 XX.XX.20XX

13 OBMA theoretical background Modal Parameter identification H ( ) jh ( ) s V ( si ) ( L jl ) ( LR jlr ) ( UR jur ) 2 Y( ) s (:, fx) (:, fy) x y 2 s x y x y Polymax can be applied in a straightforward way by using a general LSCF formulation and adapting the order of the residuals [2 0 2] for displacement order [4 2 4] for acceleration orders O( s) n v i v * T H 4 li i li 1 s * i 1 s i s i s 2 LR UR Unrestricted Siemens AG 2016 Page 13 XX.XX.20XX

14 OBMA Where? Page 14

15 OBMA When? rpm Amplitude F 129:Tacho s Time (Throughput) Tacho1 (T1) rpm Log (Peak) g Hz Frequency e-3 Page 15

16 OBMA Why? Page 16

17 OBMA Why? EMA OBMA OMA/OBMA Page 17

18 OBMA How? MEASURE Tacho_P2 (T1) rpm ANGLE DOMAIN PROCESSING order Point5:+X (CH5) db g rpm Tacho_P2 (T1) rpm Tacho_P2 (T1) 1.00 Amplitude 0.00 MODAL ANALYSIS Page 18

19 OBMA The message SIGNATURE / OPERATIONAL NVH TESTING STRUCTURAL ANALYSIS Derive operational modal models for components with dominant rotating sources Go beyond ODS to understand the structural dynamic of the system Validate numerical model in operational conditions No additional effort just measure good quality orders! Page 19

20 ODS vs OMA vs OBMA ODS OMA OBMA Auto & Cross Powers, Spectra, Orders Peak picking: Deformation at a chosen frequency line No damping information Combination of modes and forced responses Combination of closely spaced modes Phenomena observation only Auto & Cross Powers Broadband or single sine excitation Modal model: Natural frequency Damping Mode shapes Structural characteristics Separation of closely spaced modes Root causes Orders Multiple sine sweeping excitation Modal model: Natural frequency Damping Mode shapes Structural characteristics Separation of closely spaced modes Root causes Page 20

21 Application cases: Gearboxes and Transmissions Gear test rig Time s Log (Peak) g Hz Frequency e-3 Page 21

22 Application cases: Gearboxes and Transmissions Wind turbine gearbox test rig Time s Log (Peak) g e-3 Page 22

23 Application cases: Jet engine blades Jet engine blades Tacho1 (T1) rpm Log (Peak) MPa 5.52e-6 / Hz Frequency Page 23

24 Application cases: Locomotive Time s Log (Peak) g Hz Frequency e-6 Page 24

25 Application cases: Engine test bench Time s Hz Frequency Page 25

26 Application cases: Roller-bench full vehicle test Tacho1 (T1) rpm db g Hz Frequency Page 26

27 Other applications Page 27

28 Strain Based Modal Analysis

29 Content What is strain modal analysis? Why strain modal analysis? Mixed Strain & acceleration Modal Analysis Page 29

30 Introduction: Modal Analysis What is modal analysis? Vibration Modes It is the study of the dynamic behavior of vibrating structures Page 30

31 Introduction: Modal Analysis Experimental Modal Analysis: use of accelerometers Page 31

32 What is Strain Modal Analysis? Classical Modal Analysis Strain Modal Analysis Accelerometer Strain Gauge Displacement Mode Shape Strain Mode Shape Page 32

33 Strain Modal Analysis What is the difference between strain and displacement modes? A great effect on strain and displacement modeshapes comes from boundary conditions Example: cantilever beam Page 33

34 2 nd Bending 3 rd Bending Strain Modes - Cantilever Beam Example Displacement mode shape Displacement mode shape Strain mode shape Strain mode shape Page 34

35 Wind Turbine Strain Modal Analysis Cantilever boundary condition Measurement locations copyright LMS International Blade FEM model Page 35

36 Wind Turbine Strain Modal Analysis Experimental Analysis Wind Turbine Natural frequencies experiment and simulation difference and Modal Assurance Criterion Page 36

