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p a Fahrzeugkomfort und Akustik durch Weiterent- wicklungen der Transferpfadanalyse optimieren Arnd Balger Where today meets tomorrow. Unrestricted © Siemens 2020
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p

a

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Arnd Balger

Where today meets tomorrow.Unrestricted © Siemens 2020

Unrestricted © Siemens 2020

Page 2 Siemens Digital Industries Software

Typical NVH engineering challenges that can be addressed with

Transfer Path Analysis

Electric motor

Road Noise

Wind noise

HVAC

Engine

Pass-by noise

Unrestricted © Siemens 2020

Page 3 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 4 Siemens Digital Industries Software

P

a

Transfer Path Analysis

Source-transfer-receiver approach

X =Source (Fi,Qj) Transfer (NTF) Receiver (yk)

Engine

Exhaust

Tyres

EPS

(H)EV

Drive lineTransmission

HVACWiper System

Measure

d..

Tota

l

be_f:18:X

..

be_f:18:Y

..

be_f:18:Z

..

be_f:5018:X

..

be_f:5018:Y

..

be_f:5018:Z

..

be_r:

9:X

..

be_r:

9:Y

..

be_r:

9:Z

..

be_r:

5009:X

..

be_r:

5009:Y

..

be_r:

5009:Z

..

sh_f:30:X

..

sh_f:30:Y

..

sh_f:30:Z

..

sh_f:5030:X

..

sh_f:5030:Y

..

sh_f:5030:Z

..

sh_r:

32:X

..

sh_r:

32:Y

..

sh_r:

32:Z

..

sh_r:

5032:X

..

sh_r:

5032:Y

..

sh_r:

5032:Z

..

subf:20:X

..

subf:20:Y

..

subf:20:Z

..

subf:5020:X

..

subf:5020:Y

..

subf:5020:Z

..

10.00

60.00

dB

(A)

Pa

sh_r:32:Z

0.00 350.00Hz

RMS Sum

Spectrum: PRCM:0001:S

Spectrum: PRCM:0002:S

Spectrum: PRCM:0004:S

Spectrum: PRCM:0003:S

Spectrum: PRCM:0006:S

Spectrum: PRCM:0005:S

-40.00

50.00

dB

(A)

Pa

Contribution at path or group (case vs. rpm or frequency) A

Unrestricted © Siemens 2020

Page 5 Siemens Digital Industries Software

Order: 2.0 Order: 3.0 Order: 4.0 Order: 5.0 Order: 6.0

90.00Pa

Order: 2.0

80.26 FRLE

4400950 rpm

Measured

BODY:0005

FSUB:0101

BODY:0002

FSUB:0601

FSUB:0102

FSUB:0105

90

-10

dB(A

)

Pa

3800

1:1

90.00 40.00Pa 90.00Pa

90.00

Pa

90.00

Pa

FSUB:0602FSUB:0601

FSUB:0105

BODY:0603FSUB:0605

BODY:0002

BODY:0103

FSUB:0102

BODY:0001

FSUB:0101

BODY:0005

Measured

Total

Vector contribution A

Contributions at Single Cursor Complex ( values as available ) Vector View

Introduction to Transfer Path Analysis

TPA as part of Contribution Analysis

Ste

p 2

:

Path

Sourc

e T

ransfe

r

Ste

p 1

: C

ontr

ibution A

naly

sis

Pa

ths

Frequency

Amplitude Phase Modal

Force

Transfer

Contribution

Unrestricted © Siemens 2020

Page 6 Siemens Digital Industries Software

Transfer Path Analysis

Throughout the vehicle development cycle

Bench marking &

Target setting

Concept Analysis

CAE based contribution

analysis

Auralization & Optimization

Critical component & Path

Identification

Troubleshooting

What-if games &

optimization

Target Setting Concept validation Detailed Engineering Validation/Refinement

Load Identification

Classical TPA Test/CAE combined TPA Classical TPA

Unrestricted © Siemens 2020

Page 7 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 8 Siemens Digital Industries Software

P

a

Transfer Path Analysis

Source-transfer-receiver approach

X =Source (Fi,Qj) Transfer (NTF) Receiver (yk)

Engine

Exhaust

Tyres

EPS

(H)EV

Drive lineTransmission

HVACWiper System

Measure

d..

