scholarly journals Difference Equation Model-Based PM 2.5 Prediction considering the Spatiotemporal Propagation: A Case Study of Bohai Rim Region, China

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ceyu Lei ◽  
Xiaoling Han ◽  
Chenghua Gao
Keyword(s):  
Difference Equation ◽  
Prediction Accuracy ◽  
Clustering Algorithm ◽  
Absolute Error ◽  
Equation Model ◽  
Concentration Data ◽  
Comprehensive Management ◽  
Bohai Rim ◽  
Local Air Pollution ◽  
The Difference

Accurate reporting and prediction of PM 2.5 concentration are very important for improving public health. In this article, we use a spectral clustering algorithm to cluster 44 cities in the Bohai Rim Region. On this basis, we propose a special difference equation model, especially the use of nonlinear diffusion equations to characterize the temporal and spatial dynamic characteristics of PM 2.5 propagation between and within clusters for real-time prediction. For example, through the analysis of PM 2.5 concentration data for 92 consecutive days in the Bohai Rim Region, and according to different accuracy definitions, the average prediction accuracy of the difference equation model in all city clusters is 97% or 90%. The mean absolute error (MAE) of the forecast data for each urban agglomeration is within 7 units μg / m 3 . The experimental results show that the difference equation model can effectively reduce the prediction time, improve the prediction accuracy, and provide decision support for local air pollution early warning and urban comprehensive management.

scholarly journals Interpretability and variability of metamodel validation statistics in engineering system design optimization: a practical study

2014 ◽  
Vol 5 ◽  
pp. A05
Author(s):  
Husam Hamad ◽  
Awad Al-Zaben ◽  
Rami Owies
Keyword(s):  
Prediction Accuracy ◽  
Absolute Error ◽  
Engineering System ◽  
Average Absolute Error ◽  
Electronic Engineering ◽  
Deterministic Simulations ◽  
The Difference ◽  
System Design Optimization ◽  
Engineering System Design ◽  
Difference Mode

Prediction accuracy of a metamodel of an engineering system in comparison to the simulation model it approximates is one fundamental criterion that is used in metamodel validation. Many statistics are used to quantify prediction accuracy of metamodels in deterministic simulations. The most frequently used ones include the root-mean-square error (RMSE) and the R-square metric derived from it, and to a lesser degree the average absolute error (AAE) and its derivates such as the relative average absolute error (RAAE). In this paper, we compare two aspects of these statistics: interpretability of results returned by these statistics and their sample-to-sample variations, putting more emphasis on the latter. We use the difference-mode to common-mode ratio (DMCMR) as a measure of sample-to-sample variations for these statistics. Preliminary results are obtained and discussed via a number of analytic and electronic engineering examples.

scholarly journals A graphical heuristic for reduction and partitioning of large datasets for scalable supervised training

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Sumedh Yadav ◽  
Mathis Bode
Keyword(s):  
Prediction Accuracy ◽  
Clustering Algorithm ◽  
Nearest Neighbor ◽  
Large Datasets ◽  
Test Results ◽  
Accuracy Test ◽  
Reasonable Proportion ◽  
Speed Up ◽  
Run Time ◽  
Information Graph

Abstract A scalable graphical method is presented for selecting and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion to the task itself. This step is succeeded by construction of an information graph of the underlying classification patterns using approximate nearest neighbor methods. The presented method consists of two approaches, one for reducing a given training set, and another for partitioning the selected/reduced set. The heuristic targets large datasets, since the primary goal is a significant reduction in training computation run-time without compromising prediction accuracy. Test results show that both approaches significantly speed-up the training task when compared against that of state-of-the-art shrinking heuristics available in LIBSVM. Furthermore, the approaches closely follow or even outperform in prediction accuracy. A network design is also presented for a partitioning based distributed training formulation. Added speed-up in training run-time is observed when compared to that of serial implementation of the approaches.

