# Passive Fingerprinting of Same-Model Electrical Devices by Current Consumption

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## Abstract

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## 1. Introduction

- All devices have exactly the same hardware and software and, therefore, similar consumption profiles.
- A very low-frequency sampling rate of 50 kHz was applied. This sampling frequency is below the commonly applied bandwidth in RF-based fingerprinting [14] and is four times smaller than the one reported in the magnetic induction fingerprinting study reported in [2]. It is also lower than the switching frequency of common switched-mode power supplies (SMPSs) (see also Section 2 below).

## 2. Switch-Mode Power Supply Background

#### 2.1. Basic Principles

#### 2.2. Electromagnetic Interference Filtering

## 3. Time-Series Classification Considerations

#### 3.1. Data-Based Approach

#### 3.2. Feature-Based Approach

- A sequence-dependent feature-extraction (FE) stage that transforms time-series into numerical features that can be processed, while preserving the information in the original data set. It yields better results than applying machine learning directly to the raw data.
- Feature-based classification of the resulting numerical features. This stage can also include the process of reducing the number of features required for effective classification.

`Catch22`[22],

`tsfresh`[23],

`TSFEL`[24], and

`hctsa`[25], amongst others. Earlier techniques were based on Fourier and wavelet transforms [18]. Note, most of these FE libraries do not include authors’ recommended classifiers; resulting features are typically combined with random forest or logistic regression classifiers [18].

#### 3.3. Hybrid Approaches

#### 3.4. Deep-Learning-Based Approaches

#### 3.5. Classifier Selection Discussion

`sktime`[35] and

`tsai`[36] frameworks. However, even if a particular TSC method shows good results in terms of common benchmarks, see [20], this does not guarantee its performance for any specific problem. All mentioned methods suffer either from high complexity (i.e., high computation time) or from working only for some specific domain of time-series. Therefore, it is commonly required to do some additional adjustments, such as feature selection, method selection, or some domain-related modifications.

## 4. Experimental Design

#### 4.1. Electrical Setup

#### 4.2. Data Collection

#### 4.3. Database

#### 4.4. Experimental Assumptions

## 5. Evaluation

#### 5.1. Preliminary Analysis

#### 5.2. Feature-Extraction

#### 5.2.1. TSFEL

`TSFEL`(Time-Series Feature-Extraction Library) [24] was used as a sample of a fast and accurate FE framework. In the TSFEL framework, all features are extracted in an unsupervised way. The extracted features correspond to the summary statistics in the time- and frequency-domains, including Fourier and wavelet transforms. A set of 390 common features [38] was created from the data. For the wavelet decomposition, the Mexican hat wavelet with 1–10 orders (widths) was applied.

#### 5.2.2. MiniROCKET

`tsai`[36] implementation. The underlying transformation includes about 2000 random kernels with different parameters and dilation values. The particular implementation details are provided in Appendix A.1. Since the performance of the MiniROCKET algorithm depends on a set of random parameters, the classification performance has high variability, which leads to weak reproducibility. For this estimator, the best performance among 10 experiments is presented (Section 5.4).

#### 5.2.3. Empirical Wavelet Transform (EWT)

#### 5.3. Feature Classification

- Logistic regression (LR) classifier;
- Random forest (RF) classifier with Gini-index-based splitting criteria, ensemble of 100 classifiers and unlimited tree depth;
- LDA classifier with a pre-selected tolerance threshold for singular values of data decomposition (SVD). The threshold was selected using a grid search in the range from ${10}^{-5}$ up to 1. This search was done because we had noticed the significant influence of the tolerance threshold value on the obtained results;
- Naive Bayes (NB) classifier;
- k-nearest neighbors (kNN) classifier with k = 1 (1-NN). This classifier was used as a baseline due to its relatively high computational time and low classification accuracy.

`scikit-learn`Python package.

#### 5.4. Evaluation Results

- Full feature-space of the feature extraction method.
- Reduced feature-space with feature selection by correlation coefficient. Features with a correlation coefficient of 0.95 or higher were removed (cor.select).
- The previous feature subset further reduced by random-forest feature selection, i.e., selection by feature importance with threshold values 20% of importance (cor.+rf).
- Reduced feature-space only by random-forest feature selection (rf select).

