Essentially, the performance improvement of automotive systems is a multi-objective optimization problem [14] due to the challenges in both operation management and control. The interconnected dynamics inside the automotive system normally requires precise tuning and coordination of accessible system inputs. In the past, such optimization problems have been approximately solved through expensive calibration procedures or an off-line local model-based approaches where either a regressive model or a first-principle model is used. The model-based optimization provides the advantage of finding the optimal model parameters to allow the model to be used to predict the real system behavior reasonably [5]. However, other than the model complexities, there are practically two issues facing the integrity of these models: modeling uncertainty due to inaccurate parameter values and/or unmodeled dynamics, and locally effective range around operating points. As a result, the optimum solutions extracted from the model-based approach could be subject to failure of expected performance [6].

## Article

Essentially, the performance improvement of automotive systems is a multi-objective optimization problem [14] due to the challenges in both operation management and control. The interconnected dynamics inside the automotive system normally require precise tuning and coordination of accessible system inputs. In the past, such optimization problems have been approximately solved through expensive calibration procedures or off-line local model-based approaches where either a regression model or a first-principle model is used. The model-based optimization provides the advantage of finding the optimal model parameters to allow the model to be used to reasonably predict the real system behavior [5]. However, other than the model complexities, there are two practical issues facing the integrity of these models: modeling uncertainty due to inaccurate parameter values and/or unmodeled dynamics, and locally effective range around operating points. As a result, the optimum solutions extracted from the model-based approach could be subject to failure of desired performance [6].

Bearing in mind that an accurate yet computationally efficient model for automotive systems is essentially not possible in practice [7], the data-driven optimization approach has attracted a lot of research attention in recent years [8], thanks to the tremendous progress and cost reduction in computing technologies for both realtime data acquisition and processing [9]. With the input-output data available, various data-driven algorithms have been developed to achieve evolving optimization of real systems and, what is more important, the optimal solutions derived from data-driven optimization can adapt to the system operation conditions [10]. Compared to the model-based optimization designs, the data-driven optimization methods are model-free set-up by nature and normally independent of previous knowledge of the system on time horizon [10], hence, these algorithms possess strong robust performance [5]. The common drawback of data-driven optimization methods is, however, highlighted by the facts of their slow convergence time and no guaranteed transient performance, since there is no prediction conducted in these methods due to the model-free nature. Therefore, the data-driven algorithms are usually limited to applications with relaxed requirements of system performance [5, 11].

In the automotive industry, various types of models characterizing operations of automotive systems are available [2, 7]. While it is still a very challenging job in practice to derive robust optimal solutions from direct model-based optimizations with these existing models, due to highly nonlinear complexities, an interesting development would be to utilize the available modeling information to provide feedforward or feedback assistance for the data-driven optimization algorithms so that the deficiencies mentioned above could be remedied. While the idea of ‘model-guided optimization’ is still under development with no general design framework reported so far in the literature, this article presents three case studies to highlight the implementation of the so-called ‘Model-Guided Data-Driven (MGDD) optimization’ which demonstrates how the models could be applied to complement the data-driven optimization algorithms in automotive compression ignition (CI) engine systems [12,13].

## Model-Guided Data-Driven Optimization

The general structure of the MGDD optimization is schematically shown in Figure 1. Unlike the model-based optimization, in an MGDD optimization algorithm, the optimization is still conducted in a data-driven way with the measurement data of the real system. The system model, global or local, which is driven by the real system input-output data, is computed in real time to provide estimates or predictions of the system behaviors in order to complement the data-driven optimization. In case the calibration information is available at specific operating points, it can be applied to reinitialize the data-driven optimization algorithm so that the process error could be reduced. It is noted that the details in the presented general MGDD optimization structure could vary for the specific applications seen in the three case studies presented later.

