# Predicting demand of natural gas: a system identification approach

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## Predicting demand of natural gas: a system identification approach

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2

2

2

2

2

(10)

(11)

r

n

m

(12)

−1

−1

−1

1

7

2

### x(k) and y(k), based on the values of inputs u(0), u(1), . . . , u(k).

11 millimeter rainfall is the equivalent of 1 liter of water per square meter per hour.

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q

q×p

m×n

n×m

T

T

q×q

ij

kr

1

2

3

q

2

3

4

q+1

3

4

5

q+2

q

q+1

q+2

2q−1

i

(14)

n×n

n×r

m×n

m×r

p

p−2

p−3

p−4

r

p

pr

p

p

pr×N

p

p

p

p

m

p

pm

p

(15)

p

pm×N

p

p

p

p

n

n×N

n×n

m×n

p

2

p−1

k

k−1

k−2

k

k−1

p

p

p

p

p

p

p

p

p

(16)

yy

p

pT

yu

p

pT

uu

p

pT

xx

T

yx

p

T

xu

pT

yy

mp×mp

uu

rp×rp

xx

n×n

yu

mp×rp

yx

mp×n

xu

n×rp

−1

−1

−1

7

3

3

(17)

3

3

yy

yu

uu

pT

yu

p

pT

p

pT

p

p

pT

p

xu

p

uu

uu

p

−1uu

p

yu

p

xu

−1uu

yy

p

pT

p

pT

p

p

pT

p

Tyx

p

Tyu

yx

p

T

p

T

p

p

T

p

xx

p

Txu

pT

pT

yy

p

p

xx

p

Txu

T

p

Tyu

p

xx

p

p

xu

pT

p

Tyu

p

yy

p

xx

p

p

xu

pT

p

Tyu

p

xx

p

p

xu

yu

p

xu

−1uu

T

yu

p

xu

−1uu

Tyu

p

xx

Tp

p

xu

−1uu

Tyu

p

xu

−1uu

Txu

pT

yu

−1uu

Tyu

p

xu

−1uu

T

p

xx

Tp

p

xu

−1uu

Txu

pT

yu

−1uu

Tyu

(18)

yy

yu

−1uu

Tyu

p

xx

xu

−1uu

Txu

Tp

hh

yy

yu

−1uu

Tyu

xx

xx

xu

−1uu

Txu

hh

p

xx

Tp

hh

mp×mp

xx

n×n

hh

hh

2

T

n

0

2n

n×n0

n0×n

n0×n0

nT

0T

n

2n

nT

hh

0

hh

n

n

0

0

hh

p

xx

pT

n

2n

nT

p

xx

p

n

xx

2n

hh

2n

n

pm×n

p

uu

yy

yu

uu

hh

hh

(19)

n

2n

n

n

2n

n

n

n

p

n×n

p

2

3

p−1

2

p−2

p

p

p

p

p

m×n

p

(20)

N

N

N

N

1

2

r

1

2

r

i

n

i

m

rn

rm

1

2

r

1

2

r

1

2

r

N

N

N

N

N −2

N −3

N −4

m

m

m

m

m×nr

n

n

n

N −2

k=0

N −k−2

n

(21)

m×nr

m×n

m

m

1

m

2

m

r

n

n

1

n

2

n

r

m

m×m

n

n×n

N

N

N

m

m×nr

m

n

2

m

n

n

N −1

m

N −2

k=0

N −k−2

n

N

N

(22)

−4

−4

−4

−4

−5

−4

−5

−4

−3

−3

−3

−2

−2

−3

−4

−3

−2

−2

−3

−2

−3

−3

−3

−3

−4

−4

−5

−4

−3

−3

−3

−3

−3

−3

−2

−2

−3

−3

−3

−3

−2

−3

−2

−2

−5

−5

−3

−2

−3

−3

−5

−3

−3

−3

−3

−3

−3

−3

−5

−3

−3

−3

−2

−3

−5

−5

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7

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### p = 17 in the most cases, but finding the correct value for N is too time-consuming.

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