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 be treated as a physics-based dimension reduction. It can reduce high-dimensional parameter 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-Bénard 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.

Evaluation of plates in similitude by experimental tests and artificial neural networks

In the last century, the introduction of similitude theory allowed engineers to define the conditions to design a scaled-up or down version of the full-scale structure by means of a set of tools known as similitude methods: the scaled structure can be tested more easily, and then, by using the scaling laws, the prototype behavior can be recovered. However, such a response reconstruction may become hard for complex structure under incomplete or distorted similitude frameworks. Machine learning methods, with their automating characteristics, may help to circumvent these difficulties. This work is divided into two parts. First, five clamped-free-clamped-free plates in similitude are experimentally tested. In the case of complete similitude, these laws allow to accurately reconstruct the response. When the similitude is distorted, these laws are not always valid, failing to predict the dynamic behavior in some of the frequency ranges. Then, the experimental results are used to validate the prediction and identification capabilities of artificial neural networks. The artificial neural networks proved to be robust to noise and very helpful in predicting the response characteristics and identifying the model type, although an adequate number of training examples is needed. Further tests proved that the number of samples is drastically reduced by choosing accurately the features.

Support of Dynamic Measurements Through Similitude Formulations

Up to now, similitude methods have been used in order to overcome the typical drawbacks of experimental testing and numerical simulations by reconstructing the full-scale model behavior from that of the scaled model. The novelty of this work is the application of similitude theory not as a tool for predicting the prototype dynamic response, but for supporting, and eventually validating, experimental measurements polluted by noise. Two Aluminium Foam Sandwich (AFS) plates are analyzed with Digital Image Correlation (DIC) cameras. First, an algorithm for blind source separation problems is used to extract information about the excitation; then, SAMSARA (Similitude and Asymptotic Models for Structural-Acoustic Research Applications) similitude method is applied to both the force spectra and velocity responses of prototype and model. The reconstruction of force and velocity curves demonstrates that the similitude results are coherent with the quality of the experimental measurements: when the spatial pattern in resonance is recognizable, then the curves overlap. Instead, when the displacement field of just one model is not well identified, the reconstruction exhibits discrepancies. Therefore, similitude methods reveal to be an interesting tool for understanding if a set of measurements is reliable or not and their application should not be underestimated, especially in the light of the expanding range of approaches which can extract important information from noisy observations.

Overview of the innovative heat exchangers technologies

The current paper analyzed the new trends and challenges in heat exchanger technologies. The progress of the studies on mini and micro devices used in industry are presented. Particular attention is paid to the heat exchangers used in marine and chemical industries where the resistance to heat transfer increases due to the fouling or scaling. In the industry, there are very important the reduction in the size of devices, and the micro heat exchangers, due to its variety of advantages offered, are well recognized for their higher performance. The applications of them are ranging from process control to military applications. New engineering approaches for modeling the heat and fluid flow processes in micro heat exchangers are analyzed in the present paper. One of these is based on the dimensional analysis and principles of similitude theory that allow the modeling of microscale systems using a physical system at the mini scale. There are identified constant relationships between dimensions permitting the analysis of the fluid flow through micro channels.

Dynamic similarity analysis for a piezo-electromechanical system

Most research about using piezoelectric stacks to suppress vibration of mechanical structures didn’t involve the similarity problem for the piezoelectric stacks. The goal of this paper is to investigate the dynamic similarity between a prototype piezo stack and a scaled up or down piezo stack, whilst discussing the feasibility of predicting the vibration of prototype structure which use the piezoelectric stacks for vibration control. To illustrate this problem concisely, a single-DOF system consists of a proof mass and a piezo stack shunted with a series RL circuit is considered. Firstly, the governing equation of such piezo-electromechanical system in frequency domain is derived. Next the dynamic similarity of prototype and model stack is analyzed by similitude theory. After that the scaling laws are derived. Finally, a numerical simulation and relative error analysis are given to demonstrate the scaling laws.

Energy Similitude Correction Method for Free Vibration of Cylinders

Similitude theory has been applied to design scale models in many fields of engineering. As for free vibration of cylinders, the wall thickness is too thin to manufacture scale model, which leads to similitude distortion. The aim of this study is to correct the similitude distortion and establish the distorted similitude relationship for free vibration of cylinders. First, the complete and partial similitude relationships are deduced while the similitude distortion of wall thickness is discussed. Then, with analysis of similitude for energy, an equation with prediction of modal frequencies for prototype is established and the energy similitude correction method is proposed. Finally, through numerical examples, this method is verified and the influence of wall thickness variation on the accuracy of the proposed method is analyzed.

AN ANALYSIS OF SCALING METHODS FOR STRUCTURAL COMPONENTS IN THE CONTEXT OF SIZE EFFECTS AND NONLINEAR PHENOMENA

Similitude theory helps engineers to investigate system properties and behaviour with scaling methods. The application of such methods reduces the time for product development and production of prototypes. With increasing component size, the impact of size effects and nonlinear phenomena becomes more important in reduced scale model testing. The aim of this paper is to provide an overview of the scaling methods and their applicability with regard to size effects and nonlinear phenomena as well as a procedure to support the selection of a suitable method for the scaling task of structures.