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Heat stress has threatened dairy cows during periods of high temperatures. Dairy farms can often assess the respiratory rate (breahts per minute, bpm) of dairy cows, and then implement timely environmental control measures to mitigate the heat stress, thus enhancing the welfare of animals and production performance. However, previous empirical or numerical models cannot accurately predict the respiratory rate of individual dairy cows in real environments. Data-driven machine learning models can be expected to provide a better representation of the relationship between various variables, particularly on the actual respiratory rate. In this study, a random forest-based prediction model was introduced for the cow respiration rate. Five hyperparameters were fine-tuned using genetic algorithm (GA), differential evolution algorithm (DE), particle swarm optimization algorithm (PSO), and Bayesian optimization (BO). These random forest-based models were compared with the artificial neural network (ANN) and extreme gradient boosting (XGBoost) models under grid search (GS). The training data was obtained from a commercial dairy farm in North China. The thermal environment parameters (air temperature, relative humidity, wind speed, and solar radiation) were integrated with the sampling time blocks and cattlerelated variables. The thermal environment variables were utilized as the input features to construct four heat stress indices, namely the temperature-humidity index (THI), adjusted temperature-humidity index (ATHI), equivalent temperature index for cattle (STIC), and skin temperature index (STIC). The dataset was comprised of 3005 records, with 80% allocated for training and 20% for testing. Hyperparameter optimization was conducted on the training set using 5-fold cross-validation. The correlation analysis revealed that there was a highly significant correlation (P<0.01) between all thermal environment variables, heat stress indices, and the respiratory rate of cows. Additionally, significant correlations (P<0.01) were observed between the thermal environment variables and heat stress indices. In feature collinearity, the overall dataset was partitioned into five subdatasets: EP, THI, ATHI, ETIC, and STIC dataset. The differentiation among these subsets was combined with the distinct environmental variables. Specifically, the EP dataset comprised four environmental parameters, while the rest dataset's features were the corresponding indices. Results indicated that the baseline random forest model achieved the highest prediction accuracy, when utilizing the adjusted temperature-humidity index, time block, milk production of the cows, days of lactation, body posture, and the number of calving as inputs. On the test set of the ATHI feature, the performance of the RF-based model was better than those of the GS-ANN and GS-XGBoost under the four intelligent optimizations. The random forest model was optimized by the differential evolution algorithm (DE-RF), indicating the highest accuracy, with a coefficient of determination (R2 ), mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) on the testing set of 0.614, 7.708 bpm, 14.4%, and 9.730 bpm, respectively. After that, the Bayesian-optimized random forest model (BO-RF) was achieved in a coefficient of determination, mean absolute error, mean absolute percentage error, and root mean square error on the testing set of 0.614, 7.723, 14.4%, and 9.737, respectively. Notably, the BO-RF was only required 1/200 of the time taken by the DE-RF. As a result, the BO-RF displayed the most favourable overall performance, in terms of prediction accuracy and computational time. Subsequently, the relative importance (RI) of the input features was determined using the BO-RF. The feature importance analysis revealed that the adjusted temperature-humidity index held the highest importance in the model prediction (RI value = 0.73), followed by time block (RI value = 0.09), milk production of cattle (RI value = 0.07), and days of lactation (RI value = 0.06). The body posture of the cattle (RI value = 0.03) and the number of calving (RI value = 0.02) shared a marginal impact on the model predictions. This finding can offer valuable insights into the precise and intelligent control system in dairy barns. [ABSTRACT FROM AUTHOR]

Heat stress seriously affects the productivity, fertility and welfare of dairy cows. It is to be expected that, in the course of the next few decades, climate conditions for raising cattle will deteriorate. In order to reduce the risks of heat stress in dairy cows, researchers have been trying to seek a reliable method to predict or evaluate heat stress, and it has been become to a hot topic in this research field to obtain an index model by combining multiple environmental factors. To avoid blindness in selecting these environmental factors, this paper systematically analyzed the temperature-humidity index, and its modified indices based on THI combined with other factors, and compared the differences among these indices in characterizing the heat stress of dairy cows. These differences relate to the thresholds of indices, environmental factors involved and heat exchanging properties, and the relationships between physiological responses of dairy cows and indices. In this paper, the problems of heat stress index of dairy cows are also discussed. The most widely used temperature-humidity index is based on thermal sensation and thermal comfort of human, but had not been actually related to cow’s living environments. Most indices linking environmental parameters to the physiological or behavioral responses of cows were established through the statistical correlation analysis process, but it did not reflect the real physical significance of the effects of environmental parameters on the process of heat exchange between animals and its environmental factors. In addition, the indices could only be well applied to the situation where they were established properly with the sufficient information for their use. We believed that THI had played an important role in the past when environmental parameters, physiology indicators and behavior responses were hard to be obtained, but the problem of THI had been existing in its application, so other direct parameters such as heat tolerance of high-yielding cows, the change of building structure and the linkage of various cooling modes should be considered when a new THI is being designed. Otherwise, the current THI will be not to meet the future production requirements of the dairy farming industry. With the application of digital technology, multi-parameter acquisition technology has been fundamentally changed, so it is necessary to develop a more reliable index of evaluating heat stress for cows to meet the needs of increasing livestock productivity and achieving welfare. Our suggestions to achieve this goal are as follows: 1) The index should be developed to incorporate more environmental parameters reflecting heat transfer mechanism. 2) The index can be applied not only in some specific climatic conditions, but also in other climatic conditions. 3) The index is to have applicable conditions and thresholds, and the thresholds of the index should be able to be dynamically adjusted to extend the scope of its application. 4) The index should be linked to animal physiological parameters and environmental factors, and consideration could be given to constructing a new index by meeting the theory of animal thermal balance. [ABSTRACT FROM AUTHOR]