Sample-Based Continuous Approximate Method for Constructing Interval Neural Network.

In safety-critical engineering applications, such as robust prediction against adversarial noise, it is necessary to quantify neural networks' uncertainty. Interval neural networks (INNs) are effective models for uncertainty quantification, giving an interval of predictions instead of a single value for a corresponding input. This article formulates the problem of training an INN as a chance-constrained optimization problem. The optimal solution of the formulated chance-constrained optimization naturally forms an INN that gives the tightest interval of predictions with a required confidence level. Since the chance-constrained optimization problem is intractable, a sample-based continuous approximate method is used to obtain approximate solutions to the chance-constrained optimization problem. We prove the uniform convergence of the approximation, showing that it gives the optimal INN consistently with the original ones. Additionally, we investigate the reliability of the approximation with finite samples, giving the probability bound for violation with finite samples. Through a numerical example and an application case study of anomaly detection in wind power data, we evaluate the effectiveness of the proposed INN against existing approaches, including Bayesian neural networks, highlighting its capability to significantly improve the performance of applying INNs for regression and unsupervised anomaly detection.

Sample-Based Neural Approximation Approach for Probabilistic Constrained Programs.

This article introduces a neural approximation-based method for solving continuous optimization problems with probabilistic constraints. After reformulating the probabilistic constraints as the quantile function, a sample-based neural network model is used to approximate the quantile function. The statistical guarantees of the neural approximation are discussed by showing the convergence and feasibility analysis. Then, by introducing the neural approximation, a simulated annealing-based algorithm is revised to solve the probabilistic constrained programs. An interval predictor model (IPM) of wind power is investigated to validate the proposed method.

Deep Learning Models for SO2 Distribution in a 30 MW Boiler via Computational Fluid Dynamics Simulation Data.

The distribution of SO2 in a boiler is an important factor affecting tube corrosion in a furnace. To investigate the correlation between SO2 distribution and numerous variables (e.g., temperature, O2 distribution, etc.), a hybrid deep learning model is developed via the computational fluid dynamics (CFD) simulation data. First, the combustion process under typical working conditions is simulated to output the training data set. Then, a LASSO algorithm is adopted to select input variables with a high correlation with SO2 distribution. Finally, a deep belief network combined with a restricted belief machine and a fully connected layer is developed to describe the nonlinear relationship. The proposed model is the first work to use a deep learning algorithm to obtain the correlation between SO2 distribution and other products of combustion. The results show that O2 concentration has the highest influence on SO2 distribution.

Granular Description of Data Structures: A Two-Phase Design.

The study is concerned with a description of large numeric data with the aid of building a limited collection of representative information granules with the objective of capturing the structure of the original data. The proposed development scheme consists of two steps. First, a clustering algorithm characterized by high flexibility of coping with the diverse geometry of data structure and efficient computational overhead is invoked. At the second step, a clustering algorithm applied to the clusters already formed during the first phase, yielding a collection of numeric prototypes is involved and the numeric prototypes produced there are then generalized into their granular prototypes. The quality of granular prototypes is quantified while their build-up is supported by the mechanisms of granular computing such as the principle of justifiable granularity. In this paper, the clustering algorithms of DBSCAN and fuzzy C -means were used in successive phases of the processed approach. The experimental studies concerning synthetic data and publicly available data are covered and the performance of the developed approach is assessed along with a comparative analysis.

Rule-Based Modeling With DBSCAN-Based Information Granules.

Rule-based models are applicable to model the behavior of complex and nonlinear systems. Due to limited experience and randomness involving constructing information granules, an insufficient credible rules division could reduce the model's accuracy. This paper proposes a new rule-based modeling approach, which utilizes density-based spatial clustering of applications with noise (DBSCAN)-based information granules to construct the rules. First, bear in mind the advantages of density-based clustering, DBSCAN is proposed to generate data structures. Based on these data structures, two rule-based models are constructed: 1) models using DBSCAN clusters to construct granules and rules directly and 2) models generating subgranules in each DBSCAN cluster for rule formation. Experiments involving these two models are completed, and obtained results are compared with those generated with a traditional model involving fuzzy C -means-based granules. Numerical results show that the rule-based model, which builds rules from subgranules of DBSCAN structures, performs the best in analyzing system behaviors.

Quantitative Analysis of Gas Phase IR Spectra Based on Extreme Learning Machine Regression Model.

Advanced chemometric analysis is required for rapid and reliable determination of physical and/or chemical components in complex gas mixtures. Based on infrared (IR) spectroscopic/sensing techniques, we propose an advanced regression model based on the extreme learning machine (ELM) algorithm for quantitative chemometric analysis. The proposed model makes two contributions to the field of advanced chemometrics. First, an ELM-based autoencoder (AE) was developed for reducing the dimensionality of spectral signals and learning important features for regression. Second, the fast regression ability of ELM architecture was directly used for constructing the regression model. In this contribution, nitrogen oxide mixtures (i.e., N2O/NO2/NO) found in vehicle exhaust were selected as a relevant example of a real-world gas mixture. Both simulated data and experimental data acquired using Fourier transform infrared spectroscopy (FTIR) were analyzed by the proposed chemometrics model. By comparing the numerical results with those obtained using conventional principle components regression (PCR) and partial least square regression (PLSR) models, the proposed model was verified to offer superior robustness and performance in quantitative IR spectral analysis.