37 FEM Test Wind Turbine Strain Modal Analysis Modal Assurance Criterion Comparison between Experimental modes and FEM Graphical visualization Displacement Strain Page 37

38 Wind turbine blade: FRFs & coherence (m/s 2 db (m/s 2 db ue/n db Hz Hz Hz Phase Phase Phase Hz Hz Hz Real / 1.00 Real / 1.00 Real / Acceleration driving point FRF Acceleration FRF & coherence close to clamped area Strain FRF & coherence close to clamped area Hz Hz Hz Page 38

39 Why strain modal analysis?

40 Why strain modal analysis? Mostly for operational condition when an accelerometer can t be instrumented due to test condition like rotating component, high temperature FBG New technologies and challenges revive the need for strain modal testing: New sensor technologies: optical Fiber Bragg Grating (FBG) sensors, ICP High quality, multi-sensor data acquisition systems Complementary information from strain gauges and accelerometers Structural Health Monitoring systems: strain is more representative of damage and integrity ICP Strain Gauge Unrestricted Siemens AG 2016 Page 40 XX.XX.20XX

41 Instrumentation is not easy Rotating & non-rotating components in all industries Across all frequency ranges Fatigue can be either static or/and dynamic phenomena Size matters K 100K Hz Unrestricted Siemens AG 2016 Page 41 XX.XX.20XX

42 Get more out of dynamic fatigue tests Observation Intensive dynamic fatigue testing for all sorts of components Identify resonance frequency is also one of these tests Solution Increase number of strain gages on the tested component Perform a modal test and analysis based on strain data Extra processing on time data from durability test Useful for Automotive components Any machine component subject to vibration control specifications Any component subject to cyclic load tests Unrestricted Siemens AG 2016 Page 42 XX.XX.20XX

43 Get more out of static tests Observation Destructive static strength tests are required for certification Pain Instrumentation of a static strength test is time consuming & expensive but serves 1 test only Opportunity Maximize the use of the expensive static test set-up for increased engineering insight, e.g. in structural dynamics Solution Execute extra dynamic measurements prior to the destructive static tests On complete or subset of instrumentation Unrestricted Siemens AG 2016 Page 43 XX.XX.20XX Useful for Aircraft wings Spacecraft structural components Wind Turbine Blade

44 Modal analysis for rotating blades under operating condition Need identify contribution of modes to operational displacement vibration response in flight Pain Surface mounted accelerometers not possible during operating condition Solution measure strain and vibration at standstill, and strain in operation Decomposition of operational strain data using baseline data measured at standstill Apply same decomposition to vibration shapes Useful for Fans Helicopter rotor blade Wind Turbine Future investigation Strain pattern analysis Optical strain sensors Unrestricted Siemens AG 2016 Page 44 XX.XX.20XX

45 Diagnosis of root cause of failure Observation When a piece of a machine is broken, maintenance tends to simply replace the piece but the same problem might occur again & again vertical geothermal water pump Pain Modal analysis allows to identify high deformation at resonance but will indicate high stress area s Proposed Solution Characterize structure with classical modal analysis do correlation with FE model and calculate stress concentrations in simulation model Add strain gauge to instrumentation and perform strain modal analysis Perform operational measurement with strains and identify critical resonance frequency Useful for oil & gas production & transportation (also in operation) any dynamic failure investigation in operation Unrestricted Siemens AG 2016 Page 45 XX.XX.20XX

46 Flutter analysis in windtunnels based on strain data Need identify critical modes and dynamic loads on scale models in windtunnels Pain various application software environments required to complete the analysis Solution Test.Lab modal analysis & flutter analysis using strain gages data Prototype helicopter main blade section under test in windtunnel IFASD 2011 Useful for aircraft components & structures Unrestricted Siemens AG 2016 Page 46 XX.XX.20XX

