This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and integrated problem construction/solution/visualization. This paper introduces the GEKKO Optimization Suite, presents GEKKO’s approach and unique place among AMLs and optimal control packages, and cites several examples of problems that are enabled by the GEKKO library.

This paper describes nonlinear methods in model building, dynamic data reconciliation, and dynamic optimization that are inspired by researchers and motivated by industrial applications. A new formulation of the 1-norm objective with a dead-band for estimation and control is presented. The dead-band in the objective is desirable for noise rejection, minimizing unnecessary parameter adjustments and movement of manipulated variables. As a motivating example, a small and well-known nonlinear multivariable level control problem is detailed that has a number of common characteristics to larger controllers seen in practice. The methods are also demonstrated on larger problems to reveal algorithmic scaling with sparse methods. The implementation details reveal capabilities of employing nonlinear methods in dynamic applications with example code in both Matlab and Python programming languages.

Abstract:This work demonstrates the use of genetic algorithms in optimized view planning for 3D reconstruction applications using small unmanned aerial vehicles (UAVs). The quality of UAV site models is currently highly dependent on manual pilot operations or grid-based automation solutions. When applied to 3D structures, these approaches can result in gaps in the total coverage or inconsistency in final model resolution. Genetic algorithms can effectively explore the search space to locate image positions that produce high quality models in terms of coverage and accuracy. A fitness function is defined, and optimization parameters are selected through semi-exhaustive search. A novel simulation environment for evaluating view plans is demonstrated using terrain generation software. The view planning algorithm is tested in two separate simulation cases: a water drainage structure and a reservoir levee, as representative samples of infrastructure monitoring. The optimized flight plan is compared against three alternate flight plans in each case. The optimized view plan is found to yield terrain models with up to 43% greater accuracy than a standard grid flight pattern, while maintaining comparable coverage and completeness.

Increasing competitiveness of renewable power sources due to tightening restrictions on CO 2 emission from fossil fuel combustion is expected to cause a shift in power generation systems of the future. This investigation considers the impact of the Cryogenic Carbon Capture TM (CCC) process on transitional power generation. The CCC process consumes less energy than chemical and physical absorption processes and has an energy storage capability that shifts the parasitic loss of the CCC process away from peak hours. The CCC process responds rapidly to the variation of electricity demand and has a time constant that is consistent with the intermittent supply from renewable power sources. The hybrid system of conventional and renewable power generation units and the CCC process are optimized in this investigation. The system under consideration consists of load-following coal and gas-fired power units, a CCC process, and wind generation. The objective is to meet the residential and CCC plant electricity demands while maximizing the operating profit. The results demonstrate that an average profit of $35k/hr is obtained from this hybrid system over the selected days. The total electricity demand is best met using a combination of coal, gas, and wind power with grid-scale energy storage.

Structure from motion (SfM) computer vision is a remote sensing method that is gaining popularity due to its simplicity and ability to accurately characterize site geometry in three dimensions (3D). While many researchers have demonstrated the potential for SfM to be used with unmanned aerial vehicles (UAVs) to model in 3D various geologic features, such as landslides, little is understood concerning how the selection of the UAV platform can affect the resolution and accuracy of the model. This study evaluates the resolution and accuracy of 3D point cloud models of a large landslide that occurred in 2013 near Page, Arizona, that were developed from various small UAV platform and camera configurations. Terrestrial laser scans were performed at the landslide and were used to establish a comparative baseline model. Results from the study indicate that point cloud resolution improved by more than 16% when using multi-rotor UAVs instead of fixed-wing UAVs. However, accuracy of the points in the point cloud model appear to be independent of the UAV platform, but depend principally on the selected camera and the image resolution. Additional practical guidance on flying various UAV platforms in challenging field conditions is provided for geologists and engineers.