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Developing and improving process‐based models requires identifying the importance and/or influence of various processes driving system behavior. In our recent studies, important processes are identified using first‐order process sensitivity index PSK (Dai et al., 2017, ), and non‐influential processes are determined using total‐effect process sensitivity index PSTK (Yang et al., 2022, ), K denoting a given system process. Estimating these indices through the brute force Monte Carlo (MC) method is computationally intensive and often impractical. This study extends the quasi‐MC method developed by Dai et al. (2022), to concurrently estimate PSK and PSTK with reduced computational cost. The concurrent estimation is based on a rigorous theoretical framework that we leverage to provide a robust computational implementation of the quasi‐MC method. The number of model executions required for estimating PSK or PSTK associated with system process K is reduced from N2 in brute force MC method to 2N in quasi‐MC method, N being the number of samples generated for uncertain parameters. The total model executions required to concurrently estimate PSK and PSTK for all processes of an individual system model are N × (Np + 2), Np being the number of system processes associated with the system model of interest. Convergence, accuracy, and reliability of the quasi‐MC method are evaluated through an exemplary one‐dimensional groundwater flow example. Results demonstrate that the quasi‐MC method converges substantially faster and is more reliable than its brute force MC counterpart. Impacts of process model weights on estimating the two indices and their theoretical and practical limitations are also discussed.

In practical applications, an engineer is sometimes expected to execute the step test for tuning the controller without waiting much for the steady-state or a low level of disturbances. Hence, knowing that the initial settings may not be quite reliable, he/she detunes the controller by reducing its gain as a precaution against possible poor behaviour of the closed-loop system. It is up to their experience to choose by how much to detune. Therefore, the development of a practically oriented approach that would assist the engineer to choose the degree of gain reduction is the goal of this paper. The approach assumes that process parameters are determined by the least-squares approximation of the step response. Accuracy of the approximation is evaluated by a relative approximation error involving integrals of the error and the process response itself. The SIMC tuning rules are applied to choose the initial controller settings. The approach relies on detecting by simulation the worst case that may happen when the step response is triggered at any time. Detuning nomograms specify by how much to reduce the initial gain for PI-FOPTD and PID-SOPTD designs, given the relative approximation error. Two long-lasting lab experiments involving temperature control identify a plant, verify the load disturbance model through multiple step tests and demonstrate usage of the approach in the closed-loop system.

The quality of the air in underground mines is a challenging issue due to many factors, such as technological processes related to the work of miners (blasting, air conditioning, and ventilation), gas release by the rock mass and geometry of mine corridors. However, to allow miners to start their work, it is crucial to determine the quality of the air. One of the most critical parameters of the air quality is the carbon monoxide (CO) concentration. Thus, in this paper, we analyze the time series describing CO concentration. Firstly, the signal segmentation is proposed, then segmented data (daily patterns) is visualized and statistically analyzed. The method for blasting moment localization, with no prior knowledge, has been presented. It has been found that daily patterns differ and CO concentration values reach a safe level at a different time after blasting. The waiting time to achieve the safe level after blasting moment (with a certain probability) has been calculated based on the historical data. The knowledge about the nature of the CO variability and sources of a high CO concentration can be helpful in creating forecasting models, as well as while planning mining activities.

This paper aims to present a general identification procedure for fractional first-order plus dead-time (FFOPDT) models. This identification method is general for processes having S-shaped step responses, where process information is collected from an open-loop step-test experiment, and has been conducted by fitting three arbitrary points on the process reaction curve. In order to validate this procedure and check its effectiveness for the identification of fractional-order models from the process reaction curve, analytical expressions of the FFOPDT model parameters have been obtained for both situations: as a function of any three points and three points symmetrically located on the reaction curve, respectively. Some numerical examples are provided to show the simplicity and effectiveness of the proposed procedure. Good results have been obtained in comparison with other well-recognized identification methods, especially when simplicity is emphasized. This identification procedure has also been applied to a thermal-based experimental setup in order to test its applicability and to obtain insight into the practical issues related to its implementation in a microprocessor-based control hardware. Finally, some comments and reflections about practical issues relating to industrial practice are offered in this context.

Advancements in energy technologies created a new application for gas turbine generators, which are used to balance load. This usage also brought new challenges for maintenance because of harsh operating conditions that make turbines more susceptible to random failures. At the same time, reliability requirements for energy equipment are high. Reliability-centered maintenance based on forecasting the remaining useful life (RUL) of energy equipment, offers improvements to maintenance scheduling. It requires accurate forecasting methods to be effective. Defining stages in energy equipment operation allows for the improvement of quality of data used for training. At least two stages can be defined: normal operation and degradation process. A new method named Head move—Head move is proposed to robustly identify the degradation process by detecting its starting point. The method is based on two partially overlapping sliding windows moving from the start of operation to the end of life of the energy equipment and Kruskal-Wallis test to compare data within these windows. Using this data separation, a convolutional neural network-based forecasting model is applied for RUL prediction. The results demonstrate that the proposed degradation process identification (DPI) method doubles the accuracy when compared to the same forecasting model but without degradation process identification.

