# Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations

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## Abstract

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## 1. Introduction

- We conduct a structured analysis of the GOOSE network traffic in a SCN from a simulation case study that can be further applied to a network traffic from a real substation
- We model the GOOSE communication in an IEC 61850 substation using an ARFIMA model including the parameter estimation and the model prediction. We evaluate the accuracy of the suggested model using well-established criteria from the data-driven modeling field.
- We present a structured AD method based on two different approaches to detect flooding attacks using two well-known statistical tests while assuming an unknown change time and unknown model parameters under each hypothesis
- We evaluate the performance of the AD method with both detectors, in terms of basic and composite detection metrics, using a simulation case study under different rates of SNR.

## 2. Intrusion Detection Systems (IDSs) in Energy Systems

#### 2.1. Signature-Based Approaches

#### 2.2. Anomaly Detection (AD) Approaches

#### 2.3. Hybrid Approaches

## 3. Characteristics of the Process Network Traffic

#### 3.1. Diurnal Patterns

#### 3.2. Distributional Considerations of the Data

#### 3.3. Self-Similarity

#### 3.3.1. Variance-Time Plots

#### 3.3.2. Rescaled Adjusted Range R/S

## 4. ARFIMA Modeling of the Process Traffic in IEC 61850 Substations

#### 4.1. ARFIMA Model

#### 4.2. General Model Predictor

#### 4.3. Maximum Likelihood Estimation

#### Explanatory Example: Signal Embedded in WGN

#### 4.4. Description of the Process Network Traffic as an ARFIMA Model

## 5. Statistical Hypothesis Testing for the AD Method

- The algorithm starts by setting the user-defined parameters which are the order of the ARFIMA model i.e., n and a threshold ${\gamma}_{G}$ which is defined empirically based on test results for FAs and DR.
- The null-hypothesis ${\mathcal{H}}_{0}$ is computed with data contained between ${k}_{1}$ and ${N}_{0}$. ${\mathcal{H}}_{1}$ is computed using two data subsets: the bounds of the first one are represented by ${k}_{1}$ and ${k}_{2}-1$ and the second one is evaluated between ${k}_{2}$ and ${N}_{0}$. Models for ${\mathcal{H}}_{0}$ and ${\mathcal{H}}_{1}$ are computed according to Equation (24) whilst ${N}_{0}\ge N$.
- ${L}_{G}(x)$ is computed as the ration between the pdf of each hypothesis as described in Equation (23). If ${L}_{G}>{\gamma}_{G}$ holds, a change time ${k}_{2}$ is assigned to ${k}_{alarm}$ and an alarm is generated. The bounds of the dataset for ${\mathcal{H}}_{0}$ and ${\mathcal{H}}_{1}$ are also updated for further computations.
- If ${L}_{G}>{\gamma}_{G}$ does not hold, ${k}_{2}$ is incremented and ${\mathcal{H}}_{1}$ is computed in a new iteration. This procedure is repeated until ${k}_{2}>{N}_{0}$ and the bounds of the datasets for the computation of the PDFs in each hypothesis are updated.

- The algorithm starts by setting the user-defined parameters which are the order of the ARFIMA model i.e., $p,q,d$ and the size of the time windows, ${M}_{0}$ and ${M}_{1}$ used for data scanning. The threshold ${\gamma}_{C}$ is defined empirically based on test results for FAs and DR.
- As reported in [45], the model for ${\mathcal{H}}_{0}$ is computed using a dataset defined by a growing time window ${M}_{0}$ whereas the model for ${\mathcal{H}}_{1}$ is computed with data contained in a sliding fixed-size time window ${M}_{1}$. Bounds of the datasets used for the computation of models for both hypothesis are represented by ${k}_{1}$ and ${k}_{2}$. Models for ${\mathcal{H}}_{0}$ and ${\mathcal{H}}_{1}$ are computed while ${k}_{2}\le N$ holds.
- The decision function $g[k]$ is computed iteratively according to Equation (26). If $g[k]>{\gamma}_{C}$ holds, an alarm is generated indicating that anomaly is detected.
- Once an anomaly is detected, the detection time is set, the bounds ${k}_{1}$ and ${k}_{2}$ are updated and the detection function $g[k]$ is reset.

