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Recurrent Neural Networks for AFR Estimation and Control in Spark Ignition Automotive Engines 149 Since the nineties, many studies addressed the benefits achievable by replacing the PI controller by advanced control architectures, such as linear observers [42], Kalman Filter [4, 13, 26] (and sliding mode [10, 27, 51]). Nevertheless, a significant obstacle to the implementation of such strategies is represented by measuring delay due to the path from injection to O2 sensor location and the response time of the sensor itself. To overcome these barriers, new sensors have been developed [36] but their practical applicability in the short term is far from certain due to high cost and impossibility to remove transport delay. Thus, developing predictive models from experimental data might significantly contribute to promoting the use of advanced closed loop controllers. 3.1 RNN Potential Recurrent Neural Network, whose modeling features are presented in the following section, have significant potential to face the issues associated with AFR control. The authors themselves [5] and other contributions (e.g. Alippi et al. [1]) showed how an inverse controller made of two RNNs, simulating both forward and inverse intake manifold dynamics, is suitable to perform the feedforward control task. Such architectures could be developed making use of only one highly-informative data-set [6], thus reducing the calibration effort with respect to conventional approaches. Moreover, the opportunity of adaptively modifying network parameters allows accounting for other exogenous effects, such as change in fuel characteristics, construction tolerances and engine wear. Besides their high potential, when embedded in the framework of pure neural-network controller, RNN AFR estimators are also suitable in virtual sensing applications, such as the prediction of AFR in coldstart phases. RNN training during cold-start can be performed on the test-bench off-line, by pre-heating the lambda sensor before turning on the engine. Moreover, proper post-processing of training data enables to predict AFR excursions without the delay between injection (at intake port) and measuring (in the exhaust) events, thus being suitable in the framework of sliding-mode closed-loop control tasks [10, 51]. In such an application the feedback provided by a UEGO lambda sensor may be used to adaptively modify the RNN estimator to take into account exogenous effects. Finally, RNN-based estimators are well suited for diagnosis of injection/air intake system and lambda sensor failures [31]. In contrast with control applications, in this case the AFR prediction includes the measuring delay. 4 Recurrent Neural Networks The RNN are derived from the static multilayer perceptron feedforward (MLPFF) networks by considering feedback connections among the neurons. Thus, a dynamic effect is introduced into the computational system by a local memory process. Moreover, by retaining the non-linear mapping features of the MLPFF, the RNN are suitable for black-box nonlinear dynamic modeling [17, 41]. Depending upon the feedback typology, which can involve either all the neurons or just the output and input ones, the RNN are classified into Local Recurrent Neural Networks and Global or External Recurrent Neural Networks, respectively [17, 38]. This latter kind of network is implemented here and its basic scheme is shown in Fig. 3, where, for clarity of representation, only two time delay operators D are introduced. It is worth noting that in the figure a time sequence of external input data is fed to the network (i.e. the input time sequence {x(t − 1), x(t − 2)}). The RNN depicted in Fig. 3 is known in the literature as Nonlinear Output Error (NOE) [37, 38], and its general form is ŷ(t|θ) = F [ϕ(t|θ), θ], (7) where F is the non-linear mapping operation performed by the neural network and ϕ(t) represents the network input vector (i.e. the regression vector) ϕ(t, θ) = [ŷ(t − 1|θ), . . . , ŷ(t − n|θ), x(t − 1), . . . , x(t − m)], (8) where θ is the parameters vector, to be identified during the training process; the indices n and m define the lag space dimensions of external inputs and feedback variables. 150 I. Arsie et al. x (t − 1) x (t − 2 ) yˆ ( t ) yˆ ( t − 2 ) D yˆ ( t − 1) D Fig. 3. NOE Recurrent Neural Network Structure with one external input, one output, one hidden layer and two output delays Starting from the above relationships and accounting for the calculations performed inside the network, the general form of the NOE RNN can also be written as function of network weights ⎛ ⎛ ⎞⎞ nh ni

