An application of evolutionary system identification algorithm in modelling of energy production system
Introduction
The art of building mathematical models from the input–output data obtained from the System is known as System Identification. The main purpose of building the models from the system is to understand its behavior and predicts its performance for fault diagnosis. The term modeling has been extensively used in the field of SI. Basically, several types of models, systems and methods can be studied under various fields of SI as shown in Fig. A1 in Appendix A [1]. The systems modelled can be the manufacturing processes, cleaner energy production systems such as fuel cell or such as those involving the study of mechanical and thermal properties of graphene and carbon nanotubes or the stock market and weather phenomenon, etc. [1]. Among these processes, the energy storage systems such as fuel cells and batteries are the potential ones because they reduce the environmental burden arising due to toxic gases emitted by industries and by transportation vehicles. The system complexity and its functioning depends on the multiple set of input–output variables attributed to it. The cost incurred in optimization of system behavior is high because it is not economical to measure the data. The main concept behind analyzing the obtained data from the system is to unravel the useful information that is responsible for its long term efficient performance before the system is replaced. Given with the multi-functional nature of the systems, the need of modeling and optimization has been strengthened to understand its complex behavior.
The work described in this manuscript is divided into seven sections. Section 2 discusses the models and modeling methods classified under various fields of SI. Section 3 discusses the alternative methodology (evolutionary approach of Genetic programming (GP)) suggested in the latest trends in era of SI. Section 4 illustrates the application of GP in modeling of the fuel cell system. Section 5 discussed the model formulation and statistical fit on the experimental data. Section 6 provides the uncertainty analysis, 2-D and 3-D surface analysis and optimization results of GP model. Finally, Section 7 concludes the study with recommendations and novelty in work.
Section snippets
Literature review on SI
This section describes the various types of models, systems and methods being studied in SI. The methods such as those based on statistics, finite element analysis or artificial intelligence can be used to formulate models. Models are also formed using Analysis of Variance (ANOVA) or the hypothesis tests. These models however serve common purpose to understand the complex systems behavior. Models build on only the given input–output continuous data are known as regression models. The methods
Evolutionary system Identification approach of genetic programming
The literature review on SI reveals that evolutionary SI approach of GP can be suitable alternative for modeling complex systems when its behavior is completely unknown. There are hardly any statistical assumptions in the mechanism of GP. The mechanism (Fig. 1) of GP is similar to GA and being extensively used as a structural optimization methodology. Researchers have developed hybrid approach of GP such as GA-GP [30], Clustering-GP [31], FEM-GP [32], GP-OLS [33], GP-SA [34], etc. for improving
Statement of the research
Direct methanol fuel cell (DMFC) is considered as an alternative source for generating cleaner energy [36], [37]. An appropriate value of operating conditions for DMFC affects its efficiency and performance. DMFC is a complex system and therefore, the notion of mathematical modeling and optimization seems to be a suitable alternative to attain the values of these operating conditions. Among the type of mathematical models and methods discussed in Section 2, it will be interesting to explore the
Results for GP based power density model
The GP simulations are performed in MATLAB R2010b with the population size and the maximum number of genes is set at 300 and 15 respectively. For selecting the parent genes from the pool of available solutions, a Lexicographic tournament selection strategy is adopted with a tournament size of 4. The maximum depth of each tree is set to 15. The crossover, mutation and direct reproduction probabilities are taken as 0.85, 0.1 and 0.05 respectively.
The training data samples from the data set (Table
Uncertainty analysis and optimization
The power density model generated by GP is simulated in three uncertain operating conditions to check if the model formulated is providing the range of values within the permissible working conditions of DMFC. In this simulation design, each of the input is assumed to follow a normal distribution with the minimum and maximum values set same as those of the three input conditions. Fig. 4 shows that an approximate normal trend is observed with the power density values of DMFC ranging from 0.2 to
Conclusions
The present study highlights the importance of system identification (SI) approaches in modeling and optimization of complex systems such as the fuel cell. A comprehensive literature study on types of modeling methods and models in several fields of SI is conducted. Important issues such as automation of model structure and its parameter evaluation is addressed by showing the application of an evolutionary approach of GP in modeling of direct methanol fuel cell (DMFC). The models formulated
Acknowledgement
The authors wish to acknowledge that this research has been supported by Shantou University Scientific Research Foundation (Grant No. NTF 16002).
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