Resulting Prediction Error Research Articles

Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method

Wireless sensor systems often fail to provide measurements with uniform time spacing. Measurements can be delayed or even miss completely. Resampling to uniform intervals is necessary to satisfy the requirements of subsequent signal processing. Common resampling algorithms, based on symmetric finite impulse response (FIR) filters, entail a group delay of 10 s of samples, which is not acceptable regarding the typical interval of wireless sensors of seconds or minutes. The purpose of this paper is to verify the feasibility of single-delay resampling, i.e., the algorithm resamples the data without waiting for future samples. A new method to parametrize Kriging interpolation is presented and compared with two variants of Lagrange interpolation in detailed simulations for the resulting prediction error. Kriging provided the most accurate resampling in the group-delay scenario. The single-delay scenario required almost double the OSR to achieve the same signal-to-noise ratio (SNR). An OSR between 1.8 and 3.1 was necessary for single-delay resampling, depending on the required SNR and signal distortions in terms of jitter, missing samples, and noise. Kriging was the least noise-sensitive method. Especially for signals with missing samples, Kriging provided the best accuracy. The simulations showed that single-delay resampling is feasible, but at the expense of higher OSR and limited SNR.

An Online Health Monitoring Framework for Traction Motors in High-Speed Trains Using Temperature Signals

The health monitoring of traction motors is crucial for the prognostics and health management of high-speed trains. The temperature signal is an outstanding health indicator. Due to the representing of the traction motor's health conditions and low cost, accurate prediction for the motor temperature is conducive to early detection of abnormalities. However, the traditional prediction models are trained offline with high dependency on training data and cannot adapt to varying distributions of real data timely. Therefore, over time, the accuracies of these models always decrease noticeably. Concerning this issue, we propose an online health monitoring framework for traction motors using temperature signals. First, in the offline phase, multisensor signals are utilized to develop a generalized prediction model to absorb extensive information from temperature and relevant signals. Second, during the online phase, the training parameters are dynamically estimated to fulfill individualized learning by adopting a combination of the sample complexity and real-time prediction errors so as to fulfill individualized training according to the monitored data samples. Furthermore, a low-regret strategy is also presented in the online phase to determine the optimization target of the model to make the online update adaptive enough to the online prediction task. Consequently, the model can obtain new knowledge and greater understanding about the real data by online-learning continuously. Finally, the proposed framework is verified by actual data collected from Chinese high-speed trains. Compared with the conventional multilayer perceptron, gated recurrent unit, and long short-term memory, new patterns of stream data can be captured and adapted by using our framework, and the average root mean square errors of prediction results are reduced by 5%, 12%, and 11%, the average mean absolute percentage errors are reduced by 10%, 12%, and 11%, respectively. It is proven that our framework has high prediction accuracy and well-performed adaptability on real datasets.

Brand Preference Prediction Method of Cross-Border E-Commerce Consumers Based on Potential Tag Mining

There are many brands in cross-border e-commerce platforms. Obtaining consumers’ preference for brands will help promote the development of cross-border e-commerce industry. A brand preference prediction method of cross-border e-commerce consumers based on potential tag mining is proposed. Preprocess the cross-border e-commerce brand comment information obtained, build a HowNet emotion dictionary, and calculate consumers’ emotional tendency towards the brand on this basis. The projection pursuit regression model is optimized by differential evolution algorithm to reduce the dimension of the obtained consumer brand emotion information. Mining the potential labels of the information after dimensionality reduction, combined with Bayesian personalized sorting method and paired interaction tensor decomposition method, this paper constructs a brand preference’s prediction model to predict the brand preference of cross-border e-commerce consumers. The experimental results show that the proposed method has high accuracy of brand tendency calculation results, small average absolute error of prediction results, and high model accuracy.

