Complex systems represented by multivariate time series are ubiquitous in many applications, especially in industry. Understanding a complex system, its states and their evolution over time is a challenging task. This is due to the permanent change of contextual events internal and external to the system. We are interested in representing the evolution of a complex system in an intelligible and explainable way based on knowledge extraction. Our industrial context is related to energy generation: a thermal power station that burns coal and gas to produce steam in order to generate electricity. This power station has five boilers and other equipments. Each equipment is monitored through a multitude of sensors. Our dataset contains 377 times series representing the recordings of 377 sensors every 10 minutes during three years. Our main hypotheses are the following: (i) The values of the time series at a timestamp t represent the state of the system at t. Their analysis allows to detect states, and in particular “rare” states. (ii) The states of the system can be characterized by different exploratory metrics related to the evolution of the time series. (iii) The states of the system, as well as their exploratory metrics can be considered as being parts of a Finite State Automaton (FSA), for which there are efficient visual representations. (iv) The FSA is a synthetic, intelligible and comprehensible representation of the behavior of a system over time and therefore a decision making aid. (v) The level of expertise in an application domain has an impact on the acceptability and the perception of explainable representations We propose the eXplainable Representation of Complex System Behavior (XR-CSB) methodology based on three steps: (i) a time series vertical clustering using k-means to detect system states, (ii) an explainable visual representation using unfolded automaton and (iii) an explainable pre-modeling based on an enrichment via exploratory metrics (average speed, average velocity and average acceleration for each state). As explainable visual representations, four representations are proposed: (i) a FSA, (ii) a unfolded automaton, (iii) an unfolded automaton with exploratory metrics, and (iv) a simplified representation of the unfolded automaton. Scalability of XR-CSB was evaluated, and so the acceptability of the visual explanations of the complex system behavior provided by the methodology by the employees of two IT companies through a questionnaire. Company 1 has a precise knowledge about the industrial context and work on data science, whereas Company 2 works on the development of websites and interfaces of tools dedicated to data management in this industrial context but no technical knowledge of the subject. The results of the questionnaire show a difference in perception of the acceptability of a representation according to the profile of the company’s experts, the apriori knowledge of the domain, and the technical experience with the subject: the neophyte profiles of a domain prefer more information on the considered complex system (Company 2), whereas those familiar with the subject seem not to need less information (Company 1). The visual representation seems essential for the information transmission aspect as long as it is relevant and easily understandable. This highlights an important trade-off between the performance of AI approaches, the relevance of the visual explanations and its intelligibility for the target audience. To conclude, our experiments show that (i) XR-CSB is scalable, and that (ii)it allows allows generating an explainable and intelligible visual representation of the behavior of a complex system that interfaces with experts as well as neophytes. In future works, we aim to include comments from PDF with explicit temporal information about actions undertaken to make an automatic post-hoc validation process of the extracted representations.