在时间序列预测领域,精准的预测模型对于诸多实际应用场景具有重要意义。本文聚焦于基于函数型数据分析的时间序列模型预测方法,首先以构造小波基来拟合函数为例介绍了函数型数据分析在处理离散时序数据时进行降噪的方法,并阐述了主成...在时间序列预测领域,精准的预测模型对于诸多实际应用场景具有重要意义。本文聚焦于基于函数型数据分析的时间序列模型预测方法,首先以构造小波基来拟合函数为例介绍了函数型数据分析在处理离散时序数据时进行降噪的方法,并阐述了主成分分析在面对线性和非线性的高维数据的降维方法,并以LSTM为模型对比了在多类数据集当中数据降维的效果。在此理论基础上,本文将所研究的方法应用于中国大兴安岭地区部分气象站的森林火险指数(Fire Weather Index, FWI)时序数据预测实践。通过对数据进行小波变换降噪、降维处理后,运用所构建的LSTM模型进行预测,并进一步对火灾风险进行科学评估。实验结果表明,所提出的基于函数型数据分析的时间序列预测方法在实际应用中展现出了较高的预测精度和良好的可靠性,为相关领域的时序预测与风险评估工作提供了新的有效途径和方法参考。In the field of time series forecasting, accurate predictive models hold significant importance for numerous practical application scenarios. This paper focuses on the forecasting methods of time series models based on functional data analysis. Firstly, it introduces the method of using wavelet basis construction to fit functions as an example, illustrating how functional data analysis can be applied to denoise discrete time series data. It also elaborates on the dimensionality reduction methods of principal component analysis (PCA) when dealing with high-dimensional linear and nonlinear data. Furthermore, the paper compares the dimensionality reduction effects of these methods on various datasets using LSTM models as a benchmark. Building on this theoretical foundation, the methods studied in this paper are applied to the practice of predicting the Forest Fire Weather Index (FWI) time series data from some meteorological stations in the Greater Khingan Region of China. After denoising and dimensionality reduction through wavelet transformation, the constructed Long Short-Term Memory (LSTM) model is employed for forecasting, followed by a scientific assessment of fire risk. The experimental results demonstrate that the proposed time series forecasting method based on functional data analysis exhibits high prediction accuracy and good reliability in practical applications, providing a new and effective approach and reference for time series forecasting and risk assessment in relevant fields.展开更多
为了对大量电力用户的稀疏、不规律的日耗电量数据进行特征分析,并对用户进行分类,文章提出一种函数性数据聚类分析方法。首先,应用kernel方法将离散的电量数据还原成连续曲线;然后,受Sobolev空间距离的启发,定义了新的函数距离,用于k-m...为了对大量电力用户的稀疏、不规律的日耗电量数据进行特征分析,并对用户进行分类,文章提出一种函数性数据聚类分析方法。首先,应用kernel方法将离散的电量数据还原成连续曲线;然后,受Sobolev空间距离的启发,定义了新的函数距离,用于k-means算法进行聚类。以某城市10 000户居民538天的实际用电数据进行实验,得到了用户在不同距离和聚类个数下的聚类原型。实验结果显示,由于选取的用户主要是城市居民,其用电模式比较相似:大高峰时段主要在6—9月,小高峰时段主要在1—2月,日消耗波动较小。而不同用户类别的主要区别体现在用电量的范围上:低耗电用户整体低于13 k W?h/天,高耗电用户接近100 k W?h/天。展开更多
用户电力数据的爆炸式增长给原始数据修正带来许多难点。文章提出用函数型数据分析(Functional Data Analysis,FDA)对错误和缺失数据进行修正与补全。通过函数估计方法,将原有观测个体的离散数据映射到一个新的函数空间,将数据中缺失的...用户电力数据的爆炸式增长给原始数据修正带来许多难点。文章提出用函数型数据分析(Functional Data Analysis,FDA)对错误和缺失数据进行修正与补全。通过函数估计方法,将原有观测个体的离散数据映射到一个新的函数空间,将数据中缺失的成分利用相似用户曲线特征进行修复,并搭建了针对电力大数据的数据清洗整体框架。在真实数据集上的测试结果表明,该算法能够准确地提取用户的用电特征曲线,并对错误数据和缺失数据进行准确地修复。展开更多
