Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the los...Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.展开更多
In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sam...In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.展开更多
In this work,multivariate detection limits(MDL)estimator was obtained based on the microelectro-mechanical systems–near infrared(MEMS–NIR)technology coupled with two sampling accessories to assess the detection capa...In this work,multivariate detection limits(MDL)estimator was obtained based on the microelectro-mechanical systems–near infrared(MEMS–NIR)technology coupled with two sampling accessories to assess the detection capability of four quality parameters(glycyrrhizic acid,liquiritin,liquiritigenin and isoliquiritin)in licorice from di®erent geographical regions.112 licorice samples were divided into two parts(calibration set and prediction set)using Kennard–Stone(KS)method.Four quality parameters were measured using high-performance liquid chromatography(HPLC)method according to Chinese pharmacopoeia and previous studies.The MEMS–NIR spectra were acquired from¯ber optic probe(FOP)and integrating sphere,then the partial least squares(PLS)model was obtained using the optimum processing method.Chemometrics indicators have been utilized to assess the PLS model performance.Model assessment using chemometrics indicators is based on relative mean prediction error of all concentration levels,which indicated relatively low sensitivity for low-content analytes(below 1000 parts per million(ppm)).Therefore,MDL estimator was introduced with alpha error and beta error based on good prediction characteristic of low concentration levels.The result suggested that MEMS–NIR technology coupled with fiber optic probe(FOP)and integrating sphere was able to detect minor analytes.The result further demonstrated that integrating sphere mode(i.e.,MDL0:05;0:05,0.22%)was more robust than FOP mode(i.e.,MDL0:05;0:05,0.48%).In conclusion,this research proposed that MDL method was helpful to determine the detection capabilities of low-content analytes using MEMS–NIR technology and successful to compare two sampling accessories.展开更多
分数阶微分(fractional order derivative,FOD)是重要的数学分支,它将经典的整数阶扩展到任意阶,可进一步捕捉到光谱的细节特征。该文基于高光谱影像和野外土壤样本铬(Cr)元素含量建立土壤重金属高光谱反演模型,首先,根据野外样本坐标...分数阶微分(fractional order derivative,FOD)是重要的数学分支,它将经典的整数阶扩展到任意阶,可进一步捕捉到光谱的细节特征。该文基于高光谱影像和野外土壤样本铬(Cr)元素含量建立土壤重金属高光谱反演模型,首先,根据野外样本坐标信息提取像元光谱,同时按照欧式距离最短原则提取邻近像元光谱扩充样本数量;其次,对扩充后样本进行Savitzky-Golay(SG)滤波、多元散射校正处理,在此基础上进行FOD光谱变换,采用竞争自适应重加权采样算法(competitive adaptive reweighted sampling,CARS)筛选特征波段组合;最后,根据筛选的特征组合,建立偏最小二乘回归(partial least squares regression,PLSR)模型,并进行精度评价。结果发现,扩充样本可有效缓解反演模型的“过拟合”现象,提升模型的精度和稳定性;当FOD的阶数为1.8时,PLSR反演模型的训练集和测试集精度最高,模型适应性、稳定性最强,训练集R^(2)为0.8962、相对分析误差为3.1044,测试集R^(2)为0.7556、相对分析误差为2.0226,均方根误差均最小,分别为16.331 mg/kg和17.094 mg/kg,模型为能够近似预测级别。该文基于国产高光谱ZY-102E数据建立硫铁矿区Cr元素含量反演模型,可在一定程度上促进国产高光谱数据土壤重金属含量反演研究,为硫铁矿区土壤重金属污染防治提供技术支撑。展开更多
In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially acc...In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.展开更多
With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair compar...With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.展开更多
As important components of air pollutant,volatile organic compounds(VOCs)can cause great harm to environment and human body.The concentration change of VOCs should be focused on in real-time environment monitoring sys...As important components of air pollutant,volatile organic compounds(VOCs)can cause great harm to environment and human body.The concentration change of VOCs should be focused on in real-time environment monitoring system.In order to solve the problem of wavelength redundancy in full spectrum partial least squares(PLS)modeling for VOCs concentration analysis,a new method based on improved interval PLS(iPLS)integrated with Monte-Carlo sampling,called iPLS-MC method,was proposed to select optimal characteristic wavelengths of VOCs spectra.This method uses iPLS modeling to preselect the characteristic wavebands of the spectra and generates random wavelength combinations from the selected wavebands by Monte-Carlo sampling.The wavelength combination with the best prediction result in regression model is selected as the characteristic wavelengths of the spectrum.Different wavelength selection methods were built,respectively,on Fourier transform infrared(FTIR)spectra of ethylene and ethanol gas at different concentrations obtained in the laboratory.When the interval number of iPLS model is set to 30 and the Monte-Carlo sampling runs 1000 times,the characteristic wavelengths selected by iPLS-MC method can reduce from 8916 to 10,which occupies only 0.22%of the full spectrum wavelengths.While the RMSECV and correlation coefficient(Rc)for ethylene are 0.2977 and 0.9999 ppm,and those for ethanol gas are 0.2977 ppm and 0.9999.The experimental results show that the iPLS-MC method can select the optimal characteristic wavelengths of VOCs FTIR spectra stably and effectively,and the prediction performance of the regression model can be significantly improved and simplified by using characteristic wavelengths.展开更多
This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by...This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.展开更多
The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerate...The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.展开更多
基金Project supported by the Key National Natural Science Foundation of China(Grant No.62136005)the National Natural Science Foundation of China(Grant Nos.61922087,61906201,and 62006238)。
文摘Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.