ŷ(t|θ) = f ⎝ vi g ⎝ wij ϕj (t)⎠⎠, (9) i=1 j=1 where nh is the number of nodes in the hidden layer and ni the number of input nodes, vi represents the weight between the i-th node in the hidden layer and the output node, while wij is the weight connecting the j-th input node and the i-th node in the hidden layer. These weights are the components of the parameters vector and ϕj (t) is the j-th element of the input vector (8). The activation function g(.) in the hidden layer nodes is the following non-linear sigmoid function: g(x) = 2 − 1 [−1; 1], 1 + exp(−2x + b) (10) where b is an adjustable bias term; at the output node the linear activation function f (.) is assumed. Then, accounting for all the weights and biases the parameters vector is θ = [v1 , . . . vnh , w11 , . . . wnh,ni , b1 , . . . bnh , bno ]. 4.1 Dynamic Network Features Like the static MLPFF networks, RNN learning and generalization capabilities are the main features to be considered during network development. The former deals with the ability of the learning algorithm to find the set of weights which gives the desired accuracy, according to a criterion function. The generalization expresses the neural network accuracy on a data set different from the training set. A satisfactory generalization can be achieved when the training set contains enough information, and the network structure (i.e. number of layers and nodes, feedback connections) has been properly designed. In this context, large networks should be avoided because a high number of parameters can cause the overfitting of the training pattern through an overparametrization; whilst under-sized networks are unable to learn from the training pattern; in both cases a loss of generalization occurs. Furthermore, for a redundant network, the initial weights may affect the learning process leading to different final performance, not to mention computational penalty. This problem has not been completely overcome yet and some approaches are available in the literature: notably the works of Atiya and Ji [8] and Sum et al. [46] give suggestions on the initial values of the network parameters. The authors themselves have faced the problem of network weights uniqueness, making use of clustering methods in the frame of a MonteCarlo parameters identification algorithm [34], in case of steady state networks. Recurrent Neural Networks for AFR Estimation and Control in Spark Ignition Automotive Engines 151 Following recommendations provided by Thimm and Fiesler [48] and Nørgaard et al. [38], the weights are initialized randomly in the range [−0.5 to 0.5] to operate the activation function described by (10) in its linear region. Several studies have also focused on the definition of the proper network size and structure through the implementation of pruning and regularization algorithms. These techniques rearrange the connection levels or remove the redundant nodes and weights as function of their marginal contribution to the network precision gained during consecutive training phases [17, 43]. For Fully Recurrent Neural Networks the issue of finding the network topology becomes more complex because of the interconnections among parallel nodes. Thus, specific pruning methodologies, such as constructive learning approach, have been proposed in the literature [15, 28]. Some approaches have been followed to improve the network generalization through the implementation of Active Learning (AL) Techniques [3]. These methods, that are derived from the Experimental Design Techniques (EDT), allow reducing the experimental effort and increase the information content of the training data set, thus improving the generalization. For static MLPFF networks the application of information-based techniques for active data selection [14, 29] addresses the appropriate choice of the experimental data set to be used for model identification by an iterative selection of the most informative data. In the field of Internal Combustion Engine (ICE), these techniques search in the independent variables domain (i.e. the engine operating conditions) for those experimental input–output data that maximize system knowledge [3]. Heuristic rules may be followed to populate the learning data set if AL techniques are awkward to implement. In such a case, the training data set must be composed of experimental data that span the whole operating domain, to guarantee steady-state mapping. Furthermore, in order to account for the dynamic features of the system, the input data must be arranged in a time sequence which contains all the frequencies and amplitudes associated with the system and in such a way that the key features of the dynamics to be modeled will be excited [38]. As it will be shown in the following section, a pseudo-random sequence of input data has been considered here to meet the proposed requirements. The RNN described through the relationships (7) and (8) is a discrete time network, and a fixed sampling frequency has to be considered. To build the time dependent input–output data set, the sampling frequency should be high enough to guarantee that the dynamic behaviour of the system is well represented in the input–output sequence. Nevertheless, as reported in Nørgaard et al. [38], the use of a large sampling frequency may generate numerical problems (i.e. ill-conditioning); moreover, when the dimension of the data sequence becomes too large an increase of the computational burden occurs. A fundamental feature to be considered for dynamic modeling concerns with the stability of the solution. RNNs behave like dynamic systems and their dynamics can be described through a set of equivalent nonlinear Ordinary Differential Equations (ODEs). Hence, the time evolution of a RNN can exhibit a convergence to a fixed point, periodic oscillations with constant or variable frequencies or a chaotic behavior [41]. In the literature studies on stability of neural networks belong to the field of neurodynamics which provides the mathematical framework to analyze their dynamic behavior [17]. 