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摘要: 為了系統性地歸納工業場景下時序預測方法及應用，首先介紹了統計學習、集成學習、深度學習三類時序預測算法，并圍繞工業數據分析與決策問題，重點分析了循環神經網絡、卷積神經網絡、編碼?解碼器模型三類深度學習模型的優缺點及適用的工業應用場景。為了清晰全面地評估模型性能，介紹了面向點預測、序列預測問題的統計指標和誤差計算方法。同時，整理了經典的公開工業數據集，以便研究者快速評估算法性能。并以過程工業中的采礦、冶金為例，介紹了時序預測方法在真實工業場景下的應用和效果。最后，總結了工業領域中應用深度學習技術所面臨的低穩健性和弱可解釋性等問題，并探討了工業場景下時序預測方法研究的未來發展方向。Abstract: This review outlined recent developments in deep learning time series forecasting technology for the needs of industrial applications. With the advances in industrial automation, the storage and analysis of massive production data have become possible. Traditional mechanism modeling methods based on statistics encounter difficulties in dealing with high-dimensional industrial problems. Thus, time series forecasting for complex processes and products has played an important role in industrial scenarios, such as device modeling, production forecasting, remaining life prediction, and precise control, thereby receiving considerable attention from both academia and industry. To methodically review the time series forecasting method and its industrial applications, this review first introduced the three types of time series forecasting, namely, statistical learning, integrated learning, and deep learning, and compared their ease of use, complexity, and applicability issues. Focusing on industrial data analysis and decision-making, this review analyzed the three types of deep learning models, namely, recurrent neural network, convolutional neural network, and encoder–decoder network. The advantages and disadvantages of these three types of models and the applicable industrial environment were given, and how they can be embedded in industrial application sites to reduce costs and improve production efficiency was described. Afterward, to evaluate the performance of different algorithms clearly and comprehensively, statistical metrics and loss functions for the point prediction sequence and shape (motif) prediction problems were presented. At the same time, this review compiled classic public datasets of the industry for researchers to quickly find authoritative assessment data for an industry sector or issue. Taking mining and metallurgy in the process industry as examples, this review presented some widespread problems in this field, such as nonlinearity, long time delays, and unobservability of variables. This review also showed how deep-learning-based time series forecasting techniques can solve the aforementioned problems, build soft sensors, create digital twins, and achieve the visualization of complex processes. This review revealed that the application of deep learning in the process industry requires highly robust and strongly interpretable or explainable algorithms. For the robustness problem, the use of the ordinary differential equation model and Kalman filter method to solve the modeling of irregularly sampled time series and the use of the deep learning method to detect online sensor abnormalities were proposed. For the interpretability problem, sample-based, structure-based interpretable, and external co-explanation methods were introduced. This review also analyzed how explainable techniques can be applied to industrial deep learning models. Finally, the future directions of time series research were discussed in terms of both deep learning methods and industrial applications.
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Key words:
- process industry /
- time series forecasting /
- deep learning /
- model interpretability /
- evaluation metric
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表 1 時間序列預測算法對比
Table 1. Comparison of time series forecasting algorithms
Method Interpretability Design difficulty Efficiency Applicable scenario Statistical Algorithms High Easy Low Stationary random process Ensemble Learning Middle Hard High Experienced experts Deep Learning Low Middle High The predicted system has complex nonlinearity and sufficient data 
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表 2 指標定義
Table 2. Definitions of the mathematical metrics
Metric name Formula Metric name Formula Mean squared error, MSE $ \text{MSE}=\dfrac{1}{n}\sum\limits _{i=1}^{n}{e}_{i}{}^{2} $ Mean absolute error, MAE $ \text{MAE}=\dfrac{1}{n}\sum\limits _{i=1}^{n}\left|{e}_{i}\right| $ Normalized quantile error $ {Q_\rho } = \dfrac{{\sum\limits_{i = 1}^n {2\left( {\rho {e_{i;}}_{{P_i} > {A_i}} - (1 - \rho ){e_{i;{P_i} \leqslant {A_i}}}} \right)} }}{{\sum\limits_{i = 1}^n {{A_i}} }} $ R-squared $ {R^{\text{2}}} = \left( {1 - \dfrac{{\sum\limits_{i = 1}^n {{e_i}^2} }}{{\sum\limits_{i = 1}^n {{{({A_i} - \overline A )}^2}} }}} \right) \times 100\% $ Mean absolute scaled error, MASE $ \begin{array}{l}\text{MASE}=\text{MAE}/Q\text{ where}\\ Q=\dfrac{1}{n-1}\sum\limits _{i=2}^{n}\left|{A}_{i}-{A}_{i-1}\right|\end{array} $ Pearson correlation coefficient $ \begin{gathered} {r_{xy}} = \frac{{\sum\limits_{i = 1}^n {({X_i} - \bar X)({Y_i} - \bar Y)} }}{{\left( {\sqrt {\sum\limits_{i = 1}^n {{{\left( {{X_i} - \bar X} \right)}^2}} } } \right)\left( {\sqrt {\sum\limits_{i = 1}^n {{{\left( {{Y_i} - \bar Y} \right)}^2}} } } \right)}} \\ = \frac{{\sum\limits_{i = 1}^n {({A_i} - \overline A )} ({P_i} - \overline P )}}{{\left( {\sqrt {\sum\limits_{i = 1}^n {{{\left( {{A_i} - \overline A } \right)}^2}} } } \right)\left( {\sqrt {\sum\limits_{i = 1}^n {{{\left( {{P_i} - \overline P } \right)}^2}} } } \right)}} \\ \end{gathered} $ Mean absolute percentage error, MAPE $ \text{MAPE}=\dfrac{100}{n}{\displaystyle \sum _{n=1}^{i}{\left(\frac{{e}_{i}}{{A}_{i}}\right)}^{2}} $ KL divergence $ {D}_{\text{KL}}(P\Vert Q)={\displaystyle \sum _{i=1}^{n}P({x}_{i})\mathrm{log}\left(\frac{P({x}_{i})}{Q({x}_{i})}\right)} $ Root relative squared error, RRSE $ \text{RRSE}=\sqrt{\sum\limits _{i=1}^{n}\dfrac{{e}_{i}^{2}}{{\left({A}_{i}-\overline{A}\right)}^{2}}} $
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