An In-situ Solid Fuel Ramjet Thrust Monitoring and Regulation Framework Using Neural Networks and Adaptive Control

Ankit Goel; Parham Oveissi; Ryan DeBoskey; Venkat Narayanaswamy

REVIEW 3 major objections 5 minor 45 references

An In-situ Solid Fuel Ramjet Thrust Monitoring and Regulation Framework Using Neural Networks and Adaptive Control

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that neural-network thrust estimation from limited in-situ sensors, coupled with a retrospective-cost adaptive controller, can regulate a solid fuel ramjet's thrust in numerical simulation across multiple command types.

desk verdict A competent engineering extension — ANN + RCAC with variable-inlet actuation for a quasi-1D SFRJ model — publishable with revisions but not a breakthrough. read the letter →

arxiv 2506.08157 v1 pith:O7YXLTFS submitted 2025-06-09 math.OC

Ryan DeBoskey , Parham Oveissi , Venkat Narayanaswamy , Ankit Goel This is my paper

classification math.OC MSC 93C4068T07

keywords solidfuelramjetthrustestimationneuralnetworkretrospectivecostadaptivecontrolPIDin-situsensingcommandfollowing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a solid fuel ramjet (SFRJ) can monitor and regulate its own thrust without a direct thrust sensor, using only measurements that are practical in flight. A neural network is trained on synthetic data from a quasi-one-dimensional SFRJ model to estimate thrust from altitude, combustor pressure, exhaust carbon monoxide fraction, and the variable inlet position. An online adaptive controller, built on retrospective cost adaptive control, then adjusts the inlet geometry to follow thrust commands using those estimates as feedback. Numerical simulations show the same controller tracks step, doublet, ramp, and harmonic commands without retuning. The payoff, if the result transfers beyond the model, is a route to closed-loop SFRJ thrust control with a minimal sensing footprint.

What carries the argument

The framework's three coupled components are: (1) a quasi-one-dimensional SFRJ plant model whose inlet conditions come from curve fits to axisymmetric RANS simulations and whose fuel regression uses empirical constants, (2) a single-hidden-layer neural network (20 sigmoid neurons) that estimates thrust from altitude, total combustor pressure, exhaust CO fraction, and cowl radius, and (3) an RCAC-based adaptive PID controller whose gains are updated online by minimizing a retrospective cost using recursive least squares. The load-bearing link is that the controller treats the network's estimated thrust as the measured output, so the quality of the closed loop is bounded by the estimator's accuracy on the operating trajectory.

What would settle it

Compare the neural network's thrust estimates against direct load-cell thrust measurements on a ground-test SFRJ with the same geometry and cruise conditions; if the estimates deviate beyond the training tolerance under realistic sensor noise, the framework's in-situ monitoring claim fails.

Watch

Extended reading notes

Core claim

The central claim is that combining an artificial neural-network thrust estimator with a retrospective-cost adaptive controller yields effective thrust regulation for a solid fuel ramjet with variable-cowl inlet, using limited in-situ measurements instead of direct thrust measurement. The paper demonstrates this on a quasi-one-dimensional feed-forward SFRJ model, with the neural network trained on 125,000 synthetic samples spanning altitude, cowl radius, and port radius. The trained network maps the available on-board measurements to thrust, and the adaptive controller, an RCAC-optimized PID, recursively updates its gains from past tracking error and input data alone. In the reported simulations the closed loop follows step, doublet, ramp, and harmonic thrust commands without changing controller hyperparameters, and the response is insensitive to those hyperparameters over a tested range.

Load-bearing premise

The neural network and the controller are both built and tested on the same quasi-one-dimensional SFRJ model; if that model's inlet curve fits and regression-rate constants do not match a real engine, the thrust estimates and control actions will not transfer.

Editorial extensions

If this is right

If the results hold, SFRJ thrust can be regulated using only sensors that can plausibly fly on a supersonic vehicle, avoiding a direct thrust sensor.
The same controller, with fixed hyperparameters, tracks step, doublet, ramp, and harmonic commands, so no per-mission retuning is needed.
The closed-loop response is robust over a range of RCAC hyperparameters, which helps in practice when plant conditions drift.
The neural network's sensitivity analysis gives a simple guideline: hidden-layer width matters more than activation function or batch size for this thrust-estimation task.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The natural next step is to train the network on experimental data (or a validated higher-fidelity model) and test on a hardware-in-the-loop rig; the current evidence is entirely synthetic, so transfer is not yet established.
Because the estimator uses CO, the framework could be extended to estimate and regulate equivalence ratio or combustion efficiency, not just thrust, as long as the corresponding sensors exist.
A robustness gap remains: sensor noise, bias, and time delays in real CO and pressure measurements are not modeled here, so the controller's margins under realistic sensing are an open question.
The paper notes it only sketches the RCAC update proof due to page limits, so a complete stability analysis of the coupled NN-plus-RCAC loop is not provided.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a solid engineering extension, not a breakthrough. The genuinely new bit is using the variable-geometry inlet as the actuator and feeding an ANN thrust surrogate (inputs: cowl radius, altitude, Pt4, CO mole fraction) into an RCAC adaptive PID for a quasi-1D SFRJ model. Prior RCAC-SFRJ work used direct thrust feedback and heat-flux input, so this is a legitimate increment for the in-situ sensing problem.