Model Predictive Control and Transfer Learning of Hybrid Systems Using Lifting Linearization Applied to Cable Suspension Systems

Model Predictive Control (MPC) of nonlinear hybrid systems using lifting linearization underpinned by Koopman Operator is presented. Unlike standard linearization, which is valid only locally, lifting linearization provides a global linear representation of a nonlinear system in a lifted space. This allows us to obtain a unified linear model for a class of hybrid systems, which are otherwise modeled as a collection of dynamic modes that are constantly switching. This linear model created with lifting linearization is utilized to control a multi-cable robot exhibiting hybrid dynamics due to switching between taut and slack conditions of each cable. Applying MPC to the cable suspension robot, we show that even though the highly complex computation is reduced to a straightforward convex optimization, MPC can still find dexterous control actions for manipulating an object by taking into account the hybrid nature of the dynamics. A drawback of lifting linearization is that the learned model must be relearned when parameters of the system change. Here, we exploit the linearity of the model for transfer learning of a tuned model, adapted to a similar system with different parameters. Using a recursive updating method for the linear model, we demonstrate that the transferred model is able to adapt to the dynamics of the new nonlinear system and decrease prediction error over time. The resulting prediction error is comparable to that of the original model trained on its original dataset.

Application of BP neural network to prediction of recovery effect of air-foam flooding in heavy oil

Air-foam flooding is an effective technology to enhance oil recovery in heavy oil production. In this study, Back Propagation (BP) neural network model is built and optimized to predict the recovery effect of heavy oil with the injection parameters data of the oxygen-reduced air-foam flooding obtained through experiments. The study shows that the prediction results of the BP neural network is quite accurate, and the average absolute relative error of prediction results is less than 0.21%. This also illustrates the feasibility of using the BP network prediction model in predicting heavy oil recovery effect.

Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg-de Vries Equation

In this paper, with the aid of symbolic computation system Python and based on the deep neural network (DNN), automatic differentiation (AD), and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithms, we discussed the modified Korteweg-de Vries (mkdv) equation to obtain numerical solutions. From the predicted solution and the expected solution, the resulting prediction error reaches10−6. The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.

Using Multi-Factor Analysis to Predict Urban Flood Depth Based on Naive Bayes

With global warming, the number of extreme weather events will increase. This scenario, combined with accelerating urbanization, increases the likelihood of urban flooding. Therefore, it is necessary to predict the characteristics of flooded areas caused by rainstorms, especially the flood depth. We applied the Naive Bayes theory to construct a model (NB model) to predict urban flood depth here in Zhengzhou. The model used 11 factors that affect the extent of flooding—rainfall, duration of rainfall, peak rainfall, the proportion of roads, woodlands, grasslands, water bodies and building, permeability, catchment area, and slope. The forecast depth of flooding from the NB model under different rainfall conditions was used to draw an urban inundation map by ArcGIS software. The results show that the probability and degree of urban flooding in Zhengzhou increases significantly after a return period of once every two years, and the flooded areas mainly occurred in older urban areas. The average root mean square error of prediction results was 0.062, which verifies the applicability and validity of our model in the depth prediction of urban floods. Our findings suggest the NB model as a feasible approach to predict urban flood depth.

Predictive Quantization for Data Volume Reduction in Staggered SAR Systems

Staggered synthetic aperture radar (SAR) is an innovative SAR acquisition concept which exploits digital beamforming (DBF) in elevation to form multiple receive beams and continuous variation of the pulse repetition interval to achieve high-resolution imaging of a wide continuous swath. Staggered SAR requires an azimuth oversampling higher than an SAR with constant pulse repetition interval (PRI), which results in an increased volume of data. In this article, we investigate the use of linear predictive coding, which exploits the correlation properties exhibited by the nonuniform azimuth raw data stream. According to this, the prediction of each sample is calculated onboard as a linear combination of a set of previous samples. The resulting prediction error is then quantized and downlinked (instead of the original value), which allows for a reduction of the signal entropy and, in turn, of the onboard data rate achievable for a given target performance. In addition, the a priori knowledge of the gap positions can be exploited to dynamically adapt the bit rate allocation and the prediction order to further improve the performance. Simulations of the proposed dynamic predictive block-adaptive quantization (DP-BAQ) are carried out considering a Tandem-L-like staggered SAR system for different orders of prediction and target scenarios, demonstrating that a significant data reduction can be achieved with a modest increase of the system complexity.

