Response surface methodology modeling of protein concentration, coagulum cut size, and set temperature on curd moisture loss kinetics during curd stirring

peer-reviewedThe effects of the independent variables protein concentration (4–6%), coagulum cut size (6–18 mm3), and coagulation temperature (28–36°C) on curd moisture loss during in-vat stirring were investigated using response surface methodology. Milk (14 kg) in a cheese vat was rennet coagulated, cut, and stirred as per semihard cheesemaking conditions. During stirring, the moisture content of curd samples was determined every 10 min between 5 and 115 min after cutting. The moisture loss kinetics of curds cut to 6 mm3 followed a logarithmic trend, but the moisture loss of curds from larger cut sizes, 12 or 18 mm3, showed a linear trend. Response surface modeling showed that curd moisture level was positively correlated with cut size and negatively correlated with milk protein level. However, coagulation temperature had a significant negative effect on curd moisture up to 45 min of stirring but not after 55 min (i.e., after cooking). It was shown that curds set at the lower temperature had a slower syneresis rate during the initial stirring compared with curds set at a higher temperature, which could be accelerated by reducing the cut size. This study shows that keeping a fixed cut size at increasing protein concentration decreased the level of curd moisture at a given time during stirring. Therefore, to obtain a uniform curd moisture content at a given stirring time at increasing protein levels, an increased coagulum cut size is required. It was also clear that breakage of the larger curd particles during initial stirring can also significantly influence the curd moisture loss kinetics. Both transmission and scanning electron micrographs of cooked curds (i.e., after 45 min of stirring) showed that the casein micelles were fused at a higher degree in curds coagulated at 36°C compared with 28°C, which confirmed that coagulation temperature causes a marked change in curd microstructure during the earlier stages of stirring. The present study showed the dynamics of curd moisture content during stirring when using protein-concentrated milk at various set temperatures and cut sizes. This provides the basis for achieving a desired curd moisture loss during cheese manufacture using protein-concentrated milk as a means of reducing the effect of seasonal variation in milk for cheesemaking

Response Surface Methodology for Optimizing Hyper Parameters

The performance of an algorithm often largely depends on some hyper parameter which should be optimized before its usage. Since most conventional optimization methods suffer from some drawbacks, we developed an alternative way to find the best hyper parameter values. Contrary to the well known procedures, the new optimization algorithm is based on statistical methods since it uses a combination of Linear Mixed Effect Models and Response Surface Methodology techniques. In particular, the Method of Steepest Ascent which is well known for the case of an Ordinary Least Squares setting and a linear response surface has been generalized to be applicable for repeated measurements situations and for response surfaces of order o ?Ü 2. --repeated measurements,Random Intercepts Model,deterministic error terms,Method of Steepest Ascent,Support Vector Machine

The Response Surface Methodology

Thesis (M.A.) -- Indiana University South Bend, 2007.The experimentation plays an important role in Science, Engineering, and Industry. The experimentation is an application of treatments to experimental units and then measurement of one or more responses. It is a part of scientific method. It requires observing and gathering information about how process and system works. In an experiment, some input x’s transform into an output that has one or more observable response variables y. Therefore, useful results and conclusions can be drawn by experiment. In order to obtain an objective conclusion an experimenter needs to plan and design the experiment, and analyze the results. There are many types of experiments used in real-world situations and problems. When treatments are from a continuous range of values then the true relationship between y and x’s might not be known. The approximation of the response function y = f (x1, x2,...,xq) + e is called Response Surface Methodology. This thesis puts emphasis on designing, modeling, and analyzing the Response Surface Methodology. The three types of Response Surface Methodology, the first-order, the second-order,and three-level fractional factorial, will be explained and analyzed in depth. The thesis will also provide examples of application of each model by numerically and graphically using computer software

Robust optimization in simulation: Taguchi and response surface methodology

Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a `robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Response Surface Methodology (RSM). George Box originated RSM, and Douglas Montgomery recently extended RSM to robust optimization of real (non-simulated) systems. We combine Taguchi's view with RSM for simulated systems. We illustrate the resulting methodology through classic Economic Order Quantity (EOQ) inventory models, which demonstrate that robust optimization may require order quantities that differ from the classic EOQ

Application of response surface methodology to stiffened panel optimization

In a multilevel optimization frame, the use of surrogate models to approximate optimization constraints allows great time saving. Among available metamodelling techniques we chose to use Neural Networks to perform regression of static mechanical criteria, namely buckling and collapse reserve factors of a stiffened panel, which are constraints of our subsystem optimization problem. Due to the highly non linear behaviour of these functions with respect to loading and design variables, we encountered some difficulties to obtain an approximation of sufficient quality on the whole design space. In particular, variations of the approximated function can be very different according to the value of loading variables. We show how a prior knowledge of the influence of the variables allows us to build an efficient Mixture of Expert model, leading to a good approximation of constraints. Optimization benchmark processes are computed to measure time saving, effects on optimum feasibility and objective value due to the use of the surrogate models as constraints. Finally we see that, while efficient, this mixture of expert model could be still improved by some additional learning techniques

Robust Optimization in Simulation: Taguchi and Response Surface Methodology

Optimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a 'robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Response Surface Methodology (RSM). George Box originated RSM, and Douglas Montgomery recently extended RSM to robust optimization of real (non-simulated) systems. We combine Taguchi's view with RSM for simulated systems, and apply the resulting methodology to classic Economic Order Quantity (EOQ) inventory models. Our results demonstrate that in general robust optimization requires order quantities that differ from the classic EOQ.Pareto frontier;bootstrap;Latin hypercube sampling

Optimal design of single-tuned passive filters using response surface methodology

This paper presents an approach based on Response Surface Methodology (RSM) to find the optimal parameters of the single-tuned passive filters for harmonic mitigation. The main advantages of RSM can be underlined as easy implementation and effective computation. Using RSM, the single-tuned harmonic filter is designed to minimize voltage total harmonic distortion (THDV) and current total harmonic distortion (THDI). Power factor (PF) is also incorporated in the design procedure as a constraint. To show the validity of the proposed approach, RSM and Classical Direct Search (Grid Search) methods are evaluated for a typical industrial power system