## 6. Discussion

#### 6.1. MiniROCKET

#### 6.2. TSFEL and Empirical Wavelet Transform

#### 6.3. General Aspects

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Configuration Details

#### Appendix A.1. MiniROCKET Configuration

- kernel size set 9;
- kernel weights are initialized with values −1 and 2 in proportion 2:1, so as to have a sum of values equal to 0 (at all 84 kernels);
- kernel dilation rates from 1 to 903 with algorithmically increasing steps (at all 23 values, but 21 rest unique with float32 precision);
- kernel padding calculated as $\lfloor (k-1)*d)/2\rfloor ,$ where k is the kernel size; d is the dilation rate; $\lfloor \rfloor $ is the floor (integer part) operation.
- the bias values taken during training are $[0.25,0.5,0.75]$ quantiles from the kernel acting (convolution) output for one randomly selected example. Either just one quantile or more quantiles could be used.

#### Appendix A.2. EWT-Based FE

- For all segments, the auto-covariance function was calculated and 19 peaks were selected using a common find-peaks routine with an adjusted peak value threshold and peak-peak distance.
- Start and stop cutting frequencies for filtration bands were determined as middle points between peak positions. For all these bands, we take bands that include one peak, then two peaks, and so on.
- Filtration is implemented by a rectangular window in the frequency domain. The same filtering, but mirrored and shifted on one point to the left, is performed for a range from ${f}_{s}/2$ up to ${f}_{s}$ in order to avoid Hilbert filtration.

- band summary statistics (mean value, standard deviation, kurtosis, skewness, median value);
- absolute values of band summary statistics (mean value, standard deviation, kurtosis, skewness, median value);
- first-order autoregression coefficient for band;
- variance of residuals from 1-order autoregression for band;
- barycetner frequency, calculated as$$\widehat{f}=\frac{{\sum}_{k=0}^{N/2-1}S\left[k\right]{f}_{k}}{{\sum}_{k=0}^{N/2-1}S\left[k\right]},$$
- correlation-based point-wise frequency, calculated as$$\widehat{f}=\frac{{f}_{s}}{2\pi}arccos\left(\frac{{\sum}_{n=1}^{N-1}s\left(n\right)\xb7s(n-1)}{{\sum}_{n=0}^{N-1}{\left|s\left(n\right)\right|}^{2}}\right).$$

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**Figure 5.**Confusion plots for the best results for EWT-based (

**a**) and MiniROCKET-based (

**b**) approaches; medium amount $\in [100,600)$; large amount $\in [600,1250)$.

Method | Feature-Space | LR | RF | LDA | NB | 1-NN |
---|---|---|---|---|---|---|

TSFEL | 390 features | 0.63 | 0.85 | 0.91 | 0.84 | 0.63 |

cor.select (248) | 0.59 | 0.78 | 0.87 | 0.83 | 0.59 | |

cor.+rf (30) | 0.65 | 0.85 | 0.89 | 0.84 | 0.70 | |

rf select (24) | 0.63 | 0.93 | 0.91 | 0.91 | 0.83 | |

0]1.4cmMini ROCKET | 1924 features | 0.67 | 0.84 | 0.81 | 0.72 | 0.69 |

cor.select (435) | 0.59 | 0.76 | 0.80 | 0.70 | 0.67 | |

cor.+rf (18) | 0.65 | 0.90 | 0.94 | 0.85 | 0.78 | |

rf select (19) | 0.63 | 0.92 | 0.88 | 0.92 | 0.88 | |

0]*EWT | 2658 features | 0.65 | 0.88 | 0.94 | 0.81 | 0.57 |

cor.select (781) | 0.57 | 0.64 | 0.92 | 0.57 | 0.54 | |

cor.+rf (19) | 0.56 | 0.89 | 0.89 | 0.88 | 0.66 | |

rf select (145) | 0.88 | 0.92 | 0.92 | 0.91 | 0.75 |

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**MDPI and ACS Style**

Ronkin, M.; Bykhovsky, D.
Passive Fingerprinting of Same-Model Electrical Devices by Current Consumption. *Sensors* **2023**, *23*, 533.
https://doi.org/10.3390/s23010533

**AMA Style**

Ronkin M, Bykhovsky D.
Passive Fingerprinting of Same-Model Electrical Devices by Current Consumption. *Sensors*. 2023; 23(1):533.
https://doi.org/10.3390/s23010533

**Chicago/Turabian Style**

Ronkin, Mikhail, and Dima Bykhovsky.
2023. "Passive Fingerprinting of Same-Model Electrical Devices by Current Consumption" *Sensors* 23, no. 1: 533.
https://doi.org/10.3390/s23010533