RealTime Anomaly Detection for an ADMMBased Optimal Transmission Frequency Management System for IoT Devices
Abstract
:1. Introduction
 1.
 The key focus of our previous work [10] was to propose an optimisation framework for an IoT network so that the transmission frequency of the connected IoT devices can be dynamically adjusted to their optimal values through an ADMMbased iterative optimisation method. In this work, we focus on the design of an anomaly detector on top of the system we proposed in [10], which is able to infer anomalies that may occur in the underlying IoT transmission management system in real time. Thus, the scope of work is significantly extended in comparison to [10].
 2.
 We propose both mathematicalrulebased and deeplearningbased approaches for detecting anomalies in the IoT transmission frequency management system. In particular, the rulebased approach is designed to reveal anomalies of the system based on fundamental optimisation theory, and the deep learning approach aims to establish a prediction model based on sequential data analysis in system implementations.
 3.
 We conduct a comprehensive comparative study using both anomaly detector strategies and demonstrate the strengths and weaknesses for the two approaches in both simulated and practical working environments.
2. Related Works
2.1. Transmission Frequency Management System
Algorithm 1 Decentralised ADMM algorithm. 

2.2. Related Solution for Anomaly Detection
 Point: Anomalies happen randomly without clear reason and always with irregularity. For instance, network sensors can catch a sudden fluctuation in video signals [20] due to abnormal noises.
 Contextual: Anomalies happen given the specific context, including the spatial and temporal cues. For example, in [21], the pattern related to traffic accident varies between longterm and shortterm prediction (e.g., daylevel and hourlevel prediction) in different areas.
 Collective: Anomalies happen when the central node and edge devices work incongruously or the observation in a group has unusual patterns with other groups. For instance, in [22], anomalies can be defined as cascading delays in railway traffic, and these delays are common in traffic data across different weeks.
3. Problem Statement
 1.
 Manipulation on utility function input only: The independent variable of the utility function is manipulated by adding an input factor with a small given range, ${h}_{j}\left({x}_{j}\right)\Rightarrow {h}_{j}({x}_{j}+\mathit{input}\mathit{factor})$.
 2.
 Manipulation on utility function type and input: The utility function can be totally changed to anther type of concave function specified by the utility function set of the system, i.e., ${h}_{j}\left({x}_{j}\right)\Rightarrow {h}_{j}^{*}({x}_{j}+\mathit{input}\mathit{factor})$. Note that this setting maps to the “multiple userdefined utility functions” example in Section 2.1.
 3.
 Manipulation on transmission data size: The data size ${a}_{j}$ required for the j’th device per writing request is manipulated by adding a size factor with a small given range, ${a}_{j}\Rightarrow {a}_{j}+\mathit{size}\mathit{factor}$.
 1.
 We assume that at every given time only one edge device is manipulated, which is the fundamental basis for detecting an anomaly when multiple devices are manipulated in our system.
 2.
 We assume that the anomaly detector is a separate process running on the gateway, and it can only access limited information on the gateway but not all. More specifically, we assume that the anomaly detector can only access the value of $\mathit{z}$ and the sum of $\mathit{x}$ and $\mathit{u}$, denoted by $\mathit{v}$, from the ADMM iterative process at the gateway. It will never access the exact transmission frequency $\mathit{x}$ directly from the local devices and other resources/parameters shared between devices and the gateway.
 3.
 We assume that the anomaly detector starts to monitor anomalies in real time once the ADMM algorithm converges and local devices start pushing data to the gateway. The device setting will be reset when any anomalies are detected, and the optimisation process will be reactivated to reset the optimal solutions for fair resource allocation as per the normal situation. To further illustrate this point, the process of anomaly detection is shown in Figure 3.
4. Proposed Approach
4.1. RuleBased Anomaly Detection
4.1.1. Situation ${g}_{1}\left(\mathit{x}\right)=0$, ${g}_{2}\left(\mathit{x}\right)<0$
4.1.2. Situation ${g}_{1}\left(\mathit{x}\right)<0$, ${g}_{2}\left(\mathit{x}\right)=0$
4.1.3. Situation ${g}_{1}\left(\mathit{x}\right)<0$, ${g}_{2}\left(\mathit{x}\right)<0$
4.2. Limitations on the RuleBased Anomaly Detection
 A.
 The rulebased approach mainly relies on the optimality criteria without fully leveraging information from the iterative process, and as a result it cannot further distinguish different types of anomalies when a manipulation happens on the edge device.
 B.
 As we shall see, system parameters, i.e., $\mathit{z}$, may fluctuate during the optimisation process, and this can easily result in misjudgements when using the rulebased approach.
 C.
 Furthermore, when there are network delays in the IoT network, transmission frequencies of the devices may not change simultaneously, which can also lead to misjudgements when using the rulebased approach.
4.3. IoT Anomaly Detection with LSTMBased Approaches
5. Experimental Setup
5.1. Setup for Manipulations
 Manipulation on utility function type and input: The utility function is changed from ${f}_{j}\left({x}_{j}\right)$ to ${f}_{j}^{*}\left({x}_{j}\right)$ (i.e., see Table 2) with input factor, resulting in manipulation ${f}_{j}\left({x}_{j}\right)\Rightarrow {f}_{j}^{*}({x}_{j}+$ input factor), labelled as type 1.
 Manipulation on transmission data size: The data size factor is set as a random value from the set of $[1,1]$ and the ${a}_{j}$ is manipulated as ${a}_{j}\Rightarrow {a}_{j}+$ size factor, labelled as type 2.
 Manipulation on utility function input only: In this case, the $\mathit{inputfactor}$ is set as a random value from the set of $[3,3]$ for the manipulation ${f}_{j}\left({x}_{j}\right)\Rightarrow {f}_{j}({x}_{j}+$ input factor), which is labelled as type 3.
5.2. System Setup
5.3. Data Generation
5.4. Setup for LSTMBased Networks
6. Experimental Results
6.1. Anomaly Detection on SS
6.2. Anomaly Detection on RS
7. Discussion
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
MWF  Maximum writing frequency 
DFWF  Data flow writing frequency 
SS  Simulation system 
RS  Realworld system 
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Index  Utility Functions 

