Source-linked AI summary
Closed-loop separation control using machine learning
Nicolas Gautier, Thomas Duriez, Jean-Luc Aider, Bernd Noack, Marc Segond, Markus Abel
TL;DR
The paper addresses the need for robust, model-free closed-loop control of separated flows. It uses genetic programming to evolve feedback laws from real-time recirculation measurements and applies them to a backward-facing step controlled by a slotted jet. The resulting law effectively reduces recirculation, remains adaptive to operating-condition changes, and achieves performance similar to periodic forcing through different dynamics.
Problem
The study seeks a model-free alternative to model-based control designs for robust closed-loop control of nonlinear separated flows.
Method
Genetic programming evolves candidate feedback laws from sensor input using replication, mutation, crossover, and cost-based selection.
Results
The evolved law reduces the average recirculation area by 80%, achieving J_MLC = 0.419 versus J_periodic = 0.423 for periodic forcing.
Takeaways & Limitations
The recirculation-based law adapts to operating-condition changes and exploits different flow dynamics from periodic forcing while retaining similar effectiveness.
Takeaways & Limitations
The 500-individual generation size is described as a compromise between performance, diversity, and experimental testing time.
Abstract
from arXiv · showhide
A novel, model free, approach to experimental closed-loop flow control is implemented on a separated flow. Feedback control laws are generated using genetic programming where they are optimized using replication, mutation and cross-over of best performing laws to produce a new generation of candidate control laws. This optimization process is applied automatically to a backward-facing step flow at Re=1350, controlled by a slotted jet, yielding an effective control law. Convergence criterion are suggested. The law is able to produce effective action even with major changes in the flow state, demonstrating its robustness. The underlying physical mechanisms leveraged by the law are analyzed and discussed. Contrary to traditional periodic forcing of the shear layer, this new control law plays on the physics of the recirculation area downstream the step. While both control actions are fundamentally different they still achieve the same level of effectiveness. Furthermore the new law is also potentially easier and cheaper to implement actuator wise.
1. Introduction
The study addresses the challenge of designing robust closed-loop control laws for separated flows without relying on reduced-order models. It applies machine learning control based on genetic programming to a backward-facing-step recirculation bubble.
- Closed-loop flow control combines fluid mechanics, sensing and actuation, control theory, optimization, and machine learning.
- Model-based designs often use locally linear reduced-order models that ignore frequency cross-talk, while low dimensionality supports experimental robustness and online operation.
- Evolutionary algorithms can search for nonlinear control laws, and genetic programming optimizes functions against a problem-specific cost functional.
- The study applies Machine Learning Control for the first time to a separated flow, targeting the recirculation bubble downstream of a backward-facing step.
2. Experimental Setup
The experiments study a backward-facing step flow at Re_h = 1350 and control it through an upstream spanwise slotted jet. Real-time velocity fields are used to identify the instantaneous recirculation area for feedback.
- Flow facility: The experiment uses a gravity-driven hydrodynamic channel with flow conditioning, and the selected Reynolds number is Re_h = 1350.The free-stream velocity is U∞ = 7.3 × 10−2 m.s−1; the Reynolds number was chosen because of injection-system limitations.
- Backward-facing step geometry: The backward-facing step creates a separated shear layer susceptible to Kelvin–Helmholtz instability and downstream disturbances.The step height is h = 1.5 × 10−2 m.
- Backward-facing step geometry: The geometry includes an upstream injection slot located at d/h = 2 from the step edge, with expansion and aspect ratios defined for the channel.
- Sensor: Real-time velocity fields are computed from seeded-flow images using optical flow, with 42 image pairs processed per second.The measurements use 20 µm neutrally buoyant particles, laser illumination, and a CMOS camera.
- Sensor: The feedback sensor represents the instantaneous recirculation area relative to the time-averaged uncontrolled area.Figure 2 pairs an instantaneous velocity snapshot with its corresponding recirculation region.
- Actuator: Actuation uses an upstream spanwise slotted jet whose amplitude is controlled by tank pressure and can provide both blowing and suction.The jet is oriented at 45° to the wall and has a maximum actuation frequency of about 2 Hz.
3. Machine Learning Control
Machine learning control uses genetic programming to evolve model-free feedback laws for separated-flow control. Candidate laws are evaluated with a cost function balancing recirculation-area reduction and actuation energy, then evolved across generations.
- 3. Machine Learning Control: Machine learning control optimizes model-free nonlinear control laws using genetic programming for a problem-specific objective function.Candidate laws are evaluated by the flow system and evolved across generations.