Development of a PLS approach for the determination of the conversion in UV-cured white-pigmented coatings by NIR chemical imaging and its transfer to other substrates

Near-infrared (NIR) chemical imaging was used for in-line monitoring of the conversion in thick UV-cured white-pigmented acrylate coatings applied to various substrates such as glass, stainless steel, PVC and glass fiber reinforced plastic (GRP) boards. Quantitative results were obtained by means of chemometric calibration models based on the partial least square (PLS) algorithm. Two spectroscopic techniques were tested for their potential for the characterization of the conversion after UV irradiation with a broad range of UV doses in order to provide reliably precise reference data for the calibration. NIR reflection spectroscopy using band integration of the acrylate band at 1620 nm was selected as method of choice. Using glass as substrate for the coatings at the beginning, a PLS model was established and evaluated for its performance to predict the conversion in independent samples. The acrylate conversion was predicted with an error of 2%. Generally, any calibration model is specific to a well-defined sample system (e.g. material and thickness of substrate and coating). In order to reduce the effort required for the development of specific calibration models for each substrate used in this study, methods for calibration transfer were developed. It was found that the requirements for such transfer depend on the optical properties of the substrate. In case of stainless steel and PVC boards, simple preprocessing of the spectra by baseline correction and normalization (similar to samples on glass) led to satisfactory results, which is confirmed by prediction of the conversion with similar error margins as for coatings on glass. In case of glass fiber boards, the spectrum of the pristine GRP board had to be subtracted from the spectrum of the coated sample before the transfer of the PLS model. The resulting prediction error (RMSEP) was found to be 3.6%. The comparison between this transferred and a specific PLSGRP model that was built up for evaluation only proved the high performance of the transferred PLS model. These results clearly demonstrate the high efficiency of the transfer of specific PLS models to different (but similar) sample systems such as coatings applied to other substrates. In addition to the quantitative determination of the conversion, the developed calibration models were also used for the evaluation of its spatial distribution across the surface of UV-cured coatings.

Characterization of Toad Skin for Traditional Chinese Medicine by Near-Infrared Spectroscopy and Chemometrics

ABSTRACTExtraction is a widely used manufacturing protocol for medicinal materials. Near-infrared spectroscopy was implemented to simultaneously and nondestructively monitor toad skin extraction and to determine the ideal end point. A fiber optic probe was coupled to the extraction setup to collect real-time spectra. Four mathematical algorithms, including spectra dissimilarity, moving block standard deviation, mean square, and principal component analysis, were investigated to find a suitable method to determine the end point of extraction. The moving block standard deviation was the most effective method to evaluate the end point. Multivariate models based on partial least square regression were established to monitor changes. Four quantitative models for the indole alkaloid concentration and total solids in two extraction processes provided favorable statistics, and the determination coefficients of the calibration models exceeded 0.95. For indole alkaloids and total solids in the first and second extractions, the latent variables were 8, 5, 5, and 4, respectively; the root mean square error of cross-validation values were 8.26 mg mL−1, 0.18%, 7.50 mg mL−1, and 0.16%; and the root mean square error of prediction results were 11.10 mg mL−1, 0.27%, 4.89 mg mL−1, and 0.14%. The extraction monitoring system was able to ensure product quality and batch consistency while providing lower cost and faster analysis for pharmaceutical applications.

Organic Matter Modeling at the Landscape Scale Based on Multitemporal Soil Pattern Analysis Using RapidEye Data

This study proposes the development of a landscape-scale multitemporal soil pattern analysis (MSPA) method for organic matter (OM) estimation using RapidEye time series data analysis and GIS spatial data modeling, which is based on the methodology of Blasch et al. The results demonstrate (i) the potential of MSPA to predict OM for single fields and field composites with varying geomorphological, topographical, and pedological backgrounds and (ii) the method conversion of MSPA from the field scale to the multi-field landscape scale. For single fields, as well as for field composites, significant correlations between OM and the soil pattern detecting first standardized principal components were found. Thus, high-quality functional OM soil maps could be produced after excluding temporal effects by applying modified MSPA analysis steps. A regional OM prediction model was developed using four representative calibration test sites. The MSPA-method conversion was realized applying the transformation parameters of the soil-pattern detection algorithm used at the four calibration test sites and the developed regional prediction model to a multi-field, multitemporal, bare soil image mosaic of all agrarian fields of the Demmin study area in Northeast Germany. Results modeled at the landscape scale were validated at an independent test site with a resulting prediction error of 1.4 OM-% for the main OM value range of the Demmin study area.

