## 4 Conclusions
### Brief Description and Strengths of the Proposed Methodology  
Therefore, the purpose of this article is, first and foremost, to present a theoretical and methodological framework that combines thermoeconomic diagnosis with machine learning techniques identifying anomalies and quantifying their effects. Thus, this is the first time in the literature that learning through PINNs is incorporated in the field of thermoeconomics for maintenance applications, based on the previously validated characteristic-curve methodology.  
The objective is to compare the current operating condition with a reference condition without anomalies, in order to evaluate the existence of overconsumption attributable to both intrinsic anomalies and induced effects. For this comparison, while, on the one hand, the operating condition is determined directly from the system sensors, on the other hand, the corresponding analogue reference condition needs to be defined for each operating  
Figure 7: Summary of the procedure for learning, locking, and implementation of the reference operator and the system.  
mode; which is precisely proposed to be conducted with PINNs. Therefore, the described approach is applied in two main phases:  
* Phase (1): Applied only once at the beginning of the implementation, where the reference characteristic curves and the reference system model are obtained with PINNs;
* Phase (2): Applied continuously over time, where thermoeconomic diagnosis is applied according to the data obtained from the sensors in real time.  
It is important to note that this second phase, corresponding to the thermoeconomic diagnosis, has already been validated and documented from simulation models using Trnsys v17 software (see references [14; 15]). As explained, applying thermoeconomic techniques may appear complex, but does not require additional variables beyond those necessary to carry out energy balances. Additionally, and currently, thermoeconomics applied to buildings is at an advanced stage and there are free thermoeconomic tools that adapt to the corresponding operating modes of the system at any given time, through the concept of super-productive superstructure [31].  
Therefore, the complexity and novelty of the presented approach lies mainly in the first phase, where PINNs are used to implement the method of characteristic curves and the modular model in reference condition. This process makes it possible to obtain the reference variables that have traditionally been obtained by simulation. Accordingly, modelling the thermal system using PINNs may seem challenging in terms of implementation, but it has the advantage of decoupling from conventional simulation models and adapting more accurately to the real behaviour of the components, instead of relying on libraries of previously characterised models. In this way, PINN-based models represent the reality of the component under study more closely, and require only a one-time training, validation, and locking process, which significantly reduces the computational cost over time.  
Thus, the use of neural networks enables the prediction of the reference behaviour of each component individually, facilitating the identification of intrinsic anomalies. In addition, these individual PINNs are proposed to be integrated into a modular model to quantify the overconsumption induced in the other components.  
As a conclusion, the proposed methodology locates and quantifies the effects of anomalies, addressing and resolving the challenges associated with the various configurations that can occur in a dynamic system managed by a control system, a rare situation in industrial systems. Furthermore, this proposal takes into account both the casuistry of a single anomaly and the coexistence of multiple anomalies that superimpose their induced effects on the rest of the components, making it challenging to disaggregate and discriminate their origin.