What it does well: the model is described in enough detail to be reproduced, the training data generation is clear, and the RCAC formulation is standard. The paper reports command following for step, doublet, ramp, and harmonic commands with fixed RCAC hyperparameters, plus a hyperparameter sensitivity sweep. The conclusion explicitly states that simulations used the neural network predictions as the proxy for thrust, which answers the main stress-test worry: the feedback path appears to be the ANN output, not model truth. That said, the main text would be much clearer if Section IV said this directly, and the authors should show a comparison against direct-thrust feedback to prove the surrogate is not silently degrading the loop.

Soft spots, in order of importance. First, the feedback-path ambiguity in Section IV is a real readability flaw, though not a fatal one given the conclusion. Second, there is no baseline: no summary statistics for tracking error, no comparison to a fixed-gain PID or RCAC with true thrust. The claim of robustness to hyperparameter variation is supported only by eyeballing Figure 9. Third, the testing loss is not shown for brevity, a needless omission; one number or a learning curve would remove a lot of doubt about whether the ANN is actually accurate on held-out points. Fourth, the load-bearing assumption is that the quasi-1D model with curve fits from [8] and regression rate constants from [35] represents a real SFRJ. Since both the training data and the plant come from the same model, the framework inherits its fidelity. That is not circularity in the derivation, but it caps the practical claims; the abstract is appropriately careful in saying the SFRJ model.

Who this is for: people working on SFRJ or scramjet thrust control with surrogates, and anyone wanting a worked example of RCAC plus neural-network feedback. A serious referee could give useful guidance, mainly on the missing comparisons and the explicit feedback-path statement. I would not block publication on the science; I would ask for clarifications and a baseline figure.

Referee Report

3 major / 5 minor

Summary. The paper proposes a framework for thrust monitoring and regulation of a quasi-one-dimensional solid fuel ramjet (SFRJ) model using a neural network (ANN) thrust estimator coupled with retrospective cost adaptive control (RCAC). The ANN maps in-situ measurements (cowl radius, combustor total pressure, CO mole fraction, altitude) to thrust, and is trained on 125,000 synthetic samples generated from the same quasi-1D model used as the plant. An adaptive PID controller, whose gains are updated online by RCAC, modulates the cowl radius to follow commanded thrust profiles. The paper presents simulations for step, doublet, ramp, and harmonic commands, and includes sensitivity studies for ANN hyperparameters and RCAC hyperparameters. The central claim is that the combined ANN+RCAC framework can regulate thrust using limited in-situ data, based on the numerical simulations.

Significance. If the central claim is fully supported, the paper offers a useful direction for SFRJ control without direct thrust measurement, which is difficult in flight. The strengths of the manuscript are its detailed description of the quasi-1D model and data-generation procedure, the explicit ANN architecture and training setup, the complete RCAC update equations, and the hyperparameter sensitivity studies. These elements make the synthetic-data portion of the work largely reproducible. The main weakness is that the simulation section does not unambiguously identify which feedback signal is used in the RCAC loop, and the missing testing loss and lack of baseline comparisons weaken the evidence for the ANN-based regulation claim. These issues are local and fixable within the manuscript's scope.

major comments (3)

[Section IV-A, Eq. (11), and Fig. 4] The central claim that the closed-loop simulations use the ANN-predicted thrust as the feedback signal yk in Eq. (11) is not explicitly stated in the simulation section. Section III describes both an ideal scenario with true thrust feedback and a practical scenario with ANN-predicted thrust, and Fig. 4 shows the ANN in the loop, but Section IV-A does not identify which signal was used as yk for the RCAC update. Figures 5-8 plot 'commanded and generated thrust,' which could refer to the true model thrust T from Eq. (8) rather than the ANN estimate. The conclusion asserts that the ANN predictions were used as the proxy for thrust, but the simulation section must state this explicitly for each example and, ideally, provide a comparison of ANN-based feedback with direct thrust feedback. Without this, the reader cannot verify the central claim that the combined ANN+RCAC framework regulates thrust using in-situ measurements.
[Section II-B, Fig. 3] The testing loss is explicitly omitted ('not shown for brevity'), but the text states that minimization of both training and testing loss was used to evaluate ANN performance and to select 100 epochs as a compromise against overfitting. Reporting only training loss does not support the claim that the final model generalizes to the closed-loop operating region. The authors should report the testing loss, at least as a table or as an additional line in Fig. 3, and state the final training and testing mean-squared error for the selected architecture.
[Section IV-A, Figs. 5-8] The closed-loop results are reported only as time-history plots; there are no quantitative tracking metrics (e.g., RMS tracking error, settling time, overshoot) and no comparison with a baseline controller or with direct thrust feedback. The error plots on a log scale appear small, but summary statistics are needed to support the statement that the framework 'effectively regulates' thrust, especially for the ramp and harmonic commands where the tracking error may vary over time. A comparison of ANN-based feedback versus true-thrust feedback would directly address the main contribution of the paper.

