Conventional PLS Research Articles

Quantitative analysis of dried serum FTIR spectra based on correlation Analysis-Interval random Frog-Partial least squares

Serum biochemical markers are widely used in clinical practice but often require expensive, specific reagents, complex instruments, and prolonged result waiting times. Infrared spectroscopy offers multiple advantages for serum analysis, such as reagent-free testing and the ability to quickly and directly measure multiple parameters simultaneously. This study collected serum samples from 66 healthy subjects to explore the relationship between dried serum infrared spectra and biochemical parameters, and to investigate the feasibility of simultaneously quantifying nine major serum components using dried serum infrared spectra. Initially, correlation analysis was conducted between spectral data and biochemical parameters, and the correlation spectral bands of glucose, protein and lipid were determined according to the correlation results. Subsequently, the interval random frog (IRF) algorithm was utilized to select the optimal characteristic wavenumbers of the correlated spectral bands, extracting the most informative spectral variables and constructing partial least squares (PLS) quantitative models. This method successfully achieved rapid and accurate quantification of nine major components in serum, including glucose, total protein, albumin, apolipoprotein A1, apolipoprotein B, total cholesterol, triglycerides, low-density lipoprotein cholesterol, and high-density lipoprotein cholesterol. The experimental results showed that the correlation coefficient (Rp) range in the test set was 0.8892–0.9941. Among them, the quantification of total cholesterol yielded the highest Rp, corresponding to a root mean square error (RMSEP) of 7.2425 mg/dL in the test set, while the quantification of glucose yielded the lowest Rp, with an associated RMSEP of 2.3683 mg/dL. The Correlation Analysis (CA)-IRF-PLS method developed in this study outperformed the conventional PLS method, the direct use of the successive projection algorithm (SPA)-PLS quantitative method and other reported quantitative techniques, providing a novel approach for the real-time determination of clinical parameters in serum

PLS-based hellinger distance method for fault detection in chemical engineering systems

Fault detection is vital in chemical engineering systems to maintain operational efficiency, product quality, and safety through timely identification and correction of deviations from expected behavior. Although partial least squares (PLS) has proven effective in monitoring due to its ability to handle highly correlated variables, traditional detection metrics of PLS may fail to identify small abnormal changes as they rely solely on recent observations. This paper integrates PLS modeling framework with Hellinger Distance (HD)-based fault detection index to overcome the limitations of conventional detection metrics. The utilization of HD is motivated by its sensitivity to quantifying any dissimilarity between distributions, which makes it well-suited for detecting small deviations in process behavior. The HD-based index will be computed between the residuals obtained from the model in the offline stage and the online stage. The HD metric involves careful inspection and comparison of the residuals, which enables it to capture the sensitive details in the data, thus, enhancing the detection of faults. For increased flexibility, kernel density estimation is employed to establish the reference threshold of the PLS-HD approach. The performance of this approach will be evaluated using data from simulated Continuous Stirred-Tank Heater (CSTH) and Continuous Stirred-Tank Reactor (CSTR) processes, by considering various fault types such as bias, freezing, and sensor drift faults. The results demonstrate the superior performance of the proposed PLS-HD approach compared to conventional PLS monitoring methods.

A self-adaptive model for sensing total phosphorus in natural water bodies using Fourier transform mid-infrared attenuated total reflectance spectroscopy

As the most economically developed area in China, the environmental water quality of Guangdong-Hong Kong-Macao Greater Bay Area has received extensive attention, and the spatial variations of total phosphorus (TP) in the Greater Bay were significant, conventional laboratory analysis is difficult to meet the requirements of TP monitoring due to time and cost consuming, and Fourier transform infrared attenuated total reflectance spectroscopy (FTIR-ATR) technology, combined with the self-adaptive partial least squares (SA-PLS) model, was used to determine the TP concentration. The results showed that P-O vibrations were observed in the wavenumber range of 1200–900 cm−1, and prediction models were established by using this range. For the conventional partial least squares (PLS) model, the R2, RMSE and RPD were 0.817, 0.022 mg L−1 and 2.335, respectively, while for the SA-PLS model the prediction was improved with the values of 0.965, 0.010 mg L−1, 5.296, respectively, and the SA-PLS mode prediction was satisfied when the TP content in water was more than 0.05 mg L−1. It was found that the TP determination was interfered by sulfate, when the sulfate content was < 100 mg L−1, both SA-PLS and the conventional PLS model could be used for quantitative analysis of TP; when sulfate content was > 100 mg L−1, PLS model could not be used while the SA-PLS model still achieved an excellent prediction. Therefore, FTIR-ATR combined with SA-PLS model can rapidly determine TP in water, providing an alternative strategy for monitoring TP in natural water bodies.

