Granular Model of Long-Term Prediction for Energy System in Steel Industry

A Design and Optimization of a CGK-Based Fuzzy Granular Model Based on the Generation of Rational Information Granules

This study proposes an optimized context-based Gustafson Kessel (CGK)-based fuzzy granular model based on the generation of rational information granules and an optimized CGK-based fuzzy granular model with the aggregated structure. The conventional context-based fuzzy-c-means (CFCM) clustering generates clusters considering the input and output spaces. However, the prediction performance decreases when the specific data points with geometric features are used. The CGK clustering solves the above situation by generating valid clusters considering the geometric attributes of data in input and output spaces with the aid of the Mahalanobis distance. However, it is necessary to generate rational information granules (IGs) because there is a significant change in performance according to the context generated in the output space and the shape, size, and several clusters generated in the input space. As a result, the rational IGs are obtained by considering the relationship between the coverage and specificity of IG using the genetic algorithm (GA). Thus, the optimized CGK-based fuzzy granular models with the aggregated structure are designed based on rational IGs. The prediction performance was compared using the two databases to verify the validity of the proposed method. Finally, the experiments revealed that the performance of the proposed method is higher than that of the previous model.

A Design of CGK-Based Granular Model Using Hierarchical Structure

In this paper, we propose context-based GK clustering and design a CGK-based granular model and a hierarchical CGK-based granular model. Existing fuzzy clustering generates clusters using Euclidean distances. However, there is a problem in that performance decreases when a cluster is created from data with strong nonlinearity. To improve this problem, GK clustering is used. GK clustering creates clusters using Mahalanobis distance. In this paper, we propose context-based GK (CGK) clustering, which adds a method that considers the output space in the existing GK clustering, to create a cluster that considers not only the input space but also the output space. there is. Based on the proposed CGK clustering, a CGK-based granular model and a hierarchical CGK-based granular model were designed. Since the output of the CGK-based granular model is in the form of a context, it has the advantage of verbally expressing the prediction result, and the CGK-based granular model with a hierarchical structure can generate high-dimensional information granules, so meaningful information with high abstraction value granules can be created. In order to verify the validity of the method proposed in this paper, as a result of conducting an experiment using the concrete compressive strength database, it was confirmed that the proposed methods showed superior performance than the existing granular models.

Hierarchical Granular Computing-Based Model and Its Reinforcement Structural Learning for Construction of Long-Term Prediction Intervals

As one of the most essential sources of energy, byproduct gas plays a pivotal role in the steel industry, for which the flow tendency is generally regarded as the guidance for planning and scheduling in real production. In order to obtain the numeric estimation along with its reliability, the construction of prediction intervals (PIs) is highly demanded by any practical applications as well as being long term for providing more information on future trends. Bearing this in mind, in this article, a hierarchical granular computing (HGrC)-based model is established for constructing long-term PIs, in which probabilistic modeling gives rise to a long horizon of numeric prediction, and the deployment of information granularities hierarchically extends the result to be interval-valued format. Considering that the structure of this model has a direct impact on its performance, Monte-Carlo search with a policy gradient technique is then applied for reinforcement structure learning. Compared with the existing methods, the size (length) of the granules in the proposed approach is unequal so that it becomes effective for not only periodic but also nonperiodic data. Furthermore, with the use of parallel strategy, the efficiency can be also guaranteed for real-world applications. The experimental results demonstrate that the proposed method is superior to other commonly encountered techniques, and the stability of the structure learning process behaves better when compared with other reinforcement learning approaches.