4.2 Recurrent Neural Network Architectures for AFR Control Neural Network based control systems are classified into two main types: (a) Direct Control Systems and (b) Indirect Control Systems [38] as described in the following sections. Direct Control System In the Direct Control Systems (DCS) the neural network acts as a controller which processes the signals coming from the real system. The control signals are evaluated as function of the target value of the controlled variable. In this section two different DCS are presented: the Direct Inverse Model (DIM) and the Internal Model Control (IMC). A description of these two approaches is given below. Direct Inverse Model The basic principle of this methodology is to train the Neural Network (i.e. identification of the Network parameters) to simulate the “inverse” dynamics of the real process and then to use the inverse model as a 152 I. Arsie et al. D D WDUJHW r(t+1) FRQWURO IRNNM u(t) RXWSXW Plant y(t+1) D D Fig. 4. Direct Inverse Model (DIM) based on a NOE network (Inverse RNNM). The control signal is estimated at the time t as a function of the desired value r(t + 1) and the feedbacks. Note that the parameters m and n (see (12)) have been assumed equal to 2 controller. Assuming that the dynamics of the system can be described through an RNN model analogous to the one proposed in (7) and (8) ŷ(t + 1) = F [ŷ(t), . . . , ŷ(t − n + 1), x(t), . . . , x(t − m + 1)]. (11) For a generic MIMO the Inverse RNN Model (IRNNM) is obtained by isolating the most recent control input as follows: û(t) = F −1 [y(t + 1), y(t), . . . , y(t − n + 1), . . . , û(t − 1), . . . , û(t − m + 1)]. (12) It is worth remarking that the u notation in (12) replaces “x” to highlight that in control applications all or some external variables (depending on plant typology, e.g. SISO, MISO or MIMO) are control variables too. Once the network has been trained, it can be used as a controller by substituting the output ŷ(t + 1) with the desired target value r(t + 1). Assuming that the model (12) describes accurately the inverse dynamics of the system, the computed control signal û will be able to drive the system output y(t + 1) to the desired value r(t + 1). Figure 4 shows the block-diagram of a DIM. It is worth noting that the desired value r is at the time t + 1 while the control input û refers to the time t; hence the controller performs the control action one time step earlier than the desired target. The advantages of the DIM approach are the simple implementation and the Dead-Beat built-in control properties (i.e. fast response for wide and sudden variations of the state variables) [38]. Nevertheless, since the controller parameters are identified in off-line, the DIM does not perform as an adaptive control system. In order to develop an adaptive system, on-line training methodologies are required. The suitability of the inverse neural controllers to control complex dynamic processes is confirmed by several studies, particularly in the field of aerospace control systems (e.g. Gili and Battipede [16]). Internal Model Control The IMC control structure is derived from the DIM, described in the previous section, where a Forward RNN Model (FRNNM) of the system is added to work in parallel with an IRNNM. Figure 5 shows a block diagram of this control architecture. The output values predicted by the FRNNM are fed back to the IRNNM, that evaluates the control actions as function of the desired output at the next time step r(t + 1). The more the FRNNM prediction is accurate, the less the difference between FRNNM and Plant outputs will be. However, the differences between Plant and FRNNM may be used to update the networks on-line (i.e. both IRNNM and FRNNM), thus providing the neural controller with adaptive features. The stability of the IMC scheme (i.e. the closed-loop system and the compensation for constant noises) is guaranteed if both the real system and the controller are stable [22]. Despite their stringent requirements, the IMC approach seems to be really appealing, as shown by several applications in the field of chemical processes control (e.g. Hussain [23]). Recurrent Neural Networks for AFR Estimation and Control in Spark Ignition Automotive Engines 153 D r(t+1) + û(t) - Filter NN Controller System y(t+1) D NN Forward Model - + D Fig. 5. Neural Networks based Internal Model Control Structure (dashed lines – closed loop connections) Indirect Control Systems Following the classification proposed by Nørgaard et al. [38], a NN based control structure is indirect if the control signal is determined by processing the information provided from both the real system and the NN model. The Model Predictive Control (MPC) structure is an example of such control scheme. Model Predictive Control The MPC computes the optimal control signals