## Simplified Model of Compression Ignition Engine Combustion

A simplified model for automotive CI engine combustion is shown in Figure 2 [11,12]

The parameter specifications are stated below:

Heat release rate is approximated by a triangular function, бQhr:

$δQhr(ϕ,θn)=0i2⋅QhrMAXϕ−θnii−2⋅QhrMAXϕ−θCA50+dQhrMAXiii0iv$
1

ФCA50 is the crank angle of 50% accumulated heat release. ФCD is the combustion duration. LHV is the lower heating value of the fuel. mfuel is the injected fuel mass.

Woschni’s heat transfer correlation takes the following form:

where,

$i:ϕ<θnii:θn<ϕ<ϕCA50iii:ϕCA50<ϕ<θn+ϕCDiv:ϕ>θn+ϕCD$
$QhrMAX=mfuel⋅LHVϕCD$
$δQht(ϕ)=hwn(ϕ)⋅As⋅Tn(ϕ)−Twall,hwn(ϕ)=ChtB−0.2pn(ϕ)0.8Tn(ϕ)−0.55Wn(ϕ)0.8,Wn(ϕ)=C2Sp+VdTrefprefVrefpn(ϕ)−pmot(ϕ)$

where As is the surface area of the combustion chamber, B is the cylinder bore, $S¯p$ is the mean piston speed, pmot is the cylinder pressure obtained during engine motoring, Tref, pref and Vref are the reference engine states, Cht and C2 are the wall heat transfer coefficients, TwaII is the temperature of the combustion chamber wall.

This model is the one used in all three case studies in this article to provide assistance in order to improve the convergence performance of the conventional extremum seeking (ES) algorithm which is a data-driven optimization method.

## Extremum Seeking Control

There are several kinds of data-driven optimization methods [8, 14, 15], such as extremum seeking control (ESC), adaptive dynamic programming (ADP), neural network, active disturbance rejection control (ADRC), etc. While these methods differ from each other in one way or another, they share one advantage, the robust performance, and one drawback, the slow convergence rate of the algorithms. This drawback has been the major hurdle to broad applications of all data-driven optimization methods. All three case studies presented in this article showcase the discrete-time ESC, which is the gradient-descent-based data-driven optimization method [14,15,16]. The conventional structure of a continuous ESC as applied in a closed-loop configuration is shown in Figure 3, where the system is deemed as a ‘black box’ with no modeling information available. Note that the discrete-time ESC structure can be similarly implemented.

## Case 1: Model-Guided Data-Driven Optimization of Injection Timing in a Compression Ignition Engine

The convergence time required for an optimization algorithm is more or less dependent on the choice of the initial conditions for search, that is, if the initial guess of the optimizer value is close to the true optimal solution value, less searching time will be needed for convergence. However, for the conventional data-driven optimization, knowledge of the system is normally exploited so it cannot be guaranteed that the optimization search starts near the true optimal point [12,13]. An MGDD algorithm is presented in this case study (Figure 4) in which the simplified engine model is applied to generate an estimation of the injection timing set-point for the ESC in a compression ignition (CI) engine in terms of the mixed performance requirement for engine mean pressure and peak pressure rise [12]. The simplified model is an offline calibrated first-principle engine model [12, 13] and is used to provide an initial guess of the optimal injection timing whenever the engine enters a new operating zone. In this sense, the model actually ‘monitors’ the engine operation online and produces the estimated optimal solution for the specified performance function through a routine numerical optimization search that is then carried as the initial guess for the ESC algorithm. Obvious improvement of the convergence rate is observed for the said ESC algorithm [12, 13, 17]. A detailed description of the ESC algorithm can be found in [15] and for automotive systems in [16].

FIGURE 1 General structure of the MGDD Optimization.

FIGURE 1 General structure of the MGDD Optimization.

Close modal

FIGURE 2 Simplified model for CI engine combustion.

FIGURE 2 Simplified model for CI engine combustion.

Close modal

As shown in Figure 5, when model guidance is provided to initialize the ESC upon the change of the system operating point, indicated by the dotted line, the MGDD optimization consumes much less time to converge compared to the conventional perturbation-based ESC [12].

