Evaluating the performance of heuristic optimisation algorithms is essential to determine how well they perform under various conditions. Recently, the BIAS toolbox was introduced as a behaviour benchmark to detect structural bias (SB) in search algorithms. The toolbox can be used to identify biases in existing algorithms, as well as to test for bias in newly developed algorithms. In this article, we introduce a novel and explainable deep-learning expansion of the BIAS toolbox, called Deep-BIAS. Where the original toolbox uses 39 statistical tests and a Random Forest model to predict the existence and type of SB, the Deep-BIAS method uses a trained deep-learning model to immediately detect the strength and type of SB based on the raw performance distributions. Through a series of experiments with a variety of structurally biased scenarios, we demonstrate the effectiveness of Deep-BIAS. We also present the results of using the toolbox on 336 state-of-the-art optimisation algorithms, which showed the presence of various types of structural bias, particularly towards the centre of the objective space or exhibiting discretisation behaviour. The Deep-BIAS method outperforms the BIAS toolbox both in detecting bias and for classifying the type of SB. Furthermore, explanations can be derived using XAI techniques.