Multivariate statistic methods for predicting electricity consumption of Beijing

Prediction models based on multivariate statistical methods and their applications for predicting railway freight volume

The objective of this study was to compare the predictions of the protein contents and hardness values by partial least squares regression (PLSR) and principal components regression (PCR) models for bulk samples of Canadian wheat, which were obtained from different locations and crop years. Wheat samples of Canada Western Red Spring (CWRS), Canada Western Hard White Spring (CWHWS), Canada Western Soft White Spring (CWSWS), and Canada Prairie Spring Red (CPSR) classes were obtained from nearby agricultural farms in the main wheat growing locations in the Provinces of Alberta, Saskatchewan, and Manitoba from 2007, 2008, and 2009 crop years. Wheat samples were conditioned to moisture levels of 13, 16, and 19 % (wet basis) and pooled together for developing the regression models. A database of the near-infrared (NIR) hyperspectral image cubes of bulk samples of wheat classes was created in the wavelength region of 960–1,700 nm with 10 nm intervals. Reference protein contents and hardness values were determined using the Dumatherm method and single kernel characterization system (SKCS), respectively. A tenfold cross-validation was used for the ten-factor partial least squares regression (PLSR) and principal components regression (PCR) models for prediction purposes. Prediction performances of regression models were assessed by calculating the estimated mean square errors of prediction (MSEP), standard error of cross-validation (SECV), and correlation coefficient (r). Using the full data set in the protein prediction study, the ten-component PLSR model gave 1.76, 1.33, and 0.68 for the estimated MSEP, SECV, and r, respectively, which were better than the results for the ten-component PCR model (2.02, 1.42, and 0.62, respectively). For the hardness prediction, the estimated MSEP, SECV, and r values were 147.7, 12.15, and 0.82, respectively, for the ten-component PLSR model using the full data set. The PLSR models prediction performances outperformed the PCR models for predicting protein contents and hardness of wheat.

Recycled polypropylene (rPP) often contains a small amount of polyethylene (PE). Since polypropylene (PP) and PE are incompatible, the presence of PE compromises the performance of rPP materials and needs to be closely monitored. In our previous work, Raman and near-infrared (NIR) spectrometries were evaluated to monitor PE content in rPP with partial least square regression (PLSR) modeling. The NIR spectrometry exhibited a wider application range, but the accuracy of the prediction models might be further improved. In the current work, a different modeling method, principal component regression (PCR) was employed to analyze PE content in rPP with NIR spectrometry. Spectrum pretreatment methods, including multivariate scatter correction (MSC), standard normal variate transformation (SNV), smoothing, and first derivative, were investigated to improve the NIR spectrum quality. Forward and backward interval methods were used to optimize spectral range selection. The outcomes were compared with our previous PLSR modeling results. The highest accuracy in independent validation was achieved by a PCR model with an R 2 of 0.9991 and a root-mean-square error of prediction (RMSEP) of 0.1596 PE%. On the other hand, a PLSR model achieved the lowest RMSEP of 0.9712 PE% for a non-colored post-consumer rPP sample. The PCR models might be sensitive to interference and more suitable for post-industrial materials, which have a simpler chemical composition. The PLSR models might have better stability and be more suitable for complicated post-consumer samples. Both the PCR and PLSR models were successfully applied to a gray commercial rPP sample.

Among many statistical methods for linear models with the multicollinearity problem, partial least squares regression (PLSR) has become, in recent years, increasingly popular and, very often, the best choice. However, while dealing with the predicting problem from automobile market, we noticed that the results from PLSR appear unstable though it is still the best among some standard statistical methods. This unstable feature is likely due to the impact of the information contained in explanatory variables that is irrelevant to the response variable. Based on the algorithm of PLSR, this paper introduces a new method, modified partial least squares regression (MPLSR), to emphasize the impact of the relevant information of explanatory variables on the response variable. With the MPLSR method, satisfactory predicting results are obtained in the above practical problem. The performance of MPLSR, PLSR and some standard statistical methods are compared by a set of Monte Carlo experiments. This paper shows that the MPLSR is the most stable and accurate method, especially when the ratio of the number of observation and the number of explanatory variables is low.

This study aimed to compare stepwise multiple linear regression (SMLR), partial least squares regression (PLSR) and support vector machine regression (SVMR) for estimating soil total nitrogen (TN) contents with laboratory visible/near-infrared reflectance (Vis/NIR) of selected coarse and heterogeneous soils. Moreover, the effects of the first (1st) vs. second (2nd) derivative of spectral reflectance and the importance wavelengths were explored. The TN contents and the Vis/NIR were measured in the laboratory. Several methods were employed for Vis/NIR data pre-processing. The SMLR, PLSR and SVMR models were calibrated and validated using independent datasets. Results showed that the SVMR and the PLSR models had similar performances, and better performances than the SMLR. The spectral bands near 1450, 1850, 2250, 2330 and 2430 nm in the PLSR model were important wavelengths. In addition, the 1st derivative was more appropriate than the 2nd derivative for spectral data pre-processing. PLSR was the most suitable method for estimating TN contents in this study. SVMR may be a promising technique, and its potential needs to be further explored. Moreover, the future studies using outdoor and airborne/satellite hyperspectral data for estimating TN content are necessary for testing the findings.