The optimal Start of Injection (SOI) computed from the model is 357 CAD, which is very close to the true optimal SOI of the engine test bench. Therefore, the model-guided ESC converges within 708 engine cycles. For the conventional ESC, the search for the SOI at the new operating point starts from a random point. For the example shown in Figure 3, ESC takes about 2400 engine cycles to converge. One may argue that the random starting search might be from a better point by chance. It is indeed true that this might happen in practice although there is no assurance that this will be the case, so it is apparently a big advantage to conduct a model-guided ESC since it offers guaranteed fast convergence time and makes the optimization more predictable amid the changes of operating points.

FIGURE 3 Paradigm of a continuous extremum seeking control.

FIGURE 3 Paradigm of a continuous extremum seeking control.

Close modal

## Case 2: Online-Tuned Model-Guided Data-Driven Optimization of Injection Timing in a Compression Ignition Engine

While the model-guided ESC guarantees the improvement of the convergence time compared to the conventional ESC, the model accuracy plays an important role in the MGDD optimization. Therefore, whenever it is possible, an online model tuning should be introduced to update the model in real time [13,18].

FIGURE 4 An ESC with initial guess produced by the optimization based on a simplified model for a CI engine.

FIGURE 4 An ESC with initial guess produced by the optimization based on a simplified model for a CI engine.

Close modal

As shown in Figure 6, another ESC algorithm is introduced on top of the model-guided ESC in Case 1 to result in an online tuned model-guided ESC structure. This would bring in two optimization processes: one for the tuning of the model parameters online by reducing the differences between the engine measurement and the model output and then the tuned model is applied in the model-guided ESC as in Case 1 [13, 19].

An experimental example for model tuning can be found in Figure 7 [13]. Upon the change of the engine operating point, the values of the model parameters are tuned prominently with the added ESC in the lower part in Figure 6 [13, 18]. As a result, the model output tracks the engine measurement output so that the engine model preserves its fidelity. It is noted that, in order for this approach to perform appropriately, time scale separation must be held and it is also desired that the engine operation would stay at a certain state long enough to allow both processes to converge. Apparently, this optimization structure would be extremely suitable for engine calibration process.

FIGURE 5 Comparison between MGDD optimization and conventional perturbation-based ESC.

FIGURE 5 Comparison between MGDD optimization and conventional perturbation-based ESC.

Close modal

## Case 3: Pressure Sensor Data-Driven Optimization of Combustion Phase in a Diesel Engine

Various sensors have been embedded in production CI engines [20], such as temperature sensors, micromechanical pressure sensors, high-pressure sensors, NOx sensors, etc. It is a reality that a large measurement delay exists in some sensors due to either the sensor electronic dynamics or the physical transportation process, and the NOx sensor in CI engines is one of them [21]. As shown in Figure 8, upon the shift of the operating point, the NOx measurement starts to respond to the change of the operating condition. However, because of the significant volume present in the exhaust manifold between the engine cylinder and the NOx sensor, around 25 seconds is required before the sensor measurement is finally settled. It is well known that the delayed data would normally lead to a longer convergence time for the data-driven optimization algorithm. Hence, how to deal with NOx sensor delay is important for the application of the data-driven optimization in CI engines, considering that such a delay is almost impossible to characterize in practice. In this case study, a ‘soft sensor’ approach is taken to substitute the NOx sensor measurement in order to accommodate the application of data-driven optimization.

Figure 6 On-line tuned model-guided ESC.

Figure 6 On-line tuned model-guided ESC.

Close modal

Still, an ESC is considered for optimization of the CI engine combustion phase as in Figure 9 but with a mixed performance of engine efficiency as indicated by the cylinder pressure and the NOx emissions. Due to the requirement of time-scale separation in the ESC algorithm, the slow response from the NOx sensor feedback would significantly slow down the overall optimization process, which prevents the direct use of the NOx sensor in this case. When a ‘soft sensor’ is built on the calibrated engine model, the bulk gas temperature of the in-cylinder charge can be estimated as an indication of the NOx emission. The trend correlation between the soft sensor output (bulk gas temperature) and the real NOx measurement without delay is shown in Figure 10, which suggests that the estimated bulk gas temperature can be used to indicate the trend of the NOx emission of engine combustion within certain operating zones. Therefore, it can be applied to replace the NOx emission in the performance function which then allows the fast convergence of the ESC algorithm. When the engine switches to a new operating point, the feedback from the soft sensor immediately responds and settles to the new value as shown in Figure 8 in which, compared to the real measurement, the response from the soft sensor is considered to have negligible transportation delay. Hence, one should not worry about the transportation delay in the NOx measurement when executing the ESC algorithm with the virtual measurement of such a soft sensor. An experimental validation example is shown in Figure 11.

