Active Learning-Based Optimization of Hydroelectric Turbine Startup to Minimize Fatigue Damage

Arthur Favrel; Jean-Philippe Gauthier; Martin Gagnon; Quang Hung Pham; Vincent Mai

REVIEW 5 major objections 5 minor 33 references

Active Learning-Based Optimization of Hydroelectric Turbine Startup to Minimize Fatigue Damage

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Active learning finds a Francis-turbine startup that cuts peak strain by 42% using only seven measured runs.

desk verdict A real on-site active-learning optimization with a measured 42% strain reduction, but the load-bearing statistical assumption remains unvalidated and the evidence is a single success. read the letter →

arxiv 2411.14618 v2 pith:3635654V submitted 2024-11-21 cs.LG cs.SYeess.SY

Vincent Mai , Quang Hung Pham , Arthur Favrel , Jean-Philippe Gauthier , Martin Gagnon This is my paper · ORCID

classification cs.LGcs.SYeess.SY

keywords HydroelectricturbineFatiguedamageVirtualsensorActivelearningBlack-boxoptimizationFrancisStartupsequenceStrainenvelope

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 shows that a hydroelectric turbine's startup procedure can be optimized for fatigue life during a short measurement campaign, without prior data. The authors combine a fast turbine-dynamics simulator, a neural-network virtual strain sensor that predicts the envelope of blade strain, and a black-box optimizer in an active-learning loop. On a real instrumented Francis turbine, the method selected startup parameters from only seven measured sequences and cut the largest strain cycle amplitude by 42% relative to the standard startup. The result matters because more frequent startups, driven by grid integration of intermittent renewables, are a major source of turbine fatigue damage, and a procedure that reduces the governing strain amplitude could extend runner life.

What carries the argument

The load-bearing mechanism is the virtual strain sensor combined with a nested active-learning and optimization loop. The sensor is a feed-forward neural network that takes instantaneous normalized rotational speed and guide-vane opening and outputs the parameters of two conditional normal distributions for the upper and lower bounds of the strain envelope. The optimizer's cost function treats the mean-plus-one-standard-deviation as the likely extrema of the envelope, and an ensemble of five networks supplies epistemic uncertainty; during the active-learning phase the evaluator subtracts twice the epistemic standard deviation from the upper envelope and adds it to the lower envelope, an upper-confidence-bound-style exploration term. This machinery lets the system rank candidate startup sequences entirely from simulation without requiring new measurements until the next outer-loop iteration.

What would settle it

Repeat the optimized startup many times on the same turbine and record the empirical distribution of the largest strain cycle; if the observed largest cycle exceeds the predicted mean-plus-one-standard-deviation bound in substantially more than about 16% of runs, or if a nonparametric envelope model selects a different startup with a measurably lower observed largest cycle, the claim that the proxy ranks correctly would be falsified.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that an active-learning optimizer can identify a near-optimal startup parameter set using a budget of only seven measured startup trajectories on a full-scale Francis turbine. The measured largest strain cycle fell from 0.98 for the standard startup to 0.57 for the optimized startup, a 42% reduction, and a second constrained run achieved 0.73 under a shorter 60-second time limit. The discovery is that a learned probabilistic model of the strain envelope, conditioned only on instantaneous rotational speed and guide-vane opening, is sufficient inside an active-learning loop to guide the optimization toward parameter regions that genuinely reduce the largest strain cycle, and that the measured strains confirm the predictions without relying on the model for final performance.

Load-bearing premise

The load-bearing premise is that the strain envelope's distribution at any operating point is a conditional normal whose mean plus one standard deviation captures the likely extreme strain, so if that distribution is skewed or heavy-tailed, the optimizer can misrank startups.

