{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:48:47Z","timestamp":1777394927514,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T00:00:00Z","timestamp":1624233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper develops a novel soft fault diagnosis approach for analog circuits. The proposed method employs the backward difference strategy to process the data, and a novel variant of convolutional neural network, i.e., convolutional neural network with global average pooling (CNN-GAP) is taken for feature extraction and fault classification. Specifically, the measured raw domain response signals are firstly processed by the backward difference strategy and the first-order and the second-order backward difference sequences are generated, which contain the signal variation and the rate of variation characteristics. Then, based on the one-dimensional convolutional neural network, the CNN-GAP is developed by introducing the global average pooling technical. Since global average pooling calculates each input vector\u2019s mean value, the designed CNN-GAP could deal with different lengths of input signals and be applied to diagnose different circuits. Additionally, the first-order and the second-order backward difference sequences along with the raw domain response signals are directly fed into the CNN-GAP, in which the convolutional layers automatically extract and fuse multi-scale features. Finally, fault classification is performed by the fully connected layer of the CNN-GAP. The effectiveness of our proposal is verified by two benchmark circuits under symmetric and asymmetric fault conditions. Experimental results prove that the proposed method outperforms the existing methods in terms of diagnosis accuracy and reliability.<\/jats:p>","DOI":"10.3390\/sym13061096","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T13:29:58Z","timestamp":1624282198000},"page":"1096","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["A Novel Analog Circuit Soft Fault Diagnosis Method Based on Convolutional Neural Network and Backward Difference"],"prefix":"10.3390","volume":"13","author":[{"given":"Chenggong","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daren","family":"Zha","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nan","family":"Mu","sequence":"additional","affiliation":[{"name":"Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China"},{"name":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"A Novel Incipient Fault Diagnosis Method for Analog Circuits Based on GMKL-SVM and Wavelet Fusion Features","volume":"70","author":"Gao","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"23053","DOI":"10.1109\/ACCESS.2018.2823765","article-title":"Analog Circuit Incipient Fault Diagnosis Method Using DBN Based Features Extraction","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/81.974884","article-title":"Fault detection for linear analog IC-the method of short-circuit admittance parameters","volume":"49","author":"Li","year":"2002","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"18305","DOI":"10.1109\/ACCESS.2020.2968744","article-title":"Data-Driven Feature Extraction for Analog Circuit Fault Diagnosis Using 1-D Convolutional Neural Network","volume":"8","author":"Yang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5277","DOI":"10.1109\/TIE.2012.2224074","article-title":"Diagnostics and Prognostics Method for Analog Electronic Circuits","volume":"60","author":"Vasan","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.neucom.2013.11.012","article-title":"Improved diagnostics for the incipient faults in analog circuits using LSSVM based on PSO algorithm with Mahalanobis distance","volume":"133","author":"Long","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1109\/TIM.2011.2161930","article-title":"An Approach to Locate Parametric Faults in Nonlinear Analog Circuits","volume":"61","author":"Deng","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1109\/TIE.2016.2599142","article-title":"Signal Model-Based Fault Coding for Diagnostics and Prognostics of Analog Electronic Circuits","volume":"64","author":"Liu","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kim, K., and Choi, H. (2021). High-efficiency high-voltage class F amplifier for high-frequency wireless ultrasound systems. PLoS ONE, 16.","DOI":"10.1371\/journal.pone.0249034"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6640","DOI":"10.1109\/TIM.2020.2969008","article-title":"Generative Adversarial Networks With Comprehensive Wavelet Feature for Fault Diagnosis of Analog Circuits","volume":"69","author":"He","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1016\/j.isatra.2013.06.006","article-title":"Fuzzy classifier for fault diagnosis in analog electronic circuits","volume":"52","author":"Kumar","year":"2013","journal-title":"ISA Trans."