# Continual Deep Learning for Time Series Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{t}) is defined to be (weakly) stationary if all time t:

_{t}) = E[(y

_{t−1})] = μ,

_{t}) = σ

^{2}< ∞,

_{t}, y

_{t−k}) = γ(k),

^{2}by Var(.), and the covariance γ by Cov(.), respectively [11]. If the stationary conditions are no longer true, the non-stationary behaviors may pose significant difficulties for time series applications like remote sensing [12].

## 2. Advances in Deep Learning Methods for Time Series Modeling

#### 2.1. Multi-Layer Perceptron

#### 2.2. Recurrent Neural Network

#### 2.3. Long Short-Term Memory

#### 2.4. Convolutional Neural Network

#### 2.5. Graph Neural Network

#### 2.6. Others and Hybrids

#### 2.7. Advanced Preprocessing and Deep Learning Applications

## 3. Advances in Continual Learning Methods for Time Series Modeling

#### 3.1. Regularization-Based Methods

#### 3.2. Replay Methods

#### 3.3. Parameter Isolation Methods

#### 3.4. Combined Approaches

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Tree diagram for grouping the popular Deep Learning methods for sensor time series classification and forecasting tasks covered in this survey [30,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (note: if a paper uses two methods separately with similar satisfactory results, the paper will be listed under both groups).

**Figure 2.**Tree diagram for grouping the popular preprocessing methods for sensor time series classification and forecasting tasks covered in this survey [1,8,10,58,75,76,77,78,79,80,81,82,83] (note: if a paper uses two methods separately with similar satisfactory results, the paper will be listed under both groups).

**Figure 3.**Tree diagram of the taxonomy of the continual learning methods for sensor time series classification and forecasting [93,94,106,107,108,109,110,111,112,113,114,115,116] (note: if a paper uses two methods separately with similar satisfactory results, the paper will be listed under both groups).

Ref. | First Author | Year | Application Field | Datasets | Deep Learning Models | Accuracy | Details |
---|---|---|---|---|---|---|---|

[32] | Choi | 2021 | Time series anomaly detection | Water treatment test-bed, water distribution pipelines, Mars Science Laboratory rover | RNN, CNN, hybrid, attention | No clear one-size-fits-all method | Compare DL anomaly detection time series models with benchmark datasets |

[33] | Deng | 2021 | Detecting deviation from normal patterns | Sensor time series datasets of water treatment systems (SWaT and WADI) | Graph Deviation Network | 54% better F-measure than the next best baseline | Combine graph neural networks with structured learning approach |

[34] | Jiang | 2020 | Time series classification | UCR Time Series Classification Archive | MLP, CNN, ResNet | Not significantly better than 1-NN classifiers with dynamic time warping | Conduct comparison between nearest neighbor and DL models |

[35] | Ismail Fawaz | 2019 | Time series classification | Univariate time series datasets of the UCR/UEA archive | MLP, CNN, Echo State Network | SOA performance achieved with CNN and deep Residual Networks | Conduct empirical study of DNNs for TSC |

[36] | Han | 2022 | Leaf and wood terrestrial laser scanning time series classification | Seven broad-leaved trees (Ulmus americana) with a Rigel VZ-400i | Fully Convolutional Neural Network, LSTM-FCN, ResNet | Accurate separation of leaf and woody components from point clouds | Compare DL models on leaf and wood classification with a time series of geometric features |

[37] | Campos-Taberner | 2020 | Classification of land use | Sentinel-2 time series data | 2-layer Bi-LSTM network | Achieving best overall accuracy of 98.7% | Evaluate deep recurrent network 2-BiLSTM for land use classification |

[38] | Naqvi | 2020 | Real-time classification of normal and abnormal driving | Database of driver facial emotion and gaze | CNN | Superior performance vs. previous methods | Apply CNN to find changes in gaze from driver’s images |

[39] | Zheng | 2020 | Traffic flow time series forecasting | Traffic flow time series from OpenITS | LSTM | Outperform the ARIMA and BPNN | Deploy LSTM for traffic flow forecasting |

[40] | Hua | 2019 | Traffic prediction and user mobility of telecommunication problems | Traffic time series | Random Connectivity LSTM | Reduced computing complexity by 30% | Deploy the Random Connectivity LSTM for traffic and user mobility prediction |

[41] | Chen | 2020 | Equipment reliability prediction | Reliability test data of a cylinder in the small trolley of vehicle assembly plant | Deep Learning method based on MLP | Significant improvement over PCA and HMM | Employ DNN framework for reliability evaluation of cylinder |

[42] | Lim | 2021 | Time series forecasting | M4 competition (Smyl, 2020) | Exponential smoothing RNN | Hybrid model with better performance than pure methods | Conduct survey of common encoders and decoders for time series forecasting |

[43] | Yasrab | 2021 | Plant growth forecasting | Public datasets (Arabidopsis and Brassica rapa plants) | Generative Adversarial Network | Strong performance matching expert annotation | Employ generative adversarial predictive network for leaf and root predictive segmentation |