Assessing Fermentation Broth Quality of Pineapple Vinegar Production with a Near-Infrared Fiber-Optic Probe Coupled with Stability Competitive Adaptive Reweighted Sampling.

In this study, the performance of a near-infrared (NIR) fiber-optic probe coupled with stability competitive adaptive reweighted sampling (SCARS) was investigated for the analysis of acetic acid, ethanol, total soluble solids, caffeic acid, gallic acid, and tannic acid in the broth of pineapple vinegar during fermentation. The NIR spectra of the broth samples in the region of 11,536-3956 cm-1 were collected during vinegar fermentation promoted by Acetobacter aceti. This continuous biological process led to changes in the concentrations of all analytes studied. SCARS provided optimized and stabilized NIR spectral variables for the construction of a partial least squares (PLS) model for each analyte using a small number of optimal variables (under 88 variables). The SCARS-PLS model outperformed the conventional PLS model, and achieved excellent accuracy in accordance with ISO 12099:2017 for the four prediction models of acetic acid, ethanol, caffeic acid, and gallic acid, with root-mean-square error of prediction values of 0.137%, 0.178%, 0.637 μg/mL and 0.640 μg/mL, respectively. In contrast, only an acetic acid content prediction model constructed via the conventional PLS method and using the whole spectral region (949 variables) could pass with acceptable accuracy. These results indicate that the NIR optical probe coupled with SCARS is an appropriate method for the continuous monitoring of multianalytes during vinegar fermentation, particularly acetic acid and ethanol contents, which are indicators of the finished fermentation of pineapple vinegar.

Semi-supervised adaptive PLS soft-sensor with PCA-based drift correction method for online valuation of NOx emission in industrial water-tube boiler

The use of soft sensors for the prediction of Nitric Oxides (NOx) emissions to meet quality regulations has become increasingly attractive from the economic point of view. However, implementation of the standard adaptive PLS soft sensors such as the conventional adaptive block-wise recursive PLS (BW-RPLS) and just in time block-wise recursive PLS (JIT-BW-RPLS) to industrial boilers that are not equipped with an in-line hardware analyzer is impractical. This is due to the limited ability of the adaptive soft sensor to recalibrate without feedback from the actual NOx measurement. Hence, in this paper, a PCA-based drift correction method is proposed for an industrial water-tube boiler in which an in-line hardware analyzer is unavailable. The proposed drift correction factor is used to detect when drift happens and subsequently estimate the corrected NOx value to be used in a semi-supervised manner by the conventional BW-RPLS and JIT-BW-RPLS. Both the proposed semi-supervised BW-RPLS and JIT-BW-RPLS with PCA-based drift correction and estimation methods have displayed an additional 10–20% improvement in prediction accuracy relative to the performance of the conventional supervised BW-RPLS method and 50% prediction improvement compared to offline PLS model, during significant drifts in the industrial boiler operation. All the case studies have been performed using actual industrial data of a water-tube boiler.

Detection of Carbon Content from Pulverized Coal Using LIBS Coupled with DSC-PLS Method

The dust from pulverized coal weakens the acquired signal and increases the analysis difficulty for the quantitative analysis of the carbon content of pulverized coal when using laser-induced breakdown spectroscopy (LIBS). Moreover, there is a serious matrix effect and a self-absorption phenomenon. To improve the analysis accuracy, the DSC-PLS (double spectral correction-partial-least-squares) method was proposed to predict the carbon content of pulverized coal. Initially, the LIBS signal was corrected twice using P-operation-assisted adaptive iterative-weighted penalized-least-squares (P-airPLS), plasma temperature compensation, and spectral normalization algorithms. The goodness of fit of the carbon element was improved from nonlinearity to above 0.948. The modified signal was then used to establish DCS-PLS models for predicting unknown samples. In comparison to the conventional PLS model, the DSC-PLS method proposed in this paper significantly improves the ability to predict carbon content. The prediction error of the developed method was dropped from an average of 4.66% to about 0.41%, with the goodness of fit R2 of around 0.991.

