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Records with Keyword: Machine Learning
Wind Speed Prediction with Spatio⁻Temporal Correlation: A Deep Learning Approach
Qiaomu Zhu, Jinfu Chen, Lin Zhu, Xianzhong Duan, Yilu Liu
June 23, 2020 (v1)
Keywords: convolutional neural networks, deep learning, Machine Learning, spatio-temporal correlation, wind speed prediction
Wind speed prediction with spatio⁻temporal correlation is among the most challenging tasks in wind speed prediction. In this paper, the problem of predicting wind speed for multiple sites simultaneously is investigated by using spatio⁻temporal correlation. This paper proposes a model for wind speed prediction with spatio⁻temporal correlation, i.e., the predictive deep convolutional neural network (PDCNN). The model is a unified framework, integrating convolutional neural networks (CNNs) and a multi-layer perceptron (MLP). Firstly, the spatial features are extracted by CNNs located at the bottom of the model. Then, the temporal dependencies among these extracted spatial features are captured by the MLP. In this way, the spatial and temporal correlations are captured by PDCNN intrinsically. Finally, PDCNN generates the predicted wind speed by using the learnt spatio⁻temporal correlations. In addition, three error indices are defined to evaluate the prediction accuracy of the model on the... [more]
Short-Term Load Forecasting Using Smart Meter Data: A Generalization Analysis
Aida Mehdipour Pirbazari, Mina Farmanbar, Antorweep Chakravorty, Chunming Rong
June 23, 2020 (v1)
Keywords: deep learning, generalization analysis, Machine Learning, short-term load forecasting, smart meters
Short-term load forecasting ensures the efficient operation of power systems besides affording continuous power supply for energy consumers. Smart meters that are capable of providing detailed information on buildings energy consumption, open several doors of opportunity to short-term load forecasting at the individual building level. In the current paper, four machine learning methods have been employed to forecast the daily peak and hourly energy consumption of domestic buildings. The utilized models depend merely on buildings historical energy consumption and are evaluated on the profiles that were not previously trained on. It is evident that developing data-driven models lacking external information such as weather and building data are of great importance under the situations that the access to such information is limited or the computational procedures are costly. Moreover, the performance evaluation of the models on separated house profiles determines their generalization abili... [more]
Can Machine Learning Predict Stress Reduction Based on Wearable Sensors’ Data Following Relaxation at Workplace? A Pilot Study
Alessandro Tonacci, Alessandro Dellabate, Andrea Dieni, Lorenzo Bachi, Francesco Sansone, Raffaele Conte, Lucia Billeci
June 22, 2020 (v1)
Keywords: autonomic nervous system, ECG, galvanic skin response, heart rate, heart rate variability, Machine Learning, mindfulness, neural networks, relaxation, signal processing, skin conductance, wearable sensors, yoga
Nowadays, psychological stress represents a burdensome condition affecting an increasing number of subjects, in turn putting into practice several strategies to cope with this issue, including the administration of relaxation protocols, often performed in non-structured environments, like workplaces, and constrained within short times. Here, we performed a quick relaxation protocol based on a short audio and video, and analyzed physiological signals related to the autonomic nervous system (ANS) activity, including electrocardiogram (ECG) and galvanic skin response (GSR). Based on the features extracted, machine learning was applied to discriminate between subjects benefitting from the protocol and those with negative or no effects. Twenty-four healthy volunteers were enrolled for the protocol, equally and randomly divided into Group A, performing an audio-video + video-only relaxation, and Group B, performing an audio-video + audio-only protocol. From the ANS point of view, Group A sub... [more]
Machine Learning-Based Prediction of a BOS Reactor Performance from Operating Parameters
Alireza Rahnama, Zushu Li, Seetharaman Sridhar
May 22, 2020 (v1)
Keywords: Artificial Intelligence, BOS reactor, Machine Learning, neural network, steelmaking
A machine learning-based analysis was applied to process data obtained from a Basic Oxygen Steelmaking (BOS) pilot plant. The first purpose was to identify correlations between operating parameters and reactor performance, defined as rate of decarburization (dc/dt). Correlation analysis showed, as expected a strong positive correlation between the rate of decarburization (dc/dt) and total oxygen flow. On the other hand, the decarburization rate exhibited a negative correlation with lance height. Less obviously, the decarburization rate, also showed a positive correlation with temperature of the waste gas and CO2 content in the waste gas. The second purpose was to train the pilot-plant dataset and develop a neural network based regression to predict the decarburization rate. This was used to predict the decarburization rate in a BOS furnace in an actual manufacturing plant based on lance height and total oxygen flow. The performance was satisfactory with a coefficient of determination o... [more]
Gray-box Soft Sensors in Process Industry: Current Practice, and Future Prospects in Era of Big Data
Iftikhar Ahmad, Ahsan Ayub, Manabu Kano, Izzat Iqbal Cheema
April 14, 2020 (v1)
Keywords: big data analytics, internet of things, Machine Learning, sensor 4.0
Virtual sensors, or soft sensors, have greatly contributed to the evolution of the sensing systems in industry. The soft sensors are process models having three fundamental categories, namely white-box (WB), black-box (BB) and gray-box (GB) models. WB models are based on process knowledge while the BB models are developed using data collected from the process. The GB models integrate the WB and BB models for addressing the concerns, i.e., accuracy and intuitiveness, of industrial operators. In this work, various design aspects of the GB models are discussed followed by their application in the process industry. In addition, the changes in the data-driven part of the GB models in the context of enormous amount of process data collected in Industry 4.0 are elaborated.