Assessment of the human albumin in acid precipitation process using NIRS and multi-variable selection methods combined with SPA

Weather index insurance is a relatively new alternative to traditional agricultural insurance such as individual yield-based crop insurance. It is still mostly at the experimental stage, rather than in widespread use like traditional crop insurance. A major challenge for weather insurance is basis risk, where the loss estimated by the index differs from the actual loss, and this is generally believed to be the main limitation in the use of weather index insurance for crops. Variable basis risk is an important type of basis risk that occurs when there are incorrect variables or missing variables for the design of the weather index. In agriculture, there is a relatively small sample size of yields, and therefore, as the number of considered weather variables increases, the problems of limited degrees of freedom for predictive models must be overcome. The objective of this article is to demonstrate two possible approaches that could be used to construct a multivariable weather index to reduce variable basis risk. Forage insurance is used as an example, and a main focus of the research is on reducing the dimensionality of the predictive model and resolving the problem of multicollinearity among weather variables. The research uses daily weather information and county-level forage yield data from Ontario, Canada. Two multivariable indices are developed based on principal component regression (PCR) and partial least squares regression (PLSR) methods, and they are evaluated against a single-variable benchmark index based on cumulative precipitation (SVCP) using several basis risk metrics. The results show that both the PCR and PLSR models are superior compared to the single-variable weather index based on cumulative rainfall (SVCR) index and can be used to achieve the objective of reducing the dimensionality of the weather variable matrix and addressing the issue of multicollinearity. Though the PLSR indices perform better than the PCR and SVCR indices in terms of average value of basis risk (),(rom) the PCR method produces a smaller percentage of mismatch, suggesting that the PCR method may be superior in correctly detecting when the insurance payment should be triggered. The methods demonstrated in this article will assist in the development of weather index–based crop insurance.

Carbohydrate levels are important regulators of the growth and yield of tree crops. Current methods for measuring foliar carbohydrate concentrations are time consuming and laborious, but rapid imaging technologies have emerged with the potential to improve the effectiveness of tree nutrient management. Carbohydrate concentrations were predicted using hyperspectral imaging (400–1000 nm) of leaves of the evergreen tree crops, avocado, and macadamia. Models were developed using partial least squares regression (PLSR) and artificial neural network (ANN) algorithms to predict carbohydrate concentrations. PLSR models had R2 values of 0.51, 0.82, 0.86, and 0.85, and ANN models had R2 values of 0.83, 0.83, 0.78, and 0.86, in predicting starch, sucrose, glucose, and fructose concentrations, respectively, in avocado leaves. PLSR models had R2 values of 0.60, 0.64, 0.91, and 0.95, and ANN models had R2 values of 0.67, 0.82, 0.98, and 0.98, in predicting the same concentrations, respectively, in macadamia leaves. ANN only outperformed PLSR when predicting starch concentrations in avocado leaves and sucrose concentrations in macadamia leaves. Performance differences were possibly associated with nonlinear relationships between carbohydrate concentrations and reflectance values. This study demonstrates that PLSR and ANN models perform well in predicting carbohydrate concentrations in evergreen tree-crop leaves.

Motivated by recent research on two-phase flow void fraction measurement, this paper presents a study on void fraction measurements of a lubricant air-oil two-phase flow using a near infrared (NIR) optical-fiber spectrometer associated with partial least squares (PLS) regression models. To overcome the measurement inaccuracy due to interface scattering, this study used PLS regression models to analyse the spectrum of air-oil two-phase flow. First, an NIR optical-fiber spectrometer experimental system was developed. Second, a flow regime analysis was conducted for the bubble flow transition inside the experimental system. Finally, the PLS regression model validations, the void fraction measurement accuracies, and the uncertainties of the experimental system were evaluated and discussed, and the different PLS regression models were compared in detail. The results indicate that the NIR optical-fiber spectrometer combined with the PLS regression model can achieve void fraction measurements of lubricants in air-oil two-phase flow, with a maximum squared correlation coefficient (R 2) of 0.981, a minimum Type A uncertainty of 0.039% and a minimum expanded uncertainty of 0.077%.