文摘在时间序列预测领域,精准的预测模型对于诸多实际应用场景具有重要意义。本文聚焦于基于函数型数据分析的时间序列模型预测方法,首先以构造小波基来拟合函数为例介绍了函数型数据分析在处理离散时序数据时进行降噪的方法,并阐述了主成分分析在面对线性和非线性的高维数据的降维方法,并以LSTM为模型对比了在多类数据集当中数据降维的效果。在此理论基础上,本文将所研究的方法应用于中国大兴安岭地区部分气象站的森林火险指数(Fire Weather Index, FWI)时序数据预测实践。通过对数据进行小波变换降噪、降维处理后,运用所构建的LSTM模型进行预测,并进一步对火灾风险进行科学评估。实验结果表明,所提出的基于函数型数据分析的时间序列预测方法在实际应用中展现出了较高的预测精度和良好的可靠性,为相关领域的时序预测与风险评估工作提供了新的有效途径和方法参考。In the field of time series forecasting, accurate predictive models hold significant importance for numerous practical application scenarios. This paper focuses on the forecasting methods of time series models based on functional data analysis. Firstly, it introduces the method of using wavelet basis construction to fit functions as an example, illustrating how functional data analysis can be applied to denoise discrete time series data. It also elaborates on the dimensionality reduction methods of principal component analysis (PCA) when dealing with high-dimensional linear and nonlinear data. Furthermore, the paper compares the dimensionality reduction effects of these methods on various datasets using LSTM models as a benchmark. Building on this theoretical foundation, the methods studied in this paper are applied to the practice of predicting the Forest Fire Weather Index (FWI) time series data from some meteorological stations in the Greater Khingan Region of China. After denoising and dimensionality reduction through wavelet transformation, the constructed Long Short-Term Memory (LSTM) model is employed for forecasting, followed by a scientific assessment of fire risk. The experimental results demonstrate that the proposed time series forecasting method based on functional data analysis exhibits high prediction accuracy and good reliability in practical applications, providing a new and effective approach and reference for time series forecasting and risk assessment in relevant fields.
基金Projected Supported by the National High Technology Research and Development Program of China(863 Program)(2015AA050203)National Talents Training Base for Basic Research and Teaching of Natural Science of China(J1103105)~~
文摘为了对大量电力用户的稀疏、不规律的日耗电量数据进行特征分析,并对用户进行分类,文章提出一种函数性数据聚类分析方法。首先,应用kernel方法将离散的电量数据还原成连续曲线;然后,受Sobolev空间距离的启发,定义了新的函数距离,用于k-means算法进行聚类。以某城市10 000户居民538天的实际用电数据进行实验,得到了用户在不同距离和聚类个数下的聚类原型。实验结果显示,由于选取的用户主要是城市居民,其用电模式比较相似:大高峰时段主要在6—9月,小高峰时段主要在1—2月,日消耗波动较小。而不同用户类别的主要区别体现在用电量的范围上:低耗电用户整体低于13 k W?h/天,高耗电用户接近100 k W?h/天。
文摘用户电力数据的爆炸式增长给原始数据修正带来许多难点。文章提出用函数型数据分析(Functional Data Analysis,FDA)对错误和缺失数据进行修正与补全。通过函数估计方法,将原有观测个体的离散数据映射到一个新的函数空间,将数据中缺失的成分利用相似用户曲线特征进行修复,并搭建了针对电力大数据的数据清洗整体框架。在真实数据集上的测试结果表明,该算法能够准确地提取用户的用电特征曲线,并对错误数据和缺失数据进行准确地修复。