Applying convolutional neural networks (CNN) for end-to-end soil analysis based on laser-induced breakdown spectroscopy (LIBS) with less spectral preprocessing

The high variation of raw laser-induced breakdown spectroscopy (LIBS) caused by soil heterogeneity seriously reduces the accuracy and stability of the spectral analysis. Therefore, the conventional chemometrics for spectral analysis requires seeking an appropriate spectral preprocessing by a trial-and-error method before modeling, which resulted in a mutable performance. To settle this problem, the convolutional neural network (CNN), a type of deep learning approach with the advantage of end-to-end, was applied to predict soil type and soil properties based on the non-preprocessed LIBS spectra. The results indicated, when compared to conventional partial least squares (PLS), that the CNN models presented equal classification accuracy but they decreased the root mean square error in the validation set (RMSEV) by 1.48%, 4.97%, 9.56%, 10.05%, and 2.90% for pH, soil organic matter (SOM), total nitrogen (TN), total phosphorus (TP), total potassium (TK), respectively. In addition, the CNN models performed better in preventing overfitting than the conventional PLS combined with various spectral preprocessing approaches. The multi-task of CNN models also further improved the prediction of TN due to its capacity to learn inherent structures from spectra. The sensitivity analysis of spectral variables revealed that the CNN model with the Inception module discovered both the local and high abstracted features compared with other CNN models. In conclusion, the CNN architectures showed potential to end-to-end deal with raw soil LIBS spectra.

A novel dynamic nonlinear partial least squares based on the cascade structure

AbstractFor the collinearity problem of input variables in actual industrial process modeling, a novel dynamic nonlinear partial least squares (PLS) approach is presented to solve this problem. In the proposed method, a novel cascade structure which is composed of an autoregressive exogenous model and a radial basis function neural network is introduced as the inner model of the conventional PLS method, so that the newly established PLS method has both dynamic and nonlinear characteristics. In this improvement, an external model for extracting the latent variables of input and output is established through the original PLS model, which eliminates the collinearity between original dependent variables, and then the aforementioned cascade framework is employed to describe the dynamic and nonlinear relationships between the input and output score variables. Furthermore, in order to estimate the unknown parameters of the established dynamic nonlinear inner model, a stochastic gradient algorithm and a forgetting factor stochastic gradient algorithm are presented. Additionally, a simple cross validation method is used to determine the orders of the inner model. Finally, a numerical simulation example and an application example are given to demonstrate the effectiveness of the proposed approach.

Performance of three handheld NIR spectrometers for predicting grass silage quality

Description of the subject. Feed is the main variable cost in dairy farming. More efficient use of forage resources is one way to reduce production costs. Improving forage resource efficiency can start with a better assessment of the dry matter content and nutritional value of forages. Currently, analytical process time is often long and analyses are not repeatable while the quality of the fodder changes over time. Being able to analyze forages directly on-farm would make it possible to adapt the animal diet according to forage variability, in order to improve the profitability of the farm. Objectives. To propose in situ rapid analysis solutions to better characterize dry matter content and the chemical composition of fodder for assessing its feeding value. Method. The performance of three recently developed spectroscopic handheld devices, namely the Viavi’s MicroNIR 1700, the Ocean Insight’s FlameNIR and the Malvern Panalytical’s ASD FieldSpec 4, are evaluated to predict dry matter content and the chemical composition of fresh and unground grass silage in the framework of precision feeding and compared to the reference benchtop Foss’s XDS instrument. The conventional global PLS and local PLS are used as multivariate calibration methods. Results. The assessed handheld devices allow the dairy farmer to obtain a relatively precise quantitative prediction of the dry matter and crude fiber content (2.5% and 1.8% respectively on average, in terms of ratios between the local PLS error on fresh forage and the reference method error) in order to adapt the livestock diet. Crude protein, even if the prediction accuracy is lower (6.4%), is still well predicted. Higher errors are obtained for ash (9.2%), crude neutral (6.8%) and acid detergent fiber (6.9%). Conclusions. The studied devices should allow the dairy farmer to obtain a relatively precise quantitative prediction of those quality parameters in order to directly adapt the quantity of forage distributed to the animals. Performances could probably be improved by including more samples/spectra into the databases.