Editorial extensions

If this is right

Hydropower utilities can optimize startup parameters during a short, dedicated measurement campaign of about seven startups, rather than through trial-and-error over a full commissioning period.
The same active-learning loop can be applied to shutdown and load-variation transients, which also contribute to runner fatigue, using the same virtual-sensor and envelope-loss formulation.
The learned virtual sensor's envelope predictions can serve as a fast surrogate for fatigue-relevant strain in future optimization, reducing the need for additional strain-gauge campaigns.
A shorter time-to-synchronous-speed constraint still yields a 26% strain-cycle reduction at equal startup time, suggesting the method can trade startup speed against fatigue damage in a principled way.
The final optimization trajectory is measured on the turbine, so the optimized parameters' performance is validated by real strain data rather than only by model predictions.

Reading between the lines

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

The paper optimizes strain at a single gauge; a natural extension is to optimize over all instrumented gauges simultaneously, since minimizing one location's strain could shift damage to another if the strain field is not monotonic in the startup parameters.
The normal-distribution envelope assumption is the key unvalidated proxy; a testable extension would compare the selected parameters against a quantile-regression or extreme-value envelope model to see whether the ranking of candidate startups changes.
The paper's hypothesis that low-strain parameters generalize across water heads remains untested; a multi-head measurement campaign could confirm or refute it and would be the natural next industrial trial.
The active-learning phase's benefit may depend on landscape smoothness; on a rougher landscape with multiple local optima, the exploration budget of two active sequences would likely need to be larger.

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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

This paper is worth reading because it does something unusual: it runs a closed-loop, active-learning optimizer on a full-scale Francis turbine during an actual measurement campaign, and the headline 42% reduction in the largest strain cycle is a measured number, not a simulation. That alone separates it from most of the prior work, which is either model-based or post-campaign. The authors combine a fast quasi-static turbine simulator, a virtual strain sensor, NOMAD black-box optimization, and an active-learning loop that picks the next startup parameters to test. The engineering is practical: each outer loop takes about nine minutes, and the final parameters are validated on the machine, so the surrogate model is only a guide, not the evidence. I give them credit for that design and for being explicit about the limitations they do list, such as optimizing on a single gauge and ignoring water-head variation.

The soft spots are real but not disqualifying. The biggest one is the unvalidated normal assumption for the strain-envelope bounds. The cost function in Eq. 18 uses mu + sigma as the likely extreme, which is not the expected maximum of a sample from a normal distribution and is generally wrong for extreme values. The paper states flat out that this assumption was not validated. Since the entire optimization trajectory is chosen by minimizing this proxy, a systematic misranking could send NOMAD to the wrong part of the parameter space. On this test case it didn't, or at least it found a genuinely better startup, but the method's reliability across machines and operating conditions is not established. I also noticed the abstract says seven measured sequences while Table 2 lists eight; that's a minor but annoying inconsistency. And the fatigue-damage claim rests on a single measured strain amplitude rather than a rainflow-based damage calculation, so the title overpromises slightly.

That said, the measured result did happen: Optimal 1 gave 0.57 versus 0.98 for the best standard startup, with no repeats but consistent with the trend from Active 1 and 2. The method deserves a serious referee and a reader's time. This is a proof-of-concept that the closed-loop approach can work, not a fully validated statistical framework. If I were editing, I would send it to review; if I were a researcher, I would cite it as a successful demonstration while being careful about what it proves. For a reading group, it would generate a good discussion about the gap between practical optimization heuristics and statistically sound validation.

Referee Report

5 major / 5 minor

Summary. The paper presents an automated, active-learning-based framework for optimizing the startup sequence of a hydroelectric turbine to minimize fatigue damage. The startup trajectory is parameterized by four governor settings θ = {ro, oini, ωtrigger, otrigger}. The method combines a quasi-static HGU dynamics simulator, a virtual strain sensor (a feedforward neural network that models the upper and lower strain envelopes as conditionally normal distributions), and the NOMAD black-box optimizer, embedded in an active learning loop that sequentially selects startup parameters to test on the instrumented turbine. In an on-site campaign on a full-scale Francis turbine, the algorithm selected parameters that reduced the largest measured strain cycle from 0.98 (standard startup) to 0.57, a claimed 42% reduction, using eight measured sequences (the abstract says seven). A second, shorter-duration optimized startup achieved a 26% reduction. The paper is a real-world demonstration of a closed-loop optimization pipeline on a prototype machine with a very limited measurement budget.