through the minimization of an assigned Cost Function (CF). Thus, in order to optimize the future control actions, the system performance is predicted by a model of the real system. This technique is suitable for those applications where the relationships between performances, operating constraints and states of the system are strongly nonlinear [23]. In the MPCs the use of the Recurrent Neural Networks is particularly appropriate because of their nonlinear mapping capabilities and dynamic features. In the MPC scheme, a minimization of the error between the model output and the target values is performed [38]. The time interval on which the performance are optimized starts from the current time t to the time t + k. The minimization algorithm accounts also for the control signals sequence through a penalty factor ρ. Thus, the Cost Function is J(t, u(t)) = N2
i=N1 [r(t + i) − ŷ(t + i)] + ρ N3
[∆u(t + i − 1)]2 , (14) i=1 where the interval [N1 , N2 ] denotes the prediction horizon, N3 is the control horizon, r is the target value of the controlled variable, ŷ is the model output (i.e. the NN) and ∆u(t + i − 1) are the changes in the control sequences. In the literature, several examples dealing with the implementation of the MPCs have been proposed. Manzie et al. [32] have developed a MPC based on Radial Basis Neural Networks for the AFR control. Furthermore, Hussain [23] reports the benefits achievable through the implementation of NN predictive models for control of chemical processes. 5 Model Identification This section deals with practical issues associated with Recurrent Networks design and identification, such as choice of the most suitable learning approach, selection of independent variables (i.e. network external input x) and output feedbacks, search of optimal network size and definition of methods to assess RNN generalization. 154 I. Arsie et al. 5.1 RNN Learning Approach The parameters identification of a Neural Network is performed through a learning process during which a set of training examples (experimental data) is presented to the network to settle the levels of the connections between the nodes. The most common approach is the error Backpropagation algorithm due to its easy-tohandle implementation. At each iteration the error between the experimental data and the corresponding estimated value is propagated backward from the output to the input layer through the hidden layers. The learning process is stopped when the following cost function (MSE) reaches its minimum: E(θ) = N 1
(ŷ(t|θ) − y(t))2 . 2N t=1 (15) N is the time horizon on which the training pattern has been gathered from experiments. The Mean Squared Error (MSE) (15) evaluates how close is the simulated pattern ŷ(t|θ)[t = 1, N ] to the training y(t)[t = 1, N ]. The Backpropagation method is a first-order technique and its use for complex networks might cause long training and in some cases a loss of effectiveness of the procedure. In the current work, a secondorder method based on the Levenberg–Marquardt optimization algorithm is employed [17, 18, 38, 41, 43]. To mitigate overfitting, a regularization term [38] has been added to (15), yielding the following new cost function: N 1
1 E ∗ (θ) = · θT · α · θ, (ŷ(t|θ) − y(t))2 + (16) 2N t=1 2N where α is the weight decay. The above function minimization can be carried out in either a batch or pattern-by-pattern way. The former is usually preferred at the initial development stage, whereas the latter is usually employed in on-line RNN implementation, as it allows to adapt network weights in response to the exogenous variations of the controlled/simulated system. The training process aims at determining RNN models with a satisfactory compromise between precision (i.e. small error on the training-set) and generalization (i.e. small error on the test-set). High generalization cannot be guaranteed if the training data-set is not sufficiently rich. This is an issue of particular relevance for dynamic networks such as RNN, since they require the training-set not only to cover most of the system operating domain, but also to provide accurate knowledge of its dynamic behavior. Thus, the input data should include all system frequencies and amplitudes and must be arranged in such a way that the key features of the dynamics to be modeled are excited [38]. As far as network structure and learning approach are concerned, the precision and generalization goals are often in conflict. The loss of generalization due to parameters redundancy in model structure is known in the literature as overfitting [37]. This latter may occur in the case of a large number of weights, which in principle improves RNN precision but may cause generalization to decrease. A similar effect can occur if network training is stopped after too many epochs. Although this can be beneficial to precision it may negatively impacts generalization capabilities and is known as overtraining. Based on the above observations and to ensure a proper design of RNNs, the following steps should be taken: 1. Generate a training data set extensive enough to guarantee acceptable generalization of the knowledge retained in the training