An effective and rapid approach to predict molecular composition of naphtha based on raw NIR spectra

Molecular management has become an important trend in petroleum refining, which relies on the information of petroleum composition. In this contribution, a simple and effective analytical approach is proposed for the rapid prediction of the more detailed molecular composition of naphtha samples based on raw near infrared (NIR) spectroscopy for the first time. The 101 samples of reformed naphtha were collected and determined, and Tchebichef curve moments (TCMs) were calculated directly from the raw NIR spectra and employed to establish linear models for the quantitative analysis of 26 hydrocarbons (PIONA) with different carbon numbers and components. For the obtained models, the average of RMSE of prediction is 0.10. According to the ratio of performance to deviation (SD/RMSEp), the 23 obtained TCM models achieved “excellent” predictive quality. By means of the conventional PLS method with spectral pretreatment, there were only 15 models with “excellent” predictive quality, which indicated that TCM method without any spectral preprocessing could provide more simple, accurate and reliable analytical results, and meet the requirements of fast assessment. This work suggests the feasibility of the proposed method for the rapid and non-destructive analysis of molecular composition in naphtha, which is significant in the determination of refinery operating conditions.

A state-based probabilistic method for decoding hand position during movement from ECoG signals in non-human primate

Objective. In this study, we proposed a state-based probabilistic method for decoding hand positions during unilateral and bilateral movements using the ECoG signals recorded from the brain of Rhesus monkey. Approach. A customized electrode array was implanted subdurally in the right hemisphere of the brain covering from the primary motor cortex to the frontal cortex. Three different experimental paradigms were considered: ipsilateral, contralateral, and bilateral movements. During unilateral movement, the monkey was trained to get food with one hand, while during bilateral movement, the monkey used its left and right hands alternately to get food. To estimate the hand positions, a state-based probabilistic method was introduced which was based on the conditional probability of the hand movement state (i.e. idle, right hand movement, and left hand movement) and the conditional expectation of the hand position for each state. Moreover, a hybrid feature extraction method based on linear discriminant analysis and partial least squares (PLS) was introduced. Main results. The proposed method could successfully decode the hand positions during ipsilateral, contralateral, and bilateral movements and significantly improved the decoding performance compared to the conventional Kalman and PLS regression methods . The proposed hybrid feature extraction method was found to outperform both the PLS and PCA methods . Investigating the kinematic information of each frequency band shows that more informative frequency bands were (15–30 Hz) and (50–100 Hz) for ipsilateral and and (100–200 Hz) for contralateral movements. It is observed that ipsilateral movement was decoded better than contralateral movement for (5–15 Hz) and bands, while contralateral movements was decoded better for (30–200 Hz) and hfECoG (200–400 Hz) bands. Significance. Accurate decoding the bilateral movement using the ECoG recorded from one brain hemisphere is an important issue toward real-life applications of the brain-machine interface technologies.

NIR spectroscopy fruit quality detection algorithm based on the least angle regression model

To enhance the effectiveness and precision of fruit internal quality detection, the determination model of internal quality of fruit based on the least angle regression (LAR) is proposed. Compared with existing nonlinear and linear models, i.e., least squares support vector machines (LS-SVM) and partial least squares (PLS) regression (the proposed LAR model generates the best prediction results and performs better than conventional PLS. In an aspect of computational complexity, LAR and PLS are better than LS-SVM model. In aspect of interpretability, the proposed LAR is superior to the PLS model. Although the precision rate of LAR is worse than LS-SVM, it has advantages for model realisation, computation complexity, and interpretability over LS-SVM. Thus the proposed LAR model can be applied effectively in the determination of the internal quality of fruit-based on NIR (Near-infrared) spectroscopy.

In-situ FT-IR quantitative analysis of amine concentrations and CO2 loading amount in solvent mixtures for CO2 capture

An in-situ FT-IR based quantitative analysis model has been designed to track the internal state of solvent mixtures in a CO2 capture process. This approach is much faster and easier than using GC or NMR, but conventional linear multivariate analysis is not suitable due to the poor resolution of FT-IR. The conventional PLS regression also exhibits bad performance due to its inability to reflect the nonlinear behavior like peak shift, which is a common characteristic of the systems involving reactions. This paper proposes the artificial neural networks (ANNs) as an alternative nonlinear regression method. Two feature extraction methods, PCA and POD, are applied to reduce the redundancy and dimension of the input data as a preprocessing step. The neural network approach displayed higher accuracies in cross-validation and also in in-situ experiments compared to the PLS regression in a performance test involving three models. In particular, the POD-ANN method showed outstanding results with under 5 % relative error. This model can fulfill the function of an online monitoring system for CO2 capture processes and can provide information on water and solvent loss from evaporation or degradation. Furthermore, it can be utilized for control and fault detection techniques to maintain long-term operational stability of the system.