Thermal destruction systems are essential for processing hydrocarbon waste, requiring precise temperature control to ensure operational efficiency and high product quality. However, accurately modeling the thermal behavior of such systems remains a challenging task due to the need for precise identification of transient heating characteristics. This study addresses this problem by developing an advanced two-point identification approach for constructing transfer function models of temperature control objects. Unlike conventional methods that rely on fixed reference points for each model order, the proposed approach leverages predetermined empirical coefficients, enabling flexible and more accurate identification from any two points on the transient characteristic, even in the presence of noise. The effectiveness of the developed method is validated through the identification of two distinct experimental transient characteristics of a 100-liter reactor within a pilot thermal destruction system under noise conditions. Comparative analysis against three known identification techniques demonstrates that the proposed approach consistently yields the most accurate models while maintaining relatively low computational complexity, due to its versatility and ability to operate in noisy conditions. In particular, the values of the integral squared deviation were reduced by 0.126·105 for the first case and by 0.092·105 for the second case when compared with the best results achieved using the conventional two-point method. This confirms its high efficiency and the feasibility of using it to create comprehensive mathematical models of various systems for thermal destruction of hydrocarbon waste. The proposed approach is particularly well suited for rapid identification of transfer functions under varying operating conditions and can be applied to enhance control strategies, ultimately improving process stability, energy efficiency, and product quality in thermal destruction applications

SO2 emissions are known to pose great harm to both human health and atmospheric air, and flue gas generated from coal-fueled power plant is the prime source of sulfur dioxide. For this reason, flue gas desulfurization (FGD) technology has found wide applications in most coal-fired power stations. Correctly describe the dynamic behavior of an FGD process is the precondition of controlling it effectively. However, FGD process modeling is by no means an easy task, as the underlying process dynamics are highly nonlinear in nature, meanwhile time-delay effect is significant therein. Long short-term memory (LSTM) network possesses remarkable long-term memory capability, hence it is anticipated to have a powerful identification capability. In this paper, the connection between deep learning and system identification is established, further a unidirectional/bidirectional LSTM deep network is designed and employed to identify a real FGD process. Simulation results clearly demonstrate the effectiveness of deep learning-based identification approach, and the superiority of deep LSTMs over other conventional identification models is also verified.

A new analytical procedure for identifying fractional first-order plus dead-time (FFOPDT) models has recently been proposed. The technique is applicable to systems with S-shaped step responses and involves selecting three specific points on the process response curve for parameter estimation. In a simplified version of the method, the points are symmetrically positioned as x 1 = x % , x 2 = 50 % , and x 3 = ( 100 - x ) % , with 0 < x < 50 % , requiring only the optimal position of one point, x , given that the others are set automatically. This study explores the effect of adjusting the value of x 2 in the representative points ( x - x 2 - ( 100 - x ) % ) , while preserving symmetry around the center of the interval. Simulations provide insights into the influence of x 2 for more accurate estimation, revealing that the accuracy of the identified FFOPDT model is highly sensitive to the position of x 2 , and an optimal value is proposed to enhance precision. Experimental validation on a thermal-based prototype deployed on a microprocessor confirms the technique’s applicability. This approach provides new insights into selecting the central point x 2 and its implications for industrial applications.

This study focuses on modeling and dynamic identification of a reflux condenser in a batch reactor system. The model uses data from real industrial conditions, along with the Volterra series and Genocchi orthogonal polynomials, to capture the condenser’s nonlinear behavior. Identifying the dynamic behavior of the reflux condenser is essential for the safe and efficient production of phenolic resole resin in batch reactors. The condenser plays a key role in controlling the process temperature during exothermic polymerization by cooling and returning reflux material to the reactor. The model was validated with data from a 3500 kg industrial reactor, achieving a thermal energy prediction error of less than 2.5% during the critical polymerization phase. The results show that the model accurately reflects the condenser’s behavior, supporting its application in advanced control strategies for monitoring and regulating process temperature. Using these strategies can prevent uncontrolled reactions and improve operational safety and the quality of resole phenolic resin production.

The paper offers an approach to the investigation of the dynamics of nonlinear non-stationary processes with the focus on the risk of dynamic system stability loss. The risk is assessed on the basis of the accumulated knowledge about power supply system operation. New methods for power supply modes analysis are developed and applied as follows: linear discrete point knowledge-based models are developed for nonlinear non-stationary objects; wavelet analysis is used for non-stationary processes; stability loss risks are analyzed through the investigation of spectral decompositions of Gramians of these linear predictive models. Case studies are included.