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Wind-induced vibration has become increasingly prominent for long-span bridges. Flutter instability, as a type of divergent vibration, is a key component in the wind resistance investigation of long-span bridges. Based on the principle of instantaneous power balance (IPB) of the flutter critical state of bridge girders, an algorithm for predicting the flutter critical wind speed of long-span bridges was proposed by utilizing a nonlinear optimization strategy. For the bending–torsional coupling two-dimensional (2-D) motion system, the contribution of the wind-induced self-excited and structural elastic forces of the 2-D bridge section to the energy of the system was revealed to be dependent on some key parameters, such as reduced frequency, wind speed, amplitude ratio, and phase lag between vertical and torsional motions. Therefore, according to the principle of IPB during the critical flutter state, the prediction of flutter onset wind velocity can be transformed into an extreme value optimization problem of the IPB objective function. The feasibility and accuracy of the IPB algorithm were verified by comparing them with those obtained from segmental model wind tunnel tests and previous 2-D flutter prediction algorithms. Compared with the traditional methods characterized by force balance, the proposed method clearly and quantitatively presents the contribution relationship among multiple self-excited aerodynamic components on the flat plate and bridge section while flutter occurs; the method first evaluates the flutter critical state as an alternative algorithm from an energy perspective. [ABSTRACT FROM AUTHOR]