Significance. If the result holds, the paper provides an industrially relevant method for reducing turbine fatigue during startups with only a handful of prototype measurements. The main strength is that the headline 42% improvement is a measured physical quantity on a full-scale turbine, not a simulation, and the paper demonstrates an integrated pipeline (simulator + virtual sensor + derivative-free optimization + active learning) operating in real time during a measurement campaign. The work is of practical interest to hydropower utilities. However, the quantitative claim rests on a single measured pair with no repetitions of the optimal sequence, and the cost function used by the optimizer relies on an explicitly unvalidated normality assumption and a likely sign inconsistency in the lower-bound term. These issues make the reported improvement less robust than stated, though they are addressable with additional validation and more careful statistical framing.

major comments (5)

[Section 3.4, Eq. (18)] The lower-bound term in the strain cost, min_n(μ̂l_n + σ̂l_n), is not conservative and is likely a sign error. Since sl is the lower envelope defined in Eq. (10), the extreme low value should be estimated as μ̂l_n − σ̂l_n (or some lower quantile), not μ̂l_n + σ̂l_n. Adding σ̂l_n to μ̂l_n raises the lower envelope and therefore reduces the cycle amplitude cs(θ); the claim in the text that this 'ensures that the expected maximum strain cycle is not underestimated' is contradicted by the formula. Please verify the sign on actual data; if the lower envelope is negative, this underestimation can misrank candidate startups.
[Section 3.3, Eqs. (12)–(13)] The optimization objective (Eq. 18) assumes that the upper and lower envelope bounds are conditionally normal and that μ̂+σ̂ represents their likely extrema. The paper explicitly states this assumption was not validated. Because the envelope is a 10-s windowed maximum/minimum (Eqs. 9–10), the appropriate distributions are of extreme-value type, and μ̂+σ̂ is not a consistent quantile of the expected extreme. This is load-bearing: the NOMAD optimizer selects θ by minimizing cs(θ), so any systematic misranking of candidate startups invalidates the claim that the selected θ minimizes L(τM). I recommend adding a validation of the ranking: use the already-measured startups to compare the ordering of cs(θ) with the ordering of measured L(τM), e.g., by leave-one-out cross-validation.
[Section 4.2, Table 2] The reported 42% reduction is based on a single comparison between Optimal 1 (largest cycle 0.57) and Initial 5 (0.98), with no repetition of the optimal sequence. The two standard startups, Initial 1 and Initial 5, already differ by 11% (1.09 vs 0.98), which indicates substantial run-to-run variability. Without repeated measurements of the selected parameters or a statistical uncertainty interval, the 42% figure should be presented as a single-case demonstration rather than a robust performance guarantee. At minimum, the stochastic spread of the standard startup should be propagated into the claimed reduction.
[Section 3.5 and Section 5] The paper does not demonstrate that the active learning phase improves over the plain black-box optimization. The Discussion states that 'the epistemic uncertainty values were low, and the active learning phase ... was not significantly different from the optimization phase.' To substantiate the active-learning contribution, run NOMAD from the initial Ninit trajectories alone and compare the resulting θ and cost with those obtained via the full active loop. If the results are identical, the active-learning novelty should be reframed or supported with an experiment where the initial data are less informative.
[Section 3.1, Figure 4] The HGU dynamics simulator is validated visually against only two startups, with no quantitative error measure (e.g., maximum speed deviation or startup-time error). Since the optimizer evaluates hundreds of candidate trajectories, many of which lie outside the two validated cases, a quantitative validation on the available measured trajectories is needed to establish that the simulator does not introduce systematic bias into the cost function.

minor comments (5)