Extreme Learning Machine-Based Model for Solubility Estimation of Hydrocarbon Gases in Electrolyte Solutions
Narjes Nabipour, Amir Mosavi, Alireza Baghban, Shahaboddin Shamshirband, Imre Felde
February 12, 2020 (v1)
Keywords: Big Data, chemical process model, data science, deep learning, electrolyte solution, extreme learning machines, hydrocarbon gases, Machine Learning, Natural Gas, prediction model, solubility
Calculating hydrocarbon components solubility of natural gases is known as one of the important issues for operational works in petroleum and chemical engineering. In this work, a novel solubility estimation tool has been proposed for hydrocarbon gases—including methane, ethane, propane, and butane—in aqueous electrolyte solutions based on extreme learning machine (ELM) algorithm. Comparing the ELM outputs with a comprehensive real databank which has 1175 solubility points yielded R-squared values of 0.985 and 0.987 for training and testing phases respectively. Furthermore, the visual comparison of estimated and actual hydrocarbon solubility led to confirm the ability of proposed solubility model. Additionally, sensitivity analysis has been employed on the input variables of model to identify their impacts on hydrocarbon solubility. Such a comprehensive and reliable study can help engineers and scientists to successfully determine the important thermodynamic properties, which are key f... [more]
A Review of Kernel Methods for Feature Extraction in Nonlinear Process Monitoring
Karl Ezra Pilario, Mahmood Shafiee, Yi Cao, Liyun Lao, Shuang-Hua Yang
February 12, 2020 (v1)
Keywords: Fault Detection, fault diagnosis, kernel CCA, kernel CVA, kernel FDA, kernel ICA, kernel PCA, kernel PLS, Machine Learning, Multivariate Statistics
Kernel methods are a class of learning machines for the fast recognition of nonlinear patterns in any data set. In this paper, the applications of kernel methods for feature extraction in industrial process monitoring are systematically reviewed. First, we describe the reasons for using kernel methods and contextualize them among other machine learning tools. Second, by reviewing a total of 230 papers, this work has identified 12 major issues surrounding the use of kernel methods for nonlinear feature extraction. Each issue was discussed as to why they are important and how they were addressed through the years by many researchers. We also present a breakdown of the commonly used kernel functions, parameter selection routes, and case studies. Lastly, this review provides an outlook into the future of kernel-based process monitoring, which can hopefully instigate more advanced yet practical solutions in the process industries.