FIGURE 7 On-line tuning of the parameter in engine combustion model.

FIGURE 7 On-line tuning of the parameter in engine combustion model.

Close modal

FIGURE 8 A comparison of transient responses between the direct NOx measurement and the soft sensor measurement.

FIGURE 8 A comparison of transient responses between the direct NOx measurement and the soft sensor measurement.

Close modal

FIGURE 9 A soft sensor is used to estimate the emission from engine combustion.

FIGURE 9 A soft sensor is used to estimate the emission from engine combustion.

Close modal

## Future Perspectives

Combining the system model with data-driven optimization method is a viable approach to achieve robust optimization with improved convergence speed. The proposed MGDD method is easy to use as the optimization algorithm is not designed based on the system model. Reduced model accuracy is also tolerable due to the robustness of the data-driven optimization. The few examples provided in this article are just some applicable scenarios that demonstrate the power of the MGDD algorithms. It is expected that the MGDD algorithm can be extended to other applications with the utilization of different data-driven optimization algorithms that incorporate the system models in various forms.

FIGURE 10 Steady state measurement between the measurement from the NOx sensor and the soft sensor.

FIGURE 10 Steady state measurement between the measurement from the NOx sensor and the soft sensor.

Close modal

FIGURE 11 ESC of combustion phase in a CI engine with soft sensor.

FIGURE 11 ESC of combustion phase in a CI engine with soft sensor.

Close modal

Qingyuan Tan obtained the bachelor degree (B.Eng.) in Instrumentation and Control Science at Shanghai Jiaotong University, China, in 2010, the master degree in Mechanical Engineering at the University of Toronto, Canada (M.A.Sc.), in 2012, and the Ph.D. degree in Electrical and Computer Engineering at the University of Windsor, Canada, in 2018. His research interests include the real-time optimization and control of mechatronic systems, data driven learning control of nonlinear mechatronic systems, and nonlinear system modeling in automotive systems.

Xiang Chen is a Professor in the Electrical and Computer Engineering Department at the University of Windsor. He received the M.S. and PhD degrees from the Louisiana State University, USA, in 1996 and 1998, respectively. His research areas include Network-based control system, robust and nonlinear control, vision-based motion control, and control applications in automotive and manufacturing systems.

Ying Tan is an Associate Professor and Reader in the Department of Electrical and Electronic Engineering, University of Melbourne, Australia. She received the bachelor's degree from Tianjin University, China, in 1995, and the Ph.D. degree from the National University of Singapore in 2002. She was a postdoctoral fellow in the Department of Chemical Engineering, McMaster University, Canada. Since 2004, she has been with the University of Melbourne. where she was awarded the Australian Postdoctoral Fellow (2006-2008) and the Future Fellow (2009-2013) by the Australian Research Council. Her current research interests are in intelligent systems, nonlinear control systems, data-driven optimization, sampled-data distributed parameter systems, and formation control.

Ming Zheng is a Professor and Research Chair in Clean Combustion Engine Technology at the University of Windsor. He received his M.Sc. degree from Tsinghua University in 1988 and his Ph.D. degree from the University of Calgary in 1993. He is the co-founder and the Director of the Clean Combustion Engine Lab. His research areas encompass clean combustion including diesel combustion, low-temperature combustion, diesel HCCI and PCCI, adaptive combustion control, high energy spark ignition and control, EGR hydrogenreforming, active flow control aftertreatment, engine modeling, diagnosis, and dynamometer tests, biofuel and biodiesel research.

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