Cough is a vital index to evaluate the health status and postoperative recovery of patients. To realize the quantification of cough and solve the problem of excessive noise features and abnormal features in sound data during cough sound recognition, this paper proposes a PSO-GBDT-LR model to quantify cough by distinguishing cough sounds and non-cough sounds more accurately. It first leverages the Gradient Boosting Decision Tree (GBDT) to extract the leaf node index features from the original ones. Subsequently, it combines these features with the original features and puts the combined data into Logistic Regression (LR) for cough sound classification. Thanks to the powerful feature extraction of GBDT and the strong generalization ability of LR, it can effectively solve the problem of too many noisy features and abnormal features in cough recognition. Then, the hyperparameters of GBDT-LR are selected by Particle Swarm Optimization (PSO), which avoids the disadvantages of low efficiency and unsatisfactory accuracy of subjective selection of hyperparameters. In the cough recognition method flow, the cough audio signal collection device is used to collect the cough audio signals of healthy people and patients. Subsequently, the time series data is segmented using the double-threshold acoustic activity detection method. The time domain features and frequency domain features are extracted from each segment as the original features to train and test PSO-GBDT-LR. Ultimately, the effectiveness and superiority of the proposed model are demonstrated through comparison with other machine learning models. It has a mean precision of 93.965%, a mean recall of 93.93%, a mean F1 score of 93.945%, and an accuracy of 93.96%.