Session: 06-11-01: Applications of Artificial Intelligence/Machine Learning in Aerospace Engineering

Paper Number: 165693

Stochastic Framework for Analyzing Error Propagation in Digital Twins: A Two-Link Robotic Arm Case 

The digital twin concept originated in aerospace engineering, where there is a need to monitor and control remote physical assets through virtual replicas. In the literature, digital twins refer to detailed simulations with different levels of data integration: detailed simulations without data exchange (digital models), simulations with one-way data exchange from the physical asset to the digital replica (digital shadows), and fully integrated systems with two-way data exchange (true digital twins). There are many articles on conceptualizing digital twins and multiple expansive review papers. However, most of these articles are dedicated to digital models or digital shadows. Only a few articles showcase a true digital twin of a physical asset. For our definition of the digital twin, we refer to the AIAA definition: “A digital twin is a set of virtual information constructs that mimics the structure, context, and behavior of an individual/unique physical asset, is dynamically updated with data from its physical twin throughout its life cycle and informs decisions that realize value.” This definition distinguishes a digital twin from complex simulations. A true digital twin offers real-time system data, allowing for more accurate predictions than physics models alone. Furthermore, it enables monitoring and prediction and supports feedback loops, sending commands back to the system for corrective and proactive control strategies.

We will build a digital twin of a two-link robotic arm, ensuring that the digital twin framework complies with our technical definition of digital twin described earlier and includes two-way data exchange between the digital twin and physical asset. One can control the robotic arm’s position with two angular degrees of freedom. Most digital twins are built to discover anomalies in physical assets during operation and provide feedback to operators to inform their decisions. Our digital twin has three goals: 1) Identify misalignment between the desired position and the sensor readings; 2) Identify the value of misalignment; and 3) Update the predictive model to evaluate a new control input that moves the arm to the desired location.

 

At the heart of digital twins are data-driven predictive models. For this work, we will use an Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS is a hybrid intelligence system that combines the strengths of fuzzy logic and neural networks. By integrating the learning capabilities of neural networks with the flexibility of fuzzy logic, ANFIS can handle uncertainty and complex relationships in data more effectively. ANFIS employs membership functions to manage ambiguity, while the neural network component adapts and learns from data to optimize the system's parameters. Managing ambiguity is critical for creating the required inverse kinematic models for the proposed digital twin. We can achieve the same results using traditional neural networks (NN) with much larger training data sets since NN is purely data-driven, while ANFIS benefits from fuzzy logic.

 

Once the digital twin is built, we will study error propagation in the digital twin.  “Error” is defined as the discrepancy between observed (from the physical system) and predicted values (by digital twin) and can be categorized into systematic and random components. In digital twins, systematic errors are typically attributable to predictive model deficiencies or unaccounted environmental factors, while random errors result from noise and stochastic variability. Here, we employ a continuous time Markov chain model to track the propagation of error through a multi-module system. Using Monte Carlo simulations, we estimate inter-module transition rates, construct the generator matrix, and then track the distribution of error over time. We introduce an importance measure inspired by the Birnbaum measure in reliability theory which enables us to quantify how changes in transition rates affect overall system performance. This dynamic framework helps us trace how errors from measurements, and data updates propagate through the digital twin, thereby influencing predictions and decision-making. By accounting for time-dependent changes, this framework significantly enhances forecasting reliability, improves issue detection, and supports system optimization.

 

Presenting Author: Zahra Sotoudeh California State Polytechnic University, Pomona

Presenting Author Biography: Dr. Zahra Sotoudeh is a professor at Cal Poly Pomona.

Authors:

Annice Najafi Cal Poly Pomona
Shokoufeh Mirzaei Cal Poly Pomona
Zahra Sotoudeh California State Polytechnic University, Pomona