47 SISW offering for strain modal testing & analysis LMS SCADAS Universal module VB8-II/DB8-II/BDS4 ICP, DC, AC, Bridge LMS Test.Lab Structural Testing & Analysis same measurement software or strain or acceleration FRF Same modal analysis software for strain modal analysis and acceleration/displacement modal analysis (EMA/OMA) Complements FE analysis in Virtual.Lab, Samcef, Simcenter 3D Unrestricted Siemens AG 2016 Page 47 XX.XX.20XX

48 Mixed Strain & acceleration Modal Analysis

49 Strain and acceleration modal analysis Complementary? There can be benefits in combining strain and acceleration measurements: Strain modes can be very hard to interpret; But they can provide valuable information not present in displacement modeshapes; Using displacement and strain helps interpret physical meaning of modes, with additional information from strain; Example on ground vibration testing of an F-16 Unrestricted Siemens AG 2016 Page 49 XX.XX.20XX

50 F-16 Test Setup Unrestricted Siemens AG 2016 Page 50 XX.XX.20XX

51 Dynamic Piezo Strain Sensors Some characteristics: Quartz sensing element Reusable Easy to mount (but has to be on a flat surface) Titanium housing - can add stiffness to structure High sensitivity: 50mV/μE Frequency range: 0.5 Hz to 100 KHz Unrestricted Siemens AG 2016 Page 51 XX.XX.20XX

52 F-16 Test Setup - Sensor Locations Unrestricted Siemens AG 2016 Page 52 XX.XX.20XX

53 Left Wing Sensor Locations 17 strain sensors 8 triaxial accelerometers Left Wing Unrestricted Siemens AG 2016 Page 53 XX.XX.20XX

54 Displacement and Strain Modes Unrestricted Siemens AG 2016 Page 54 XX.XX.20XX

55 Displacement and Strain Modes Unrestricted Siemens AG 2016 Page 55 XX.XX.20XX

56 Displacement and Strain Modes Unrestricted Siemens AG 2016 Page 56 XX.XX.20XX

57 Displacement and Strain Modes Unrestricted Siemens AG 2016 Page 58 XX.XX.20XX

58 Acoustic Modal Analysis

59 Outline Introduction and background New sound source New modal analysis method (ML-MM) Case studies Numerical simulation of an automotive cabin Experimental: automotive (Neon & Mercedes SLK) interior cabin Experimental: aircraft (ATR42) interior cabin Conclusions Page 60

60 response Acoustic Modal Analysis Interior car sound: very important attribute in vehicle engineering Predict the acoustic behaviour with simulation models Role of testing and experimental acoustic modal analysis Understand modelling challenges and improve modelling know-how Troubleshooting Excitation Force [N] Noise [m 3 /s 2 ] Pa/(m 3/s2 ) db Real / F F B FRF 3_5:mic2:S/vvs:1:S FRF 3_5:mic2:S/vvs:2:S Coherence 3_5:mic2:S/Multiple Vibration [m/s2] Sound Pressure [Pa] Structural Dynamics Modal Model Acoustic sensitivity for structural excitation Structural sensitivity to acoustic excitation Acoustic FRF & Modal Model Hz Page 61

61 Acoustic Modal Analysis: Challenges Acoustic excitation of cavity + flexible body structure: many vibro-acoustic modes Highly-damped modes Many (8+) acoustic sources needed for homogeneous sound field inside cabin Mode shape distortions in case of too few references (See Yoshimura et al.) Many (few 100s) microphones used to get good mode shape description and to study interaction effect with body and cavities FRF matrix with many columns (many sources) is challenge for most modal parameter estimation algorithms: curvefitting quality goes down Page 62 Yoshimura et al., Modal analysis of automotive cabin by multiple acoustic excitation, ISMA 2012.

