# 2D Transformations of Energy Signals for Energy Disaggregation

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## Abstract

**:**

## 1. Introduction

- Six time-series-imaging (two-dimensional representations) techniques were compared on high- and low-frequency data.
- The convergence behavior and the influence on the sampling frequency of the two-dimensional representations were evaluated.
- The robustness to noise for the six evaluated time series imaging approaches was evaluated.

## 2. Time Series Imaging for Energy-Consumption Signals

#### 2.1. VI-Trajectory

- Normalize the waveforms to their absolute maximum values, i.e., ${\tilde{i}}_{agg}^{\tau}=\frac{{i}_{agg}^{\tau}}{max\left(\left(\right),{i}_{agg}\right)}$ and ${\tilde{v}}_{agg}^{\tau}=\frac{{v}_{agg}^{\tau}}{max\left(\left(\right),{v}_{agg}\right)}$.
- Define a uniform grid with grid size $\mathsf{\Delta}i=\frac{max\left(\right|{i}_{agg}\left|\right)}{W/2}$ and $\mathsf{\Delta}v=\frac{max\left(\right|{v}_{agg}\left|\right)}{W/2}$.
- Map the current and voltages samples ${\tilde{i}}_{agg}\left(i\right)$ and ${\tilde{v}}_{agg}\left(j\right)$ with $1\le i,j\le W$ to the $W\times W$ grid cells, obtaining the VI-Trajectory feature vector ${F}_{i,j}^{\tau}\in {\mathbb{R}}^{W\times W}$, where each element in ${F}_{i,j}^{\tau}$ indicates if a combination of current and voltage exists or not.

#### 2.2. Double Fourier Integral Analysis

#### 2.3. PQ Transformation

#### 2.4. Recurrence Plot

#### 2.5. Gramian Angular Field

#### 2.6. Markov Transition Field

## 3. NILM Using Two-Dimensional Signal Representations

## 4. Experimental Setup

#### 4.1. Datasets

#### 4.2. Pre-Processing

#### 4.3. Model Parametrization

#### 4.4. Experimental Protocols

## 5. Experimental Results

## 6. Discussion

#### 6.1. Runtime and Convergence

#### 6.2. Sampling Frequency

#### 6.3. Robustness to Noise

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**One electrical cycle for the aggregated current and voltage (

**a**) as well as the transformed signals as obtained from the time series imaging (

**b**–

**g**).

**Figure 2.**Non-Intrusive Load-Monitoring architecture using time series imaging for high-frequency data inputs.

**Figure 3.**Architecture of the evaluated two-stage NILM model utilizing a two-dimensional CNN for feature extraction and a three layer DNN for regression. For each layer, the number of filter/pooling operations (X) and the two-dimensional filter/pooling size ($Y\times Z$) is given as ($X@Y\times Z)$.

**Figure 4.**Convergence of the six time series 2D representation methods for 50 epochs of training using the REDD database during (

**a**) training and (

**b**) validation.

**Figure 5.**Performance for the REDD database for different sampling frequencies using PQ-transformed signals.

**Figure 6.**Influence of the noise level on the performance of energy disaggregation for different time series imaging methods.

Name | House | Country | Appliances | Sampling Rate | NAR |
---|---|---|---|---|---|

REDD | 3, 5 | US | 19, 22 | 16.5 kHz | 11.1–31.8% |

AMPds2 | - | CA | 22 | 60 sec | 17.8 |

**Table 2.**Hyper-parameter values of the CNN model and parameters of the Adam optimizer. HF and LF are the parameters for using high-frequency and low-frequency data, respectively.

