Quantum computing (QC) and deep learning techniques have attracted widespread attention in the recent years. This paper proposes QC-based deep learning methods for fault diagnosis that exploit their unique capabilities to overcome the computational c
hallenges faced by conventional data-driven approaches performed on classical computers. Deep belief networks are integrated into the proposed fault diagnosis model and are used to extract features at different levels for normal and faulty process operations. The QC-based fault diagnosis model uses a quantum computing assisted generative training process followed by discriminative training to address the shortcomings of classical algorithms. To demonstrate its applicability and efficiency, the proposed fault diagnosis method is applied to process monitoring of continuous stirred tank reactor (CSTR) and Tennessee Eastman (TE) process. The proposed QC-based deep learning approach enjoys superior fault detection and diagnosis performance with obtained average fault detection rates of 79.2% and 99.39% for CSTR and TE process, respectively.
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts underlying quantu
m computation and their distinctive characteristics in comparison to their classical counterparts are also discussed. Along with different hardware architecture description of two commercially available quantum systems, an example making use of open-source software tools is provided as a first step for diving into the new realm of programming quantum computers for solving systems optimization problems. The trade-off between qualities of these two quantum architectures is also discussed. Complex nature of energy systems due to their structure and large number of design and operational constraints make energy systems optimization a hard problem for most available algorithms. Problems like facility location allocation for energy systems infrastructure development, unit commitment of electric power systems operations, and heat exchanger network synthesis which fall under the category of energy systems optimization are solved using both classical algorithms implemented on conventional CPU based computer and quantum algorithm realized on quantum computing hardware. Their designs, implementation and results are stated. Additionally, this paper describes the limitations of state-of-the-art quantum computers and their great potential to impact the field of energy systems optimization.
This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extr
act distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end-to-end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county-level case study of a spatially explicit biofuel supply chain in Illinois.
Appropriate greenhouse temperature should be maintained to ensure crop production while minimizing energy consumption. Even though weather forecasts could provide a certain amount of information to improve control performance, it is not perfect and f
orecast error may cause the temperature to deviate from the acceptable range. To inherent uncertainty in weather that affects control accuracy, this paper develops a data-driven robust model predictive control (MPC) approach for greenhouse temperature control. The dynamic model is obtained from thermal resistance-capacitance modeling derived by the Building Resistance-Capacitance Modeling (BRCM) toolbox. Uncertainty sets of ambient temperature and solar radiation are captured by support vector clustering technique, and they are further tuned for better quality by training-calibration procedure. A case study that implements the carefully chosen uncertainty sets on robust model predictive control shows that the data-driven robust MPC has better control performance compared to rule-based control, certainty equivalent MPC, and robust MPC.
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical program
ming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.
Scenario programs have established themselves as efficient tools towards decision-making under uncertainty. To assess the quality of scenario-based solutions a posteriori, validation tests based on Bernoulli trials have been widely adopted in practic
e. However, to reach a theoretically reliable judgement of risk, one typically needs to collect massive validation samples. In this work, we propose new a posteriori bounds for convex scenario programs with validation tests, which are dependent on both realizations of support constraints and performance on out-of-sample validation data. The proposed bounds enjoy wide generality in that many existing theoretical results can be incorporated as particular cases. To facilitate practical use, a systematic approach for parameterizing a posteriori probability bounds is also developed, which is shown to possess a variety of desirable properties allowing for easy implementations and clear interpretations. By synthesizing comprehensive information about support constraints and validation tests, improved risk evaluation can be achieved for randomized solutions in comparison with existing a posteriori bounds. Case studies on controller design of aircraft lateral motion are presented to validate the effectiveness of the proposed a posteriori bounds.
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive
scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances.
A novel data-driven stochastic robust optimization (DDSRO) framework is proposed for optimization under uncertainty leveraging labeled multi-class uncertainty data. Uncertainty data in large datasets are often collected from various conditions, which
are encoded by class labels. Machine learning methods including Dirichlet process mixture model and maximum likelihood estimation are employed for uncertainty modeling. A DDSRO framework is further proposed based on the data-driven uncertainty model through a bi-level optimization structure. The outer optimization problem follows a two-stage stochastic programming approach to optimize the expected objective across different data classes; adaptive robust optimization is nested as the inner problem to ensure the robustness of the solution while maintaining computational tractability. A decomposition-based algorithm is further developed to solve the resulting multi-level optimization problem efficiently. Case studies on process network design and planning are presented to demonstrate the applicability of the proposed framework and algorithm.
