China
Africa
Explore chapters and articles related to this topic
Hybrid Models and Experimental Design
Published in Jarka Glassey, Moritz von Stosch, Hybrid Modeling in Process Industries, 2018
Model-based experimental design—also referred to as optimal experimental design—is commonly used to reduce the uncertainty of parameter values or to discriminate between competing models. In neural network research, a similar approach exists, typically referred to as active learning, although the idea there is to better explore the region in which the model predictions can be assumed to be of poor quality rather than to directly improve the structure or parameters (weights) of the model. For instance, the sequential pseudo-uniform design approach, which was proposed by Chang et al. (2007) and used along with a hybrid model on a simulated polymerization reactor system, seeks to explore the design region more efficiently. Brendel et al. (2008) proposed a similar approach that, in particular, seeks to extend the design region of dependent variables. Thus, in contrast to classical DoEs, the factors in their approach are not required to be independent, as long as the model describes the dependencies. Brendel and colleagues show that the approach is more efficient in exploring a process region than are classical DoEs. The incorporation of the dependencies is a particular strength of this approach, since the model will capture the process dynamics—those arising from the feedback/dependencies—much better. This is of particular importance for process control, since feedback/dependencies affect the system response and stability. The approach can be set up as an optimization problem, where the difference between the factor values of the new experiment and those of the already-executed experiments is maximized (Brendel and Marquardt 2008).
Optimization of Food Processes Using Mixture Experiments
Published in Surajbhan Sevda, Anoop Singh, Mathematical and Statistical Applications in Food Engineering, 2020
Daniel Granato, Verônica Calado, Edmilson Rodrigues Pinto
Optimal experimental design is a powerful and flexible tool for generating efficient experimental designs, enabling a reduction in the number of experimental trials and, thus, reducing costs and saving time and money. However, the optimal experimental design depends on the model considered and if the model is not suitable the design will not be appropriate.
A fuzzy mixed-integer robust design optimization model to obtain optimum settings of both qualitative and quantitative input variables under uncertainty
Published in Engineering Optimization, 2023
Response surface designs are not appropriate for experiments considering both qualitative and quantitative input variables. Therefore, computer-generated designs may be practical to construct a model matrix using qualitative and quantitative input variables. In this article, an A-optimal experimental design is selected for the design phase because it has good statistical properties, such as estimating the model parameters well. It is also noted that A-optimal experimental designs surpass D-optimal experimental designs based on the variances of individual parameter estimates (Jones, Allen-Moyer, and Goos 2021). Furthermore, the A-optimal experimental design is modified for both qualitative and quantitative input variables while dealing with uncertainty. Therefore, the model matrix can be generated under uncertainty by using the modified A-optimal experimental design, as follows: where tr denotes trace, and it is the sum of the variances of the coefficients. The modified A-optimality criterion-based model in (1) may be verified in the optimum model matrix with the Lagrangian function (Lfun) as:
A Taguchi approach for optimizing the mixture design of cold-bonded PCM aggregates
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2019
Erman Yiğit Tuncel, Bekir Yılmaz Pekmezci
An optimal experimental design should provide the maximum amount of information after the minimum number of experimental trials. Taguchi Methods serve this purpose by utilizing orthogonal arrays to study a large number of variables with a small number of experiments. An orthogonal array (OA) is a type of experiment where the columns for the independent variables are “orthogonal” to one another. It is defined by (i) number of factors to be studied, (ii) levels for each factor, (iii) the specific two-factor interactions to be estimated, and (iv) the special difficulties that would be encountered during the experiment. Since OAs are highly fractionated factorial designs, using the Taguchi approach in experimental design reduces the number of experiments required. This provides several advantages such as reduction in the experimental effort, time, and cost (Rama Rao and Padmanaban 2012).
An I-optimal experimental design-embedded nonlinear lexicographic goal programming model for optimization of controllable design factors
Published in Engineering Optimization, 2021
The term ‘optimal experimental design’ refers to designs constructed for an assumed model and statistical optimality criterion. The I-optimality criterion addresses prediction variance and is used in generating I-optimal experimental designs built to minimize the average prediction variance over the non-standard design region. For controllable design factors, an I-optimal experimental design is defined as follows: where and denotes a column vector of the design variables expanded to model form. Then, the following equation is where . Next, the following equation is found: where . The following equation is then defined as where is constant owing to the integration. E, which is the moment matrix, is defined as follows: Then, the following equation is obtained: Notice that is a constant. Thus, it has no impact on the minimization in Equations (4) and (6), or on , and can be removed (or at least it is indicated that it is a constant and can be ignored in the minimization process).