[44] | El-Sappagh | 2020 | Alzheimer’s disease progression detection | Time series data from Alzheimer’s Disease Neuroimaging Initiative | Ensemble of stacked CNN and Bidirectional LSTM | Much better than conventional ML | Deploy deep network for detecting common patterns for classification and regression tasks |

[45] | Lara-Benitez | 2021 | Twelve time series forecasting tasks | Twelve public datasets cover time series applications like finance, industry, solar energy, tourism, traffic, and internet traffic | MLP, Elman RNN, LSTM, Echo State Network, GRU, CNN, Temporal Convolutional Network | LSTM and CNN are the best choices | Evaluate seven popular DL models in terms of efficiency and accuracy |

[46] | Cao | 2020 | Investigating temporal correlations of intra-series and the correlations of inter-series | Time series datasets from energy, electrocardiogram, and traffic sectors | Spectral Temporal Graph Neural Network | Outstanding forecasting results, plus advantage of interpretability | Develop the Spectral Temporal Graph Neural Network for multivariable time series forecasting |

[30] | Rajagukguk | 2020 | Prediction of solar irradiance and photovoltaic | Time series data of temperature, humidity, and wind speed | RNN, LSTM, GRU, CNN-LSTM | Better prediction results than conventional ML | Evaluate models based on accuracy, forecasting horizon, training time, etc. |

[47] | Torres | 2018 | Solar energy generation forecasting | Two-year time series of PV power from a rooftop PV plant | Deep Learning approach, based on the H20 package with the grid search method for hyper-parameter optimization | Particularly suitable for big solar data, given its strong computing behavior | Deploy DL approach for solar photovoltaic power forecasting for the next day |

[48] | Xiao | 2019 | Prediction of sea surface temperature (SST) | SST time series data from 36-year observations by satellite | Convolutional Long Short-Term Memory | Outperform persistence model, SVR, and two LSTM models | Deploy ConvLSTM to capture correlations of SST across both space and time |

**Table 2.**Summary of the importance of advanced preprocessing techniques for real-world sensor time series DL applications.

Ref. | First Author | Year | Application Field | Preprocessing Methods | Deep Learning Models | Accuracy | Details |
---|---|---|---|---|---|---|---|

[75] | Kanani | 2020 | ECG time series signals for monitoring and classification of cardiovascular health | Squeezing and stretching of the signal along the time axis | 1D convolution | Achieved more than 99% accuracy | Develop a DL architecture for the preprocessing process for increased training stability |

[76] | Kisa | 2020 | Surface electromyography time series of human muscles for gesture classification | Empirical mode decomposition | CNN | Worst results for original signal vs. all IMFs images | Deploy EMD to segmented signal to obtain the Intrinsic Mode Functions (IMFs) images for CNN |

[8] | Zheng | 2018 | Classifying eight daily activities from wearable sensors | Segmentation and transformation methods | CNN | Achieved best results with multichannel method | Evaluate the impact of segmentation and transformation methods on DL models |

[77] | Castro Filho | 2020 | Synthetic Aperture Radar images for rice crop detection | 3D-Gamma filter and method of Savitzky and Golay | LSTM, Bidirectional LSTM | High accuracy and Kappa (>97%) | Apply 3D spatial–temporal filters and smoothing with Savitzky–Golay filter to minimize noise |

[78] | ReBwurm | 2020 | Classifying crop type based on raw and preprocessed Sentinel 2 satellite time series data | Atmospheric correction, filtering of cloud temporal observations, focusing on vegetative periods, and masking of cloud | 1D-convolutions, RNN, self-attention model | Preprocessing can increase classification performance for all models | Present the preprocessing pipeline, including atmospheric correction, temporal selection of cloud-free observations, cloud masking, etc. |

[79] | Kingphai | 2022 | Classifying mental workload levels from EEG time series signals | Independent component analysis based on ADJUST | CNN, Stacked GRU, Bidirectional GRU, BGRU-GRU, LSTM, BiLSTM, BiLSTM-LSTM | Most effective model performance can be achieved | Deploy automatic ICA-ADJUST to remove the frequently contaminated artifacts components before applying DL models |

[80] | Yokkampon | 2022 | Anomaly detection of multivariate sensor time series | Multi-scale attribute matrices | Multi-scale convolutional variational autoencoder | Achieved superior performance and robustness | Develop a new ERR-based threshold setting strategy to optimize anomaly detection performance |

[58] | Barrera- Animas | 2022 | Rainfall prediction | Correlation matrix with the Pearson correlation coefficient | LSTM, Stacked-LSTM, Bidirectional LSTM | Retained the main features of DL models | Apply Pearson correlation matric for unsupervised feature selection |

[81] | Mishra | 2020 | Wind predictions | Discrete wavelet transformation, fast Fourier Transformation, inverse transformation | Attention, DCN, DFF, RNN, LSTM | Performed best for attention and DCN with wavelet or FFT signal | Propose a preprocessing model of discrete wavelet transformation and fast Fourier transformation |