## 6. Results and Discussion

#### 6.1. Description of the Use Case and the Threat Model

#### 6.2. Evaluation of the Modeling of GOOSE IEC 61850 Traffic

#### 6.3. Performance of the Anomaly Detection (AD) Method

## 7. Conclusions & Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACF | Auto-Correlation Function |

AD | Anomaly Detection |

CPS | Cyber-Physical Security |

CUSUM | Cumulative sum |

DoS | Denial of Service |

DPI | Deep Packet Inspection |

GLRT | Generalized Likelihood Ratio Test |

GOOSE | Generic Object Oriented Substation Event |

HMI | Human-Machine Interface |

ICS | Industrial Control System |

ICT | Information and Communication Technology |

IEC | International Electrotechnical Commission |

IED | Intelligent Electronic Device |

LRD | Long-Range Dependency |

ML | Machine-Learning |

MLE | Maximum Likelihood Estimator |

MMS | Manufacturing Message Specification |

MU | Merging Unit |

NRMSE | Normalized Root Mean Square Error |

Probability Density Function | |

ROC | Receiver Operating Characteristic |

RT | Real-Time |

SCADA | Supervisory Control And Data Acquisition |

SCN | Substation Communication Network |

SG | Smart Grid |

SRD | Short-Range Dependency |

SV | Sampled Values |

TNR | True Negative Rate |

TPR | True Positive Rate |

WGN | White Gaussian Noise |

Glossary | |

B | Backshift operator. |

${C}_{ID}$ | The intrusion detection capability metric. |

${C}_{exp}$ | The expected cost metric. |

H | Hurst parameter. |

L | Length of non-overlaping intervals composing a time-series. |

${M}_{0}$ | Initial size of the dataset for the calculation of the CUSUM detector. |

${M}_{1}$ | Length of fixed-sized sliding window for the calculation of the CUSUM detector. |

N | Size of a time-series. |

${S}_{i}$ | The standard deviation of a subset x calculated over the interval $[i,i+(n-1)]$. |

${W}_{i,u}$ | The partial sum of a subset x calculated over the interval $[i,i+(n-1)]$. |

$\mathsf{\Gamma}(.)$ | The gamma (generalized factorial) function. |

$\mathsf{\Lambda}$ | The covariance matrix of the measurement noise. |

$\mathsf{\Theta}(B)$ | Moving average (MA) polynomial operator of an ARFIMA model. |

$\mathsf{\Theta}$ | The parameter vector. |

$\epsilon $ | Model residuals. |

x | Time-series. |

${\mathit{x}}^{(m)}$ | The aggregated sequence by m of x. |

B | The base rate. |

${\gamma}_{c}$ | The threshold for the CUSUM statistical detection. |

${\gamma}_{g}$ | The threshold for the GLRT statistical detection. |

$\widehat{\mu}$ | Sample mean. |

$\widehat{\sigma}$ | Sample variance. |

$\varphi (B)$ | Autoregressive (AR) polynomial operator of an ARFIMA model. |

${\widehat{\sigma}}_{e}^{2}$ | Variance of a white Gaussian noise process. |

d | The difference coefficient. |

$e[k]$ | Value of e at k. |

g | The CUSUM decision function. |

k | Discrete time index. |

${k}_{a}$ | Time at which an attack occurs. |

l | Delay order of the back-shift operator. |

m | The level of aggregation. |

n | ARFIMA model order defined by $n=(p,q)$. |

p | The order of the autoregressive process. |

q | The order of moving the average. |

$s[k]$ | Log-likelihood ratio increment. |

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**Figure 6.**GOOSE network traffic used for estimation (depicted in black) and arfima model prediction (depicted in red).