Increasing the accuracy of atmospheric ammonia concentrations calculated from Open-Path Fourier transform infrared spectra using partial least squares model by scanning and removing interference spectral data

<p>Soil properties could be assessed with reflectance spectroscopy (soil spectroscopy, SS) in vis-NIR region (400-2500 nm) through absorption features found in soil spectra. A high spectral resolution (up to 1 nm) drives to high dimensional and multicollinear data. This issue is usually addressed prior to modelling with feature extraction methods such as Principal Component Analysis, or embedded methods such as Partial Least Squares Regression (PLSR). Feature Selection (FS) wrapper methods are promising dimensionality reduction approaches barely used in SS. The objective of this study was two-fold: i) evaluate the performance of FS wrapper methods built from Random Forest (RF) algorithm to predict soil organic matter (SOM), clay and carbonates using laboratory spectroscopy, ii) test the performance of FS methods for dimensionality reduction in SS. The reflectance of 100 soil samples from Sierra de las Nieves National Park (Spain), was measured under laboratory conditions using an ASD FieldSpec Pro JR. A spectral preprocessing method, Continumm Removal (CR), was applied to raw spectra. The RF wrapper considered two different feature searching approaches: Sequential Forward Selection (SFS) and Sequential Flotant Forward Selection (SFFS). The performance of RF with FS (RF-FS) was compared to that of Partial Least Squares Regression (PLSR) and RF (without FS). Models were evaluated with R-squared, root mean squared error (RMSE) and ratio of prediction to deviation (RPD).</p><p>RF-FS models outperformed PLSR and RF models for the three SAP. RF-FS best models had a RPD of 2.19 for SOM, 1.64 for carbonates and 1.52 for clay, whereas PLSR models had RPD values of 1.59, 1.22 and 1.3, and RF 1.38, 1.23 and 1.23 for SOM, carbonates, and clay, respectively. Therefore, FS was useful in obtaining models with improved accuracy by reducing redundant features and avoiding multicollinearity (Hughes effect). The application of FS wrapper methods reduced the number of features in the RF-FS models to less than 1% of the starting features. Features were selected across all spectra from SOM and clay, and around 900, 1900 and 2350 nm for carbonates. This research, thus, shows an alternative to different feature extraction approaches for modelling soil properties based on FS methods and machine learning.</p>

Monitoring of crops during their growth period is essential to increase the profitability of production and reduce costs. Unmanned aerial vehicles (UAVs) have been introduced as an appropriate tool in precision farming, due to their affordability and high-spatial resolution data. The potential of plant height and vegetation indices derived from UAV-based RGB imagery at 12-leaf growth stage (V12) is investigated for prediction of corn forage yield. Using the structure from motion techniques, the crop height model (CHM) was created by subtracting crop surface model from digital elevation model. Next, by evaluating the CHM using ground measurements of plant height, it was shown that UAV imagery provides high capability in modeling the plant height ( R 2 = 0.85). Pearson’s correlation coefficient ( R ) between variables showed that the plant height had the highest correlation with forage yield ( R = 0.84). Furthermore, among the vegetation indices, visible atmospherically resistant index with R = 0.77, normalized difference index with R = 0.75, and excess red with R = 0.74 were better than other indices. Finally, the partial least squares regression (PLSR) model was constructed using plant height and vegetation indices to predict forage yield. The beta regression coefficients of the PLSR model were used to identify the most relevant predictors, and the final PLSR model was rebuilt with relevant predictors. The PLSR analysis confirmed that the plant height was the most important predictor, although integrating the vegetation indices in the PLSR model has slightly improved the prediction model ( R 2 = 0.74, RMSE = 0.316 kg / m2, and relative RMSE = 12.39 % ), compared to the model that used only plant height ( R 2 = 0.702, RMSE = 0.339 kg / m2, and relative RMSE = 13.29 % ). Overall, these results indicate that the UAV-based images are efficient and cost-effective data to predict corn forage yield as well as plant height modeling.

Regional regression models can be employed to estimate hydrologic statistics at ungauged river sites. The increased availability of watershed characteristics and the use of GIS-based methods to process this data have created situations where a large number of highly correlated watershed characteristics are available as potential model explanatory variables. The use of ordinary least squares (OLS) regression procedures with highly correlated variables can produce multicollinearity, creating highly sensitive parameter estimators with inflated variances, and improper model selection. A Monte Carlo simulation is developed to compare four techniques for handling multicollinearity: OLS, OLS with Variance Inflation Factor screening (VIF), principal component regression (PCR), and partial least squares regression (PLS). Results show the impact of multicollinearity is magnified at smaller samples sizes, higher correlations, and larger model error variances. Although PCR and PLS yield parameter estimators with reduced variances, there is no improvement in model prediction compared to OLS and VIF. Using VIF for screening variables produced small improvements in model predictions. The use of OLS appears warranted as the complexity of using biased regression techniques to address multicollinearity does little to improve model predictions.

Estimating economic benefit of sugar beet based on three-dimensional computer vision: a case study in Inner Mongolia, China

Fractional-order Savitzky–Golay filter for pre-treatment of on-line vis–NIR spectra to predict phosphorus in soil