Markovian-based Model Research Articles

Cascade-based multi-scale AI approach for modeling rainfall-runoff process

Abstract In this paper, runoff time series of the sub-basins in a cascade form were decomposed by Wavelet Transform (WT) to extract their dynamical and multi-scale features for modeling Multi-Station (MS) rainfall-runoff (R-R) process of the Little River Watershed (LRW) in USA. A Self-Organizing Map (SOM) clustering technique was also employed to find homogeneous extracted sub-series' clusters. As a complementary feature, extraction criterion of mutual information (MI) was utilized for proper cluster agent choice to impose to the artificial intelligence (AI) models (Feed Forward Neural Network, FFNN; Extreme Learning Machine, ELM; and Least Square Support Vector Machine, LSSVM) to predict the runoff of the LRW sub-basins. The performance of wavelet-based runoff prediction was compared to the Markovian-based MS model. The proposed method not only considers the prediction of the outlet runoff but also covers predictions of interior sub-basins behavior. The outcomes showed that the proposed AI-models combined with the SOM and MI tools enhanced the MS runoff prediction efficiency up to 23% in comparison with the Markovian-based models. Nevertheless, benefit of the seasonality of the process along with reduction of dimension of the inputs could help the AI-models to consume pure information of the recorded data.

Conjunction of wavelet transform and SOM-mutual information data pre-processing approach for AI-based Multi-Station nitrate modeling of watersheds

Accurate nitrate load predictions can elevate decision management of water quality of watersheds which affects to environment and drinking water. In this paper, two scenarios were considered for Multi-Station (MS) nitrate load modeling of the Little River watershed. In the first scenario, Markovian characteristics of streamflow-nitrate time series were proposed for the MS modeling. For this purpose, feature extraction criterion of Mutual Information (MI) was employed for input selection of artificial intelligence models (Feed Forward Neural Network, FFNN and least square support vector machine). In the second scenario for considering seasonality-based characteristics of the time series, wavelet transform was used to extract multi-scale features of streamflow-nitrate time series of the watershed’s sub-basins to model MS nitrate loads. Self-Organizing Map (SOM) clustering technique which finds homogeneous sub-series clusters was also linked to MI for proper cluster agent choice to be imposed into the models for predicting the nitrate loads of the watershed’s sub-basins. The proposed MS method not only considers the prediction of the outlet nitrate but also covers predictions of interior sub-basins nitrate load values. The results indicated that the proposed FFNN model coupled with the SOM-MI improved the performance of MS nitrate predictions compared to the Markovian-based models up to 39%. Overall, accurate selection of dominant inputs which consider seasonality-based characteristics of streamflow-nitrate process could enhance the efficiency of nitrate load predictions.

Empirical Markovian-based models for rehabilitated pavement performance used in a life cycle analysis approach

Two empirical Markovian-based models are presented in this paper to predict the transition probabilities associated with rehabilitated pavement. The first model predicts the staged-homogenous transition probabilities as required by the staged-homogenous Markov model. The second model predicts the non-homogenous transition probabilities as applicable to the non-homogenous Markov model. In both the models, the deterioration transition probabilities are predicted as a function of the corresponding values associated with original pavement and two adjustment factors reflecting the impacts of increased traffic load applications and decreased pavement strength. The predicted transition probabilities are used to estimate the future distress ratings required for developing the corresponding life cycle performance curve. The life cycle performance/cost ratio is used to evaluate the cost-effectiveness of potential long-term M&R plans. The life cycle performance is defined as the area falling under the life cycle curve. The life cycle cost is estimated to include initial construction cost, routine maintenance cost, major rehabilitation cost, and added user cost due to work zone. Two proposed cost models are used in the case study for estimating routine maintenance and added user costs. The case study indicates that the proposed empirical Markovian-based models have provided reasonable estimates of the transition probabilities as reflected by the corresponding life cycle performance curves.

A Markovian approach to determining optimum process means with inspection sampling plan in serial production systems

This paper develops Markovian-based models for determining the optimum process means with the consideration of an acceptance sampling plan in a serial production system. This paper studies a production system where products are produced continuously with specified lower and upper specification limits for each stage in the production system for quality assurance purposes. Considering the inherent variability in production processes, the quality characteristic(s) of a product might fall below the lower specification limit, resulting in scrap cost, or above the upper specification limit, resulting in rework costs. To study the dynamics of this problem, this paper first develops a Markovian-based model for the optimum process target level for a single quality characteristic assuming a single sampling inspection plan for both a single- and a two-stage production system. Then, the proposed model is extended for dual quality characteristics that are dependent for single- and two-stage production systems. Numerical examples and sensitivity analysis are performed to investigate the effect of different system parameters on the expected profit and optimum process means. The results showed that both single- and two-stage production systems have convex function for the expected profit. In addition, the results showed that the optimum process means are slightly larger than the average of the specification limits. Finally, the correlation between the quality characteristics affects the expected profit significantly.

Analysis of customer lifetime value and marketing expenditure decisions through a Markovian-based model

The general aim of this study is to provide a guide to the future marketing decisions of a firm, using a model to predict customer lifetime values. The proposed framework aims to eliminate the limitations and drawbacks of the majority of models encountered in the literature through a simple and industry-specific model with easily measurable and objective indicators. In addition, this model predicts the potential value of the current customers rather than measuring the current value, which has generally been used in the majority of previous studies. This study contributes to the literature by helping to make future marketing decisions via Markov decision processes for a company that offers several types of products. Another contribution is that the states for Markov decision processes are also generated using the predicted customer lifetime values where the prediction is realized by a regression-based model. Finally, a real world application of the proposed model is provided in the banking sector to show the empirical validity of the model. Therefore, we believe that the proposed framework and the developed model can guide both practitioners and researchers.

A Markovian approach to determining process means with dual quality characteristics

This paper studies a production system where products are produced continuously and whose specification limits are specified for screening inspection. In this paper, we consider dual quality characteristics and different costs associated with each quality characteristic that falls below a lower specification limit or above an upper specification limit. Due to these different costs, the expected total profit will greatly depend on the process parameters, especially a process mean. This paper develops a Markovian-based model for determining the optimum process means with the consideration of dual quality characteristics in a single-stage system. The proposed model is then illustrated through a numerical example and sensitivity analysis is performed to validate the model. The results showed that the optimum process mean for both quality characteristics have a significant effect on the performance of the system. Since the literature survey shows that dealing with multi-quality characteristics is extremely limited, the proposed model, coupled with the Markovian approach, provides a unique contribution to this field.

Adaptive Mixture Estimation and Unsupervised Local Bayesian Image Segmentation

This paper addresses mixture estimation applied to unsupervised local Bayesian segmentation. The great efficiency of global Markovian-based model methods is well known, but the efficiency of local methods can be competitive in some particular cases. The purpose of this paper is to specify the behavior of different local methods in different situations. Algorithms which estimate distribution mixtures prior to segmentation, such as expectation maximization (EM), iterative conditional estimation (ICE), and stochastic expectation maximization (SEM), are studied. Adaptive versions of EM and ICE, valid for nonstationary class fields, are then proposed. After applying various combinations of estimators and segmentations to noisy images, we compare the estimators' performances according to different image and noise characteristics. Results obtained attest to the suitability of adaptive versions of EM, ICE, and SEM. Furthermore, the local methods turn out to be robust in the sense that the parameter estimation step does not degrade the final segmentation results significantly, and the choice of EM, ICE, or SEM has little importance.