PG Madhavan

PG Madhavan

In this foundational expository article on the application of Causality Analysis in IoT, we establish the basic theory and algorithms for estimating Structural and Granger causality factors from measured multichannel sensor data (vector timeseries). Vector timeseries is modeled as a Structural Vector Autoregressive (SVAR) model; utilizing Kalman Filter and Independent Component Analysis (ICA) methods, Structural and generalized Granger causality factors are estimated. The estimated causal factors are presented as a Fence graph which we call Causal Digital Twin. Practical applications of Causal Digital Twin are demonstrated on NASA Prognostic Data Repository Bearing data collection. Use of Causal Digital Twin for counterfactual experiments are indicated. Causal Digital Twin is a horizontal solution that applies to diverse use cases in multiple industries such as Industrial, Manufacturing, Automotive, Consumer, Building and Smart City.

PG Madhavan

We provide some basic and sensible definitions of different types of digital twins and recommendations on when and how to use them. Following up on our recent publication of the Learning Causal Digital Twin, this article reports on a stochastic formulation and solution of the problem. Structural Vector Autoregressive Model (SVAR) for Causal estimation is recast as a state-space model. Kalman filter (and smoother) is then employed to estimate causal factors in a system of connected machine bearings. The previous neural network algorithm and Kalman Smoother produced very similar results; however, Kalman Filter/Smoother may show better performance for noisy data from industrial IoT sources.

PG Madhavan

Evidence-based Prescriptive Analytics (EbPA) is necessary to determine optimal operational set-points that will improve business productivity. EbPA results from what-if analysis and counterfactual experimentation on CAUSAL Digital Twins (CDTs) that quantify cause-effect relationships in the DYNAMICS of a system of connected assets. We describe the basics of Causality and Causal Graphs and develop a Learning Causal Digital Twin (LCDT) solution; our algorithm uses a simple recurrent neural network with some innovative modifications incorporating Causal Graph simulation. Since LCDT is a learning digital twin where parameters are learned online in real-time with minimal pre-configuration, the work of deploying digital twins will be significantly simplified. A proof-of-principle of LCDT was conducted using real vibration data from a system of bearings; results of causal factor estimation, what-if analysis study and counterfactual experiment are very encouraging.