[Abstract and Section 4.1] The abstract says 'seven measured sequences,' but Section 4.1 specifies Ninit = 5, Nact = 2, Nopt = 1, totaling eight measured sequences (and Table 2 lists eight rows, excluding the extra Optimal 2 run). Please correct the count.
[Section 4.2, Table 2] For Initial 1, tst is reported as N/A because recording was delayed for the first few seconds. Since the largest cycle is computed from the recorded portion only, the reported value 1.09 may be a lower bound on the true cycle; this caveat should be stated.
[Section 4.1] The envelope window w = 10 s and the sampling frequencies (fM = 500 Hz, fe = 10 Hz) are chosen without a sensitivity analysis; please state whether the results depend materially on these choices.
[Section 3.3] The neural network hyperparameters (two hidden layers of 32 units, three epochs, learning rate 0.001, ensemble size 5) are given without justification or sensitivity study; at least cite a reference or include a brief ablation.
[Figure 13] The text 'induces an significant standard deviation' contains a grammatical error; 'an' should be 'a'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the headline 42% reduction is a measured, out-of-sample turbine result; the virtual sensor self-citation [24] is re-validated on this campaign's own data.

full rationale

The claimed derivation is self-contained and non-circular. The key result—a 42% reduction in the largest measured strain cycle (Optimal 1: 0.57 vs standard: 0.98, Table 2)—is a physical measurement taken from the instrumented turbine after the optimization, so it does not reduce to any fitted quantity. The optimizer's cost c(θ) (Eq. 18) is a model-based proxy built from the virtual sensor, but the selected θ is then executed and measured; no fitted parameter is renamed as a prediction. The virtual sensor approach is attributed to the authors' prior work [24], but Section 3.3 estimates m_ϕ from the current campaign's measured trajectories and Figure 13 compares its predictions to the measured envelopes on the selected optimal trajectories, providing independent in-paper support for the model. The statement 'This assumption was not validated in the current study' (Section 3.3, Eqs. 12-13) exposes a real correctness risk in using μ+σ as the expected extremum, but an unvalidated modeling assumption is not a circular reduction. Finally, the abstract's 'seven measured sequences' is inconsistent with Section 4's N_init=5, N_act=2, N_opt=1 plus a ninth 60-s run in Table 2; this is a factual reporting error, not an instance of circularity.

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

The central claim rests less on new physics than on a chain of modeling choices: deterministic dynamics, a quasi-static torque surface, an unvalidated normal model for strain envelopes, and a max-min proxy for fatigue. The only fitted numbers are the neural-network weights and the bilinear torque surface, which are trained on the same few measured startups used to drive the optimization. No new physical entities are introduced.

free parameters (6)

alpha_d normalization factor = inverse of strain range in dataset D
Scales the strain cost against the time-constraint cost in c(theta) = alpha_d c_s + c_c; it is data-dependent and chosen so alpha_d c_s is at most 1, so it directly shapes which startup is called optimal.
time-constraint cost coefficients = 0.5, 0.05, 0.2 in Eq. (19)
Hand-chosen thresholds and penalty slopes that favor shorter startups and encode constraint violation; no sensitivity analysis is given.
UCB exploration coefficient = 2 in Eq. (20)
Hand-chosen weight on epistemic uncertainty for active learning; no sensitivity study, and Section 5 reports the active learning phase was not significantly different from the plain optimization phase.
neural network hyperparameters = hidden size 32, 2 layers, 3 epochs, batch 32, learning rate 0.001, ensemble of 5
Hand-chosen; no tuning or ablation is reported, and the beta weighting in the beta-NLL loss is not stated, so the model configuration is under-specified.
envelope window and sampling frequencies = w = 10 s, fM = 500 Hz, fe = 10 Hz, fD = 10 Hz
Hand-chosen values that determine the envelope definition and the resolution of trajectories fed to the virtual sensor and simulator.
quasi-static torque surface grid = not reported
The turbine dynamics surrogate is a bilinear interpolant over a uniform grid of steady-state SIMSEN torque simulations; the grid density is not given, so the surrogate error is unquantified.

