  Data collected from arrays of sensors are essential for informed
decision-making in various systems. However, the presence of anomalies can
compromise the accuracy and reliability of insights drawn from the collected
data or information obtained via statistical analysis. This study aims to
develop a robust Bayesian optimal experimental design (BOED) framework with
anomaly detection methods for high-quality data collection. We introduce a
general framework that involves anomaly generation, detection and error scoring
when searching for an optimal design. This method is demonstrated using two
comprehensive simulated case studies: the first study uses a spatial dataset,
and the second uses a spatio-temporal river network dataset. As a baseline
approach, we employed a commonly used prediction-based utility function based
on minimising errors. Results illustrate the trade-off between predictive
accuracy and anomaly detection performance for our method under various design
scenarios. An optimal design robust to anomalies ensures the collection and
analysis of more trustworthy data, playing a crucial role in understanding the
dynamics of complex systems such as the environment, therefore enabling
informed decisions in monitoring, management, and response.