Energy Efficiency On Smart Street Lighting Using Raspberry Pi Based On Scada And Internet Of Things (IoT)

One of the criteria of a city categorized as Smart city is the ability to manage infrastructure, property and human resources intelligently. A reliable, sustainable and customable electric energy source is an absolute requirement for a smart city. However, the management of electrical energy must be economically so that it does not burden the local government budget. From a number of infrastructures that consume a lot of electrical energy under the authority of the responsibility of the local government, namely Public Street Lighting (PSL). Lighting from PLS that emits too much light when unnecessary is useless. At present, conventional PLS systems are synonymous with energy waste. Monitors and controls only do locally without having the ability to monitor and control remotely so that if there is damage or theft, it is slow to handle. The solution is to build a smart PSL system and its management. This paper presents a real-world proven solution that relies on aRaspberry Pi, SCADA, and Internet of Things (IoT). This system provide an energy efficiency. Smart PSL will work intelligently in accordance with their environmental conditions. Lighting and illumination are arranged based on the presence of people and vehicles so that they can avoid over lighting and glare. SCADA and IoT technologies are used for work process monitoring systems and data viewers that are carried out continuously and in real time. The result is the smart PLS mode is 43% more efficient than conventional PLS modes.

Robust Generalized Fuzzy Systems Training From High-Dimensional Time-Series Data Using Local Structure Preserving PLS

Establishing fuzzy models from time-series data with predictive capabilities for numerical targets typically requires dimension reduction techniques to overcome the severe curse of dimensionality effects. Linear projection methods are promising candidates in this context as they—unlike nonlinear dimension reduction techniques—preserve interpretability of the resulting models. However, linear projections do not reveal the inherent (nonlinear, local) cluster structure of the data and are thus not ideally suited for the identification of fuzzy rule bases. To overcome this limitation, in this article, we present a new fuzzy modeling approach that combines generalized fuzzy systems modeling with a local structure preserving variant of partial least squares (PLS). In contrast to ordinary PLS, our approach maps a weighted (adjacency) graph on the directions associated with high covariance with the response in order to emphasize local data structures when constructing the latent variable (LV) space. This operates into the direction from which the (training of the) fuzzy model benefits, as therein local regions are represented by submodels in form of generalized Takagi-Sugeno (TS) fuzzy rules. The local structure preserving LV space is obtained by solving a new penalized objective function, which assures global optimality of the solutions by virtue of the specific properties of the Laplacian matrix. Local regions are characterized in two ways: through nearest neighbor points (assuming fixed local region sizes) and through density regions identified by clustering (achieving variable local region sizes). To establish a robust time-series-based forecast model, the training of a generalized TS fuzzy model is conducted in the LV space with reduced dimensionality. It is realized by an iterative robust version of Gen-Smart-EFS , allowing multiple passes over the complete datasets until convergence of the antecedent space. Consequent parameters are estimated by a fuzzily weighted elastic net approach, embedding a convex combination of ridge regression and Lasso to achieve robust solutions also in case of ill-posed problems and meeting the (more stable and interpretable) local learning spirit. The new approach is termed as LS-PLS-Fuzzy , short for local structure preserving PLS fuzzy regression . It was successfully evaluated on three real-world application scenarios including a total of 11 time-series-based prediction modeling problems with different proportions between the number of training samples and original input dimensionality. Our results show significantly improved model accuracy compared to related State-of-the-Art (SoA) modeling approaches, an alternative dimension reduction technique, and when using conventional PLS and/or nongeneralized fuzzy rules.

Dynamic Nonlinear Partial Least Squares Modeling Using Gaussian Process Regression

A dynamic Gaussian process regression based partial least-squares (D-GPR-PLS) model is proposed to improve estimation ability and compared to the conventional nonlinear PLS. Considering the strong ability of GPR in nonlinear process modeling, this method is used to build a nonlinear regression between each pair of latent variables in the partial least-squares. In addition, augmented matrices are embedded into the D-GPR-PLS model to obtain better prediction accuracy in nonlinear dynamic processes. To evaluate the modeling performance of the proposed method, two simulated cases and a real industrial process based on wastewater treatment processes (WWTPs) are considered. The simulated cases use data from two high fidelity simulators: benchmark simulation model no. 1 and its long-term version. The second study uses data from a real biological wastewater treatment process. The results show the superiority of D-GPR-PLS in modeling performance for both data sets. More specifically, in terms of the prediction for effluent chemical oxygen demand of the real WWTP data, the value of the root-mean-square error is decreased by 31%, 16%, and 52%, respectively, in comparison with that for linear PLS, quadratic PLS, and least-squares support vector machine based PLS.

