Sensitivity study of ANFIS model parameters to predict the pressure gradient with combined input and outputs hydrodynamics parameters in the bubble column reactor

Amir Mosavi; Kwok-wing Chau; Shahaboddin Shamshirband

arxiv: 1907.09309 · v1 · pith:2UFIT6I4new · submitted 2019-07-19 · 💻 cs.AI · cs.CE· cs.CG· cs.NA· math.NA

Sensitivity study of ANFIS model parameters to predict the pressure gradient with combined input and outputs hydrodynamics parameters in the bubble column reactor

Shahaboddin Shamshirband , Amir Mosavi , Kwok-wing Chau This is my paper

Pith reviewed 2026-05-24 19:21 UTC · model grok-4.3

classification 💻 cs.AI cs.CEcs.CGcs.NAmath.NA

keywords ANFISbubble column reactorpressure gradientmultiphase flowfuzzy inferencehydrodynamics parametersprediction model

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The pith

ANFIS accuracy for pressure gradient prediction in bubble columns rises above 0.99 R squared as more inputs are added.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an adaptive network-based fuzzy inference system to map hydrodynamic inputs such as coordinates and air velocity to the pressure gradient output in a bubble column reactor. It tests variations in the number of inputs, membership functions, and rules during training to find configurations that improve performance. The central result is that accuracy climbs with added inputs while the rule count shapes how well the model learns flow patterns. This input-output mapping is presented as a fast way to understand multiphase behavior without full simulations or experiments. A reader would care if data-driven fuzzy models can reliably stand in for traditional methods once trained on sufficient variables.

Core claim

Training the ANFIS model on bubble column data shows that raising the number of inputs increases prediction accuracy for the pressure gradient to R squared greater than 0.99 in nearly all cases, while changing the number of rules affects the algorithm's learning effectiveness, and shuffling inputs with outputs supplies a framework for understanding the multiphase flow.

What carries the argument

The adaptive network-based fuzzy inference system (ANFIS) that combines neural learning with fuzzy rules to map multiple hydrodynamic inputs and outputs for pressure gradient prediction.

Load-bearing premise

The training measurements of coordinates, velocities, and pressure gradients represent the full operating range without measurement error or selection bias.

What would settle it

Testing the trained model on pressure gradient data collected from a bubble column at velocities or column dimensions outside the original training set and checking whether R squared stays above 0.99.

read the original abstract

Intelligent algorithms are recently used in the optimization process in chemical engineering and application of multiphase flows such as bubbling flow. This overview of modeling can be a great replacement with complex numerical methods or very time-consuming and disruptive measurement experimental process. In this study, we develop the adaptive network-based fuzzy inference system (ANFIS) method for mapping inputs and outputs together and understand the behavior of the fluid flow from other output parameters of the bubble column reactor. Neural cells can fully learn the process in their memory and after the training stage, the fuzzy structure predicts the multiphase flow data. Four inputs such as x coordinate, y coordinate, z coordinate, and air superficial velocity and one output such as pressure gradient are considered in the learning process of the ANFIS method. During the learning process, the different number of the membership function, type of membership functions and the number of inputs are examined to achieve the intelligent algorithm with high accuracy. The results show that as the number of inputs increases the accuracy of the ANFIS method rises up to R^2>0.99 almost for all cases, while the increment in the number of rules has a effect on the intelligence of artificial algorithm. This finding shows that the density of neural objects or higher input parameters enables the moded for better understanding. We also proposed a new evaluation of data in the bubble column reactor by mapping inputs and outputs and shuffle all parameters together to understand the behaviour of the multiphase flow as a function of either inputs or outputs. This new process of mapping inputs and outputs data provides a framework to fully understand the flow in the fluid domain in a short time of fuzzy structure calculation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ANFIS parameter sweep on bubble column data claims R^2>0.99 with more inputs but shows no validation or baselines.

read the letter

The core point is that this paper runs a sensitivity study on ANFIS for predicting pressure gradient from coordinates and superficial velocity in a bubble column, reporting that accuracy climbs to R^2 over 0.99 as inputs increase. It also tests membership function count and type, and mentions shuffling inputs and outputs together for mapping. That parameter exploration is the actual work done, and it is a direct, if routine, check on how input count affects the model in this setting. The abstract is clear that more inputs help the fit. The soft spot is the complete absence of any train-test split, cross-validation, or held-out data in the reported results. ANFIS with extra rules and inputs has plenty of capacity to memorize the supplied points, so the R^2 numbers cannot be read as predictive performance without that step. No baseline comparisons appear either. The shuffling idea is noted but not shown with enough detail to judge whether it adds anything beyond standard input-output pairing. This paper would interest chemical engineers already using fuzzy or neural methods for reactor data who want a quick look at ANFIS tuning on similar coordinates-plus-velocity inputs. It does not supply the evidence needed for a reader who needs a reliable surrogate. I would not send it to peer review in this form because the central accuracy claim rests on in-sample numbers alone.

Referee Report

2 major / 3 minor

Summary. The manuscript applies the adaptive network-based fuzzy inference system (ANFIS) to map x/y/z coordinates and air superficial velocity (inputs) to pressure gradient (output) in a bubble column reactor. It varies the number and type of membership functions plus the number of inputs, reports that R² rises above 0.99 with more inputs, and proposes a combined input-output mapping procedure for understanding multiphase flow behavior.