Tota

l

be_f:18:X

..

be_f:18:Y

..

be_f:18:Z

..

be_f:5018:X

..

be_f:5018:Y

..

be_f:5018:Z

..

be_r:

9:X

..

be_r:

9:Y

..

be_r:

9:Z

..

be_r:

5009:X

..

be_r:

5009:Y

..

be_r:

5009:Z

..

sh_f:30:X

..

sh_f:30:Y

..

sh_f:30:Z

..

sh_f:5030:X

..

sh_f:5030:Y

..

sh_f:5030:Z

..

sh_r:

32:X

..

sh_r:

32:Y

..

sh_r:

32:Z

..

sh_r:

5032:X

..

sh_r:

5032:Y

..

sh_r:

5032:Z

..

subf:20:X

..

subf:20:Y

..

subf:20:Z

..

subf:5020:X

..

subf:5020:Y

..

subf:5020:Z

..

10.00

60.00

dB

(A)

Pa

sh_r:32:Z

0.00 350.00Hz

RMS Sum

Spectrum: PRCM:0001:S

Spectrum: PRCM:0002:S

Spectrum: PRCM:0004:S

Spectrum: PRCM:0003:S

Spectrum: PRCM:0006:S

Spectrum: PRCM:0005:S

-40.00

50.00

dB

(A)

Pa

Contribution at path or group (case vs. rpm or frequency) A

Unrestricted © Siemens 2020

Page 9 Siemens Digital Industries Software

Traditional TPA methods

Efficient & Accurate FRF Acquisition

Reciprocal FRF measurement

• Measurement of multiple/all NTF

(noise transfer functions) at once,

faster than roving hammer or

shakers

Direct FRF Measurements

• Modal Hammer

✓ Common.limited quality and

repeatability

• Shaker

✓ shakers overcome hammer

issues, if small and applicable

Receiver

Ptotal

P/F1

P/F2

Receiver

Ptotal

P/F1

P/F2

Unrestricted © Siemens 2020

Page 10 Siemens Digital Industries Software

Traditional TPA methods

Requirements: Verify data quality and gain insight – the Heatmap

Gain insight in the system dynamics

1000+ FRFs in one view

Instant verification of FRF consistency by checking reciprocity,

linearity and directions errors

Unrestricted © Siemens 2020

Page 11 Siemens Digital Industries Software

P

a

Transfer Path Analysis

Source-transfer-receiver approach

X =Source (Fi,Qj) Transfer (NTF) Receiver (yk)

Engine

Exhaust

Tyres

EPS

(H)EV

Drive lineTransmission

HVACWiper System

Measure

d..

Tota

l

be_f:18:X

..

be_f:18:Y

..

be_f:18:Z

..

be_f:5018:X

..

be_f:5018:Y

..

be_f:5018:Z

..

be_r:

9:X

..

be_r:

9:Y

..

be_r:

9:Z

..

be_r:

5009:X

..

be_r:

5009:Y

..

be_r:

5009:Z

..

sh_f:30:X

..

sh_f:30:Y

..

sh_f:30:Z

..

sh_f:5030:X

..

sh_f:5030:Y

..

sh_f:5030:Z

..

sh_r:

32:X

..

sh_r:

32:Y

..

sh_r:

32:Z

..

sh_r:

5032:X

..

sh_r:

5032:Y

..

sh_r:

5032:Z

..

subf:20:X

..

subf:20:Y

..

subf:20:Z

..

subf:5020:X

..

subf:5020:Y

..

subf:5020:Z

..