Threshold | Detection Delay * | Basic | Composite | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

FPR [%] | FNR [%] | C_{exp} | C_{ID} | |||||||||||||||||

[21] | [29] | D_G | D_C | [21] | [29] | D_G | D_C | [21] | [29] | D_G | D_C | [21] | [29] | D_G | D_C | [21] | [29] | D_G | D_C | |

0.1 | 7 | 7 | 7 | 7 | 12.27 | 20.22 | 11.29 | 13 | 7.54 | 7.91 | 7.6 | 7.41 | 0.1224 | 0.2078 | 0.1161 | 0.1613 | 1.9172 | 1.5655 | 1.9541 | 1.6069 |

0.2 | 8 | 9 | 8 | 8 | 12.39 | 19.38 | 9.79 | 11.26 | 7.53 | 7.85 | 7.66 | 7.62 | 0.1229 | 0.1998 | 0.105 | 0.145 | 1.916 | 1.5875 | 2.0424 | 1.6803 |

0.3 | 8 | 9 | 8 | 8 | 12.25 | 18.19 | 8.61 | 9.98 | 7.56 | 7.9 | 7.71 | 7.66 | 0.1238 | 0.1907 | 0.1001 | 0.1331 | 1.9048 | 1.615 | 2.1143 | 1.746 |

0.4 | 7 | 10 | 11 | 9 | 12.29 | 16.85 | 7.62 | 8.62 | 7.55 | 7.91 | 7.79 | 7.74 | 0.1243 | 0.1804 | 0.0969 | 0.1206 | 1.9016 | 1.6506 | 2.1921 | 1.8298 |

0.5 | 9 | 14 | 11 | 9 | 12.23 | 15.19 | 6.5 | 7.66 | 7.57 | 8.01 | 7.99 | 7.86 | 0.1244 | 0.1693 | 0.0938 | 0.112 | 1.8999 | 1.6983 | 2.3059 | 1.8993 |

0.6 | 8 | 13 | 9 | 9 | 12.21 | 14.01 | 5.77 | 6.67 | 7.57 | 8.1 | 8.13 | 7.96 | 0.1248 | 0.1622 | 0.0915 | 0.1032 | 1.8976 | 1.737 | 2.4017 | 1.9864 |

0.7 | 8 | 13 | 8 | 8 | 12.28 | 12.78 | 5.05 | 6 | 7.56 | 8.19 | 8.24 | 8.09 | 0.1249 | 0.1551 | 0.0891 | 0.0975 | 1.8971 | 1.7839 | 2.5178 | 2.0538 |

0.8 | 8 | 14 | 8 | 11 | 12.25 | 11.86 | 4.52 | 5.24 | 7.56 | 8.31 | 8.39 | 8.29 | 0.1249 | 0.1498 | 0.0849 | 0.0912 | 1.8967 | 1.8245 | 2.6187 | 2.1425 |

0.9 | 8 | 13 | 9 | 8 | 12.29 | 10.89 | 4.01 | 4.69 | 7.56 | 8.55 | 8.69 | 8.56 | 0.1255 | 0.1442 | 0.0815 | 0.0873 | 1.8933 | 1.8715 | 2.728 | 2.212 |

1 | 9 | 11 | 14 | 8 | 12.24 | 9.8 | 3.49 | 4.12 | 7.56 | 8.91 | 8.98 | 8.79 | 0.1252 | 0.1376 | 0.0781 | 0.083 | 1.8952 | 1.9328 | 2.862 | 2.3 |

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## Share and Cite

**MDPI and ACS Style**

Elbez, G.; Keller, H.B.; Bohara, A.; Nahrstedt, K.; Hagenmeyer, V.
Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations. *Energies* **2020**, *13*, 5176.
https://doi.org/10.3390/en13195176

**AMA Style**

Elbez G, Keller HB, Bohara A, Nahrstedt K, Hagenmeyer V.
Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations. *Energies*. 2020; 13(19):5176.
https://doi.org/10.3390/en13195176

**Chicago/Turabian Style**

Elbez, Ghada, Hubert B. Keller, Atul Bohara, Klara Nahrstedt, and Veit Hagenmeyer.
2020. "Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations" *Energies* 13, no. 19: 5176.
https://doi.org/10.3390/en13195176