62 Experimental Acoustic Modal Analysis Basic Formulation Governing equation for 3D closed acoustic system with rigid boundaries p 2 c 2 1 p q p q c Sound pressure [N/m2] Volume velocity per unit volume [1/s] Speed of sound [m/s] Density of medium [kg/m3] Adding damping (Spatial) discretization A p B p C p q A, B, C Acoustical mass, damping, stiffness matrices Page 63

63 Outline Introduction and background New sound source New modal analysis method (ML-MM) Case studies Numerical simulation of an automotive cabin Experimental: automotive (Neon & Mercedes SLK) interior cabin Experimental: aircraft (ATR42) interior cabin Conclusions Page 64

64 LMS Qsources Low Mid Frequency Volume Source (Q-LMF) Miniature Volume Source (Q-IND) Frequency range: 10 ~ 800 Hz Dimension: x 0.38 x 0.79 m Powering mode: ICP Measuring source quantity: m 3 /s 2 Page 65 Frequency range: 50 ~ 1000 Hz Dimension: φ 21 mm, 70 mm length Powering mode: voltage Measuring source quantity: m 3 (volume displacement) The measured FRF should be double integrated [the unit of FRF: Pa/m 3 Pa/(m 3 /s 2 )]

65 Newly developed LMS Qsources sound source Requirements No distortion of cavity High excitation levels in the low frequency range (for measuring acoustic FRFs in highly-damped high-end class vehicles) Solution: newly developed sound source Monopole sound source High noise levels at low frequencies Omnidirectional Real-time sound source strength measurement Architecture: two high performant magnetic drives with a voice coil stroke assembled in a rigid body Page 66

66 Directivity Omnidirectional sound source Sound pressure variations < 1.5dB at 630Hz FRF comparison: new source versus Miniature Source FRFs very similar Despite significantly different source dimensions 71mm x φ21mm: Miniature Source 200mm x φ70mm: new source db Pa/(m 3/s2 ) db 10dB Directivity plot at 1 meter in semi anechoic conditions dB New source Miniature source Hz Hz 1000 Page 67

67 FRF example and signal-to-noise assesment Source strength sufficient Source in trunk, microphone in front row foot area: Good quality FRF and coherence Sound level due to source versus background noise Trunk microphone: source on/off Above 10Hz: response up to 50dB higher Pa/(m 3/s2 ) db Pa 2 /Hz db 20dB 20dB / Amplitude e-3 Hz Page Hz 500

68 Outline Introduction and background New sound source New modal analysis method (ML- MM) Case studies Numerical simulation of an automotive cabin Experimental: automotive (Neon & Mercedes SLK) interior cabin Experimental: aircraft (ATR42) interior cabin Conclusions Page 69

69 ML-cost function New modal parameter estimation method: ML-MM Maximum Likelihood estimation of a Modal Model A modal parameter estimator that combines the following benefits: Clear stabilization chart in a fast way (user friendliness) Optimized modal model (ML estimation) Confidence bounds on all the modal parameters (freq, damp, shapes, ) Continuous-time model without numerical conditioning problem 2 ML 1 5% Measurement Data Polymax Noise Initial values: Poles Mode shapes Participation factors Lower and upper residual terms Maximum Likelihood based on Modal Model (ML-MM) ( ) H θ, s k = No N N i f H oi (, ) H 2 o 1 i 1 k 1 H ( oi k N m r=1 ML k L r ψ r L r + ψ r s k λ r s k λ r oi ) ( ) k 2 + LR s k 2 + UR Gauss-Newton optimization ML-cost function Iteration Iteration Page 71 VUB-LMS collaboration Improved estimates for all the modal parameters together with their confidence bounds

70 Outline Introduction and background New sound source New modal analysis method (ML-MM) Case studies Numerical simulation of an automotive cabin Experimental: automotive (Neon & Mercedes SLK) interior cabin Experimental: aircraft (ATR42) interior cabin Conclusions Page 73

71 Case study 1 Numerical simulation of an automotive cabin Acoustic Modal Analysis of car cavity with rigid boundaries (non-confidential finite element (FE) model of an Audi car) Introducing damping: Modeling the cavity boundaries as complex impedance Here alternative approach: assign modal damping to the undamped modes Uncoupled Acoustic Modes Mode Frequency [Hz] Damping ratio [%] Page 74

72 Case study 1 Numerical simulation of an automotive cabin Real acoustic mode shapes directly calculated from the FEM (a) First Longitudinal (86.49 Hz) (b) First Lateral ( Hz) (c) First Vertical ( Hz) (d) First Lateral + First Longitudinal ( Hz) (e) First Vertical + First Longitudinal ( Hz) (f) ( Hz) (g) Second Lateral ( Hz) Page 75

