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For the safe operation of nuclear power plants (NPPs), it is significant to promptly and correctly identify malfunctions/transients, which is difficult for the operators by monitoring the variation of important parameters. In this paper, a novel method is proposed for the transient identification in NPPs. It directly models the transients in a linear space that is represented by a matrix instead of a training process. Then a transient can be represented via a linear combination of the columns of the modeling matrix, and the coefficient vector encodes the identity of the transient. To obtain the coefficient vector, the smoothed ℓ0 -norm optimization (SL0) algorithm is adopted, where the truncated singular value decomposition (TSVD) method is combined to improve the stability. Then the identification of a transient can be accomplished by examining the property of the solution using three quantities. The proposed method can correctly classify the transients and successfully reject “unknown” types, and it is applicable under a wide range of operational conditions. It is verified by simulator data of pebble-bed modular high temperature gas-cooled reactor nuclear power plant (HTR-PM) developed by Institute of Nuclear and New Energy Technology with Tsinghua University.