GC-MS Fingerprints Profiling Using Machine Learning Models for Food Flavor Prediction
Kexin Bi, Dong Zhang, Tong Qiu, Yizhen Huang
February 12, 2020 (v1)
Keywords: convolutional neural network, fingerprint modeling, GC-MS/O profiling, Machine Learning, odor compounds
Food flavor quality evaluation is attracting continuous attention, but a suitable evaluation system is severely lacking. Gas chromatography-mass spectrometry/olfactometry (GC-MS/O) is widely used to solve the food flavor evaluation problem, but the olfactometry evaluation is unfeasible to be carried out in large batches and is unreliable due to potential issue of an operator or systematic laboratory effect. Thus, a novel fingerprint modeling and profiling process was proposed based on several machine learning models including convolutional neural network (CNN). The fingerprint template was created by the data analysis of existing GC-MS spectrum dataset. Then the fingerprint image generation program was applied for structuring the complex instrumental data. Food olfactometry result was obtained by a machine learning method based on CNN using fingerprint image as the input. The case study on peanut oil samples demonstrated the model accuracy of around 93%. By structure optimization and f... [more]
Data Augmentation Applied to Machine Learning-Based Monitoring of a Pulp and Paper Process
Andréa Pereira Parente, Maurício Bezerra de Souza Jr., Andrea Valdman, Rossana Odette Mattos Folly
January 19, 2020 (v1)
Keywords: data-driven, FDD, Machine Learning, Monte Carlo technique, neural networks, pulp and paper industry, study case
Industrial archived process data represent a convenient source of information for data-driven models, such as artificial neural network (ANN), that can be used for safety and efficiency improvement like early or even predictive fault detection and diagnosis (FDD). Nonetheless, most of the data used for model generation are representative of the process nominal states and therefore are not enough for classification problems intended to determine abnormal process conditions. This work proposes the use of techniques to augment the original real data standards, dismissing the need for experiments that could jeopardize process safety. It uses the Monte Carlo technique to artificially increase the number of model inputs coupled to the nearest neighbor search (NNS) by geometric distances to consistently classify the generated patterns in normal or faulty statuses. Finally, a radial basis function neural network is trained with the augmented data. The methodology was validated by a study case... [more]
Using Real-Time Electricity Prices to Leverage Electrical Energy Storage and Flexible Loads in a Smart Grid Environment Utilizing Machine Learning Techniques
Moataz Sheha, Kody Powell
January 2, 2020 (v1)
Keywords: artificial neural networks, duck curve, dynamic real-time optimization, Energy Storage, Machine Learning, real-time pricing, Renewable and Sustainable Energy, smart grid, smart houses, solar energy
With exposure to real-time market pricing structures, consumers would be incentivized to invest in electrical energy storage systems and smart predictive automation of their home energy systems. Smart home automation through optimizing HVAC (heating, ventilation, and air conditioning) temperature set points, along with distributed energy storage, could be utilized in the process of optimizing the operation of the electric grid. Using electricity prices as decision variables to leverage electrical energy storage and flexible loads can be a valuable tool to optimize the performance of the power grid and reduce electricity costs both on the supply and demand sides. Energy demand prediction is important for proper allocation and utilization of the available resources. Manipulating energy prices to leverage storage and flexible loads through these demand prediction models is a novel idea that needs to be studied. In this paper, different models for proactive prediction of the energy demand... [more]
A Holonic-Based Self-Learning Mechanism for Energy-Predictive Planning in Machining Processes
Seung-Jun Shin, Young-Min Kim, Prita Meilanitasari
December 10, 2019 (v1)
Keywords: cyber-physical production systems, holonic manufacturing systems, Machine Learning, predictive analytics, self-learning factory, transfer learning
The present work proposes a holonic-based mechanism for self-learning factories based on a hybrid learning approach. The self-learning factory is a manufacturing system that gains predictive capability by machine self-learning, and thus automatically anticipates the performance results during the process planning phase through learning from past experience. The system mechanism, including a modeling method, architecture, and operational procedure, is structured to agentize machines and manufacturing objects under the paradigm of Holonic Manufacturing Systems. This mechanism allows machines and manufacturing objects to acquire their data and model interconnection and to perform model-driven autonomous and collaborative behaviors. The hybrid learning approach is designed to obtain predictive modeling ability in both data-existent and even data-absent environments via accommodating machine learning (which extracts knowledge from data) and transfer learning (which extracts knowledge from e... [more]
