A Study on Optimal Time of Artificial Insemination in Cows using Hurst Exponent based on L1 Norm

Abstract

Artificial insemination of cows is closely related to a number of indicators of the stock farms, such as conception rates, income, productivity, etc. Importantly, the success of insemination depends on timely detection of estrus the most. In other words, estrus detection is the most important prerequisite for predicting optimal time of artificial insemination. However, most of the domestic farms rely on a passive method, visual detection, by inseminators for a limited period of time, and thus the average failure rate generally reaches 43.4%. This study proposes an estrus detection method using hurst exponents based on L1 norm to predict optimal time of cow insemination. The hurst exponent, a measure of long-term memory, can play a key role to account for the periodical nature of temporal data. Many studies verified its effectiveness in classifying state categories in a variety of areas. Thus, we applied the hurst exponent to classify the estrus state of cows. Time series data collected from accelerometers were equally divided into windows with a period of 2^13 seconds for monitoring purpose. Wavelet spectrum analysis was then applied across the windows to estimate the local hurst exponents. In the process of complex wavelet transform, we confirmed that most of the wavelet coefficients were sparse signals. For wavelet energy, L2 norm, a common way to get the magnitude, was then substituted with a L1 norm to preserve the magnitudes of the sparse signals. Finally, the estimates of the hurst exponents were obtained from simple linear regression models whose response variable is the wavelet spectrum lying on the resolution level. Applied to physical activity data of the cows, the proposed method is shown to detect the change in activity during estrus, and to have superior performance compared with existing methods.