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Evaluating Parshall flume aeration with experimental observations and advance soft computing techniques

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Abstract

A Parshall flume is a versatile device due to its diverse applications in irrigation canals, mine discharge, dam seepage, sewage treatment plants and many more. It is an economical due to its construction and installation and an accurate in discharge measurement in open channel and non-full pipe. Exchange of oxygen between water and air is termed as aeration. In the study, advance soft computing models; Multivariate Adaptive Regression Splines (MARS) and Generalized Structure- Group Method of Data Handling (GS-GMDH) have used to predict aeration efficiency (E20) values at Parshall flumes and its modified forms and also compared with existing conventional models. The performance of the models was assessed using four evaluating metrics; coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE) and Nash Sutcliffe model efficacy. Agreement plot of GS-GMDH and MARS models showed that the MARS model has the maximum exactness in predicting E20 values at Parshall flumes and its modified forms with the lowest RMSE = 0.0020, MAE = 0.0015. MARS model with input combination of ratio of throat width to throat length (W/L), ratio of sill height to throat length (S/L) and Froude number is performing better than that of all other input combinations used for models and found to be more suitable for predicting the E20. Overall comparison among conventional and advance soft computing models suggests that advance soft computing models perform better than conventional models.

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Abbreviations

K L a :

Volumetric oxygen transfer coefficient or absorption coefficient

C s :

Saturation concentration of oxygen in water

C 0 :

Concentration of oxygen in water at time t = 0

C t :

Concentration of oxygen in water at time t in seconds

A :

Linked with the volume over which oxygen transfer occurs

V :

Volume

T :

Time

U :

Illustrative of upstream zone

D :

Illustrative of downstream zone

R :

Oxygen aeration deficient ratio

f :

Aeration exponent

W :

Throat width

L :

Throat length

S :

Sill height

x :

Independent parameter for MARS

k :

Border value for MARS

BFs:

Basic functions

Y :

Dependent parameter which is predicted using function f(x)

a 0 :

Constant value for MARS

n :

Number of BFs

α n :

Coefficient multiplied in BFs

β n :

Demonstrates the BFs

N :

Number of data

C(H):

Complexity penalty that increases by number of BFs

D :

Penalty number for each BFs

H :

Number of BFs derived from MARS method

w i :

Coefficient of transfer function

x i and x j :

Pair of inputs

a :

Number of observations

y :

Actual values

\(\hat{y}\) :

Estimated values

M :

Number of adjustable parameters

j i :

Observed values for soft computing techniques

k i :

Predicted values from soft computing techniques

m :

Total number of observations for soft computing techniques

E :

Oxygen aeration efficiency of tape water for any room temperature

E 20 :

Oxygen transfer efficiency for 20 °C

DO:

Dissolved oxygen

ANN:

Artificial neural network

FL:

Fuzzy logic

ANFIS:

Adaptive neuro fuzzy inference system

MARS:

Multivariate adaptive regression splines

GMDH:

Group method of data handling

GS-GMDH:

Generalized structure-group method of data handling

GCV:

Generalized cross-validation

Na2SO3 :

Sodium sulphite

CoCl2 :

Cobalt chloride

Fr:

Froude number

Re:

Reynolds number

AIC:

Akaike information criterion

R 2 :

Coefficient of determination

MAE:

Mean absolute error

RMSE:

Root mean square error

NSE:

Nash–Sutcliffe model efficiency

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Authors and Affiliations

  1. Water Technology Center, Indian Agricultural Research Institute, New Delhi, India, 110012

    Sangeeta Bhoria

  2. Department of Civil Engineering, Shoolini University, Solan, India

    Parveen Sihag

  3. Department of Civil Engineering, Panipat Institute of Engineering and Technology, Panipat, India

    Balraj Singh

  4. Department of Soils and Agri-Food Engineering, Laval University, Québec, G1V0A6, Canada

    Isa Ebtehaj & Hossein Bonakdari

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  1. Sangeeta Bhoria
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Correspondence to Balraj Singh.

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Bhoria, S., Sihag, P., Singh, B. et al. Evaluating Parshall flume aeration with experimental observations and advance soft computing techniques. Neural Comput & Applic 33, 17257–17271 (2021). https://doi.org/10.1007/s00521-021-06316-9

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