Proposing a normalized Biot number: For simpler determination of Fourier exponents and for evaluating the sensitivity of the Biot number

This paper presents a normalization of the Biot number, which enables the Fourier exponents to be fitted with a simple 3rd order polynomial (R2 > 0.9999). The method is validated for Biot numbers ranging from 0.02 to ∞, and presented graphically for both the Fourier exponents and the lag factors needed in the series expansion. The lag factors and Fourier exponents are validated with an average variation coefficient (CVRMSD) less than 0.006. The resulting prediction error of the thermal response is < 0.6 °C for spheres and <0.3 °C for slabs and cylinders. The normalized Biot number also facilitates an easy investigation of the sensitivity in heat transfer calculations. The simplicity of the solution facilitates its implementation in the industry and curricula for engineers that needs crude calculation methods for thermal calculations, e.g. food science and food technology educations.

Study on Prediction Model of Grain Yield Based on Principal Component Analysis and BP Neural Network

Taking the grain yield data from 1980 to 2012 of Jilin Province for example, this paper analyzes the main factors that influences the grain yield based on the principle component analysis method. According to these main factors, the input samples of BP neutral network are definite. Thereby, the BP neutral networks could be trained to predict. The results show that the fertilizer consumption, large cattle head number, end grain sowing area, effective irrigation area and rural per capita living space are the main effect factor on grain yield. The BP neural network was built by using it as the input samples. The number of input nodes of the network is determined. Then build the prediction model of grain production in Jilin province. The simulation results show that, the average error of prediction results of BP neural network model based on principal component analysis is 4.48%.

Reliable estimation of prediction errors for QSAR models under model uncertainty using double cross-validation.

BackgroundGenerally, QSAR modelling requires both model selection and validation since there is no a priori knowledge about the optimal QSAR model. Prediction errors (PE) are frequently used to select and to assess the models under study. Reliable estimation of prediction errors is challenging – especially under model uncertainty – and requires independent test objects. These test objects must not be involved in model building nor in model selection. Double cross-validation, sometimes also termed nested cross-validation, offers an attractive possibility to generate test data and to select QSAR models since it uses the data very efficiently. Nevertheless, there is a controversy in the literature with respect to the reliability of double cross-validation under model uncertainty. Moreover, systematic studies investigating the adequate parameterization of double cross-validation are still missing. Here, the cross-validation design in the inner loop and the influence of the test set size in the outer loop is systematically studied for regression models in combination with variable selection.MethodsSimulated and real data are analysed with double cross-validation to identify important factors for the resulting model quality. For the simulated data, a bias-variance decomposition is provided.ResultsThe prediction errors of QSAR/QSPR regression models in combination with variable selection depend to a large degree on the parameterization of double cross-validation. While the parameters for the inner loop of double cross-validation mainly influence bias and variance of the resulting models, the parameters for the outer loop mainly influence the variability of the resulting prediction error estimate.ConclusionsDouble cross-validation reliably and unbiasedly estimates prediction errors under model uncertainty for regression models. As compared to a single test set, double cross-validation provided a more realistic picture of model quality and should be preferred over a single test set.Electronic supplementary materialThe online version of this article (doi:10.1186/s13321-014-0047-1) contains supplementary material, which is available to authorized users.

The Prediction Error of Bornhuetter/Ferguson

Together with the Chain Ladder (CL) method, the Bornhuetter/Ferguson (BF) method is one of the most popular claims reserving methods. Whereas a formula for the prediction error of the CL method has been published already in 1993, there is still nothing equivalent available for the BF method. On the basis of the BF reserve formula, this paper develops a stochastic model for the BF method. From this model, a formula for the prediction error of the BF reserve estimate is derived.Moreover, the model gives important advice on how to estimate the parameters for the BF reserve formula. E.g. it turns out that the appropriate BF development pattern is different from the CL pattern. This is a nice add-on as it makes BF to a standalone reserving method which is fully independent from CL. The other parameter required for the BF reserve is the well-known initial estimate for the ultimate claims amount. Here the stochastic model clearly shows what has to be meant with ‘initial’.In order to apply the formula for the prediction error, the actuary must assess his uncertainty about both sets of parameters, about the development pattern and about the initial ultimate claims estimates. But for both, much guidance can be drawn from the estimates itself and from the run-off data given. Finally, a numerical example shows how the resulting prediction error compares to the one of the CL method.

