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To estimate the parameters and time\u2010delay simultaneously, a redundant rule method is introduced, which turns the time\u2010delayed model into an augmented model. Then, two GD algorithms can be used to identify the time\u2010delayed model. Compared with the traditional GD algorithms, these two modified GD algorithms have the following advantages: (1) avoid a high\u2010order matrix eigenvalue calculation, thus, are more efficient for large\u2010scale systems; (2) have faster convergence rates, therefore, are more practical in engineering practices. 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