# An Analog Circuit Fault Diagnosis Method Based on Circle Model and Extreme Learning Machine
## 1 Introduction  
Since the 1970s, analog circuit fault diagnosis has become a research hotspot in the field of electronic testing, and gradually formed a relatively complete theoretical system [1]. In order to ensure the test quality of circuits under test (CUT) at a low cost, many fault models and methods have been proposed [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. One of the most widely used is the fault dictionary method [6]. The fault dictionary method is based on the simulation of circuit faults and the mapping relationship between fault features and fault components to form a fault dictionary. But it also has the following shortcomings: it can only diagnose catastrophic faults (hard faults) and discrete parameter fault types and the fault dictionary increases with the increase of components. Parameter fault diagnosis (also known as soft fault) is still an Non-deterministic (NP)-hard problem. With the development of modern information processing technology and artificial intelligence, starting from 1990's, a new generation of the analog circuit fault diagnosis method represented by machine learning algorithms has been widely developed. Modernanalog circuit fault diagnosis methods can be divided into two main categories: model-based fault diagnosis methods and classifier based fault diagnosis methods. The model-based fault diagnosis methods include the discrete parameter model, slope fault diagnosis, symbolic analysis, and so on. However, the discrete parameter model cannot characterize the fault completely, for the input/output (I/O) signals and element parameters all change continuously. The slope fault diagnosis only applies to linear circuits [3; 4]. The fault of an element can be modeled with the slope as the fault feature. Nonetheless, slope fault diagnosis only works when the measuring points outnumber the faults to be modeled. The applicable scope of symbolic analysis is limited by its reliance on the transfer function [5]. Based on complex domain modeling, [PERSON] et al. [6] and [PERSON] et al. [9] proposed a method that creates a unified fault model called the circle model for all parameters, using only a few measuring points. Due to the presence of tolerances, this method cannot diagnose the critical regions of different circuit states accurately, which suppresses the test accuracy. The classifier-based fault diagnosis methods are generally implemented in three steps: collecting features of the circuit in different states, training the collected features with a classifier, and diagnosing the fault based on the training data. These methods typically adopt classifiers like support vector machine (SVM) [7], least squares support vector machine (LS-SVM) [8], extreme learning machine (ELM) [15; 20], and so on. The SVM or LS-SVM algorithm is used to map the lower-dimensional nonlinear response space into the higher-dimensional feature space for effective classification. However, this algorithm has a much higher time cost because of complex computation of SVM, processes of test signal generator and test structure, and has unstable testing accuracy because of reduced precision in case of compressing the sampled space. The computational complexity of ELM algorithm in sample classification is much lower than that of SVM. Furthermore, trade-off parameters are not sensitive to the accuracy of ELM classification, so ELM has a good classification performance without optimization of trade-off parameters in case of compressing sampled space. For modern intelligent diagnosis of analog circuit faults, the key lies in the extraction of fault features and the design of classification algorithms. In fact, the calculation rate and diagnosis efficiency of the diagnosis system directly hinge on the excellence of the fault feature extraction methods, especially those capable of extracting the features that clearly distinguishes between different types of faults.