assumptions (6)

domain assumption HGU dynamics are deterministic for a fixed parameter set theta
Section 2 states 'Under the hypothesis that HGU dynamics are deterministic'; this justifies mapping theta to a single dynamic trajectory and lets the simulator stand in for the real machine.
domain assumption Quasi-static torque from steady-state simulations approximates transient torque
Section 3.1 replaces SIMSEN co-simulation with a bilinear interpolant of steady-state torque in (omega, o), neglecting water-hammer and unsteady fluid effects during startup; validated only against two measured startups.
domain assumption Strain envelope bounds are conditionally normal given (omega, o)
Section 3.3 states the normal distribution 'was chosen because it is simple and generally a good approximation. This assumption was not validated in the current study.' This underpins the mu plus sigma cost in Eq. (18).
domain assumption Largest strain cycle amplitude is an adequate proxy for fatigue damage
Section 2 says the largest cycle 'has the most impact on fatigue' and defines the loss as the max-min of strain; this is an explicit approximation, not a rainflow-based fatigue calculation.
domain assumption A virtual sensor trained on a few trajectories generalizes across the startup parameter space
Section 5 admits the active learning phase depended on a smooth landscape and good initial coverage; the model is assumed to be trustworthy in regions not yet measured.
domain assumption Nominal constant head and negligible bearing friction
Section 3.1 fixes gross head at nominal and neglects friction in Eq. (7); Section 5 notes water head may affect strain, so this assumption is acknowledged as a limitation.

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Cite this review

Pith. "Pith review of Active Learning-Based Optimization of Hydroelectric Turbine Startup to Minimize Fatigue Damage." pith.science (2026). https://pith.science/paper/3635654V

@misc{pith2026241114618,
  author       = {Pith},
  title        = {Pith review of: Active Learning-Based Optimization of Hydroelectric Turbine Startup to Minimize Fatigue Damage},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3635654V}},
  note         = {Machine review of arXiv:2411.14618}
}

read the original abstract

Hydro-generating units (HGUs) play a crucial role in integrating intermittent renewable energy sources into the power grid due to their flexible operational capabilities. This evolving role has led to an increase in transient events, such as startups, which impose significant stresses on turbines, leading to increased turbine fatigue and a reduced operational lifespan. Consequently, optimizing startup sequences to minimize stresses is vital for hydropower utilities. However, this task is challenging, as stress measurements on prototypes can be expensive and time-consuming. To tackle this challenge, we propose an innovative automated approach to optimize the startup parameters of HGUs with a limited budget of measured startup sequences. Our method combines active learning and black-box optimization techniques, utilizing virtual strain sensors and dynamic simulations of HGUs. This approach was tested in real-time during an on-site measurement campaign on an instrumented Francis turbine prototype. The results demonstrate that our algorithm successfully identified an optimal startup sequence using only seven measured sequences. It achieves a remarkable 42% reduction in the maximum strain cycle amplitude compared to the standard startup sequence. This study paves the way for more efficient HGU startup optimization, potentially extending their operational lifespans.

Figures

Figures reproduced from arXiv: 2411.14618 by the authors.

**Figure 1.** Startup sequence parameters and phases Under the hypothesis that HGU dynamics are deterministic, two startups with identical parameter sets θ i lead to the same dynamic trajectory τ i D. This trajectory is discretized in time at frequency fD, and defined as: τ i D .= (ω i 0 , oi 0 , ωi 1 , oi 1 , ..., ωi n i D,st , oi n i D,st ) (2) 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** HGU dynamics block diagram At time t, the strain s(t) at a given location of a turbine blade can be measured by strain gauges, usually in microstrains (µS), at frequency fM. During a startup process, the measured trajectory can be captured as τ i M, defined as the combination of the dynamic trajectory τ i D and the strain measurements s i n : τ i M .= ω i 0 , oi 0 , si 0 , ωi 1 , oi 1 , si 1 , ..., ωi n i M,st , o… view at source ↗