10.00

60.00

dB

(A)

Pa

sh_r:32:Z

0.00 350.00Hz

RMS Sum

Spectrum: PRCM:0001:S

Spectrum: PRCM:0002:S

Spectrum: PRCM:0004:S

Spectrum: PRCM:0003:S

Spectrum: PRCM:0006:S

Spectrum: PRCM:0005:S

-40.00

50.00

dB

(A)

Pa

Contribution at path or group (case vs. rpm or frequency) A

Unrestricted © Siemens 2020

Page 12 Siemens Digital Industries Software

Load identification methods

Mount stiffness and Matrix inversion

Matrix InversionMount Stiffness

2

))()(()()(

−=

piai

ii

aaKF )()()(

1 aHF =

Unrestricted © Siemens 2020

Page 13 Siemens Digital Industries Software

Matrix InversionMount Stiffness OPAX

Solution for load identification

Traditional methods

ASQ/Panel

Contribution

Reduced number of

required measurements

Fast troubleshooting

method

Quantify airborne

contributions of nozzles,

panels or component

housings

Works for all kind of

connections (soft & rigid)

No stiffness curves

required

Fast and easy setup

Requires mount stiffness

curves

Load identification techniques for fast troubleshooting to detailed structural &

airborne load determination

2

))()(()()(

−=

piai

ii

aaKF )()()(

1 aHF =

PHQ PQ *1−

=

Unrestricted © Siemens 2020

Page 14 Siemens Digital Industries Software

TPA method: Strain sensors based

Separating nearby paths

Strain FRF

Acceleration FRF

)()()(1

aHF =−

Advanced approach:

Strain Indicators

→ Strain responses are

dominated by a high

amount of local

structural body modes

→ Extended possibilities for

load separation /

identification

Classic approach:

Acceleration Indicators

→ Acceleration responses

are dominated by a

limited amount of global

structural body modes

→ Potential limitation for

force estimation

possibilities

Unrestricted © Siemens 2020

Page 15 Siemens Digital Industries Software

Time domainStrain-based Multi-reference

Solution for load identification

Advanced methods

Multi-source noise &

vibration issues

Road noise analysis

Analyze transient

phenomena

Listen to partial

contributions

Separate strongly

coupled forces

Low Frequency Analysis

Tackle issues from every possible angle – from simple systems to complex

structures

Unrestricted © Siemens 2020

Page 16 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 17 Siemens Digital Industries Software

Frequency-domain vs. Time-domain TPA

FIR Filter =

=X

NTF

Auralization, Signature Analysis, Sound Quality metrics ...

Loads (orders,

spectra)

Path contributions

(orders, spectra)

Frequency

transfer

model

Loads (time traces) Path contributions

(time traces)

440.0020.00 Hz

FSUB:0105:+Y (CH1)

4500.00

900.00

rpm

Tacho1 (

T1)

20.00

-80.00

dB N

440.0020.00 Hz

FRLE:S (CH2)

4500.00

900.00

rpm

Tacho1 (

T1)

70.00

-30.00

dB Pa

120.000.00 s

24.00

-24.00

Real

N

1.00

0.00

Am

plit

ude

120.000.00 s

0.10

-0.12

Real

Pa

1.00

0.00

Am

plit

ude

Frequency-domain TPA

➔ Order analysis

➔ Spectrum analysis

✓ Run-up & run-down

✓ Stationary: e.g road noise

Time-domain TPA

➔ Time traces

✓ Run-up & run-down

✓ Stationary: e.g road noise

✓ Transient: e.g. engine start-up

✓ Semi-stationary: e.g. idle noise,

frequency modulation …

Unrestricted © Siemens 2020

Page 18 Siemens Digital Industries Software

Time-domain TPA for Tip-in/Tip-out

Application Example

…Transfer Path Analysis (TPA)

Insights in contribution

to NVH Comfort

…in “full NVH Context”

To link transient loads

to Dynamic Interface Forces…

Transient Load identification

Strain gage technology

Low frequency

Strain responses

(right) during Tip-in

Typical Tip-in / Tip-out

Response

Transient torque oscillations in the driveline

Amplified by P/T, suspension and body modes

Resulting seat and steering-wheel vibrations

Time-domain Transfer Path Analysis for Transient Phenomena Applied to Tip-in/Tip-out (Shock & Jerk)

H. Shiozaki, Y.Iwanaga, MMC, T. Geluk ,F. Daenen, J, Van Herbruggen, LMS, SAE 2012-01-1545

Time domain Path

Contribution Analysis for

Seat vibrations X-direction

Unrestricted © Siemens 2020

Page 19 Siemens Digital Industries Software

Transfer Path Analysis:

More insight with TPA Synthesis

Immediate

assessment of design

modifications. real-

time filtering and

auralization of partial

contributions for

subjective sound

qualification and A/B

comparisons

Unrestricted © Siemens 2020

Page 20 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 21 Siemens Digital Industries Software

Automotive OEMs have to reduce full vehicle testing to

handle wide variety of vehicles

Body Component

• Increasing testing effort

• Prototype availability?