文摘In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.
基金This work was financially supported fromthe National Natural Science Foundation of China(81303218)Doctoral Fund of China (20130013120006)Special Fund of Outstanding Young Teachers and Innovation Team.
文摘In this work,multivariate detection limits(MDL)estimator was obtained based on the microelectro-mechanical systems–near infrared(MEMS–NIR)technology coupled with two sampling accessories to assess the detection capability of four quality parameters(glycyrrhizic acid,liquiritin,liquiritigenin and isoliquiritin)in licorice from di®erent geographical regions.112 licorice samples were divided into two parts(calibration set and prediction set)using Kennard–Stone(KS)method.Four quality parameters were measured using high-performance liquid chromatography(HPLC)method according to Chinese pharmacopoeia and previous studies.The MEMS–NIR spectra were acquired from¯ber optic probe(FOP)and integrating sphere,then the partial least squares(PLS)model was obtained using the optimum processing method.Chemometrics indicators have been utilized to assess the PLS model performance.Model assessment using chemometrics indicators is based on relative mean prediction error of all concentration levels,which indicated relatively low sensitivity for low-content analytes(below 1000 parts per million(ppm)).Therefore,MDL estimator was introduced with alpha error and beta error based on good prediction characteristic of low concentration levels.The result suggested that MEMS–NIR technology coupled with fiber optic probe(FOP)and integrating sphere was able to detect minor analytes.The result further demonstrated that integrating sphere mode(i.e.,MDL0:05;0:05,0.22%)was more robust than FOP mode(i.e.,MDL0:05;0:05,0.48%).In conclusion,this research proposed that MDL method was helpful to determine the detection capabilities of low-content analytes using MEMS–NIR technology and successful to compare two sampling accessories.
基金Supported by National Natural Science Foundation of China(11271039)
文摘In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.
基金supported by the National Natural Science Foundation of China (52075420)the National Key Research and Development Program of China (2020YFB1708400)。
文摘With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.
基金supported by National Key Scientific Instrument and Equipment Development Project of China,Grant Nos.2013YQ220643the National 863 Program of China,Grant Nos.2014AA06A503.
文摘As important components of air pollutant,volatile organic compounds(VOCs)can cause great harm to environment and human body.The concentration change of VOCs should be focused on in real-time environment monitoring system.In order to solve the problem of wavelength redundancy in full spectrum partial least squares(PLS)modeling for VOCs concentration analysis,a new method based on improved interval PLS(iPLS)integrated with Monte-Carlo sampling,called iPLS-MC method,was proposed to select optimal characteristic wavelengths of VOCs spectra.This method uses iPLS modeling to preselect the characteristic wavebands of the spectra and generates random wavelength combinations from the selected wavebands by Monte-Carlo sampling.The wavelength combination with the best prediction result in regression model is selected as the characteristic wavelengths of the spectrum.Different wavelength selection methods were built,respectively,on Fourier transform infrared(FTIR)spectra of ethylene and ethanol gas at different concentrations obtained in the laboratory.When the interval number of iPLS model is set to 30 and the Monte-Carlo sampling runs 1000 times,the characteristic wavelengths selected by iPLS-MC method can reduce from 8916 to 10,which occupies only 0.22%of the full spectrum wavelengths.While the RMSECV and correlation coefficient(Rc)for ethylene are 0.2977 and 0.9999 ppm,and those for ethanol gas are 0.2977 ppm and 0.9999.The experimental results show that the iPLS-MC method can select the optimal characteristic wavelengths of VOCs FTIR spectra stably and effectively,and the prediction performance of the regression model can be significantly improved and simplified by using characteristic wavelengths.
文摘This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.
文摘The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.