Effects of Conventional Flotation Frothers on the Population of Mesophilic Microorganisms in Different Cultures
Mohammad Jafari, Mehdi Golzadeh, Sied Ziaedin Shafaei, Hadi Abdollahi, Mahdi Gharabaghi, Saeed Chehreh Chelgani
December 3, 2019 (v1)
Subject: Biosystems
Keywords: bioleaching, flotation, frother, Machine Learning, mixed culture
Bioleaching is an environment-friendly and low-investment process for the extraction of metals from flotation concentrate. Surfactants such as collectors and frothers are widely used in the flotation process. These chemical reagents may have inhibitory effects on the activity of microorganisms through a bioleaching process; however, there is no report indicating influences of reagents on the activity of microorganisms in the mixed culture which is mostly used in the industry. In this investigation, influences of typical flotation frothers (methyl isobutyl carbinol and pine oil) in different concentrations (0.01, 0.10, and 1.00 g/L) were examined on activates of bacteria in the mesophilic mixed culture (Acidithiobacillus ferrooxidans, Leptospirillum ferrooxidans, and Acidithiobacillus thiooxidans). For comparison purposes, experiments were repeated by pure cultures of Acidithiobacillus ferrooxidans and Leptospirillum ferrooxidans in the same conditions. Results indicated that increasing... [more]
A Comparison of Clustering and Prediction Methods for Identifying Key Chemical−Biological Features Affecting Bioreactor Performance
Yiting Tsai, Susan A. Baldwin, Lim C. Siang, Bhushan Gopaluni
November 24, 2019 (v1)
Keywords: bioinformatics, Machine Learning, statistics
Chemical−biological systems, such as bioreactors, contain stochastic and non-linear interactions which are difficult to characterize. The highly complex interactions between microbial species and communities may not be sufficiently captured using first-principles, stationary, or low-dimensional models. This paper compares and contrasts multiple data analysis strategies, which include three predictive models (random forests, support vector machines, and neural networks), three clustering models (hierarchical, Gaussian mixtures, and Dirichlet mixtures), and two feature selection approaches (mean decrease in accuracy and its conditional variant). These methods not only predict the bioreactor outcome with sufficient accuracy, but the important features correlated with said outcome are also identified. The novelty of this work lies in the extensive exploration and critique of a wide arsenal of methods instead of single methods, as observed in many papers of similar nature. The results show... [more]
Development of a Two-Stage ESS-Scheduling Model for Cost Minimization Using Machine Learning-Based Load Prediction Techniques
Minsu Park, Jaehwi Kim, Dongjun Won, Jaehee Kim
August 14, 2019 (v1)
Keywords: bagging, energy storage system, ensemble learning, load prediction, Machine Learning, random forest, two-stage algorithm
Effective use of energy storage systems (ESS) is important to reduce unnecessary power consumption. In this paper, a day-ahead two-stage ESS-scheduling model based on the use of a machine learning technique for load prediction has been proposed for minimizing the operating cost of the energy system. The proposed algorithm consists of two stages of ESS. In the first stage, ESS is used to minimize demand charges by reducing the peak load. Then, the remaining capacity is used to reduce energy charges through arbitrage trading, thereby minimizing the total operating cost. To achieve this purpose, accurate load prediction is required. Machine learning techniques are promising methods owing to the ability to improve forecasting performance. Among them, ensemble learning is a well-known machine learning method which helps to reduce variance and prevent overfitting of a model. To predict loads, we employed bootstrap aggregating (bagging) or random forest technique-based decision trees after Ho... [more]
An Accurate Clinical Implication Assessment for Diabetes Mellitus Prevalence Based on a Study from Nigeria
Muhammad Noman Sohail, Ren Jiadong, Musa Uba Muhammad, Sohaib Tahir Chauhdary, Jehangir Arshad, Antony John Verghese
July 31, 2019 (v1)
Subject: Biosystems
Keywords: clinical implications, cluster, data mining, Decision table, diabetes, epidemiology, forecast, Machine Learning, PART, real-life patients, regression, Weka
The increasing rate of diabetes is found across the planet. Therefore, the diagnosis of pre-diabetes and diabetes is important in populations with extreme diabetes risk. In this study, a machine learning technique was implemented over a data mining platform by employing Rule classifiers (PART and Decision table) to measure the accuracy and logistic regression on the classification results for forecasting the prevalence in diabetes mellitus patients suffering simultaneously from other chronic disease symptoms. The real-life data was collected in Nigeria between December 2017 and February 2019 by applying ten non-intrusive and easily available clinical variables. The results disclosed that the Rule classifiers achieved a mean accuracy of 98.75%. The error rate, precision, recall, F-measure, and Matthew’s correlation coefficient MCC were 0.02%, 0.98%, 0.98%, 0.98%, and 0.97%, respectively. The forecast decision, achieved by employing a set of 23 decision rules (DR), indicates that age, ge... [more]