• Impact of modification?

• …

How to ensure NVH performance while keeping development

time and cost under control?

Powertrain

Front-loading vehicle

level component

NVH testing

Frontloading# of vehicle variantsIC

PHEV

EV

Unrestricted © Siemens 2020

Page 22 Siemens Digital Industries Software

Component-based TPA for full vehicle NVH assessmentEnable NVH what-if analysis from concept to final troubleshooting

Unrestricted © Siemens 2020

Page 23 Siemens Digital Industries Software

Component-based TPA for full vehicle NVH assessment

Testlab NVH Synthesis – Concept

NVH

synthesis

Solver

Digital Twin

Model

Methods

Scenarios

-7.00 10.00m

65.00

75.00

dB

(A)

Pa

65.00

75.00

dB

(A)

Pa

F Left Side

F Left Side Virtual

B Right Side

B Right Side Virtual

Compare Contribution Analysis

Sound Synthesis Result

Pass-by Noise Synthesis

NVH Driving Simulator Evaluation

Combining

Test & Simulation

data

Vehicle

Architectures

Stiffness

FRF

Forces

Component

Library

Target

Requirements

Unrestricted © Siemens 2020

Page 24 Siemens Digital Industries Software

Component-based TPA

Invariant load characterization

Structure-borne:

Airborne:

Blocked Forces

Volume Velocities

Receiver independent, allowing:

• Validating sources against

receiver independent targets

• Benchmarking or validating

modifications

• Predicting NVH performance in

arbitrary source-receiver

assemblies

Invariant load characterization

Unrestricted © Siemens 2020

Page 25 Siemens Digital Industries Software

1. Blocked Force

Source A

12

F source

𝑭2,𝐵𝑙𝑜𝑐𝑘𝑒𝑑

2. Free Velocity/Acceleration

Source A

12

F source𝒂𝟐,𝑭𝒓𝒆𝒆

𝑯22𝐴 −𝟏𝒂𝟐,𝑭𝒓𝒆𝒆 = 𝑭2,𝐵𝑙𝑜𝑐𝑘𝑒𝑑

3. In-Situ TPA

Source A Receiver B

12

5

4

F source

4

𝑯24𝐴𝐵

𝑭2,𝐵𝑙𝑜𝑐𝑘𝑒𝑑 = 𝑯24𝐴𝐵 +𝒂𝟒

Source:Elliott, Moorhouse, Characterization of the structure borne

sound sources from measurements in-situ, 2008

Source: Mondot, Petersson, Characterization of structure-borne

sound sources: The source descriptor and the coupling function

1987

Three possible methodologies to obtain independent source description

Rigid test rig → Often not possible Source in free free conditions (ISO 9611) Any receiver is valid (ISO 20270-2019)

Component-based TPA

Invariant load characterization for structural paths

3

Unrestricted © Siemens 2020

Page 26 Siemens Digital Industries Software

50020 50 100 150 200 250 300 350 400 450

Hz

20

-60

-50

-40

-30

-20

-10

0

10

dBg

180.00

-180.00

Phase

°

Harmonic Spectrum P3:T1:+Z Measured

Harmonic Spectrum P3:T1:+Z<Total Contact bench

Example: Source-Receiver interaction

Strong coupling case – Structure Borne

Test Bench

Source`

Vehicle / Receiver

Source

Predict Target Response

Test bench

CONTACT

FORCES

Predicted target

deviates from

measured target!