73 Case study 1 Numerical simulation of an automotive cabin FRF calculations from the FEM FRFs are calculated through a dynamicresponse mode based solver The following I/O points were defined Input: 8 input points: Front right foot Front left foot Front right ear Front left ear Rear right foot Rear left foot Rear right ear Rear left ear Output: 611 output points at the boundaries of the FE model Page 76

74 Numerical simulations uncoupled Mode shape distortion at loudspeaker location For each analysis, only 1 loudspeaker selected (1 column of FRF matrix) Perfect estimation of frequency and damping Very good FRF synthesis True mode shape for comparison: But Distorted mode shapes Source: Rear right ear Source: Front right foot Source: Rear right foot Source: Front right ear Page 77

75 Numerical simulations uncoupled Mode shape distortion at loudspeaker location Improving mode shape estimates with increasing number of references MAC with respect to true values (FE mode shapes) 1 Ref (4) 2 Ref (4,7) 4 Ref (3,4,7,8) 8 Ref (all) Avg. diag MAC: 98.5 Avg. diag MAC: 99.8 Page 78

76 From the Numerical Model Case Study 2: many-reference vehicle cabin test Preliminary Analysis An acoustic FE model of the interior case-study-car was created in LMS Virtual.Lab Acoustics Rigid wall assumption Number of modes and their shape Proper distribution of sources to avoid nodal lines Test geometry (Wireframe) of the measurements points Guideline for selecting meaningful modes Page 79 Frequency range: [0-200] Hz

77 Microphones When the purpose is the validation, correlation and updating of the FE numerical model, an accurate description of the acoustic modes is necessary Microphones were positioned: On roving arrays With a spacing equal to 20 cm Both at the boundary surface and inside the cavity Also in extreme positions (foot regions, hat shelf) 527 locations Page 80

78 Sources 12 sources spread over the cavity Geometrically symmetric positioning Close to the edge, corners and at the maximum amplitude location S:01S:02 S:09S:10 S:03S:04 S:05S:06 S:07S:08 S:11S:12 Source:02 (Front Windshield RH) Source:04 (Rear Passenger Ears RH) Source:06 (Trunk RH) Source:08 (Front Foot Region RH) Source:10 (Front Seat Passenger RH) Source:12 (Rear Foot Region LH) Page 81

79 Measurements Procedure and consistency 18 microphone runs to cover entire cavity 12 sources used sequentially White noise excitation FRF: H1, 150 averages Pa/m 3 db db (m 3 ) 2 Amplitude Pa/m 3 db / F F B B B2 B2 FRF Reference_Point:01:S/Source:01:S FRF Reference_Point:01:S/Source:01:S AutoPow er Source:01:S AutoPow er Source:01:S Coherence Reference_Point:01:S/Source:01:S Coherence Reference_Point:01:S/Source:01:S Phase Hz Consistency: 1 st run versus last run Page Hz Consistency: FRFs from 18 runs

80 Measurements Reciprocity Pa/m 3 db FRF Source_Mic:01:S/Source:12:S FRF Source_Mic:12:S/Source:01:S FRF Source_Mic:01:S/Source:11:S FRF Source_Mic:11:S/Source:01:S Phase Hz Page 83

81 Measurements: comparison of 6-sources experiment with single-source experiment Conclusions OK to measure with all sources together OK to measure with sequential sources (but without moving the Q-LMF sources) FRF Reference_Point:01/Source:09 FRF Reference_Point:02/Source:09 FRF Reference_Point:03/Source:09 FRF Reference_Point:04/Source:09 FRF Reference_Point:01:S/Source:09:S FRF Reference_Point:02:S/Source:09:S FRF Reference_Point:03:S/Source:09:S FRF Reference_Point:04:S/Source:09:S Pa/m 3 db FRF Reference_Point:01/Source:01 FRF Reference_Point:02/Source:01 FRF Reference_Point:03/Source:01 FRF Reference_Point:04/Source:01 FRF Reference_Point:01:S/Source:01:S FRF Reference_Point:02:S/Source:01:S FRF Reference_Point:03:S/Source:01:S FRF Reference_Point:04:S/Source:01:S Phase Phase Pa/(m 3/s2 ) db Hz Hz Page 84

