Many years back I was looking for good algorithms for an online estimation of the parameters of a parallel robot mainly for self-calibration. I applied traditional nonlinear Optimization after modelling higher-degree nonlinearities as noises. To my surprise, I found that near some configurations of the robot, my algorithm was not converging. After careful evaluation, I found through physics equations that those were zones of physical singularities. Straightforward for a person with knowledge of numerical systems isn’t it? Not so simple. Without that knowledge of parallel robot dynamics and associated equations modelled as constraints, it would have been impossible to predict, quantify and design the robust algorithm for the robot I was looking for.
Fast forward two and half decades: AI/ML has made tremendous progress and has become omnipresent in the tech world. I regularly work on and give talks on predictive maintenance, condition monitoring, and digital twins for cyber-physical systems. I see a definite tendency to generalize AI problems of cyber-physical systems as data and model problems. This in my view is wrong, more in the case of many cyber-physical objects (patient monitoring devices, robots, e-bikes etc.. ML and AI can augment engineering and can make cyber-physical systems smarter but there is an urgent need for modellers and data scientists to understand the engineering of the system if the effort to make them intelligent needs to be successful. The progress of physics-guided machine learning is a resolute step in that direction.
There are two main ways of modelling cyber-physical systems – data-driven modelling and engineering equation-driven modelling. If a realistic system needs to model with all its nonlinearities and stochastic variabilities a combination of both types of analysis is the most suitable approach. Here comes physics-guided machine learning.
Physics-guided Machine Learning:
Physics-guided Machine Learning ( ML, DL, NN etc) utilises the guiding physics/engineering equations of the system to improve the accuracy of prediction. There are various ways to include the knowledge of the traditional physics-based approximate equations ( yes most of the equations in engineering and physics are derived after a lot of assumptions which lead to a loss of accuracy ) in an ML model:
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1. Use equations to do feature engineering
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2. Use of equations as a constraint in the loss function of neural network models
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3. Validating the available data for equal distribution of the whole solution space
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4. Generation of initial data set for quick convergence of the algorithm
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5. Removal of spurious data to reduce bias
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6. Avoid generalization
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7. Develop explainability of the system
Completely trained and updated Digital twins are just the opposite of what is done in physics-guided ML. In physics-guided ML, the ML model is augmented with the knowledge of equations whereas the digital twins with appropriate models for nonlinearity/noise leverages ML models to augment physics-guided digital twins.
Digital twins with Parameter Estimation
Digital twins digital replicas of a cyber-physical system that allows two-way data communication to improve the accuracy of replication. In most real-life cases, the twin equations, either closed form or CAE modelled, approximate the physics and model manufacturing variabilities through a statistical/ML method. Real-life cyber-physical systems do calibration/training when they start operation. Various statistical/ML models are used to model these calibration processes in which
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1. Major system parameters can be estimated
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2. Complicated non-linear effects can be approximated
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3. The accuracy of the system can be improved and maintained
In real cyberphysical systems equations and machine learning can work as complementary methods improving the predictability of the systems and hence better operations. Not all systems need these complementary methods to be employed simultaneously. The value of the asset and level of accuracy required always determine how the compute power needs to be employed
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