A difference equation model of partial series

1994 ◽  
Vol 61 (2-3) ◽  
pp. 301-305
Author(s):  
K.J. Bunch ◽  
R.W. Grow
Keyword(s):  
Difference Equation ◽  
Equation Model

Curved Exponential Models in Econometrics

1997 ◽  
Vol 13 (6) ◽  
pp. 771-790 ◽  
Author(s):  
Kees Jan van Garderen
Keyword(s):  
Structural Equation ◽  
Equation Model ◽  
Econometric Models ◽  
Demand Systems ◽  
Likelihood Ratios ◽  
Sufficient Statistics ◽  
Sufficient Statistic ◽  
Exponential Models ◽  
Minimal Sufficient Statistic ◽  
The Difference

Curved exponential models have the property that the dimension of the minimal sufficient statistic is larger than the number of parameters in the model. Many econometric models share this feature. The first part of the paper shows that, in fact, econometric models with this property are necessarily curved exponential. A method for constructing an explicit set of minimal sufficient statistics, based on partial scores and likelihood ratios, is given. The difference in dimension between parameterand statistic and the curvature of these models have important consequences for inference. It is not the purpose of this paper to contribute significantly to the theory of curved exponential models, other than to show that the theory applies to many econometric models and to highlight some multivariate aspects. Using the methods developed in the first part, we show that demand systems, the single structural equation model, the seemingly unrelated regressions, and autoregressive models are all curved exponential models.

scholarly journals On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn−1)/(1+xn) for q>1+p>1

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Weiyong Yu ◽  
Jinfeng Zhao
Keyword(s):  
Difference Equation ◽  
Boundedness Of Solutions ◽  
The Difference

Multisensor Degradation Data Fusion and Remaining Life Prediction

2017 ◽  
Author(s):  
Changxi Wang ◽  
E. A. Elsayed ◽  
Kang Li ◽  
Javier Cabrera
Keyword(s):  
Data Fusion ◽  
Prediction Accuracy ◽  
Life Prediction ◽  
Clustering Algorithm ◽  
Partial Information ◽  
Degradation Process ◽  
Sensor Data ◽  
Multiple Sensors ◽  
Degradation Data ◽  
Degradation Monitoring

Multiple sensors are commonly used for degradation monitoring. Since different sensors may be sensitive at different stages of the degradation process and each sensor data contain only partial information of the degraded unit, data fusion approaches that integrate degradation data from multiple sensors can effectively improve degradation modeling and life prediction accuracy. We present a non-parametric approach that assigns weights to each sensor based on dynamic clustering of the sensors observations. A case study that involves a fatigue-crack-growth dataset is implemented in order evaluate the prognostic performance of the unit. Results show that the fused path obtained with the proposed approach outperforms any individual sensor data and other paths obtained with an adaptive threshold clustering algorithm in terms of life prediction accuracy.

Diagnosis of infertility from adenomyosis and endometriosis through entroxon based intelligent water drop back propagation neural networks

2022 ◽  
pp. 1-9
Author(s):  
P. Vijayalakshmi ◽  
K. Muthumanickam ◽  
G. Karthik ◽  
S. Sakthivel
Keyword(s):  
Clustering Algorithm ◽  
Water Drop ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
Uterine Wall ◽  
Health Issues ◽  
Testing Dataset ◽  
Proposed Model ◽  
Fuzzy C Means Clustering ◽  
The Difference

Adenomyosis is an abnormality in the uterine wall of women that adversely affects their normal life style. If not treated properly, it may lead to severe health issues. The symptoms of adenomyosis are identified from MRI images. It is a gynaecological disease that may lead to infertility. The presence of red dots in the uterus is the major symptom of adenomyosis. The difference in the extent of these red dots extracted from MRI images shows how significant the deviation from normality is. Thus, we proposed an entroxon-based bio-inspired intelligent water drop back-propagation neural network (BIWDNN) model to discover the probability of infertility being caused by adenomyosis and endometriosis. First, vital features from the images are extracted and segmented, and then they are classified using the fuzzy C-means clustering algorithm. The extracted features are then attributed and compared with a normal person’s extracted attributes. The proposed BIWDNN model is evaluated using training and testing datasets and the predictions are estimated using the testing dataset. The proposed model produces an improved diagnostic precision rate on infertility.

scholarly journals An inequality with application to a difference equation

2004 ◽  
Vol 69 (3) ◽  
pp. 519-528 ◽  
Author(s):  
Jong-Yi Chen ◽  
Yunshyong Chow
Keyword(s):  
Heat Conduction ◽  
Difference Equation ◽  
Heat Conduction Problem ◽  
The Difference

In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence satisfies The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

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