Relevance Vector Machines-Based Time Series Prediction for Incomplete Training Dataset: Two Comparative Approaches

Considering that real-life time series mixed with missing points cannot be directly modeled by using most of the supervised machine learning methods, this paper proposes a novel time series prediction method based on relevance vector machines for incomplete training dataset. Given the regularity between the missing inputs and outputs constructed by the phase space reconstruction, this paper imputes the missing inputs during the learning process by the values of their corresponding missing outputs such that the elements in kernel matrix related to the missing inputs are capable of being updated. This paper designs two strategies to estimate the missing outputs. The first one is based on the expectation maximization formulation in which a joint posterior distribution over the missing outputs and the weights vector is derived as a multivariate Gaussian form, and the another maximizes the marginal likelihood function with respect to the missing outputs and other hyperparameters. To verify the performance of the two proposed computing strategies, two synthetic time series and a real-life dataset are employed. The results indicate that the proposed methods have robust and better performance over the other methods when dealing with incomplete time series training dataset.

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.

Granular Prediction and Dynamic Scheduling Based on Adaptive Dynamic Programming for the Blast Furnace Gas System

A timely and effective scheduling of the byproduct gas system plays a pivotal role in realizing intelligent manufacturing and energy conservation in the steel industry. In order to realize real-time dynamic scheduling of the blast furnace gas (BFG) system, a granular prediction and dynamic scheduling process based on adaptive dynamic programming is proposed in this paper. To reflect the specificity of production reflected in the fluctuation of data, a series of information granules is constructed and described. In the dynamic scheduling phase, based on the granular feature description, a scheduling action network is established and further updates of information granules are realized. Considering a slow adjustment process and delay characteristics of the BFG system, the cumulative reward of the critic network is calculated on the basis of the data partition to construct a tendency attenuation-based cost function. In order to determine the future trends of the gas tank level that targets real-time determination of the scheduling moment, a reinforcement learning-based granulation and prediction process is also proposed. To demonstrate the performance of the proposed method, a number of comparative experiments are presented by using the practical industrial data. The results indicate that the proposed method exhibits high accuracy and can deliver an effective solution to justified scheduling of the BFG system.

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.

Attribute-Driven Granular Model for EMG-Based Pinch and Fingertip Force Grand Recognition

Fine multifunctional prosthetic hand manipulation requires precise control on the pinch-type and the corresponding force, and it is a challenge to decode both aspects from myoelectric signals. This paper proposes an attribute-driven granular model (AGrM) under a machine-learning scheme to solve this problem. The model utilizes the additionally captured attribute as the latent variable for a supervised granulation procedure. It was fulfilled for EMG-based pinch-type classification and the fingertip force grand prediction. In the experiments, 16 channels of surface electromyographic signals (i.e., main attribute) and continuous fingertip force (i.e., subattribute) were simultaneously collected while subjects performing eight types of hand pinches. The use of AGrM improved the pinch-type recognition accuracy to around 97.2% by 1.8% when constructing eight granules for each grasping type and received more than 90% force grand prediction accuracy at any granular level greater than six. Further, sensitivity analysis verified its robustness with respect to different channel combination and interferences. In comparison with other clustering-based granulation methods, AGrM achieved comparable pinch recognition accuracy but was of lowest computational cost and highest force grand prediction accuracy.

Optimization by Context Refinement for Development of Incremental Granular Models

Optimization by refinement of linguistic contexts produced from an output variable in the construction of an incremental granular model (IGM) is presented herein. In contrast to the conventional learning method using the backpropagation algorithm, we use a novel method to learn both the cluster centers of Gaussian fuzzy sets representing the symmetry in the premise part and the contexts of the consequent part in the if–then fuzzy rules. Hence, we use the fundamental concept of context-based fuzzy clustering and design with an integration of linear regression (LR) and granular fuzzy models (GFMs). This GFM is constructed based on the association between the triangular membership function produced both in the input–output variables. The context can be established by the system user or using an optimization method. Hence, we can obtain superior performances based on the combination of simple linear regression and local GFMs optimized by context refinement. Experimental results pertaining to coagulant dosing in a water purification plant and automobile miles per gallon prediction revealed that the presented method performed better than linear regression, multilinear perceptron, radial basis function networks, linguistic model, and the IGM.

