Data-driven discovery of dimensionless numbers and scaling laws from experimental measurements

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a highly-multivariable system with incomplete governing equations. In this study, we embed the principle of dimensional invariance into a two-level machine learning scheme to automatically discover dominant and unique dimensionless numbers and scaling laws from data. The proposed methodology, called dimensionless learning, can reduce high-dimensional parametric spaces into descriptions involving just a few physically-interpretable dimensionless parameters, which significantly simplifies the process design and optimization of the system. We demonstrate the algorithm by solving several challenging engineering problems with noisy experimental measurements (not synthetic data) collected from the literature. The examples include turbulent Rayleigh-Benard convection, vapor depression dynamics in laser melting of metals, and porosity formation in 3D printing. We also show that the proposed approach can identify dimensionally-homogeneous differential equations with minimal parameters by leveraging sparsity-promoting techniques

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10$\times$ acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research

A novel intelligent adaptive control of laser-based ground thermal test

AbstractLaser heating technology is a type of potential and attractive space heat flux simulation technology, which is characterized by high heating rate, controlled spatial intensity distribution and rapid response. However, the controlled plant is nonlinear, time-varying and uncertainty when implementing the laser-based heat flux simulation. In this paper, a novel intelligent adaptive controller based on proportion–integration–differentiation (PID) type fuzzy logic is proposed to improve the performance of laser-based ground thermal test. The temperature range of thermal cycles is more than 200K in many instances. In order to improve the adaptability of controller, output scaling factors are real time adjusted while the thermal test is underway. The initial values of scaling factors are optimized using a stochastic hybrid particle swarm optimization (H-PSO) algorithm. A validating system has been established in the laboratory. The performance of the proposed controller is evaluated through extensive experiments under different operating conditions (reference and load disturbance). The results show that the proposed adaptive controller performs remarkably better compared to the conventional PID (PID) controller and the conventional PID type fuzzy (F-PID) controller considering performance indicators of overshoot, settling time and steady state error for laser-based ground thermal test. It is a reliable tool for effective temperature control of laser-based ground thermal test

Vapor-induced flow and its impact on powder entrainment in laser powder bed fusion

A 2D axisymmetric transient Thermal-Fluid-Evaporation model coupled with melt pool dynamics and gas kinetics is developed to study the formation mechanisms of vapor-induced flow and the resulting powder entrainment in powder bed fusion using laser beam (PBF-LB) for 316 L powders. The interactions between keyhole formation inside the melt pool, vapor plume flow, and vapor-induced shielding gas flow are investigated. Vapor plume flow results in powder spattering with much higher speed, while vapor-induced gas flow significantly contributes to powder denudation with lower speed. It is also reported that powder spattering is stronger in 1 atm argon than that in 1 atm helium because the drag force for spattering is 2.72 times larger in 1 atm argon, but powder denudation becomes greater in 1 atm helium as the ratio of drag force for denudation in 1 atm argon to that in 1 atm helium is only 0.582. Furthermore, the vapor plume results in more spatters with the decrease of ambient pressure from 1 atm to 0.05 atm in argon because the plume is diluted faster with a twofold wider plume head and the two times higher peak velocity as a result of the pressure drop-induced significant reduction of viscosity restriction. A larger divergency angle in 0.05 atm argon is also recorded at the same time for the weaker restriction and faster dilusiton. In combination with in-situ observations, the proposed model provides insights into the vapor-induced flow, and its impact on powder entrainment under different gas types and ambient pressures

Vapor-induced flow and its impact on powder entrainment in laser powder bed fusion

A 2D axisymmetric transient Thermal-Fluid-Evaporation model coupled with melt pool dynamics and gas kinetics is developed to study the formation mechanisms of vapor-induced flow and the resulting powder entrainment in powder bed fusion using laser beam (PBF-LB) for 316 L powders. The interactions between keyhole formation inside the melt pool, vapor plume flow, and vapor-induced shielding gas flow are investigated. Vapor plume flow results in powder spattering with much higher speed, while vapor-induced gas flow significantly contributes to powder denudation with lower speed. It is also reported that powder spattering is stronger in 1 atm argon than that in 1 atm helium because the drag force for spattering is 2.72 times larger in 1 atm argon, but powder denudation becomes greater in 1 atm helium as the ratio of drag force for denudation in 1 atm argon to that in 1 atm helium is only 0.582. Furthermore, the vapor plume results in more spatters with the decrease of ambient pressure from 1 atm to 0.05 atm in argon because the plume is diluted faster with a twofold wider plume head and the two times higher peak velocity as a result of the pressure drop-induced significant reduction of viscosity restriction. A larger divergency angle in 0.05 atm argon is also recorded at the same time for the weaker restriction and faster dilution. In combination with in-situ observations, the proposed model provides insights into the vapor-induced flow, and its impact on powder entrainment under different gas types and ambient pressures

A novel intelligent adaptive control of laser-based ground thermal test

Laser heating technology is a type of potential and attractive space heat flux simulation technology, which is characterized by high heating rate, controlled spatial intensity distribution and rapid response. However, the controlled plant is nonlinear, time-varying and uncertainty when implementing the laser-based heat flux simulation. In this paper, a novel intelligent adaptive controller based on proportion–integration–differentiation (PID) type fuzzy logic is proposed to improve the performance of laser-based ground thermal test. The temperature range of thermal cycles is more than 200K in many instances. In order to improve the adaptability of controller, output scaling factors are real time adjusted while the thermal test is underway. The initial values of scaling factors are optimized using a stochastic hybrid particle swarm optimization (H-PSO) algorithm. A validating system has been established in the laboratory. The performance of the proposed controller is evaluated through extensive experiments under different operating conditions (reference and load disturbance). The results show that the proposed adaptive controller performs remarkably better compared to the conventional PID (PID) controller and the conventional PID type fuzzy (F-PID) controller considering performance indicators of overshoot, settling time and steady state error for laser-based ground thermal test. It is a reliable tool for effective temperature control of laser-based ground thermal test

Mechanistic data-driven prediction of as-built mechanical properties in metal additive manufacturing

Abstract Metal additive manufacturing provides remarkable flexibility in geometry and component design, but localized heating/cooling heterogeneity leads to spatial variations of as-built mechanical properties, significantly complicating the materials design process. To this end, we develop a mechanistic data-driven framework integrating wavelet transforms and convolutional neural networks to predict location-dependent mechanical properties over fabricated parts based on process-induced temperature sequences, i.e., thermal histories. The framework enables multiresolution analysis and importance analysis to reveal dominant mechanistic features underlying the additive manufacturing process, such as critical temperature ranges and fundamental thermal frequencies. We systematically compare the developed approach with other machine learning methods. The results demonstrate that the developed approach achieves reasonably good predictive capability using a small amount of noisy experimental data. It provides a concrete foundation for a revolutionary methodology that predicts spatial and temporal evolution of mechanical properties leveraging domain-specific knowledge and cutting-edge machine and deep learning technologies