Improved decision support for engine-in-the-loop experimental design optimization.

Experimental optimization with hardware in the loop is a common procedure in engineering and has been the subject of intense development, particularly when it is applied to relatively complex combinatorial systems that are not completely understood, or where accurate modelling is not possible owing to the dimensions of the search space. A common source of difficulty arises because of the level of noise associated with experimental measurements, a combination of limited instrument precision, and extraneous factors. When a series of experiments is conducted to search for a combination of input parameters that results in a minimum or maximum response, under the imposition of noise, the underlying shape of the function being optimized can become very difficult to discern or even lost. A common methodology to support experimental search for optimal or suboptimal values is to use one of the many gradient descent methods. However, even sophisticated and proven methodologies, such as simulated annealing, can be significantly challenged in the presence of noise, since approximating the gradient at any point becomes highly unreliable. Often, experiments are accepted as a result of random noise which should be rejected, and vice versa. This is also true for other sampling techniques, including tabu and evolutionary algorithms.

After the general introduction, this paper is divided into two main sections (sections 2 and 3), which are followed by the conclusion. Section 2 introduces a decision support methodology based upon response surfaces, which supplements experimental management based on a variable neighbourhood search and is shown to be highly effective in directing experiments in the presence of a significant signal-to-noise ratio and complex combinatorial functions. The methodology is developed on a three-dimensional surface with multiple local minima, a large basin of attraction, and a high signal-to-noise ratio.

In section 2, the methodology is applied to an automotive combinatorial search in the laboratory, on a real-time engine-in-the-loop application. In this application, it is desired to find the maximum power output of an experimental single-cylinder spark ignition engine operating under a quasi-constant-volume operating regime. Under this regime, the piston is slowed at top dead centre to achieve combustion in close to constant volume conditions.

As part of the further development of the engine to incorporate a linear generator to investigate free-piston operation, it is necessary to perform a series of experiments with combinatorial parameters. The objective is to identify the maximum power point in the least number of experiments in order to minimize costs. This test programme provides peak power data in order to achieve optimal electrical machine design.

The decision support methodology is combined with standard optimization and search methods — namely gradient descent and simulated annealing— in order to study the reductions possible in experimental iterations. It is shown that the decision support methodology significantly reduces the number of experiments necessary to find the maximum power solution and thus offers a potentially significant cost saving to hardware-in-the-loop experimentation.