examples 2. Select the proper stopping criteria to prevent overtraining 3. Define the network structure with the minimum number of weights As far as the impact of point (1) on the current application, AFR dynamics can be learned well by the RNN estimator once the trajectories of engine state variables (i.e. manifold pressure and engine speed) described in the training set are informative enough. This means that the training experiments on the testbench should be performed in such a way to cover most of the engine working domain. Furthermore a proper description of both low- and high-frequency dynamics is necessary, thus the experimental profile should be obtained by alternating steady operations of the engine with both smooth and sharp acceleration/deceleration maneuvers. Recurrent Neural Networks for AFR Estimation and Control in Spark Ignition Automotive Engines 155 Point (2) is usually addressed by employing the early stopping method. This technique consists of interrupting the training process, once the MSE computed on a data set different from the training one stops decreasing. Therefore, when the early stopping is used, network training and test require at least three data sets [17]: training-set (set A), early stopping test-set (set B) and generalization test-set (set C). Finally, point (3) is addressed by referring to a previous paper [6], in which a trial-and-error analysis was performed to select the optimal network architecture in terms of hidden nodes and lag space. Although various approaches on choosing MLPFF network sizing are proposed in the specific literature, finding the best architecture for recurrent neural network is a challenging task due to the presence of feedback connections and (sometimes) past input values [38]. In the current work the trial-and-error approach is used to address (3). 5.2 Input Variables and RNNs Formulation Based on experimental tests, the instantaneous port air mass flow is known to be mainly dependent on both manifold pressure and engine speed (i.e. engine state variables) [21]. On the other hand, the actual fuel flow rate results from the dynamic processes occurring into the inlet manifold (see Fig. 1 and (1), (2)), therefore the manifold can be studied as a Multi Input Single Output (MISO) system. In case of FRNNM for AFR prediction, the output, control and external input variables are ŷ = AF R, u = tinj , x = [rpm, pm ], respectively and the formulation resulting from (7) and (8) will be AF̂ R(t, θ) = F [AF̂ R(t − 1|θ1 ), . . . , AF̂ R(t − n|θ1 ), tinj (t − 1), . . . , tinj (t − m), rpm(t − 1), . . . , rpm(t − m), pm (t − 1), . . . , pm (t − m)]. (17) It is worth noting that the output feedback in the regressors vector (i.e. AF̂ R in (17)) is simulated by the network itself, thus the FRNNM does not require any AFR measurement as feedback to perform the on-line estimation. Though such a choice could reduce network accuracy [38], it allows to properly address the AFR measurement delay issue due to mass transport, exhaust gas mixing and lambda sensor response [39]. This NOE feature is also very appealing because it enables AFR virtual sensing even when the oxygen sensor does not supply a sufficiently accurate measurement, as it happens during cold start phases. Regarding AFR control, a DIM structure (see Fig. 4) is considered for the current application. Hence the IRNNM can be obtained by inverting (7), yielding the following RNN expression: t̂inj (t − 1|θ2 ) = G[AF̂ R(t|θ1 ), . . . , AF̂ R(t − n|θ1 ), t̂inj (t − 2|θ2 ), . . . , t̂inj (t − m|θ2 ) rpm(t − 1), . . . , rpm(t − m), pm (t − 1), . . . , pm (t − m)], (18) where AF̂ R is the estimate provided by FRNNM and θ2 is the IRNNM parameters vector. Afterwards, substituting AF̂ R(t + 1|θ1 ) by the future target value AF Rdes , the control action can be computed as t̂inj (t − 1|θ2 ) = G[AF Rdes (t), . . . , AF̂ R(t − n|θ1 ), t̂inj (t − 2|θ2 ), . . . , t̂inj (t − m|θ2 ) rpm(t − 1), . . . , rpm(t − m), pm (t − 1), . . . , pm (t − m)]. (19) 6 Experimental Set-Up The RNN AFR estimator and controller were trained and tested vs. transient data sets measured on the engine test bench at the University of Salerno. The experiments were carried out on a commercial engine, four cylinders, 1.2 liters, with Multi-Point injection. It is worth noting that due to the absence of a camshaft sensor, the injection is not synchronized with the intake stroke, therefore it takes place twice a cycle for each cylinder. The test bench is equipped with a Borghi & Saveri FE-200S eddy current dynamometer. A data acquisition system, based on National Instruments cards PCI MIO 16E-1 and Sample & Hold Amplifier SC-2040, is used to measure engine variables with a sampling frequency up to 10 kHz. An AVL gravimetric balance is used to measure fuel consumption in steady-state conditions to calibrate the injector flow rate. 156 I. Arsie et al. Dyno rpm Engine β AVL-Puma tinj, θs Pm, rpm Micro Autobox Fig. 6. Lay-out of the experimental plant. β = throttle opening, θs = spark advance, tinj = injection time Fig. 7. Location of the UEGO sensor (dotted oval) c MicroAutobox equipment and a power conditioning The engine control system is