**Figure 3.** Turbine dynamics model The HGU simulator is built by combining Equation 7 with the underlying equations of the speed governor model described above, resulting in a system of Neq nonlinear ordinary differential equations with adjustable parameters θ: dq dt = F(t, q, θ) (8) with the unknowns’ vector q(t) = [ω(t), o(t), u(t), q4(t), q5(t), . . . , qNeq (t)]T , where q4(t) through qNeq (t) are internal variables of the … view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Comparison of simulated startup sequences with experimental data [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Example of startup measured strains and the corresponding resampled envelope [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Different components of the black box given measured trajectories dataset D To ensure compliance with the time constraint, cc(θ i ) in the event of a time constraint violation must be higher than any possible strain-related cost αdcs(θ i ). Therefore, αd is set as the …

**Figure 7.** Figure 7: Active learning nested loop for startup parameter optimization. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

**Figure 8.** Figure 8: Positions of the uniaxial gauge and rosettes on the Francis turbine runner, as [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

**Figure 9.** Figure 9: Standard startup trajectory measurements, including the strains for three dif [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

**Figure 10.** Figure 10: Measured turbine dynamic trajectories mapped on the opening - rotational speed space. The color map (white is better) represents the latest trained virtual sensor’s predictions of ˆµ + ˆσ for the upper (a) and lower bounds (b) of the strain envelope [PITH_FULL_IMAGE:…

**Figure 11.** Figure 11: Strain measurements τM and envelopes τe for the sequential startups run on the turbine. The optimized startups have significantly lower strain amplitude than the standard ones. during the optimal trajectories are shown in higher temporal resolution in figure 12 [PITH…

**Figure 12.** Figure 12: Comparison of measured strain envelopes for initial (Ini 5 ) and optimized startups (Opt 1 is limited to t¯st = 90s, Opt 2 is limited to t¯st = 60s). While the optimization process is also able to reduce the strain amplitude by 26% for similar durations to the initi…

**Figure 13.** Figure 13: Black box strain predictions given optimal startup parameters [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

Discussion (0). Continue with ORCID to comment.

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M. Gagnon, Q. H. Pham, V. Mai, and A. Favrel, “Virtual sensors for indirect strain measurement during Francis turbine startup,” in Pro- ceedings of the 9th IAHR Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, (Timisoara, Romania)...

2023
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Response spectra and expected fatigue reliability: A look at hydroelectric turbines behavior,

M. Gagnon and D. Thibault, “Response spectra and expected fatigue reliability: A look at hydroelectric turbines behavior,” Procedia Engi- neering, vol. 133, p. 613–621, 2015

2015
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Nicolet, Hydroacoustic modelling and numerical simulation of un- steady operation of hydroelectric systems

C. Nicolet, Hydroacoustic modelling and numerical simulation of un- steady operation of hydroelectric systems. PhD thesis, EPFL, 2007

2007
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Batch normalization: Accelerating deep network training by reducing internal covariate shift,

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” Mar 2015. arXiv:1502.03167

2015 arXiv
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On the pitfalls of heteroscedastic uncertainty estimation with probabilistic neural net- works,

M. Seitzer, A. Tavakoli, D. Antic, and G. Martius, “On the pitfalls of heteroscedastic uncertainty estimation with probabilistic neural net- works,” Apr 2022. arXiv:2203.09168 [cs, stat]

2022 arXiv
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Algorithm 1027: NOMAD version 4: nonlinear optimization with the MADS algo- rithm,

C. Audet, S. Le Digabel, V. R. Montplaisir, and C. Tribes, “Algorithm 1027: NOMAD version 4: nonlinear optimization with the MADS algo- rithm,” ACM Transactions on Mathematical Software, vol. 48, p. 1–22, Sep 2022

2022
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Finite-time analysis of the multiarmed bandit problem,

P. Auer, N. Cesa-Bianchi, and P. Fischer, “Finite-time analysis of the multiarmed bandit problem,” Machine Learning, vol. 47, no. 2/3, p. 235–256, 2002

2002
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Obtaining stress measurements on runners as a key contribution to reducing their degradation and improv- ing the reliability of hydroelectric production units,