Improvement of quantitative analysis of molybdenum element using PLS-based approaches for laser-induced breakdown spectroscopy in various pressure environments

An experimental setup has been designed and realized in order to optimize the characteristics of laser-induced breakdown spectroscopy system working in various pressure environments. An approach combined the normalization methods with the partial least squares (PLS) method are developed for quantitative analysis of molybdenum (Mo) element in the multi-component alloy, which is the first wall material in the Experimental Advanced Superconducting Tokamak. In this study, the different spectral normalization methods (total spectral area normalization, background normalization, and reference line normalization) are investigated for reducing the uncertainty and improving the accuracy of spectral measurement. The results indicates that the approach of PLS based on inter-element interference is significantly better than the conventional PLS methods as well as the univariate linear methods in the various pressure for molybdenum element analysis.

Using elastic net regression to perform spectrally relevant variable selection

AbstractMultivariate data such as spectra frequently contain measured variables that are uninformative, and removal of such variables requires the use of methods that can be used to select informative variables. Partial least squares (PLS) regression may incorporate information from uninformative measured variables, and so it is important to select variables before performing the PLS regression. Elastic net (EN) regression can be used to perform variable selection automatically. An EN regression can be used to select groups of correlated variables or to select either sparse or nonsparse sets of variables. However, the predictive performance of the EN regression can be significantly worse than competing 1‐step variable selection methods such as variable importance in projection (VIP). In the present work, the use of the EN to select variables, followed by conventional PLS regression on the selected variables (EN‐PLS), has been investigated. Variable selection by using EN‐PLS was compared with that from EN regression, sparse PLS regression, VIP, and from selectivity ratio selection on 2 data sets of visible/near‐infrared spectra. In all cases, the wavelengths selected were compared with reference data. The variables selected by using EN‐PLS offered advantages in interpretability and gave more robust prediction performance as compared with those obtained from full‐spectrum PLS and the other variable selection methods. This paper reports a method for variable selection by using an EN regression prior to a second regression by using PLS, a 2‐step method termed EN‐PLS. Variables selected by using EN‐PLS are compared with variables selected from the EN regression, as well as VIP, selectivity ratio, and the sparse PLS regression, 3 commonly used methods for variable selection in chemometrics. The EN‐PLS is shown to select variables that were more easily interpreted. In addition, EN‐PLS performed more robustly than a PLS regression performed on all variables, as well as reduced PLS regressions by using variables selected from either the sparse PLS regression algorithm or a VIP variable selection followed by PLS modeling.

Robust boosting neural networks with random weights for multivariate calibration of complex samples

Neural networks with random weights (NNRW) has been used for regression due to its excellent performance. However, NNRW is sensitive to outliers and unstable to some extent in dealing with the real-world complex samples. To overcome these drawbacks, a new method called robust boosting NNRW (RBNNRW) is proposed by integrating a robust version of boosting with NNRW. The method builds a large number of NNRW sub-models sequentially by robustly reweighted sampling from the original training set and then aggregates these predictions by weighted median. The performance of RBNNRW is tested with three spectral datasets of wheat, light gas oil and diesel fuel samples. As comparisons to RBNNRW, the conventional PLS, NNRW and boosting NNRW (BNNRW) have also been investigated. The results demonstrate that the introduction of robust boosting greatly enhances the stability and accuracy of NNRW. Moreover, RBNNRW is superior to BNNRW particularly when outliers exist.

Locally weighted kernel partial least squares regression based on sparse nonlinear features for virtual sensing of nonlinear time-varying processes

Virtual sensing technology is crucial for monitoring product quality when real-time measurement is not available. To deal with both strong nonlinearity and time-varying dynamics of industrial processes, we propose a novel locally weighted kernel PLS (LW-KPLS) based on sparse nonlinear features in this research. Unlike the conventional locally weighted PLS (LW-PLS), the proposed method weights the training samples by using sparse kernel feature characterization factors (SKFCFs), which take account of the strength of nonlinear dependency between samples in the Hilbert feature space. By integrating the nonlinear features into the locally weighted regression framework, LW-KPLS not only can cope with the time-varying characteristics but also is more suitable for highly nonlinear processes. The proposed method was validated through a numerical example, a penicillin fermentation process, and a real industrial cleaning process for residual drug substances. The results have demonstrated that the proposed LW-KPLS outperforms the conventional PLS, KPLS, LW-PLS, and eLW-KPLS in the prediction performance.