CDL4CDRP: A Collaborative Deep Learning Approach for Clinical Decision and Risk Prediction
Mingrui Sun, Tengfei Min, Tianyi Zang, Yadong Wang
July 30, 2019 (v1)
Keywords: clinical diagnosis, decision support systems, Machine Learning, prediction algorithms, recommender systems
(1) Background: Recommendation algorithms have played a vital role in the prediction of personalized recommendation for clinical decision support systems (CDSSs). Machine learning methods are powerful tools for disease diagnosis. Unfortunately, they must deal with missing data, as this will result in data error and limit the potential patterns and features associated with obtaining a clinical decision; (2) Methods: Recent years, collaborative filtering (CF) have proven to be a valuable means of coping with missing data prediction. In order to address the challenge of missing data prediction and latent feature extraction, neighbor-based and latent features-based CF methods are presented for clinical disease diagnosis. The novel discriminative restricted Boltzmann machine (DRBM) model is proposed to extract the latent features, where the deep learning technique is adopted to analyze the clinical data; (3) Results: Proposed methods were compared to machine learning models, using two diffe... [more]
Extracting Valuable Information from Big Data for Machine Learning Control: An Application for a Gas Lift Process
Ana Carolina Spindola Rangel Dias, Felipo Rojas Soares, Johannes Jäschke, Maurício Bezerra de Souza Jr, José Carlos Pinto
July 28, 2019 (v1)
Keywords: echo state network, gas lift, Machine Learning, model predictive control (MPC)
The present work investigated the use of an echo state network for a gas lift oil well. The main contribution is the evaluation of the network performance under conditions normally faced in a real production system: noisy measurements, unmeasurable disturbances, sluggish behavior and model mismatch. The main pursued objective was to verify if this tool is suitable to compose a predictive control scheme for the analyzed operation. A simpler model was used to train the neural network and a more accurate process model was used to generate time series for validation. The system performance was investigated with distinct sample sizes for training, test and validation procedures and prediction horizons. The performance of the designed ESN was characterized in terms of slugging, setpoint changes and unmeasurable disturbances. It was observed that the size and the dynamic content of the training set tightly affected the network performance. However, for data sets with reasonable information co... [more]
A Systematic Grey-Box Modeling Methodology via Data Reconciliation and SOS Constrained Regression
José Luis Pitarch, Antonio Sala, César de Prada
July 25, 2019 (v1)
Keywords: grey-box model, Machine Learning, process modeling, SOS programming
Developing the so-called grey box or hybrid models of limited complexity for process systems is the cornerstone in advanced control and real-time optimization routines. These models must be based on fundamental principles and customized with sub-models obtained from process experimental data. This allows the engineer to transfer the available process knowledge into a model. However, there is still a lack of a flexible but systematic methodology for grey-box modeling which ensures certain coherence of the experimental sub-models with the process physics. This paper proposes such a methodology based in data reconciliation (DR) and polynomial constrained regression. A nonlinear optimization of limited complexity is to be solved in the DR stage, whereas the proposed constrained regression is based in sum-of-squares (SOS) convex programming. It is shown how several desirable features on the polynomial regressors can be naturally enforced in this optimization framework. The goodnesses of the... [more]
Data-Mining for Processes in Chemistry, Materials, and Engineering
Hao Li, Zhien Zhang, Zhe-Ze Zhao
July 25, 2019 (v1)
Keywords: chemistry, data-mining, Energy, engineering, Machine Learning, materials, neural networks
With the rapid development of machine learning techniques, data-mining for processes in chemistry, materials, and engineering has been widely reported in recent years. In this discussion, we summarize some typical applications for process optimization, design, and evaluation of chemistry, materials, and engineering. Although the research and application targets are various, many important common points still exist in their data-mining. We then propose a generalized strategy based on the philosophy of data-mining, which should be applicable for the design and optimization targets for processes in various fields with both scientific and industrial purposes.