- 3. Machine Learning Control: Control laws are represented as expression trees built from user-defined functions, basic operations, constants, and the sensor input s(t).The first generation varies in tree depth and density, with all individuals different to maintain diversity.
- 3. Machine Learning Control: 500 individuals form each generation, providing a compromise between population diversity, performance, and experimental testing time.The population size is reported as sufficient to converge on most single-input cases.
- 3.2. Evaluation: The cost function combines time-averaged recirculation-area reduction with a penalty for actuation energy.The sensor is normalized by the uncontrolled time-averaged recirculation area, while actuation is normalized by maximum jet velocity; w = 3/2 strongly penalizes high actuation costs.
- 3.2. Evaluation: One-minute evaluations provide sufficient statistics to discriminate candidate performance, while approximately 1000 individuals are evaluated over 24 hours.Refilling the jet supply tank can extend the interval between evaluations to two minutes.
- 3.3. Breeding of subsequent generations and stop criteria: Each generation is ranked by cost, its five best individuals are re-evaluated five times, and subsequent individuals are produced by replication, mutation, or crossover.The respective probabilities are 10%, 20%, and 70%; evolution iterates until the cost reaches 0 or a stopping condition is met.
4. Results
Machine learning control converged toward an effective nonlinear law for the backward-facing-step flow, reducing recirculation through low-frequency feedback. It performed similarly to periodic forcing while remaining robust to Reynolds-number changes.
- 4.1. Convergence of machine learning control: The first generation was ineffective, but effective control laws appeared in the second generation and subsequent generations improved over their predecessors.The cost-function slope as a function of individual index also improved through the evolution.
- 4.1. Convergence of machine learning control: After the 9th generation, the best individuals appeared to converge, while averaging the five best laws reached convergence after the 8th generation.The authors suggest stopping when the average cost of the first five individuals no longer improves.
- 4.2. Analysis of the best control law obtained by MLC: The final control law combines blowing and suction, with a non-monotonic dependence on normalized recirculation area.Its graph is simple over 0 ≤ s ≤ 1 despite the complex mathematical expression, and actuation generally decreases toward suction at intermediate s before increasing again in the post-transient regime.
- 4.2. Analysis of the best control law obtained by MLC: 80% reduction in average recirculation area was achieved after control began at t = 25 s.The actuation consisted of short suction periods followed by longer blowing periods at approximately b ≈ 0.45.
- 4.2. Analysis of the best control law obtained by MLC: 0.1 Hz oscillations characterized the feedback actuation, close to the recirculation-bubble flapping frequency and below the approximately 1 Hz shear-layer shedding frequency.The low-frequency actuation may allow slower actuators to affect higher-Reynolds-number flows.
- 4.3. Comparison to periodic forcing: Jperiodic = 0.423 and JMLC = 0.419 showed similar effectiveness, although periodic forcing operated near 1 Hz while MLC exploited approximately 0.1 Hz dynamics.The MLC law performed slightly better in the reported comparison.
- 4.4. Robustness: 20% was the maximum reported increase in cost function when Reynolds number changed by a factor of 2.The MLC law adapted through its dependence on recirculation area, whereas fixed-frequency open-loop forcing performed poorly away from its design Reynolds number.
5. Conclusion
Machine learning control converges to an efficient, robust law for reducing recirculation in backward-facing-step flow, achieving an 80% reduction without deriving an input-output model.
- MLC converged toward an efficient and robust control law linking real-time recirculation measurements to actuation values.The law was obtained without deriving a model for the input-output system.
- 80% reduction of the recirculation area was achieved with a simple experimental design.
- The optimization stopped when statistical indicators suggested that further improvement was unlikely, although optimality cannot be proven.
- Genetic programming may support additional control outputs and sensor inputs for multi-input/multi-output problems.
Appendix A.
The appendix explains how control laws are represented as expression trees and how genetic-programming mutation and crossover generate new candidate laws.
- A.1. Control laws and expression trees.: Expression trees represent control functions, with user-defined operations as nodes, constants and sensor inputs as leaves, and the root returning the control value.The same tree can also be represented and manipulated as a LISP expression.
- A.1. Control laws and expression trees.: LISP notation places operators before operands, enabling recursive generation, evaluation, and manipulation of individuals.
- A.2. Genetic programming operations on expression trees.: Mutation replaces a selected node and its subtree with a randomly grown subtree, preserving some information while exploring the search space with larger steps.This operation increases population diversity.
- A.2. Genetic programming operations on expression trees.: Crossover selects one node from each of two individuals and exchanges the corresponding substructures.