minor comments (5)

[Section II-A] The physical fidelity of the quasi-1D SFRJ model, including the inlet curve fits from Ref. [8] and the regression-rate constants from Ref. [35], is the load-bearing premise for transfer to a real engine. Because the ANN is trained on synthetic data from this same model and the closed-loop plant is the same model, the demonstration is self-consistent but inherits any model bias. This limitation should be stated explicitly in the conclusions, along with an indication of what experimental validation would be needed.
[Section IV-A, Eq. (19)] The symbol r0 is used both for the cowl radius state and for the nominal value in the recurrence r0 = r0 + 0.001uk; using a different symbol for the nominal value would avoid confusion.
[Section II-B] The statement that the sigmoid activation function is applied on all layers 'to return a normalized value of [0,1]' is only strictly correct for the output layer; hidden-layer sigmoid activations do not normalize the network output, and the sentence should be clarified.
[Fig. 3] The three panels of Fig. 3 appear to lack axis labels, legends, and clear association with the hyperparameter cases in Table III, making it difficult to interpret the sensitivity study. Please add labels or a caption that maps each panel to a specific hyperparameter sweep.
[Throughout] There are several typographical and notation issues: the title header contains 'Regulati on', Section IV reads 'In all subsequence examples', and 'P0 = 10 −5I3' should be typeset as 10^{-5} I_3. These should be corrected in revision.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity: RCAC adaptation is genuinely online, but the in-situ monitoring claim is self-referential (ANN fitted to the same model used as plant) and the feedback signal used in Eq. (11) is never specified.

fitted input called prediction [Section V (Conclusions), cf. Sections II-B (Eqs. 8-9) and IV-A.1 (Eq. 11)]
"With the neural network predictions as the proxy for thrust generated by the SFRJ, numerical simulations demonstrated successful command following response for several thrust commands without the need to retune the adaptive controller."

The claim that the framework 'can effectively regulate the thrust produced by the SFRJ model using limited in-situ data' rests on simulations whose plant is the same quasi-1D model whose thrust output (Eq. 8) was the ANN's training label, fit via MSE (Eq. 9) on 125,000 synthetic points (Section II-B). Section V asserts the simulations used 'the neural network predictions as the proxy for thrust,' but Section IV never states whether yk in Eq. (11) was true thrust T or the ANN estimate. If T was used, the result contains no ANN and the central claim is unsupported; if the ANN estimate was used, in-situ monitoring reduces to the surrogate's in-distribution fit to the controlled plant, with testing loss withheld ('not shown for brevity') and no direct-vs-ANN comparison.

full rationale

The derivation chain is: (i) a quasi-1D SFRJ model with variable cowl (Section II-A) creates synthetic data; (ii) an ANN maps in-situ measurements (r0, Pt4, XCO, H) to model thrust (Section II-B, Eq. 9); (iii) RCAC adapts PID gains online (Section III, Eqs. 17-18); (iv) closed-loop simulations show command following (Section IV). The control result is not circular: RCAC gains are adapted online from measured data, the update law is a standard RLS specialization cited to external literature [45], and the closed-loop demonstration could have failed. No fitted parameter is renamed as a derived result, and no uniqueness theorem is imported from the authors' prior work. Self-citations [8], [11]-[13] are contextual: the prior SFRJ RCAC papers assumed heat-flux input and direct thrust measurement, which the paper explicitly distinguishes from the present variable-inlet, in-situ setup; the plant model from [8] is an input assumption, not the derived result. The genuinely self-referential element is that the ANN's training target and the closed-loop plant are the same quasi-1D model, so the in-situ monitoring capability is demonstrated only on the ANN's own training distribution. Per the reviewing rule, the following in-text limitations are flagged and weighed: the testing loss is omitted ('not shown for brevity') though hyperparameters were selected on it; the proof of Prop. 3.1 is only a sketch (but points to an external RLS reference); and Section IV never states whether yk was the true thrust or the ANN estimate, even though Section V asserts the proxy was used. These omissions weaken verifiability and make the monitoring claim partially reduce to the surrogate fit, but the central adaptive-control claim retains independent dynamical content, so the overall circularity is minor (score 2).

