In nonlinear system identification, one of the main challenges is how to select a nonlinear model. The accuracy of nonlinear subspace identification depends on the accuracy of the nonlinear feedback force that the user chooses. Considering the uncertainties in the selection process of an appropriate nonlinear model, a novel Bayesian probability method calculation framework based on response data is established to improve the accuracy of nonlinear subspace identification. Three implementation steps are introduced: 1) establish the candidate model database; 2) the reconstructed signal can be calculated by nonlinear subspace identification; and 3) the posterior probability of each candidate model is estimated to get the optimal nonlinear model and determine the nonlinear coefficients of the nonlinearities. Two numerical simulations are investigated: a two-degree-of-freedom spring-mass system with nonlinear damping and a cantilever beam with nonlinear stiffness. The influence of the noise on the robustness of the algorithm is considered. The experimental investigation is eventually undertaken considering a device showing elastic and damping nonlinearities. The latter is represented by a friction model depending on both velocity and displacement. Results indicate that the proposed approach can effectively identify the nonlinear system behavior with high accuracy.

在非线性系统辨识中，主要挑战之一是如何选择非线性模型。非线性子空间识别的精度取决于用户选择的非线性反馈力的精度。考虑到在选择合适的非线性模型过程中存在的不确定性，建立了一种基于响应数据的新型贝叶斯概率方法计算框架，以提高非线性子空间识别的准确性。介绍了三个实现步骤：1）建立候选模型数据库；2）重构信号可以通过非线性子空间识别计算得到；3)估计每个候选模型的后验概率，得到最优的非线性模型，确定非线性的非线性系数。研究了两个数值模拟：具有非线性阻尼的二自由度弹簧质量系统和具有非线性刚度的悬臂梁。考虑了噪声对算法鲁棒性的影响。最终进行实验研究，考虑到显示弹性和阻尼非线性的设备。后者由取决于速度和位移的摩擦模型表示。结果表明，所提出的方法可以有效地识别非线性系统的行为，并且具有很高的准确度。后者由取决于速度和位移的摩擦模型表示。结果表明，所提出的方法可以有效地识别非线性系统的行为，并且具有很高的准确度。后者由取决于速度和位移的摩擦模型表示。结果表明，所提出的方法可以有效地识别非线性系统的行为，并且具有很高的准确度。