Comparison and estimation of different linear and nonlinear lactation curve submodels in random regression analyses on dairy cattle

In the random regression model (RRM) for milk yield, by replacing empirical lactation curves with the five-order Legendre polynomial to fit fixed groups, the RRM can be transformed to a hierarchical model that consisted of a RRM in the first hierarchy with Legendre polynomials as individuals’ lactation curves resolved by restricted maximum likelihood (REML) software, and a multivariate animal model for phenotypic regression coefficients in the second hierarchy resolved by DMU software. Some empirical lactation functions can be embedded into the RRM at the first hierarchy to well fit phenotypic lactation curve of the average observations across all animals. The functional relationship between each parameter and time can be described by a Legendre polynomial or an empirical curve usually called submodel, and according to three commonly used criteria, the optimal submodels were picked from linear and nonlinear submodels except for polynomials. The so-called hierarchical estimation for the RRMs in dairy cattle indicated that more biologically meaningful models were available to fit the lactation curves; moreover, with the same number of parameters, the empirical lactation curves (MIL1, MIL5, and MK1 for 3, 4, and 5 parameters, respectively) performed higher goodness of fit than Legendre polynomial when modelling individuals’ phenotypic lactation curves.

A triangulation estimation and forecasting framework for agricultural time series

This study proposes a framework implementing triangular estimation for better modeling and forecasting time series. In order to improve the performance of estimation, we employ two sources of triangulation to generate a time series, which is statistically indistinguishable with the latent time series hidden in a system. Thanks to Bayesian hierarchical estimation, which is akin to deep learning but more sophisticate and longer history, the framework has been validated by a large amount of records in vegetable auctions. The hierarchical Bayesian estimation and Monte Carlo Markov Chain particle filters used in hidden Markov model are appreciated during the massive bootstrapping of data. Our results demonstrate excellent estimation performance in discovering hidden states.

Multi-Level Hierarchical Estimation for Thermal Management Systems of Electrified Vehicles

This paper presents a multi-level model-based hierarchical estimation framework for complex thermal management systems of electrified vehicles. System dynamics are represented by physics-based lumped parameter models derived from a graph-based modeling approach. The complexity of hierarchical models is reduced by applying an aggregation-based model order reduction technique that preserves the physical correspondence between a physical system and its reduced-order model. The paper presents a case study in which a hierarchical observer is designed to estimate the dynamics of a candidate system. The hierarchical observer is connected to a hierarchical controller for closed-loop control. A comparison between the proposed hierarchical observer and a centralized observer shows that a hierarchical observer enables a reduction in the required computational power.

Multilevel Hierarchical Estimation for Thermal Management Systems of Electrified Vehicles With Experimental Validation

This paper presents a multilevel model-based hierarchical estimation framework for complex thermal management systems of electrified vehicles. System dynamics are represented by physics-based lumped parameter models derived from a graph-based modeling approach. The complexity of the hierarchical models is reduced by applying an aggregation-based model-order reduction technique that preserves the physical correspondence between a reduced-order model and the physical system. This paper also presents a case study in which a hierarchical observer is designed to estimate the dynamics of a candidate system. The hierarchical observer is connected to a previously developed hierarchical controller for closed-loop control, and the closed-loop performance is demonstrated through simulation and real-time experimental results. A comparison between the proposed hierarchical observer and a centralized observer shows the tradeoff between the estimation accuracy and the computational complexity of the two approaches.