Parameter | Value HF | Values LF |
---|---|---|

Input size | 55 × 55 | 30 × 30 |

Batch size | 50 | 1000 |

Epochs | 100 | 50 |

Patience | 15 | 10 |

Learning rate | 0.001 | 0.001 |

Beta-1 | 0.9 | 0.9 |

Beta-2 | 0.999 | 0.999 |

Epsilon | $1\times {10}^{8}$ | $1\times {10}^{8}$ |

Protocol | Dataset | Model | Appliances | Train | Validation | Test |
---|---|---|---|---|---|---|

#1 | REDD | HF-CNN | ALL | 90% | 10% of Train | 10% |

#2 | AMPds2 | LF-CNN | ALL | 90% | 10% of Train | 10% |

#3 | AMPds2 | LF-CNN | DEF | 90% | 10% of Train | 10% |

**Table 4.**Results for protocols $\#1$ in terms of ${E}_{ACC}$, MAE, and SAE for the high-frequency data of REDD-3/5.

2D Method | REDD-3 HF | REDD-5 HF | ||||
---|---|---|---|---|---|---|

E_{ACC} | MAE | SAE | E_{ACC} | MAE | SAE | |

VI | 83.66% | 6.69 | 0.053 | 65.62% | 13.32 | 0.655 |

DFIA | 85.31% | 5.73 | 0.077 | 73.10% | 10.40 | 0.036 |

PQ | 86.26% | 5.60 | 0.068 | 76.33% | 9.73 | 0.055 |

REC | 84.21% | 6.16 | 0.077 | 76.51% | 9.35 | 0.098 |

GAF | 84.38% | 6.30 | 0.074 | 77.43% | 9.16 | 0.099 |

MKF | 75.50% | 9.74 | 0.074 | 67.25% | 13.24 | 0.013 |

**Table 5.**Results for protocols $\#2$ and $\#3$ in terms of ${E}_{ACC}$, MAE, and SAE for the low-frequency data of AMPds2.

2D Method | AMPds2 ALL | AMPds2 DEF | ||||
---|---|---|---|---|---|---|

E_{ACC} | MAE | SAE | E_{ACC} | MAE | SAE | |

DFIA | 80.85% | 0.22 | 0.246 | 81.84% | 0.31 | 0.263 |

PQ | 89.94% | 0.12 | 0.048 | 94.78% | 0.09 | 0.048 |

REC | 80.91% | 0.22 | 0.216 | 80.04% | 0.34 | 0.352 |

GAF | 79.18% | 0.24 | 0.273 | 77.86% | 0.38 | 0.408 |

MKF | 77.94% | 0.25 | 0.311 | 77.49% | 0.39 | 0.423 |

**Table 6.**Comparison of the best-performing proposed 2D transformation method (PQ) with state-of-the-art performances reported in the literature in terms of ${E}_{ACC}$ and MAE (* the approach utilizes the next-to-active and reactive power and current and apparent power as its input features).

2D Method | PQ | SSHMM [10] | WaveNILM [24] | BiLSTM [26] | EnerGAN [29] | EnerGAN++ [30] |
---|---|---|---|---|---|---|

DEF | 95.2% | 94.0% | 94.7% | - | - | - |

ALL | 90.0% | - | 90.2% * | - | - | - |

DR,HO,WO | 13.2 | - | - | 38.6 | 35.3 | 38.5 |

Imaging Method | VI | PQ | DFIA | REC | GAF | MKF |
---|---|---|---|---|---|---|

AET | 670 us | 33 us | 170 us | 950 us | 920 us | 980 us |

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**MDPI and ACS Style**

Schirmer, P.A.; Mporas, I.
2D Transformations of Energy Signals for Energy Disaggregation. *Sensors* **2022**, *22*, 7200.
https://doi.org/10.3390/s22197200

**AMA Style**

Schirmer PA, Mporas I.
2D Transformations of Energy Signals for Energy Disaggregation. *Sensors*. 2022; 22(19):7200.
https://doi.org/10.3390/s22197200

**Chicago/Turabian Style**

Schirmer, Pascal A., and Iosif Mporas.
2022. "2D Transformations of Energy Signals for Energy Disaggregation" *Sensors* 22, no. 19: 7200.
https://doi.org/10.3390/s22197200