Dealing With Uncertainty in Engineering and Management Practices

Peng, Wei
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Faculty of Graduate Studies and Research, University of Regina

A set of methodologies is proposed for dealing with uncertainties in five fields. These fields are: (1) traffic noise impact assessment, (2) hydraulic reliability assessment and reliability based optimization, (3) binary linear programming, (4) real-time multiple source water
blending optimization, and (5) process control of an industrial rotary kiln. The proposed methods are applied to several engineering and management cases to demonstrate their explicabilities and advantages.

In the field (1), an integrated approach is presented to assess traffic noise impact under uncertainty (Peng and Mayorga, 2008). Three uncertain inputs, namely, traffic flow, traffic speed and traffic components, are represented by probability distributions. Monte Carlo simulation is performed to generate these noise distributions. Further, fuzzy sets and binary fuzzy relations are employed in the qualitative assessment. Finally, the quantification of noise impact is evaluated using the probability analysis.

In the field (2), two innovative approaches are developed under uncertainty (Peng and Mayorga, 2010e). One is to assess hydraulic reliability that accounting for the deterioration of both structural integrity and hydraulic capacity of each pipe; another is to design a reliability- based optimal rehabilitation/upgrade schedule that considering both hydraulic failure potential and mechanical failure potential. In these two approaches, all uncertain hydraulic parameters are treated as random values. The main methodologies used are: Monte Carlo simulation, EPANET simulation, genetic algorithms, Shamir and Howard’s exponential model, threshold break rate model, and two-stage optimization model. Eventually, two universal codes, the hydraulic reliability assessment code and the long-term schedule code,were written in MATLAB and linked with EPANET.

In the field (3), an interval coefficient fuzzy binary linear programming (IFBLP) and its solution are built under uncertainty (Peng and Mayorga, 2010c, 2010d). In the IFBLP, the parameter uncertainties are represented by the interval coefficients, and the model structure uncertainties are reflected by the fuzzy constraints and a fuzzy goal. The solution includes a defuzzification process and a crisping process. An alpha-cut technique is utilized for the defuzzification process, and an interval linear programming algorithm is used to the crisping process. One mixed technique (links the alpha-cut technique and min-operator technique) is used to determine a single optimal alpha value on a defuzzified crisp-coefficient BLP. Finally, the IFBLP is converted into two extreme crisping BLP models: a best optimum model and a worst optimum model.

Uncertainties in the field (4) include the modeling uncertainty and dynamic input uncertainty (Peng et al, 2010a, 2010b). This dissertation provides a fuzzy multiple response surface methodology (FMRSM) to deal with these kinds of uncertainties. In the FMRSM, the experimental data sets are fitted into the first quadratic models and their residuals are fitted into the second quadratic models; the multiple objectives are optimized using a fuzzy optimization method. Six scenarios are designed based on a real-time operation. The results show the FMRSM is a robust, computational efficient and overall optimization approach for the real-time multi-objective nonlinear optimization problems.

In the field (5), a dual-response-surface-based process control (DRSPC) programming is developed to address the uncertainty and dynamic calcination process (Peng, et al, 2010f). Several response surface models are appropriately fitted for an industrial rotary kiln. The proposed
approach is applied on a real case. The application shows that the proposed approach can rapidly provide the optimal and robust outputs to the industrial rotary kiln. Other properties of the proposed approach include a solution for the time delay problem and a statistical elimination of measurement errors.