Table 4 Optimal parameters values of Mitscherlich model (Eqs. 5, 9, 10, 11, 12) and thinned model (Eqs. 5, 8, 10, 11, 12)

\(\phantom {\dot {i}\!}Y_{max_{th_{m}}}\)

4220

5370

6000

\(\phantom {\dot {i}\!}Y_{max_{{th}}}\)

1.36

1.96

2.78

\(\phantom {\dot {i}\!}\omega _{yth_{m}}\)

0.99

1

1

ω_yth

0.95

0.97

0.99

\(\phantom {\dot {i}\!}\gamma _{yth_{m}}\)

1.610⁻³

1.910⁻³

2.510⁻³

γ_yth

1.410⁻²

1.810⁻²

2.110⁻²

\(\phantom {\dot {i}\!}\sigma _{yth_{m}}\)

33.8

41.4

50.1

σ_yth

29.6

36.6

44.2

N₀

1590

2070

2630

N₀

15000

18600

22200

ω_N

3.810⁻²

4.710⁻²

5.710⁻²

ω_N

4.310⁻²

5.210⁻²

6.210⁻²

γ_N

0.09

0.11

0.13

γ_N

0.08

0.10

0.11

σ_N

508

604

717

σ_N

505

598

707

a_B

0.06

0.11

0.19

a_B

6.210⁻²

0.14

0.24

b_B

0.89

1.01

1.11

b_B

0.85

0.98

1.13

σ_B

0.88

1.12

1.41

σ_B

0.92

1.18

1.4

a_L

1.510⁻⁶

0.03

0.72

a_L

0.1

0.96

2.6

b_L

2.42

5.8

9.5

b_L

2.05

3.39

4.96

\(\phantom {\dot {i}\!}W_{L_{{max}}}\)

17.6

18.5

19.4

\(\phantom {\dot {i}\!}W_{L_{{max}}}\)

17.6

18.5

19.4

σ_WL

1.42

1.8

2.22

σ_WL

1.4

1.8

2.2