replaced with a dSPACE unit. Such a system allows to control all the engine tasks and to customize the control laws. To guarantee the controllability and reproducibility of the transient maneuvers, both throttle valve and engine speed are controlled through an AVL PUMA engine automation tool (see Fig. 6). The exhaust AFR is sensed by an ETAS Lambda Meter LA4, equipped with a Bosch LSU 4.2 UEGO sensor. This is placed right after the exhaust valve of the first cylinder (see Fig. 7) to investigate the air– fuel mixing process in one cylinder only. This choice allows to remove the dynamic effects induced by gas transport and mixing phenomena occurring in the exhaust pipes. Also non predictable effects generated by cylinder-to-cylinder unbalance due to uneven processes such as air breathing, thermal state and fuel injection can be neglected. Therefore, the time shift between injection timing and oxygen sensor measurement mostly accounts for pure engine cycle and lack of synchronization between injection and intake valve timing. This latter term can be neglected in case of synchronized injection. As mentioned before, the time delay could represent a significant problem for control applications [10, 24, 32, 42] and the accomplishment of this task is described in Sect. 6.1. 6.1 Training and Test Data The training and test sets were generated by running the engine on the test bench in transient conditions. In order to span most of the engine operating region, perturbations on throttle and load torque were imposed during the transients. Fast throttle actions, with large opening-closing profiles and variable engine speed set points, were generated off-line and assigned through the bench controller to the engine and the dyno, respectively (see Fig. 6). Regarding fuel injection, only the base injection task (see Fig. 2) was executed, thus allowing to investigate the dynamic behavior of the uncontrolled plant, without being affected by neither feedforward nor feedback compensation. Furthermore, in order to excite the wall wetting process Recurrent Neural Networks for AFR Estimation and Control in Spark Ignition Automotive Engines 157 Fig. 8. Training data set (SET A) independently from the air breathing dynamics, a uniform random perturbation was added to the injection base time, limiting the gain in the range ±15% of the nominal fuel injection time (i.e. duration of time when the injector is open). Such an approach protects the RNN from unacceptable accuracy of predictions in the case of injection time deviation at constant engine load and speed as it is the case when a different AFR target is imposed. This matter is extensively described in our previous work [6]. In Fig. 8 the measured signals of throttle opening (a), engine speed (b), manifold pressure (c), injection time (d) and AFR (e) used as training-data (Set A) are shown. The throttle opening transient shown in Fig. 8a allows exciting the filling-emptying dynamics of the intake manifold and the engine speed dynamics, as a consequence of both engine breathing and energy balance between engine and load torque. Fig. 8b, c indicate that the transient spans most of the engine operating domain with engine speed and manifold pressure ranging from 1,000 to 4,000 rpm and from low to high load, respectively. The variation of manifold pressure and engine speed affects the intake air flow rate and consequently the amount of fuel to be injected to meet the target AFR. It is worth noting that the manifold pressure signal was filtered in order to cancel the process noise that has negligible effects on the AFR dynamic response. This enhances the FRNNM in learning the main manifold dynamics without being perturbed by second order phenomena (e.g. intake manifold pressure fluctuation). 158 I. Arsie et al. Fig. 9. Test data set (SET B) The injection time trajectory (Fig. 8d), commanded by the ECS, excites the wall wetting dynamics, which in turn influences the in-cylinder AFR in a broad frequency range. It is also worth to mention that engine speed and throttle opening are decoupled to generate more realistic engine speed–pressure transients. Furthermore, the speed dynamics is more critical as compared to what occur on a real vehicle, due to the lower inertia of the engine test-bench. Figure 9 shows the time histories of throttle opening, engine speed, manifold pressure and injected fuel measured for the test-set (SET B). SET B was obtained imposing square wave throttle maneuvers (Fig. 9a) to excite the highest frequencies of the air dynamics, while keeping the engine speed constant (Fig. 9b) and removing the fuel pulse random perturbation. Figure 9d, e evidence that the resulting step variations of injected fuel generate wide lean/rich spikes of AFR, due to uncompensated effects of wall wetting dynamics during abrupt throttle opening/closing transients. Such features make SET B suitable as test data-set since RNN accuracy in predicting high frequency dynamic response is demanded. Moreover, the step variations of injected fuel are also appropriate to estimate the AFR delay. Thus, SET B is also very suitable to assess the ability of RNN to cope with the pure time delay.