WAVE HISTOGRAM - CONDITIONAL PROBABILITY CURVE

EXAMPLE:

Observed Wave Height intervalsH (aralık, m) 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10H (m.) 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5n (adet) 6 29 88 180 247 260 133 42 10 5

0.0060 0.0290 0.0880 0.1800 0.2470 0.2600 0.1330 0.0420 0.0100 0.00501000 =N, total number of observations

H * n = 3.00 43.50 220.00 630.00 1111.50 1430.00 864.50 315.00 85.00 47.50Hort 4.75 m. (Ağırlıklı ortalama)

Hort aynı zamanda H * n% ile de direk hesaplanabilir.H * n% = 0.003 0.0435 0.22 0.63 1.1115 1.43 0.8645 0.315 0.085 0.0475

Hort= 4.75 m.

NORMDIST 0.005 0.026 0.087 0.188 0.261 0.233 0.135 0.050 0.012 0.002ILE

Dikkat: Dalga gözlem sayısı ağırlık alınarak Ağırlıklı Standart Sapma hesaplanıyor.0.1084 0.3063 0.4455 0.2813 0.0154 0.1463 0.4073 0.3176 0.1406 0.1128

1.51053.78617 n: number of observation

: ağırlıklı ortalama.

x, burada bizim için Dalga Yüksekliği (H)!p(H) computes the predictive n/(N DH) values , red line in the chart.

p(H) 0.005 0.026 0.087 0.188 0.261 0.233 0.135 0.050 0.012 0.002p(H) 0.005 0.026 0.087 0.188 0.261 0.233 0.135 0.050 0.012 0.002

rms H computation1.5 65.25 550 2205 5001.75 7865 5619.25 2362.5 722.5 451.25

rms H= 4.98438 (root mean square H)

Histogram of the wave observation

n/(N DH)

compute ss=

s*(2*p)^.5

s: Ağırıklı Standart sapma

1 2 3 4 5 6 7 8 9 10

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

p(H)=(1/3.785)*exp{-0.5[((H-4.75)^2)/1.5105]}

wave observation data

prob dens func

H (m)

n/(

N D

H)

p(H)=(1/3.786)*exp{-0.5 [( H-4.75) / 1.5105 ) ) ^2 ]}

Wave hegiht measurements of irregular seaway is a good example of a random event. The measurements can be shown in a histogram form by defining the probabilities of the wave heights. The problem is to obtain analytical expression of a continuous curve fitting to the histogram values. The computation below shows such an example.

These fitted curves called as Probabiliy Density Function. Typical probability density functions are - Normal or Gauss Density Function- Logarithmic Normal (Log-normal) Density Function- Rayleigh Density Functionand the like.

Wave measurement data is given corresponding to different wave height intervals. Obtain probability of each wave height and show them in a histogram. Further find the best fitting probability density function and show it in the histogram.

x̄

σ n=√∑i=1

n( x i−x )

2wi

∑i

nw i

x̄

Red line represents the predictive probability curve (best-fit) for wave histogram.

1 2 3 4 5 6 7 8 9 10

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

p(H)=(1/3.785)*exp{-0.5[((H-4.75)^2)/1.5105]}

wave observation data

prob dens func

H (m)

n/(

N D

H)

HİSTOGRAM

verilenler

ortalama alınır.

n% = wi / topl(wi)

ağırlıklı ortalama için.

Toplamı Hort'yı verecektir.

3 m. İçin %n ?

p(H) ve NORMDIST excelfonksiyonları NORMAL DAĞILIM

0 FONKSİYONU olmaktadır.p(H) computes the predictive n/(N DH) values , red line in the chart.

1 2 3 4 5 6 7 8 9 10

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

p(H)=(1/3.785)*exp{-0.5[((H-4.75)^2)/1.5105]}

wave observation data

prob dens func

H (m)

n/(

N D

H)

Wave measurement data is given corresponding to different wave height intervals. Obtain probability of each wave height and show them in a histogram. Further find the best fitting probability density function and show it in the histogram.

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.50.00

0.05

0.10

0.15

0.20

0.25

0.30

H

H

Red line represents the predictive probability curve (best-fit) for wave histogram.

1 2 3 4 5 6 7 8 9 10

0.0000

0.0500

0.1000

0.1500

0.2000

0.2500

0.3000

p(H)=(1/3.785)*exp{-0.5[((H-4.75)^2)/1.5105]}

wave observation data

prob dens func

H (m)

n/(

N D

H)