1  ${f}_{1}\left({x}_{1}\right)={({x}_{1}9)}^{2}+{x}_{1}^{3}$ 
2  ${f}_{2}\left({x}_{2}\right)={({x}_{2}4)}^{2}$ 
3  ${f}_{3}\left({x}_{3}\right)={(2{x}_{3}6)}^{2}+{x}_{3}^{3}$ 
Utility Functions 

${f}_{j}\left({x}_{j}\right)={({x}_{j}9)}^{2}+{x}_{j}^{3}$ 
${f}_{j}^{*}\left({x}_{j}\right)=exp({x}_{j}9)$ 
${f}_{j}^{*}\left({x}_{j}\right)=1/({x}_{j}9)$ 
${f}_{j}^{*}\left({x}_{j}\right)=log(1+exp({x}_{j}9))$ 
Anomaly Types  Simulation  RealWorld System 

Function input only  98.14% ± 0.52%  82.84% ± 3.81% 
Function type and input  99.82% ± 0.01%  93.90% ± 1.52% 
Data size  93.91% ± 1.00%  92.65% ± 0.85% 
General (twoclass)  98.81% ± 0.38%  96.28% ± 0.89% 
General (fourclass)  92.35% ± 0.84%  78.88% ± 3.80% 
Anomaly Types  Simulation  RealWorld System 

Function input only  97.48%  86.53% 
Function type and input  99.65%  80.21% 
Data size  65.26%  66.59% 
General (twoclass)  91.78%  83.34% 
Complexity  LSTM  biLSTM  StackedLSTM  LSTMatt.  LSTMen. 

Num. of model parameters  43,204  86,404  123,604  73,204  124,210 
Simulation inference (s)  0.66  1.05  0.93  0.56  0.36 
Realworld inference (s)  0.60  1.13  0.93  0.52  0.33 
Thresholds  RealWorld System 

1% optimal frequency  86.53% 
5% optimal frequency  87.90% 
10% optimal frequency  87.02% 
15% optimal frequency  86.62% 
30% optimal frequency  83.23% 
50% optimal frequency  77.10% 
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Wu, H.; O’Connor, N.E.; Bruton, J.; Hall, A.; Liu, M. RealTime Anomaly Detection for an ADMMBased Optimal Transmission Frequency Management System for IoT Devices. Sensors 2022, 22, 5945. https://doi.org/10.3390/s22165945
Wu H, O’Connor NE, Bruton J, Hall A, Liu M. RealTime Anomaly Detection for an ADMMBased Optimal Transmission Frequency Management System for IoT Devices. Sensors. 2022; 22(16):5945. https://doi.org/10.3390/s22165945
Chicago/Turabian StyleWu, Hongde, Noel E. O’Connor, Jennifer Bruton, Amy Hall, and Mingming Liu. 2022. "RealTime Anomaly Detection for an ADMMBased Optimal Transmission Frequency Management System for IoT Devices" Sensors 22, no. 16: 5945. https://doi.org/10.3390/s22165945