L. Marcouiller and D. Thibault, “Obtaining stress measurements on runners as a key contribution to reducing their degradation and improv- ing the reliability of hydroelectric production units,” in HYDRO 2015, (Bordeaux, France), Oct. 2015. 27

2015
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Fatigue strength analysis of a prototype fran- cis turbine in a multilevel lifetime assessment procedure part ii: Method application and numerical investigation,

E. Doujak, J. Unterluggauer, G. Fillinger, A. Nocker, F. Haller, M. Maier, and S. Stadler, “Fatigue strength analysis of a prototype fran- cis turbine in a multilevel lifetime assessment procedure part ii: Method application and numerical investigation,” Energies, vol. 15, 02 2022

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Parallel space decomposi- tion of the mesh adaptive direct search algorithm,

C. Audet, J. E. Dennis, and S. L. Digabel, “Parallel space decomposi- tion of the mesh adaptive direct search algorithm,” SIAM Journal on Optimization, vol. 19, p. 1150–1170, Jan 2008. 28 Appendix A. Notation table HGU dynamics n Time step ωn Turbine rotation speed on Guide va...

2008

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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The new role of sustainable hydropower in flexible energy systems and its technical evolution through innovation and digitalization,

E. Vagnoni, D. Gezer, I. Anagnostopoulos, G. Cavazzini, E. Doujak, M. Hoˇ cevar, and P. Rudolf, “The new role of sustainable hydropower in flexible energy systems and its technical evolution through innovation and digitalization,” Renewable Energy, vol. 230, p. 120832, 2024

work page 2024

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Effect of transients on Fran- cis turbine runner life: a review,

M. Trivedi, B. Gandhi, and M. Cervantes, “Effect of transients on Fran- cis turbine runner life: a review,” Journal of Hydraulic Research, vol. 51, no. 2, p. 121–132, 2013

work page 2013

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A review on fatigue damage mechanism in hydro turbines,

X. Liu, Y. Luo, and Z. Wang, “A review on fatigue damage mechanism in hydro turbines,” Renewable and Sustainable Energy Reviews, vol. 54, p. 1–14, 2016

work page 2016

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Analysis of the part load helical vortex rope of a Francis turbine using on-board sensors,

F. Duparchy, A. Favrel, P.-Y. Lowys, C. Landry, A. M¨ uller, K. Ya- mamoto, and F. Avellan, “Analysis of the part load helical vortex rope of a Francis turbine using on-board sensors,” Journal of Physics: Con- ference Series, vol. 656, p. 012061, nov 2015

work page 2015

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Swirl number based transposition of flow-induced me- 24 chanical stresses from reduced scale to full-size Francis turbine runners,

A. Favrel, J. Gomes Pereira Junior, A. M¨ uller, C. Landry, K. Yamamoto, and F. Avellan, “Swirl number based transposition of flow-induced me- 24 chanical stresses from reduced scale to full-size Francis turbine runners,” Journal of Fluids and Structures, vol. 94, p. 102956, 2020

work page 2020

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Rainflow-counting matrix interpolation over different operating condi- tions for hydroelectric turbine fatigue assessment,

Q. H. Pham, M. Gagnon, J. Antoni, A. Tahan, and C. Monette, “Rainflow-counting matrix interpolation over different operating condi- tions for hydroelectric turbine fatigue assessment,” Renewable Energy, vol. 172, p. 465–476, Jul 2021

work page 2021

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Transient CFD simula- tion of a Francis turbine startup,

J. Nicolle, J.-F. Morissette, and A.-M. Giroux, “Transient CFD simula- tion of a Francis turbine startup,” IOP Conference Series: Earth and Environmental Science, vol. 15, pp. 2014–, 11 2012

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On the stochastic simulation of hydroelectric turbine blades transient response,

M. Gagnon, A. Tahan, P. Bocher, and D. Thibault, “On the stochastic simulation of hydroelectric turbine blades transient response,” Mechan- ical Systems and Signal Processing, vol. 32, pp. 178–187, 2012. Uncer- tainties in Structural Dynamics

work page 2012