Ensemble Learning Approach for Probabilistic Forecasting of Solar Power Generation
Azhar Ahmed Mohammed, Zeyar Aung
February 27, 2019 (v1)
Keywords: ensemble models, Machine Learning, probabilistic forecasting, regression, solar power
Probabilistic forecasting accounts for the uncertainty in prediction that arises from inaccurate input data due to measurement errors, as well as the inherent inaccuracy of a prediction model. Because of the variable nature of renewable power generation depending on weather conditions, probabilistic forecasting is well suited to it. For a grid-tied solar farm, it is increasingly important to forecast the solar power generation several hours ahead. In this study, we propose three different methods for ensemble probabilistic forecasting, derived from seven individual machine learning models, to generate 24-h ahead solar power forecasts. We have shown that while all of the individual machine learning models are more accurate than the traditional benchmark models, like autoregressive integrated moving average (ARIMA), the ensemble models offer even more accurate results than any individual machine learning model alone does. Furthermore, it is observed that running separate models on the da... [more]
A Review of Classification Problems and Algorithms in Renewable Energy Applications
María Pérez-Ortiz, Silvia Jiménez-Fernández, Pedro A. Gutiérrez, Enrique Alexandre, César Hervás-Martínez, Sancho Salcedo-Sanz
January 7, 2019 (v1)
Keywords: applications, classification algorithms, Machine Learning, Renewable and Sustainable Energy
Classification problems and their corresponding solving approaches constitute one of the fields of machine learning. The application of classification schemes in Renewable Energy (RE) has gained significant attention in the last few years, contributing to the deployment, management and optimization of RE systems. The main objective of this paper is to review the most important classification algorithms applied to RE problems, including both classical and novel algorithms. The paper also provides a comprehensive literature review and discussion on different classification techniques in specific RE problems, including wind speed/power prediction, fault diagnosis in RE systems, power quality disturbance classification and other applications in alternative RE systems. In this way, the paper describes classification techniques and metrics applied to RE problems, thus being useful both for researchers dealing with this kind of problem and for practitioners of the field.
Principal Component Analysis of Process Datasets with Missing Values
Kristen A. Severson, Mark C. Molaro, Richard D. Braatz
July 31, 2018 (v1)
Keywords: chemometrics, Machine Learning, missing data, multivariable statistical process control, principal component analysis, process data analytics, process monitoring, Tennessee Eastman problem
Datasets with missing values arising from causes such as sensor failure, inconsistent sampling rates, and merging data from different systems are common in the process industry. Methods for handling missing data typically operate during data pre-processing, but can also occur during model building. This article considers missing data within the context of principal component analysis (PCA), which is a method originally developed for complete data that has widespread industrial application in multivariate statistical process control. Due to the prevalence of missing data and the success of PCA for handling complete data, several PCA algorithms that can act on incomplete data have been proposed. Here, algorithms for applying PCA to datasets with missing values are reviewed. A case study is presented to demonstrate the performance of the algorithms and suggestions are made with respect to choosing which algorithm is most appropriate for particular settings. An alternating algorithm based... [more]
On the Use of Multivariate Methods for Analysis of Data from Biological Networks
Troy Vargason, Daniel P. Howsmon, Deborah L. McGuinness, Juergen Hahn
July 31, 2018 (v1)
Keywords: autism spectrum disorder, classification, Fisher discriminant analysis, Machine Learning, Multivariate Statistics, one carbon metabolism, probability density function, transsulfuration, urine toxic metals
Data analysis used for biomedical research, particularly analysis involving metabolic or signaling pathways, is often based upon univariate statistical analysis. One common approach is to compute means and standard deviations individually for each variable or to determine where each variable falls between upper and lower bounds. Additionally, p-values are often computed to determine if there are differences between data taken from two groups. However, these approaches ignore that the collected data are often correlated in some form, which may be due to these measurements describing quantities that are connected by biological networks. Multivariate analysis approaches are more appropriate in these scenarios, as they can detect differences in datasets that the traditional univariate approaches may miss. This work presents three case studies that involve data from clinical studies of autism spectrum disorder that illustrate the need for and demonstrate the potential impact of multivariate... [more]
Deterministic Global Optimization with Artificial Neural Networks Embedded
Global deterministische Optimierung von Optimierungsproblemen mit künstlichen neuronalen Netzwerken
Artur M Schweidtmann, Alexander Mitsos
October 15, 2018 (v2)
Subject: Optimization
Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and concave envelopes of the nonlinear activation function of ANNs. The optimization problem is solved using our in-house global deterministic solver MAiNGO. The performance of the proposed method is shown in four optimization examples: an illustrative function, a fermentation process, a compressor plant and a chemical process optimization. The results show that computational solution time is favorable compared to the global general-purpose optimization solver BARON.
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