82 ML-MM Modal parameter estimation based on 527 x 12 FRFs: Polymax & ML-MM Pa/m 3 db v ss s s v ss v v s v s v s v s ss vs s vvsssv s vvss s v s s s sv s sv vs 128 v vs s v v vs v s v s v s v s vs vv s vssv vvvs v s v sv vv s sv v 126 o ss s v vs v s v s sv s vsv v s v ssv vsvs v v sv s s vs v 120 vs s v ss v s v s vv s v v s v svv vvvs v v v sv s s v v 114 v ss s v s s s s v s sv s v s s vvssv vs v v v s v s vs v 108 o vs s o s s v s v s s s vv v s vsv vs v v v s v s s sv 102 s s v s o s s v s vv v svs v s s vv s v s vs v 96 v vs s o s s s s s v v vss vvs v s vs s s sv Linear Hz Initial modal model Fitting error % Fitting Corr. % Computational time <5 min Optimized modal model Fitting error % Fitting Corr. % Page 85

83 Neon: acoustic mode shapes extracted from FRF measurements Page 86

84 Case study 2 Experimental: automotive (Mercedes SLK) interior cabin 2 Acoustic Volume Velocity Sources Positioned on driver and passengers seat 195 Microphone positions Measured in 32 runs Pa/(m 3/s2 ) db Amplitude / db (m 3/s2 ) 2 F B B2 B2 FRF 3_2:mic1:S/vvs:1:S Coherence 3_2:mic1:S/Multiple AutoPow er vvs:1:s AutoPow er vvs:2:s Hz Page 88

85 Case study 2 Experimental: automotive (Mercedes SLK) interior cabin ML-MM mode shapes Page 89

86 Case Study 3 Experimental: aircraft (ATR42) interior cabin ATR42 Twin Propeller Aircraft Trimmed aircraft cabin High, non-uniform damping Overlapping modes Complex mode shapes of cavity walls Acoustic ground test Identify acoustic cabin system Explain in-flight acoustic behaviour Page 91 ATR 42 aircraft interior

87 Case study 3 Experimental: aircraft (ATR42) interior cabin Measurement Setup Inputs 4 sources (2 longitudinal + 2 lateral loudspeakers) Outputs 20 simultaneous microphones: 1 section 12 section 240 pressure measurements Page 92

88 Case study 3 Experimental: aircraft (ATR42) interior cabin Modal parameter estimation results Model with 37 poles Comparison: Polymax and ML-MM FRF fitting quality FRF fitting quality Polymax ML-MM Cost Function 15 x Minimization of cost function during ML-MM iterations Mean error 61% 7% Mean correlation 74% 94% Iteration Measured PolyMAX Synthesis ML-MM Synthesis Pa/V db Pa/V db Measured PolyMAX Synthesis ML-MM Synthesis Hz Hz Page 93

89 Case study 3 Experimental: aircraft (ATR42) interior cabin ML-MM mode shapes Page 94

90 Conclusions Increased interest in acoustic characterization of automotive cabins Improved modelling capabilities validated by test Vehicle development and troubleshooting projects Call for enhanced testing capabilities New sound source Compact, omnidirectional and capable of generating high noise levels in the low frequency range Detailed experimental study: new source excellently suited for automotive cabin acoustic modal analysis New modal analysis method Maximum Likelihood Estimation based on the Modal Model (MLMM) Deals properly with FRF matrices with many references Provides superior FRF synthesis results Case studies Numerical simulations: study mode shape distortions Confirmation of benefits of new MLMM solver Page 96

91 Thank you! Advanced Modal Seminar Brasil, Februari 2017 Unrestricted Siemens AG 2016 Realize innovation.