## 1 Introduction
PID control remains the majority of all control loops over decades and in decades to come in industrial process control because of its simple structure, easy implementation, and effective control of some industrial objects or processes. However, there are some limitations of conventional PID control [15]: (1) it is difficult to establish an accurate mathematical model when the controlled object has complex nonlinear characteristics; (2) the parameters of the controlled system in the industrial process control are unknown; and (3) the time-varying phenomenon of parameters or the non-negligible existence of random disturbances led by the changes in raw materials, environment, and working conditions raise considerable hardness for conventional PID control to carry out online parameter tuning, which is studied under the premise that the controlled object is linear. Hence, more sophisticated controlling strategies with error detection and abnormal behavior are urgently required to solve the problems including great inertia, long time delay, and strong nonlinearity in drum control. Several advanced control strategies have been applied to steam generators in the serial communication industry to realize system health monitoring. Based on the triumph of intelligent control theory, the PID can be refined in various ways, like IMC (internal model control), DMC (dynamic matrix control), MPC (model predictive control), and fuzzy logic. [PERSON] et al. [16] compared and discussed the performance of a boiler evaporator system controlled by a traditional PID strategy and fuzzy logic block, which brings some advantages to the previous three-element boiler feed-water controller; likewise, [PERSON] [17] and [PERSON] [14] acquired an improvement over the boiler drum level controller by embedding a cascade model predictive control scheme. However, not all the prevalent smart control methods are suitable for drum pressure control. Generally, for real-world control problems, phenomenological and empirical models, like the IMC and MPC mentioned above, are available and the selection of these two categories is concerned mainly with the practical problems approached, available technology, and the goal of the simulations. These two models are based on the fundamental theory and simplification of a chemical process, which makes it difficult to develop an accurate model quantifying the phenomenology of unknown or partially unknown parameters. Moreover, numerous experimental records desired for expertise database establishment of expert control and rules determination of fuzzy control confines their implementation in the chemical control system, in spite of the fact that modeling of the controlled object is not demanded in these two control schemes. In this context, a neural network [18; 19; 20; 21; 22], capable of learning and adapting and thus providing good models, is a recommended tool, which is useful in the frequently encountered cases when researchers do not fully know the laws that govern the systems. In neural network modeling, there is no need for a good understanding of the process's internal laws, like a \"black box\" [23]. Neural networks [24] with good modeling capabilities have been widespread in chemical processes and the applications will increase broadly and continuously, such as sensor data analysis, fault detection, and nonlinear process identification. Three different types of neural networks (MLP, recurrent, and probabilistic) are applied by [PERSON] [25] to solve the problem of anomaly detection, confirming that neural network-based data-driven modeling has the potential to be integrated into real-time health monitoring systems of thermal power plants. [PERSON] [26] utilized a radial basis function neural network (RBFNN) for the FTS slurry reactor control and modeling, successfully predicting the reactor temperature. Favorable control equality was reached by the introduction of a neural network and different air-water loop configurations as well [27; 28; 29].