[10] | Livieris | 2020 | Time series data from energy section, stock market, and cryptocurrency | Iterative transformations and Augmented Dickey–Fuller test | LSTM, CNN-LSTM | Considerably improved the DL forecasting performance | Propose transformation method for enforcement of stationarity of the time series |

[1] | Asadi | 2020 | Traffic flow time series | Time series decomposition method | Convolution-LSTM | Outperformed SOA models | Deploy time series decomposition method for separating short-term, long-term, and spatial patterns |

[82] | Wen | 2021 | Survey of data augmentation methods | Data augmentation methods (like time domain and frequency domain), decomposition-based methods, statistical generative models | Deep generative models | Show successes in time series tasks | Compare data augmentation methods for enhancing the quality of training data |

[83] | Azar | 2020 | Wireless network with smart sensors | Discrete wavelet transform and the error-bound compressor Squeeze | Resnet, LSTM-FCN, GRU-FCN, FCN | Achieve the optimal trade-off between data compression and quality | Develop a compression approach with discrete wavelet transform and error-bound compressor |

Ref. | First Author | Year | Application Field | Motivations for Deploying CL | Continual Learning Models | Accuracy | Details |
---|---|---|---|---|---|---|---|

[107] | Sah | 2022 | Wearable sensors for activity recognition | Addressing the catastrophic forgetting in the non-stationary sequential learning process | A-GEM, ER-Ring, MC-SGD | Still need improvement for multitask training | Compare CL approaches for sensor systems |

[108] | Matteoni | 2022 | Human state monitoring of domain- incremental scenario | Overcoming the non-stationary environments | Replay, elastic weight consolidation, learning without forgetting, naive and cumulative strategies | Existing strategies struggle to accumulate knowledge | Assess the ability of existing CL methods for knowledge accumulation over time |

[93] | Kiyasseh | 2021 | Multiple clinics with various sensors for cardiac arrhythmia classification | Temporal data in clinics are often non-stationary | Buffer strategy to construct the continual learning model CLOPS | Outperform GEM and MIR | Apply uncertainty-based acquisition functions, for instance, replay |

[109] | Kwon | 2021 | Deployment in mobile and embedded sensing devices | Addressing the resources requirements and limitations of the mobile and embedded sensing devices | CL approaches- regularization, replay and replay with examples | Best results for replay with exemplars schemes | Compare three main CL approaches for mobile and embedded sensing applications like activity recognition |

[110] | Cossu | 2021 | Sensors of the robotics system | Achieving walk learning in different environments | Continual learning in RNNs | Highlight the importance of a clear specification | Evaluate CL approaches in class-incremental scenarios for speech recognition and sequence classification |

[111] | He | 2022 | Identification of anomalies | Addressing the lack of transparency for CL modules | Explainability module based on dimension reduction methods and visualization methods | Proposed evaluation score based on metric | Propose the conceptual design of explainability module for CL techniques |

[112] | Doshi | 2022 | Video anomaly detection (VAD) | Overcoming practical VAD challenges | Incremental updating of the memory module, experience replay | Outperform existing methods significantly | Develop a two-stage CL approach with feature embedding and kNN-based RNN model |

[113] | Maschler | 2021 | Metal-forming time series dataset of a discrete manufacturing | Providing automatic capability for adapting formerly learned knowledge to new settings | Continual learning approach based on regularization strategies | Improved performance vs. no regularization | Compare CL approaches of regularization strategies on industrial metal-forming data for fault prediction |

[114] | Maschler | 2020 | Fault prediction in a distributed environment | Real-world restrictions like industrial espionage and legal privacy concern prevent the centralizing of data from factories for the DL training | LSTM algorithm with elastic weight consolidation | Promising results for industrial automation scenarios | Apply elastic weight consolidation for distributed, cooperative learning |

[115] | Bayram | 2020 | Auditory scene analysis | Addressing high-value background noise and high computational demands | Continual learning approach based on Hidden Markov Model | Achieve high accuracy | Develop an HMM-based CL approach with UED and retraining for time series classification |

[106] | Xiao | 2022 | Evolving long-term streaming traffic flow | Addressing the non-stationary data distribution during policy evolution | Prioritized experience replay strategy for transferring learned knowledge into the model | Able to continuously learn and predict traffic flow over time | Formulate the traffic flow prediction problem as continuous reinforcement learning task |

[116] | Schillaci | 2021 | Transferring the knowledge gained from the greenhouse research facilities to greenhouses | Addressing problems like the requirement of large-scale re-training in the new facility | Continual learning RNN model with episodic memory replay and consolidation | Outperform standard memory consolidation approaches | Present a CL approach of an episodic memory system and memory consolidation |

[94] | Gupta | 2021 | In-process quality prediction by manufacturers | Addressing the lack of practical variability among industrial sensor networks | Generator-based RNN continual learning module | Possible significant performance enhancement | Deploy task-specific generative models to augment data for target tasks |

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Ao, S.-I.; Fayek, H.
Continual Deep Learning for Time Series Modeling. *Sensors* **2023**, *23*, 7167.
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Continual Deep Learning for Time Series Modeling. *Sensors*. 2023; 23(16):7167.
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