Unrestricted © Siemens 2020

Page 27 Siemens Digital Industries Software

50020 50 100 150 200 250 300 350 400 450

Hz

30

-60

-50

-40

-30

-20

-10

0

10

20

dBg

180.00

-180.00

Phase

°

Harmonic Spectrum P3:T1:+Z Measured

Harmonic Spectrum P3:T1:+Z<Total Blocked forces

Example: Source-Receiver interaction

Strong coupling case – Structure Borne

Test Bench

Source`

Vehicle / Receiver

Source

Predict Target Response

Predicted target

matches measured

target!

Test Bench

BLOCKED

FORCES

• + Invariant Load Strength

• +- Conditioning similar to classical Matrix

Inversion TPA

• - Combining with FBS puts high demands

towards data quality

Unrestricted © Siemens 2020

Page 28 Siemens Digital Industries Software

Virtual Point Transformation

Accurate FRFs at interface connection points

Solution:

▪ Geometrical Reduction / Virtual Point

Transformation

▪ Assumption: local rigidity in the connection

▪ Input: Geometry Information and FRFs

Challenge:

▪ High quality transfer functions at precise

locations.

▪ Transfer functions at difficult to access

positions

▪ Translational and rotational transfer

functions (DOFs)1000.000.00 Hz

80.00

-80.00

dBN

180.00

-180.00

Phase

°

Blocked force

at connection

Blocked force

off connection

VP for correct blocked force estimation

VP for correct assembly using FBS

VP

Unrestricted © Siemens 2020

Page 29 Siemens Digital Industries Software

Component-based TPA

Application example of a steering system

Source MechanismInvariant

Source Synth. ModelSub-Receiver Receiver

Steering

System

Blocked

Forces &

Impedances

Mount Pos.

SubframeFEM/TEST

FRF

BodyFEM/TEST

FRF

Invariant Source Load (TEST) Full System Transfer Function

bench

1

A

𝑎𝑖xx

x

𝐻𝑖1𝐴𝐶

𝐹𝑏𝑙𝐴

𝐹𝑏𝑙𝐴 = 𝐻𝑖1

𝐴𝐶 −1∗ 𝑎𝑖

𝐹𝑏𝑙𝐴

3𝑝

1 2

A

B

𝐹𝑟

𝑝 = 𝐻32𝐴𝐵 ∗ 𝐹𝑏𝑙

𝐴

1. Measure Coupled FRF

Unrestricted © Siemens 2020

Page 30 Siemens Digital Industries Software

Component-based TPA

Application example of a steering system

Source MechanismInvariant

Source Synth. ModelSub-Receiver Receiver

Steering

System

Blocked

Forces &

Impedances

Mount Pos.

SubframeFEM/TEST

FRF

BodyFEM/TEST

FRF

Invariant Source Load (TEST) Full System Transfer Function

bench

1

A

𝑎𝑖xx

x

𝐻𝑖1𝐴𝐶

𝐹𝑏𝑙𝐴

𝐹𝑏𝑙𝐴 = 𝐻𝑖1

𝐴𝐶 −1∗ 𝑎𝑖

𝐹𝑏𝑙𝐴 , 𝐻11

𝐴

3𝑝

1 2

A

B

𝐹𝑟

𝐹𝑟 = 𝐻11𝐴 + 𝐻22

𝐵 + 𝐾−1 −1 ∗ 𝐻11𝐴 ∗ 𝐹𝑏𝑙

𝐴

𝑝 = 𝐻32𝐵 ∗ 𝐹𝑟

2. Calculate Coupled FRF

Unrestricted © Siemens 2020

Page 31 Siemens Digital Industries Software

2. Load & Contribution Prediction1. Assembly Definition

Component-based TPA

Assembly & Prediction (Simcenter Testlab 2019.1)

The complete Component Based TPA process fully integrated in Simcenter Testlab

Unrestricted © Siemens 2020

Page 32 Siemens Digital Industries Software

Airborne example application:

PBN Performance Prediction

SOURCE

Invariant description of

sources

Recombine with selected

components to synthesize

SYSTEMS

Predict NVH performance

VA

RIA

NT

A

VA

RIA

NT

B

All Design Variants

VE

HIC

LE

1

VE

HIC

LE

VA

RIA

NT

S

Vehicle Variants

Unrestricted © Siemens 2020

Page 33 Siemens Digital Industries Software

2. NVH Synthesis Applications

Simcenter Testlab NVH Synthesis

Model Based Development for NVH

1. NVH Component Definition

Enable NVH what-if analysis from concept to final troubleshooting

Unrestricted © Siemens 2020

Page 34 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 35 Siemens Digital Industries Software

Model-base TPA

Gearbox Noise – Multi-Body Dynamics + Structural Dynamics

SOURCE PATH TRANSFER RECEIVER

Operational surface vibrations

Operational connection forces (to body)Gear rattle or meshing forces in

function of volute profile, misalignment,

torque load, …

Full system of gears, axles and body

including their respective flexibility

Unrestricted © Siemens 2020

Page 36 Siemens Digital Industries Software

Gearbox Noise – Structural Dynamics and Acoustics

Operational surface vibrations

(Airborne noise)

Operational connection forces

(structure borne noise) Vibro-Acoustic FRFs

Acoustic FRFs SPL/ surface vibration

Cabin Powertrain Noise

Installed condition

Free radiation condition

Exterior Pass-By Noise

Ext. Component Noise

SOURCE PATH TRANSFER RECEIVER

Unrestricted © Siemens 2020

Page 37 Siemens Digital Industries Software

Model-based TPA

Application example: Low frequency driveline booming

Vibro-acoustic

response

TPA Analysis

Driveline properties

Geometric & mount design

Driveline + Chassis

& Vehicle

Controls development Traditional NVH Engineering

Transmission Model

Clutch +

Transmission +

Torque Converter

ECU / TCU

Combustion

Pressure Engine Model

Extending TPA to system simulation and controls development

Unrestricted © Siemens 2020

Page 38 Siemens Digital Industries Software

Einführung

Klassische Methoden der TPA

TPA im Zeitbereich

Komponenten-TPA

Modellbasierte TPA

Zusammenfassung + Ausblick

Fahrzeugkomfort und Akustik durch Weiterent-

wicklungen der Transferpfadanalyse optimieren

Unrestricted © Siemens 2020

Page 39 Siemens Digital Industries Software

Predictive

Analysis

Contribution

Analysis

Load

Identification

Operational

measurements

FRF

measurements

Transfer Path Analysis Process

Complete process supported on one single platform

Accurate FRF and NTF

measurements for load

identification and

contribution analysis

Simcenter Structures

Acquistion

Simcenter provides

a fully integrated environment for streamlined work- and data flows

Simcenter Signature

Acquisition

Simcenter Transfer

Path Analysis

Simcenter Transfer

Path Analysis

Simcenter Component

Based TPA

Operational

measurements for

operational load

identification

Load identification using

the appropriate

technique

Load identification and

validation based on

different techniques

Predict full vehicle

performance for each

variant and load case

Spe

ctru

m: P

RC

M:0

001:

S..

Spe

ctru

m: P

RC

M:0

002:

S..

Spe

ctru

m: P

RC

M:0

003:

S..

Spe

ctru

m: P

RC

M:0

004:

S..

Spe

ctru

m: P

RC

M:0

005:

S..

Spe

ctru

m: P

RC

M:0

006:

S..

RM

S S

um..

10.00

60.00

dB(A

)

Pa

Spectrum: PRCM:0001:S

0.00 350.00Hz

-40.00

60.00

dB(A

)

Pa

99.00

1:1

0.0050.00 Pa 50.00Pa

50.00

Pa

50.00

Pa

be_f:5018:X

be_f:18:Xsubf:5020:X

subf:20:X

sh_f:5030:Y

be_f:5018:Z

be_r:5009:X

be_f:18:Y

be_r:5009:Y

be_r:5009:Z

Measured

Vector contribution A

=

)(a

)(a

)(a

.

)(H)(H)(H

)(H)(H)(H

)(H)(H)(H

)(F

)(F

)(F

v

2

1

1

nvv2v1

2n2212

1n2111

n

2

1

2

piaiii

))(a)(a(*)(K)(F

−=

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