(117g) What Does the Industry Want from Machine Learning? Interpretable Modelling Algorithm and Robust Optimisation for the Energy-Efficient Operation of Power Plants Case Study

Machine learning (ML) algorithms have demonstrated reliable utilisation in various fields of applications, including natural language processing, image classification, speech recognition, object detection, etc. However, the chemical process industries and power sector are still reluctant to deploy ML-based autonomous control of their industrial systems, given the black-box nature of the results obtained by using ML. The lack of interpretability in the ML model-based predictions raises numerous concerns for safety-critical industrial processes where one wrong action can be catastrophic for the operation and safety of the industrial systems. Moreover, industrial processes are inherently uncertain, i.e., aleatoric (un-explainable randomness in the system) or epistemic (lack of system-knowledge) level of uncertainties are entwined in the operations. The computation of the robust optimal solution for the large-scale industrial systems suffers from computational and resource challenges and it is quite difficult to determine the robust solution for the dynamic mode of operation [1]. The lack of interpretability, complemented with the challenges of robust optimisation further compromises confidence in the computation and implementation of ML based decision-making, decision support system and production planning and scheduling of industrial systems. Therefore, extensive research is needed in the domain of interpretable ML and robust optimisation to overcome the limitations and challenges of the ML and optimisation algorithms that can open a plethora of applications in industrial systems – true candidate customers of the ML.

Motivated by the existing research challenges in the domain of ML and optimisation, this paper presents a novel modelling algorithm called Data Information-Integrated Neural Network (DINN) that incorporates the information extracted from the dataset for the development of a better interpretable ML model [2]. Pearson correlation coefficient (PCC) measures the linear dependence between the pair of variables and indicates the nature of either linear or nonlinear relationships between the variables [3]. We have embedded the PCC information in the loss function of DINN that contributes to the parameter updates (weights and biases) during the DINN training. The loss function of DINN is customized to minimise the mean squared deviation between the true and model-simulated responses, as well as minimising the mean squared deviation between the PCC computed between the set of input variables with the true responses and the PCC computed between the set of input variables with the model-simulated responses. The gradient descent with momentum algorithm is applied to derive the analytical expressions for the parameter updates for DINN training. Moreover, a constraint is incorporated into the stopping condition that checks the absolute deviation of the PCC measured for a set of input variables with true and model-simulated responses and stops the model training when the deviation reaches the specified goal. The iterative training of the DINN on the customized loss function, along with the stopping constraint, tunes the parameters to better capture the information hidden in the training dataset and can offer improved interpretable performance.

A two-stage methodological framework is proposed for the data-driven robust optimisation that integrates the ML model like DINN for the estimation of the robust solution under different states of power generation from the industrial power stations. The mathematical rigor of nonlinear programming (NLP) technique offers to determine the solution corresponding to the initial conditions in the first stage. Whereas, in the second stage, the space around the estimated solution is extensively explored through Monte Carlo technique based constructed experiments to compute the variance in the objective function’s responses. A solution is regarded as robust out of the candidate solutions when the variance produced in the objective function’s responses for the simulated experiments is less than the user-defined threshold [4]. The ML models have the advantage of modelling the system with high accuracy and low computational resource utilisation for the simulation tasks. These features of ML expedite the search for robust solution under large number of simulated experiments that extensively investigate the system response under different operating values of the input variables corresponding to the state of power generation from industrial power stations.

The DINN algorithm is applied to model the thermal efficiency, power generation, and heat rate of a 660 MW supercritical coal power plant and an 1180 MW combined cycle gas power plant. The operation of a combined cycle gas power plant is maintained through the synchronized operation of sub-power systems like gas turbines and steam turbines. We have modeled the thermal efficiency, power generation, and heat rate of the gas turbine systems (gas turbine 1 and gas turbine 2) while power generation and heat rate are modelled for the steam turbine system by the operationally relevant input variables selected by domain knowledge and a literature survey. The output variables of the sub-power systems are deployed to predict the thermal efficiency, power generation, and heat rate at the complex-level of the combined cycle gas power plant. The historical operation data of the two power stations is taken which is cleaned and processed for the modelling tasks. Extensive hyperparameter tuning is carried out to train the DINN models for the considered output variables of the coal and combined cycle gas power plants, and the DINN models are further validated (a minimum R² > 0.7 is observed) to ensure the good predictive performance of the models. Monte Carlo technique-based variable significance analysis is carried out to establish the order of significance of the input variables impacting the output variables. It is computed that steam cycle-based variables have the percentage significance of 79%, 74%, and 66%, while gas turbines have a percentage significance of 85%, 93%, and 78% towards the thermal efficiency, power, and heat rate of coal and combined cycle gas power plants, respectively. It is noted that DINN based variable significance order is better aligned with the existing operational knowledge of the power plants than that of traditional artificial neural network, thereby indicating the advantage of integrating the PCC for the DINN training.

A multi-objective optimisation function is formulated that maximises the power and thermal efficiency while minimising the turbine heat for the coal and combined cycle gas power plants. A sequential quadratic solver is used to determine the solution for the formulated problem. Later, Gaussian noise based simulated experiments are designed for the NLP based estimated solution to investigate the impact of uncertainty on the response of the formulated multi-objective function. The robust optimal solutions are verified on the coal and combined cycle gas power plants’ operation, the improvement in the energy efficiency of the two power stations leads to the highest annual reduction in CO₂ measuring 200 ± 10 kt and 62 ± 20 kt respectively, corresponding to the mid-load capacity generation operation of the coal and combined cycle gas power stations. The DINN based process modelling has demonstrated the comparative advantage to interpret the model’s predictions, and robust optimisation is implemented for the estimation of a robust solution to enhance the energy efficiency of the power stations, leading to a reduction in CO₂ emissions. Machine intelligence, domain knowledge, and robust optimisation unified in an analytical framework can enhance the performance of industrial systems that contribute to the smart operation of industries and the net-zero goal.

Reference

1. Shang, C., X. Huang, and F. You, Data-driven robust optimization based on kernel learning. Computers & Chemical Engineering, 2017. 106: p. 464-479.
2. Ashraf, W.M. and V. Dua, Data Information integrated Neural Network (DINN) algorithm for modelling and interpretation performance analysis for energy systems. Energy and AI, 2024: p. 100363.
3. Zhang, W., et al., Machine learning based prediction and experimental validation of arsenite and arsenate sorption on biochars. Science of The Total Environment, 2023. 904: p. 166678.
4. Mirjalili, S., A. Lewis, and J.S. Dong, Confidence-based robust optimisation using multi-objective meta-heuristics. Swarm and Evolutionary Computation, 2018. 43: p. 109-126.