Nonlinear viscous dampers can efficiently improve the seismic performance of structures by dissipating large amounts of earthquake-induced energy. In common practice, the spectral analysis of structures with nonlinear viscous dampers is generally conducted based on an estimated equivalent damping ratio. To this end, the stochastic linearization technique can be used as an effective probabilistic approach to take into account the evolutionary characteristics of the input earthquake excitation. This study aims to present optimal non-Gaussian probability density functions to improve the accuracy of the stochastic linearization technique for nonlinear viscous dampers in both firm and soft soil-based structures. It is shown that by using the optimum probability density functions, the computational error of the stochastic linearization technique for a single-degree-of-freedom structure under simulated ground motions, with a range of peak ground accelerations between 0.1 and 0.6 g, is reduced by up to 70%. The efficiency of the proposed probability density functions is then demonstrated for multi-degree-of-freedom structures, by estimating the roof displacements of a six-story steel frame with nonlinear viscous dampers under a set of natural ground motions using different linearization methods. The comparison of the stochastic linearization technique estimated responses with the exact values confirms that using the proposed probability density functions leads to considerably lower errors in both firm and soft soil-based structures compared with the other linearization techniques.

非线性粘性阻尼器可以通过耗散大量的地震感应能量来有效地改善结构的抗震性能。在通常的实践中，通常基于估计的等效阻尼比对具有非线性粘性阻尼器的结构进行光谱分析。为此，随机线性化技术可以用作一种有效的概率方法，以考虑输入地震激励的演化特征。这项研究的目的是提出最佳的非高斯概率密度函数，以提高非线性粘性阻尼器在坚固和软土地基结构中的随机线性化技术的准确性。结果表明，通过使用最佳概率密度函数，对于单自由度结构在模拟地面运动下（峰值地面加速度范围在0.1到0.6 g之间）的随机线性化技术，其计算误差最多可降低70％。然后，通过使用一组不同的线性化方法，通过估算一组自然地震动下带有非线性粘性阻尼器的六层钢框架的屋顶位移，证明了所提出的概率密度函数对于多自由度结构的效率。随机线性化技术的估计响应与精确值的比较证实，与其他线性化技术相比，使用建议的概率密度函数可以在坚固和软土基结构中导致更低的误差。