W. B. Roush

Kalman filter and an example of its use to detect changes in poultry production responses

Abstract The Kalman filter, a recursive algorithm for making short-term predictions, was written in BASIC and applied to feed consumption data of a commercial laying hen flock. The results showed that trends such as steady state, slope changes and transient responses could be monitored daily. Early detection of a change in response as differentiated from normal data variation allows the manager to make appropriate management adjustments for the flock.

Prediction of amino acid profiles in feed ingredients : Genetic algorithm calibration of artificial neural networks

Linear regression (LR) has been used to predict the amino acid (AA) profiles of feed ingredients, given proximate analysis (PA) input. Artificial neural networks (ANN) have also been trained to predict AA levels, generally with better results. Past projects have indicated that ANN more effectively identified the complex relationship between nutrients and feed ingredients than did LR. It was shown that the maximum R2 value, a measurement of the amount of variability explained by the model, was highest when a general regression neural network (GRNN) with iterative calibration (GRNNIT) was used to train the ANN. This was in comparison to LR, Ward backpropagation (WBP) or 3-layer backpropagation (3BP) architectures. The current study investigated the potential of a new, advanced method of calibration using the genetic algorithm (GA) to optimize GRNN smoothing values. Calibration of an ANN allows the neural network to generalize well and therefore provide good results on new data. A GRNN architecture (NeuroShell 2® Software) with GA calibration (GRNNGA) was used to train an ANN to predict AA levels in maize, soya bean meal (SBM), meat and bone meal, fish meal and wheat, based on proximate analysis input. Within the GRNNGA architecture, ANN were trained with either an Euclidean or City Block distance metric and a (0,1), (−1,1), (logistic) or (tanh) input scale. Predictive performance was judged on the basis of the maximum R2 value. In general, maximum R2 values were higher when the GA calibration was used in comparison to LR. For example, the highest methionine (MET) R2 value for SBM was 0.54 (LR), 0.81 (3BP), 0.87 (WBP), 0.92 (GRNNIT) and 0.98 (GRNNGA). Genetic algorithm calibration of GRNN architecture led to further improvements in ANN performance for AA level predictions in most of the cases studied. Exceptions were the TSAA level in SBM (0.94 with GRNNIT vs. 0.90 with GRNNGA) and the TRY level in maize (0.88 with GRNNIT vs. 0.61 with GRNNGA).

Stochastic true digestible amino acid values

Abstract The concept of using amino acid digestibility coefficients has been reported to be valuable in formulating diets to meet the requirements of livestock. Digestibility coefficients of nutrients reflect the amounts of components of a feedstuff that become available to meet livestock requirements. Most biological factors, including feed ingredient amino acid means and their digestibility values, have variabilities associated with them. Chance constrained (stochastic) programming for feed formulation has been suggested as a method that accounts for variability. The ingredient matrix for stochastic formulation requires means and standard deviations (S.D.s) for all nutrients involved in the formulation. Several references were used to provide ingredient amino acid means and S.D.s, and true digestibility coefficient means and S.D.s. When there is variability associated with two or more variables in a calculation (e.g. nutrient mean and S.D., coefficient of true digestibility mean and S.D.), it is a nonlinear problem involving the application of the principles of probability theory for a solution. It is a mathematical oversimplification to multiply an amino acid S.D. by the coefficient of true digestibility for the calculation of the digestibility S.D. This technique would result in an under-estimation of the S.D. associated with the digestibility of the amino acid. A Microsoft Excel

Grazing incidence optics for wide-field x-ray survey imaging: a comparison of optimization techniques

Discussions of optimizing wide-field x-ray optics, with field-of-view less-than 1.1 degree-squared, have been made previously in the literature. However, very little has been published about the optimization of wide-field x-ray optics with larger field-of-views, which technology could greatly enhanced x-ray surveys. We have been working on the design of a wide-field (3.1 degree-squared field-of-view), short focal length (190.5 cm), grazing incidence mirror shell set, with a desired rms image spot size of 15 arcsec. The baseline design consists of Wolter 1 type mirror shells with polynomial perturbations applied to the baseline design. The overall optimization technique is to efficiently optimize the polynomial coefficients that directly influence the angular resolution, without stepping through the entire multi-dimensional coefficient space. We have investigated optimization techniques such as the downhill simplex method, fractional factorial, and response surface (including Box- Behnken and central composite) design. We have also investigated the use of neural networks, such as backpropagation, general regression, and group method of data handling neural networks. We report our findings to date.

Partitioning of variance in true metabolizable energy determinations: an example using wheat data

A variance statistic was used to partition the total variance into that attributable to each step of a TMEN assay procedure. Estimation of the TMEN of wheat was used as an example. The variance statistic can also be used to optimize the design of a TMEN experiment with respect to cost of the experiment and desired accuracy of the result. Experimental design optimization is accomplished by providing a functional relationship between the accuracy of the estimate and the number of replicates of feed, the number of birds used in the experiment, and the cost of each step. The variance statistic is also a useful tool for identifying and removing outliers and highly variable measurements. This feature was demonstrated with the chosen example data. Gross energy of the feed will explain approximately 50% of the variance of the TMEN estimate depending on how many replicates are evaluated. Nitrogen content of the feed sample will explain approximately 40% of the total variance. It is recommended to replicate this measurement as many times as possible. Ten replicates were recommended for the example data. The energy content of excreta from fed birds represented the next largest source of variance, at approximately 4% of the total variance, respectively. If within-bird variance is large, better homogenization of the sample and more replicates are recommended. If among-bird variance is significantly different, more birds should be used. Nitrogen content of excreta from fed birds represented less than 2.5% of the total variance. Energy and nitrogen content of excreta from unfed birds combined represented less than 2% of the total variance, suggesting that the number of unfed birds and the amount of excreta sub-samples may be reduced without adversely affecting the accuracy of the TMEN estimate. Variance due to the amount of excreta collected from the fed birds, and variance due to the amount of feed consumed by the birds, are expected to be small. This result suggested that force-feeding may not be necessary for accurate TMEN estimates.