# A Novel Low-Complexity Fault Diagnosis Algorithm for Energy Internet in Smart Cities
## 1 Introduction  
The components a smart city include smart infrastructure, smart buildings, smart transportation, smart energy, smart health care, smart technology, smart governance, smart education, and smart citizens [1; 2; 3; 4; 5], among which the concept of smart energy can be viewed as an \"Energy Internet\" model [6; 7; 8; 9; 10; 11]. The backbone of a smart energy system is the smart energy grid, the smart energy metering of which is an important component. For example, the smart meter records consumption of electric energy in certain time intervals and communicates that information to the utility for monitoring and billing. To ensure a green model for smart cities [12], minimal energy consumption is required. To serve such a purpose, fault diagnosis in green smart cities should be efficient in low complexity [13; 14; 15]. There exist many filter-based fault diagnosis algorithms specifically designed for nonlinear time-varying stochastic systems. In Reference [16], [PERSON] et al. proposed a fault-related parameter estimation method based on a strong tracking filter for state assessment, as well as a logistic regression algorithm for root cause classification. In Reference [17], [PERSON] et al. designed a particle filter-based dual estimation strategy for both time-varying parameters and states. In Reference [18], [PERSON] and [PERSON] proposed an intelligent particle filter to solve the problem of misleading state estimation due to the particle impoverishment. They designed a genetic-operators-based strategy to improve the particle diversity. [PERSON] et al. [19] developed an optimal unbiased finite impulse response filter,the estimator of which is used to minimize the mean square error subject to the unbiasedness constraint. In Reference [20], [PERSON] et al. used the residual signal to detect sensor bias faults first and then employed residual analysis for faults isolation. [PERSON] et al. [21] studied a performance comparison of the strong tracking filter and Kalman filter. In Reference [22], [PERSON] et al. designed an adaptive robust square-root cubature Kalman filter (\(CKF\)) with the noise statistic estimator to solve the decline or divergence problem of the accuracy of the \(CKF\). Residual \(\chi^{2}\) test is a system-level fault detection algorithm [23] that can judge whether a set of measurement information in the Kalman filter system is effective in real time, based on which interactive residual fault detection method was proposed to identify both hard and soft faults, which are similar to the jump type fault and the soft fault, respectively. [PERSON] and [PERSON] [24] utilized two Bernoulli random variables to model the dead-zone effect. In addition, a Tobit Kalman filter is brought forward to generate a residual that can indicate the occurrence of an intermittent fault. The time-domain uncensored Kalman filter state estimation methodology is applied to address short circuit faults and transient load conditions [25]. On the other hand, researchers have been working on non-filter-based fault diagnosis algorithms for decades. [PERSON] et al. [26] proposed a centralized diagnosis algorithm based on end-to-end transmission time, and then they employed the Bayes' classification to improve the diagnosis accuracy. In Reference [27], [PERSON] et al. used the Pearson test to find faulty nodes within a square grid based network. [PERSON] et al. [28] proposed an optimal deducing model to locate faulty nodes based on the return message from the sink node. [PERSON] [29] developed a two-phase fault detection algorithm based on the majority voting. [PERSON] and [PERSON] [30] applied a three Sigma test to locate faulty nodes. In Reference [31], [PERSON] et al. proposed a decentralized algorithm based on spatio-temporal correlation. In Reference [32], [PERSON] et al. integrated the network cut set and majority voting to detect the faulty nodes. Recently, [PERSON] et al.