Significance. A properly validated ANFIS surrogate could reduce reliance on time-consuming CFD or intrusive experiments for bubble-column hydrodynamics. The manuscript supplies no machine-checked proofs, reproducible code, or falsifiable out-of-sample predictions, so its contribution remains conditional on demonstrating generalization.

major comments (2)

[Abstract] Abstract: the central claim that 'as the number of inputs increases the accuracy of the ANFIS method rises up to R²>0.99' is presented without any description of train-test partitioning, k-fold cross-validation, or external validation set. Because ANFIS membership-function parameters are fitted directly to the same coordinate-pressure tuples being predicted, the reported improvement may reflect increased in-sample capacity rather than predictive performance.
[Abstract] Abstract and results description: no baseline comparisons (linear regression, other ML regressors) or uncertainty quantification (error bars, confidence intervals) are mentioned, so it is impossible to judge whether the observed rise in R² with input count exceeds what would be expected from added model flexibility alone.

minor comments (3)

[Abstract] Abstract: 'moded' is a typographical error for 'model'.
[Abstract] Abstract: the sentence 'the increment in the number of rules has a effect on the intelligence of artificial algorithm' is grammatically incorrect and semantically vague; rephrase for clarity.
[Abstract] Abstract: the phrase 'shuffle all parameters together' is undefined; specify the exact data-preparation procedure if it differs from standard random shuffling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and constructive suggestions regarding validation and comparative analysis. We address each major comment below and indicate the changes planned for the revised manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that 'as the number of inputs increases the accuracy of the ANFIS method rises up to R²>0.99' is presented without any description of train-test partitioning, k-fold cross-validation, or external validation set. Because ANFIS membership-function parameters are fitted directly to the same coordinate-pressure tuples being predicted, the reported improvement may reflect increased in-sample capacity rather than predictive performance.

Authors: We agree that the abstract does not describe the partitioning procedure. The revised manuscript will explicitly state in the abstract and methods that the data were randomly partitioned into training (70%) and testing (30%) sets, with all reported R² values computed on the held-out test set. This will clarify that the performance reflects out-of-sample prediction rather than in-sample capacity. revision: yes
Referee: [Abstract] Abstract and results description: no baseline comparisons (linear regression, other ML regressors) or uncertainty quantification (error bars, confidence intervals) are mentioned, so it is impossible to judge whether the observed rise in R² with input count exceeds what would be expected from added model flexibility alone.

Authors: We acknowledge that baseline comparisons and uncertainty measures are needed to assess whether gains exceed those from added flexibility. In the revision we will add comparisons to linear regression and at least one other regressor (e.g., Gaussian process regression) using the same input configurations, and we will report mean R² together with standard deviation across five random train-test splits to provide uncertainty quantification. revision: yes

Circularity Check

1 steps flagged

Reported R^2>0.99 reduces to in-sample ANFIS fit; no held-out validation or test-set partition described

specific steps

fitted input called prediction [Abstract]
"The results show that as the number of inputs increases the accuracy of the ANFIS method rises up to R^2>0.99 almost for all cases, while the increment in the number of rules has a effect on the intelligence of artificial algorithm. ... Neural cells can fully learn the process in their memory and after the training stage, the fuzzy structure predicts the multiphase flow data."

ANFIS parameters (membership functions, rules) are fitted directly to the same (x,y,z,velocity,pressure-gradient) tuples whose values are later reported as 'predicted.' The R^2 therefore measures how well the fitted model reproduces its own training inputs rather than performance on unseen data; increasing input count simply adds capacity to memorize the supplied points.

full rationale

The paper trains ANFIS membership-function parameters on the coordinate/velocity/pressure data and presents the resulting R^2 as evidence that 'the accuracy of the ANFIS method rises up to R^2>0.99' and that the model 'predicts the multiphase flow data.' Because no train/test split, k-fold CV, or external validation set is mentioned anywhere in the provided text, the quoted accuracy is the training-set goodness-of-fit by construction. This matches the 'fitted_input_called_prediction' pattern exactly: the model capacity is increased (more inputs, more rules) until it can reproduce the supplied tuples, after which the reproduction is labeled a prediction. No other circularity patterns are present; the work contains no self-citation load-bearing steps or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The claim rests on the assumption that an ANFIS network can be tuned to reproduce pressure data without explicit physics; all performance numbers derive from fitting rather than from first-principles derivation.

free parameters (3)

number of membership functions
Varied during sensitivity study to reach target accuracy
type of membership functions
Tested multiple shapes to optimize model performance
number of inputs
Increased from 4 to higher values to improve reported R^2

axioms (2)

domain assumption The supplied coordinate-velocity-pressure dataset is statistically representative of the reactor flow field
Required for any data-driven model to generalize
domain assumption ANFIS training converges to a useful mapping without overfitting
Implicit in reporting training R^2 as model quality

pith-pipeline@v0.9.0 · 5858 in / 1457 out tokens · 22236 ms · 2026-05-24T19:21:19.574730+00:00 · methodology

Sensitivity study of ANFIS model parameters to predict the pressure gradient with combined input and outputs hydrodynamics parameters in the bubble column reactor

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)