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Specifically, we study the cases where the unitaries are applied periodically, quasiperiodically, aperiodically and randomly. For a periodic protocol, when $U_1 = e^{-i H_1 T/2}$ and $U_2 = e^{-i H_2 T/2}$ are applied alternately, we find that end modes may appear, but the number of end modes does not always agree with the winding number which is a $Z$-valued topological invariant. 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Specifically, we study the cases where the unitaries are applied periodically, quasiperiodically, aperiodically and randomly. For a periodic protocol, when $U_1 = e^{-i H_1 T/2}$ and $U_2 = e^{-i H_2 T/2}$ are applied alternately, we find that end modes may appear, but the number of end modes does not always agree with the winding number which is a $Z$-valued topological invariant. 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