High-Order Temporal Correlation Model Learning for Time-Series Prediction

Time-series prediction has become a prominent challenge, especially when the data are described as sequences of multiway arrays. Because noise and redundancy may exist in the tensor representation of a time series, we focus on solving the problem of high-order time-series prediction under a tensor decomposition framework and develop two novel multilinear models: 1) the multilinear orthogonal autoregressive (MOAR) model and 2) the multilinear constrained autoregressive (MCAR) model. The MOAR model is designed to preserve as much information as possible from the original tensorial data under orthogonal constraints. The MCAR model is an enhanced version that is developed by replacing orthogonal constraints with an inverse decomposition error term. For both models, we project the original tensor into subspaces spanned by basis matrices to facilitate the discovery of the intrinsic temporal structure embedded in the original tensor. To build connections among consecutive slices of the tensor, we generalize a traditional autoregressive model to tensor form to better preserve the temporal smoothness. Experiments conducted on four publicly available datasets demonstrate that our proposed methods converge within a small number of iterations during the training stage and achieve promising results compared with state-of-the-art methods.

Clustering Homogeneous Granular Data: Formation and Evaluation

In this paper, we develop a comprehensive conceptual and algorithmic framework to cope with a problem of clustering homogeneous information granules. While there have been several approaches to coping with granular (viz. non-numeric) data, the origin of granular data themselves considered there is somewhat unclear and, as a consequence, the results of clustering start lacking some full-fledged interpretation. In this paper, we offer a holistic view at clustering information granules and an evaluation of the results of clustering. We start with a process of forming information granules with the use of the principle of justifiable granularity (PJG). With this regard, we discuss a number of parameters used in this development of information granules as well as quantify the quality of the granules produced in this manner. In the sequel, Fuzzy C -Means is applied to cluster the derived information granules, which are represented in a parametric manner and associated with weights resulting from the usage of the PJG. The quality of clustering results is evaluated through the use of the reconstruction criterion (quantifying the concept of information granulation and degranulation). A suite of experiments using synthetic and publicly available datasets is reported to quantify the performance of the proposed approach and highlight its key features.

Incremental Granular Model Improvement Using Particle Swarm Optimization

This paper proposes an incremental granular model (IGM) based on particle swarm optimization (PSO) algorithm. An IGM is a combination of linear regression (LR) and granular model (GM) where the global part calculates the error using LR. However, traditional CFCM clustering presents some problems because the number of clusters generated in each context is the same and a fixed value is used for fuzzification coefficient. In order to solve these problems, we optimize the number of clusters and their fuzzy numbers according to the characteristics of the data, and use natural imitative optimization PSO algorithm. We further evaluate the performance of the proposed method and the existing IGM by comparing the predicted performance using the Boston housing dataset. The Boston housing dataset contains housing price information in Boston, USA, and features 13 input variables and 1 output variable. As a result of the prediction, we can confirm that the proposed PSO-IGM shows better performance than the existing IGM.

Adaptive Granulation-Based Prediction for Energy System of Steel Industry

The flow variation tendency of byproduct gas plays a crucial role for energy scheduling in steel industry. An accurate prediction of its future trends will be significantly beneficial for the economic profits of steel enterprise. In this paper, a long-term prediction model for the energy system is proposed by providing an adaptive granulation-based method that considers the production semantics involved in the fluctuation tendency of the energy data, and partitions them into a series of information granules. To fully reflect the corresponding data characteristics of the formed unequal-length temporal granules, a 3-D feature space consisting of the timespan, the amplitude and the linetype is designed as linguistic descriptors. In particular, a collaborative-conditional fuzzy clustering method is proposed to granularize the tendency-based feature descriptors and specifically measure the amplitude variation of industrial data which plays a dominant role in the feature space. To quantify the performance of the proposed method, a series of real-world industrial data coming from the energy data center of a steel plant is employed to conduct the comparative experiments. The experimental results demonstrate that the proposed method successively satisfies the requirements of the practically viable prediction.