The Prediction Error of Bornhuetter/Ferguson

Together with the Chain Ladder (CL) method, the Bornhuetter/Ferguson (BF) method is one of the most popular claims reserving methods. Whereas a formula for the prediction error of the CL method has been published already in 1993, there is still nothing equivalent available for the BF method. On the basis of the BF reserve formula, this paper develops a stochastic model for the BF method. From this model, a formula for the prediction error of the BF reserve estimate is derived.Moreover, the model gives important advice on how to estimate the parameters for the BF reserve formula. E.g. it turns out that the appropriate BF development pattern is different from the CL pattern. This is a nice add-on as it makes BF to a standalone reserving method which is fully independent from CL. The other parameter required for the BF reserve is the well-known initial estimate for the ultimate claims amount. Here the stochastic model clearly shows what has to be meant with ‘initial’.In order to apply the formula for the prediction error, the actuary must assess his uncertainty about both sets of parameters, about the development pattern and about the initial ultimate claims estimates. But for both, much guidance can be drawn from the estimates itself and from the run-off data given. Finally, a numerical example shows how the resulting prediction error compares to the one of the CL method.

On‐line assessment of prediction risk for wind power production forecasts

AbstractThe article introduces a new methodology for assessing on‐line the prediction risk of short‐term wind power forecasts. The first stage of this methodology consists in computing confidence intervals with a confidence level defined by the end‐user. The resampling approach is used, which, in contrast to existing methods for wind forecasting, does not need to make a restrictive hypothesis on the distribution of the errors. To account for the non‐linearity of the power curve and the cut‐off effect, the errors are classified using appropriate fuzzy sets. The confidence intervals are then fine‐tuned to reduce their width in the case of stable weather conditions. For this purpose an appropriate index, called the ‘meteo‐risk index’ (MRI), is defined reflecting the spread of the available numerical weather predictions. A linear relation between that index and the resulting prediction error is shown. The second part of the methodology is to use the MRI itself as a preventive on‐line tool to derive signals for the operator on the meteorological risk, i.e. the probabilities of the occurrence of high prediction errors depending on the weather stability. Evaluation results of this methodology over a 1 year period on the case study of Ireland are given, where the output of several wind farms is predicted using a dynamic fuzzy neural network‐based model. The proposed methodology is generic and can be applied to all kinds of wind power prediction models. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Structural health monitoring of offshore structures using ambient excitation

This work explores the role of ambient excitation and empirical modeling in detecting damage in offshore structures. Two simple models of an articulated offshore structure are excited with the output of a stochastic process conforming to the ambient Pierson–Moskowitz wave distribution. Because ambient excitation (hence the resulting response) is typically modeled as a narrow-band process, the resulting response is ‘practically’ low-dimensional allowing for phase space methods of analysis to be applied. Based on the structure's response to this excitation empirical phase space models are constructed. Structural response data from an undamaged structure are used to make predictions on the response of a damaged structure. As damage is incurred, the resulting prediction error increases. The result is a data-driven approach which can successfully detect a stiffness degradation in model offshore structures. This technique is demonstrated effective for diagnosing the presence, and in one of the examples the magnitude, of the degradation.

Information transfer and nontrivial collective behavior in chaotic coupled map networks.

The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local unit possesses about the collective dynamics. Applications to locally and globally coupled map systems are considered. The prediction error exhibits phase transitions at critical values of the coupling for the onset of ordered collective behavior in these networks. This information measure may be used as an order parameter for the characterization of complex behavior in extended chaotic systems.

Lossless image compression with a codebook of block scans

When applying predictive compression on image data there is an implicit assumption that the image is scanned in a particular order. Clearly, depending on the image, a different scanning order may give better compression. In earlier work, we had defined the notion of a prediction tree (or scan) which defines a scanning order for an image. An image can be decorrelated by taking differences among adjacent pixels along any traversal of a scan. Given an image, an optimal scan that minimizes the absolute sum of the differences encountered can be computed efficiently. However, the number of bits required to encode an optimal scan turns out to be prohibitive for most applications. In this paper we present a prediction scheme that partitions an image into blocks and for each block selects a scan from a codebook of scans such that the resulting prediction error is minimized. Techniques based on clustering are developed for the design of a codebook of scans. Design of both semiadaptive and adaptive codebooks is considered. We also combine the new prediction scheme with an effective error modeling scheme. Implementation results are then given, which compare very favorably with the JPEG lossless compression standard. >