Inverse Problem Modeling

Inverse Problem Modeling

Citation for published version (APA):

Schijndel, van, A. W. M. (2009). Inverse Problem Modeling. conference; Contribution Workshop on Modeling using Matlab SimuLink Comsol; 2009-06-17; 2009-06-17.

Document status and date: Published: 01/01/2009

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The Exploration of an Inverse

Problem Technique to

Obtain Material Properties of a

Building Construction

Contents

•

Introduction

•

Measurements

•

Modeling

•

The inverse problem

Background

Hunting Lodge St. Hubertus

•

Conservation

Problem

•

What we could do

• Model current moisture

problems

• Simulate possible solutions

•

But ….

•

How to get material properties?

• Taking samples not allowed!

• No ‘spare’ masonry available

Methodology

Inverse problem

•

Input data (time series)

•

Objective data (time series)

•

Data (signal) analysis

•

Model

•

Simulate data

•

Compare with objective data

Measurements

Sensors

•

External

• T

• RH

• Rain

• Wind

• Solar

•

Internal

• T

• RH

•

Surface

• T

• RH

Data set

Input data 1/2

•

External

• T

• RH

•

Rain

•

Wind

•

Solar

•

Internal

• T

• RH

•

Surface

•

T

•

RH

Data set

Input data 2/2

•

External

•

T

•

RH

• Rain

•

Wind

• Solar

•

Internal

•

T

•

RH

•

Surface

•

T

•

RH

Data set

Objective data

•

External

•

T

•

RH

•

Rain

•

Wind

•

Solar

•

Internal

•

T

•

RH

•

Surface

• T

• RH

Modeling

•

PDEs

•

PDE coefficients from

material properties

•

Verification

Modeling

PDEs

)

(

)

(

22 21 12 11

LPc

K

T

K

t

LPc

C

LPc

K

T

K

t

T

C

LPc T

∇

+

∇

⋅

∇

=

∂

∂

∇

+

∇

⋅

∇

=

∂

∂

, , ) log( 22 12 11 10 RT M Psat LPc Pc LPc Pc K K LPc Pc Pc w C RT M Psat LPc Pc l K K c C Pc LPc a w p LPc a w p lv T ⋅ ⋅ ∂ ∂ ⋅ ⋅ − ∂ ∂ ⋅ − = ∂ ∂ ⋅ ∂ ∂ = ⋅ ⋅ ∂ ∂ ⋅ ⋅ ⋅ − = = ⋅ = = ρ φ δ ρ φ δ λ ρ

•

Potential T, LPc

•

PDE coefficients formulation

• Material properties

• function of T, LPc

Calculating PDE coefficients

using material properties, method 1/2

)

(

)

(

22 21 12 11

LPc

K

T

K

t

LPc

C

LPc

K

T

K

t

T

C

LPc T

∇

+

∇

⋅

∇

=

∂

∂

∇

+

∇

⋅

∇

=

∂

∂

•

PDE coefficients lookup

tables calculated in MatLab

using:

• heat conduction

coefficients

• specific heat

• density

• liquid permeability

• moisture retention curve

• vapour permeability

)

(

)

(

22 21 12 11

LPc

K

T

K

t

LPc

C

LPc

K

T

K

t

T

C

LPc T

∇

+

∇

⋅

∇

=

∂

∂

∇

+

∇

⋅

∇

=

∂

∂

Calculating PDE coefficients

Verification

HAMSTAD Benchmark no 1

)

(

)

(

)

(

p

p

g

p

p

l

T

T

h

q

_{i i lv i}

−

⋅

=

−

⋅

⋅

+

−

⋅

=

β

β

0

)

(

=

−

⋅

=

g

T

T

h

q

_{e e}

Verification

Verification

Heat

Verification

Moisture

The inverse problem

•

Signal analysis

•

First guess simulation

The inverse problem

Signal analysis, Crest factor

•

Crest factor

• Impacting versus random noise

• The lower the better

2

))

(

max(

u

t

u

C

_f

=

The inverse problem

Signal analysis, Crest factor

Signal

Crest factor

T

_i

7.0

T

_e

12.7

pv

_i

7.9

pv

_e

10.2

Irrad

_sol

4.6

Rain

17.8 (10 occurrences)

T

_oppi

9.1

RH

_oppi

23.8 (problem?)

First guess Simulation vs Measurements

Sensitivity indoor surface conditions

change in heat conduction of concrete

•

Heat coefficient

concrete doubled (1)

and halved (2)

•

Surface conditions

compared:

• T1 – T2

• RH1 – RH2

•

No effect first 4 days

Sensitivity of change in surface heat

transfer coefficient

•

Heat surface transfer

coefficient doubled (1)

and halved (2)

•

Surface conditions

compared:

• T1 – T2

• RH1 – RH2

•

Similar to previous

•

No effect first 4 days

Conclusion

•

It is quite clear that there are still

major problems

to

be solved before the suggested methodology of the

inverse problem technique will be useful for

estimating material properties.

•

Before going into the drawbacks of the approach, the

reader should notice that the

major benefit

, in case

of a successful method,

could be

that

material

properties are easy obtained

in situ and without

damaging the construction by quite simple

Limitations

•

All measurements errors must be known

. This means that there is also

a systematic error in measuring the inside surface conditions.

•

The (measured) signals itself should deliver enough input power

into

the system. For example in this research, the rain intensity has a

relative high Crest factor due to the less than 10 rain events in one

month.

•

The simulated objective data

(in this case inside surface conditions)

Recommendations

•

It is recommended, in case of applying inverse

problem techniques, to

simulate the sensitivity

of the

objective data on the material properties

before

starting measurements

.

•

Furthermore, if this simulated sensitivity is

promising, the measurement error should be an

order lower than the sensitivity

•

Thank you