Development of a fast, robust numerical tool for the design, optimization, and control of IC engines

This paper discusses the development of an integrated tool for the design, optimization, and real-time control of engines from a performance and emissions standpoint. Our objectives are threefold: (1) develop a tool that computes the engine performance and emissions on the order of a typical engine cycle (25-50 milliseconds); (2) enable the use of the tool for a wide variety of engine geometries, operating conditions, and fuels with minimal user changes; and (3) couple the engine module to an efficient optimization module to enable real-time control and optimization. The design tool consists of two coupled modules: an engine module and an optimization module. The engine module consists of three components: a two-zone quasi-dimensional engine model to compute the temporal variation of temperature and pressure during the compression and power stroke, a thermal model to compute the cyclic variation of the engine wall temperature, and a reaction-rate-controlled emission model to compute engine-out NO and CO. The optimization solver is an extension of the model-based, derivative-free POUNDER and is designed to limit the number of engine model evaluations. The outputs of the engine model, thermal model, and emissions model can be used for optimizations under various design constraints. By more thoroughly using the output from the simulations, our optimization scheme reduces the number of simulation evaluations by two orders of magnitude compared with parameter sweeps and one order of magnitude compared with the standard black-box optimizer in MATLAB. These results highlight the proposed tool’s potential for use in design, optimization, and real-time control of engines. INTRODUCTION Modern automotive engines (both SI and CI) are complex systems that pose several multiobjective, multiconstraint problems from an engine control and optimization standpoint. These are largely due to the ever-increasing demand for higher power output, increased fuel economy, and reduced emissions. Real-time control of IC engines poses even greater challenges in terms of computational cost, robustness of the control algorithms, and fidelity of the underlying physical models. Given the large parameter space (engine geometry, engine RPM, air-fuel-ratio, spark/fuel injection timing, etc.) over which an engine has to be optimized for performance and emissions, formulation of a generalized mathematical optimization problem can be difficult. Typically, design engineers focus on examining localized regions of the overall operating parameter space in order to evaluate the relative effect of changing one particular parameter with respect to another. For instance, one could pose questions such as What is the minimum percent reduction in engine torque needed in order to obtain a 2 percent reduction in fuel consumption? or What is the percent increase in overall engine-out NO/CO for a 5 percent increase in overall average torque over a typical driving cycle? Design, optimization, and control of conventional engines can be carried out by using available engine data. For newer engine concepts and/or operating regimes and for engines powered by alternative fuels or fuel blends, one can complement limited engine data through the use of reliable physics-based engine models for making design and/or optimization decisions. Development of reliable, physics-based engine modeling tools can thus play an integral role in the design and optimization studies of engines. Transient multidimensional numerical simulation of the entire engine cycle that models the effects of complex Page 2 of 18 combustion chemistry and turbulence is extremely challenging. Such simulations can take several hours to days, depending on factors such as complexity of the flow or chemistry model and size of the computational domain. Hence, the required computational effort precludes using multi-dimensional simulations in the early stages of design, development, and engine optimization in terms of performance and emissions. On the other hand, computationally fast, robust, physics-based, quasi-dimensional modeling tools require minimal computational resources, and the computational time for solutions is usually on the order of seconds. Development of such quasi-dimensional modeling tools can greatly aid the design, analysis, and optimization of IC engines. Several quasi-dimensional models have been developed since the early 1980s to study both gasoline and diesel engines (see, for example, [1-8]) with varying degrees of fidelity. With few exceptions (for instance, [3] and [7]), however, these studies do not discuss the wall-clock time required for the computation of an engine cycle (a single compression and expansion stroke). The level of fidelity in the quasi-dimensional model and the wall-clock time required for the computation of an engine cycle are important considerations, especially for real-time optimization and control, which require the computational time to be on the order of an engine cycle (typically, 25-50 milliseconds). In this paper we discuss a methodology to greatly increase the computational speed of engine optimization problems by using a fast, robust engine module designed for use with an efficient optimization scheme. Several investigators have published results for engine optimization based on various optimization techniques [9-21]. Most of these studies discuss optimization of engine performance alone. Relatively fewer studies report on engine optimization from both a performance and an emissions standpoint [19-21]. These latter optimization studies have focused primarily on black-box global optimization algorithms, such as genetic algorithms, particle swarm optimization, simulated annealing, and the DIRECT method [22-24]. Although their internal optimization parameters must often be tuned to the particular problem, these methods tend to be robust to computational noise and discontinuities, provided the number of parameters is small (typically 1-3) or a large number of simulation evaluations (often in the millions) are possible. In this paper we consider local optimization methods, which begin from a user-provided initial design vector and search for a local minimum/maximum. Because these methods do not need to asymptotically obtain a global solution, they require fewer simulation evaluations than do their global counterparts. We restrict our focus to so-called derivative-free methods [25], which operate even when the objective and/or constraint function derivatives with respect to the design parameters are unavailable. Under idealized circumstances, the dependence of the underlying differential algebraic equations (DAEs) on the design parameters is algebraically available to first order; and derivative-based or even linear programming methods could be employed (see, e.g., [26]). Alternatively, when explicit derivatives are unavailable, algorithmic (sometimes called “automatic”) differentiation (AD) is often a viable option [27]. We focus on the derivativefree case in recognition of many of the practical obstacles that remain, such as truncation of crank angle degrees and look-up tables based on experimental data. Within the class of derivative-free local optimization methods, we focus on model-based methods, which have been shown to perform well when relatively few simulation evaluations are available [28]. These methods seek to fully exploit the information obtained from each simulation evaluation by building local surrogate models based on the simulation output. Another benefit of these methods is that they can exploit additional knowledge of structure (temporal variation of temperature/pressure, derived quantities such as engine torque, emissions, etc.) in the problem, rather than aggregating the simulation output into a single “black-box” scalar objective. Such information is often present in many real-world problems and can be used to further reduce the number of simulation evaluations required in order to solve the optimization problem and/or to obtain more accurate solutions. Our method employs quadratic interpolation models [29]. Examples of this approach exploiting structure include parameter fitting (nonlinear least squares) problems [30] and simulation-based, nonlinear constraints [31]. We illustrate its application here on a bilevel problem of determining the equivalence ratio at which engine-out NO is maximum under maximum brake torque (MBT) conditions. The main focus of this work was to develop an integrated design tool with the following features: (1) a physics-based engine module where different components (or models) can be coupled or uncoupled easily, (2) flexibility and ease of use for exploring a large parameter space, (3) capability of computing performance and emission characteristics on the order of an engine cycle (25-50 milliseconds), and (4) use of inputs from the engine module to conduct optimization. Figure 1 shows a block diagram of the approach used in this work. Figure 1: Block diagram showing the modules and models in the design/optimization tool.