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/TIM.2009.2025068","article-title":"A New Neural-Network-Based Fault Diagnosis Approach for Analog Circuits by Using Kurtosis and Entropy as a Preprocessor","volume":"59","author":"Yuan","year":"2009","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.1016\/j.neucom.2010.12.003","article-title":"A novel approach for analog fault diagnosis based on neural networks and improved kernel PCA","volume":"74","author":"Xiao","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.neucom.2015.12.131","article-title":"An improved SVM classifier based on double chains quantum genetic algorithm and its application in analogue circuit diagnosis","volume":"211","author":"Chen","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s10470-016-0721-5","article-title":"Statistical property feature extraction based on FRFT for fault diagnosis of analog circuits","volume":"87","author":"Song","year":"2016","journal-title":"Analog. Integr. Circuits Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10554","DOI":"10.1016\/j.eswa.2011.02.087","article-title":"A SVDD approach of fuzzy classification for analog circuit fault diagnosis with FWT as preprocessor","volume":"38","author":"Luo","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yuan, X., Miao, Z., Liu, Z., Yan, Z., and Zhou, F. (2020). Multi-Strategy Ensemble Whale Optimization Algorithm and Its Application to Analog Circuits Intelligent Fault Diagnosis. Appl. Sci., 10.","DOI":"10.3390\/app10113667"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1752","DOI":"10.1016\/j.neucom.2015.09.050","article-title":"Analog circuit fault diagnosis based UCISVM","volume":"173","author":"Zhang","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1002\/cta.2075","article-title":"Analog circuits fault diagnosis using multi-valued Fisher\u2019s fuzzy decision tree (MFFDT)","volume":"44","author":"Cui","year":"2016","journal-title":"Int. J. Circ. Theor. App."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.measurement.2015.11.041","article-title":"A novel approach for analog fault diagnosis based on stochastic signal analysis and improved GHMM","volume":"81","author":"Luo","year":"2016","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.asoc.2016.11.012","article-title":"Research on WNN soft fault diagnosis for analog circuit based on adaptive UKF algorithm","volume":"50","author":"Zhe","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/TIM.2018.2836058","article-title":"RideNN: A New Rider Optimization Algorithm-Based Neural Network for Fault Diagnosis in Analog Circuits","volume":"68","author":"Binu","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6690","DOI":"10.1109\/TGRS.2019.2907932","article-title":"Deep Learning for Hyperspectral Image Classification: An Overview","volume":"57","author":"Li","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.neucom.2016.12.038","article-title":"A survey of deep neural network architectures and their applications","volume":"234","author":"Liu","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.measurement.2018.02.044","article-title":"A novel approach for analog circuit fault diagnosis based on Deep Belief Network","volume":"121","author":"Zhao","year":"2018","journal-title":"Measurement"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s10470-020-01732-8","article-title":"A deep network solution for intelligent fault detection in analog circuit","volume":"107","author":"Shokrolahi","year":"2021","journal-title":"Analog. Integr. Circuits Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Deng, Y., and Zhou, Y. (2020). Fault Diagnosis of an Analog Circuit Based on Hierarchical DVS. Symmetry, 12.","DOI":"10.3390\/sym12111901"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1109\/TII.2017.2690940","article-title":"Capturing High-Discriminative Fault Features for Electronics-Rich Analog System via Deep Learning","volume":"13","author":"Liu","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"106330","DOI":"10.1016\/j.ymssp.2019.106330","article-title":"Deep separable convolutional network for remaining useful life prediction of machinery","volume":"134","author":"Wang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","first-page":"1097","article-title":"Imagenet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_31","unstructured":"Ioffe, S., and Szegedy, C. (2015). Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4681","DOI":"10.1109\/TII.2019.2943898","article-title":"Deep Residual Shrinkage Networks for Fault Diagnosis","volume":"16","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4949","DOI":"10.1109\/TII.2020.2967557","article-title":"Multibranch and Multiscale CNN for Fault Diagnosis of Wheelset Bearings under Strong Noise and Variable Load Condition","volume":"16","author":"Peng","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2996","DOI":"10.1109\/TIM.2019.2929669","article-title":"Roller Bearing Degradation Assessment Based on a Deep MLP Convolution Neural Network Considering Outlier Regions","volume":"69","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"108122","DOI":"10.1016\/j.measurement.2020.108122","article-title":"An adaptive data fusion strategy for fault diagnosis based on the convolutional neural network","volume":"165","author":"Li","year":"2020","journal-title":"Measurement"},{"key":"ref_37","first-page":"249","article-title":"Understanding the difficulty of training deep feedforward neural networks","volume":"9","author":"Glorot","year":"2010","journal-title":"J. Mach. Learn. Res."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1096\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:20:07Z","timestamp":1760163607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/6\/1096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,21]]},"references-count":37,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["sym13061096"],"URL":"https:\/\/doi.org\/10.3390\/sym13061096","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,21]]}}}