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a quasi-1D SFRJ model assembled from several empirical correlations and assumptions: regression-rate constants from Ref. [35], inlet curve fits from Ref. [8], constant combustion and nozzle efficiencies, equilibrium chemistry from an external solver, and sensor sufficiency for thrust estimation. The paper does not provide the numerical values of these empirical inputs, nor does it test the sensitivity of the closed-loop result to the main model assumptions. The neural network surrogate and the controller are built on top of this set of assumptions.

free parameters (6)

Regression rate constants alpha, a, b, c = not given (from Ref. [35])
Used in Eq. (1) to compute fuel regression rate; empirically derived in prior literature and not reproduced in this paper.
Inlet isolator exit curve-fit coefficients = not given (from Ref. [8])
Mass flow, stagnation pressure, and Mach number at the isolator exit are curve-fitted functions of r0 from RANS; these coefficients are cited but not provided.
Combustion efficiency eta_c = 0.75
Assumed constant in Eq. (6) to scale equilibrium flame temperature; no sensitivity analysis of this value is reported.
Nozzle efficiency eta_n = 0.95
Assumed constant and used to compute actual exhaust velocity from the theoretical value in Section II-A; not varied.
RCAC hyperparameters P0 and N1 = P0 = 10^-5 I3, N1 = 1
Selected by a 'trivial grid search' in Section IV; the choice is not justified by analysis and affects the transient response.
ANN hyperparameters (nodes, activation, batch size, epochs) = 20 nodes, sigmoid, batch 100, 100 epochs
Selected via sensitivity study on training loss only; testing loss is not reported, so the selection may not represent the best generalization performance.

assumptions (6)

domain assumption The SFRJ can be adequately represented by a static quasi-1D feed-forward model
The entire methodology rests on the quasi-1D model described in Section II-A, inherited from Ref. [8] with modifications; no validation against experimental data is provided.
domain assumption Fuel regression follows the empirical power law of Eq. (1) with constants from Ref. [35]
Equation (1) is an empirical correlation from prior experiments; the constants are not given in this paper.
domain assumption Isolator exit conditions are curve-fitted functions of cowl radius r0 obtained from RANS
Section II-A relies on curve fits from Ref. [8] without providing the fits or their accuracy.
domain assumption Equilibrium chemistry via CANTERA with the skeletal 1,3-butadiene mechanism gives accurate flame temperature and composition
The equilibrium solver and mechanism from Ref. [38] are used to compute T4, gamma4, R4, and XCO; no verification of the mechanism's accuracy for this configuration is shown.
standard math The RLS recursion is valid for the RCAC cost function
Proposition 3.1 is stated with a proof sketch citing Ref. [45]; the result is standard and not the paper's contribution.
domain assumption The selected sensors (H, Pt4, XCO, r0) provide sufficient information to estimate thrust
Section II-B defines the sensor set without a formal observability analysis or a sensitivity study over alternative sensor combinations.

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Cite this review

Pith. "Pith review of An In-situ Solid Fuel Ramjet Thrust Monitoring and Regulation Framework Using Neural Networks and Adaptive Control." pith.science (2026). https://pith.science/paper/O7YXLTFS

@misc{pith2026250608157,
  author       = {Pith},
  title        = {Pith review of: An In-situ Solid Fuel Ramjet Thrust Monitoring and Regulation Framework Using Neural Networks and Adaptive Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O7YXLTFS}},
  note         = {Machine review of arXiv:2506.08157}
}

read the original abstract

Controlling the complex combustion dynamics within solid fuel ramjets (SFRJs) remains a critical challenge limiting deployment at scale. This paper proposes the use of a neural network model to process in-situ measurements for monitoring and regulating SFRJ thrust with a learning-based adaptive controller. A neural network is trained to estimate thrust from synthetic data generated by a feed-forward quasi-one-dimensional SFRJ model with variable inlet control. An online learning controller based on retrospective cost optimization is integrated with the quasi-one-dimensional SFRJ model to regulate the thrust. Sensitivity studies are conducted on both the neural network and adaptive controller to identify optimal hyperparameters. Numerical simulation results indicate that the combined neural network and learning control framework can effectively regulate the thrust produced by the SFRJ model using limited in-situ data.

Figures

Figures reproduced from arXiv: 2506.08157 by the authors.

**Figure 2.** Final artificial neural network architecture diagra [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Resulting training loss of ANN hyperparameter sensi [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Control architecture to regulate the thrust generat [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Closed-loop response of the SFRJ to a single step comm [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: Closed-loop response of the SFRJ to a sequence of ramp [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 9.** Figure 9: Effect of RCAC hyperparameters P0 and N1 on the closedloop response of the SFRJ. in 47th AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit, 2011, p. 5756. [31] J. P. Reardon, J. A. Schetz, and K. T. Lowe, “Computational analysis of unstart in variable-geometry …

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