2. Experimental set-up

Experiments were conducted in an 8-metre-long duct with a $7 \times{30}\,\textrm {cm}^{2}$ rectangular cross-section leading to an aspect ratio of $4.28$ . A centreline velocity of $U_0 = {3.2}{\,\textrm {m s}}^{-1}$ was imposed. The friction velocity was $u_\tau = {0.162}{\,\textrm {m s}}^{-1}$ , which leads to a friction Reynolds number of $\textit{Re}_\tau \approx 350$ , a viscous length of $l_\tau = \nu /u_\tau = {9.89\times {10}^{-05}}\,\textrm {m}$ and a viscous time of $t_\tau = \nu /u_\tau ^2 = {6.1\times {10}^{-4}}\,\textrm {s}$ . The instantaneous velocity components $(U, V, W)$ , respectively streamwise, wall-normal and spanwise components, can be decomposed in a mean contribution $(\overline {U}, \overline {V}, \overline {W})$ and a fluctuating one $(u, v, w)$ . Channel flow statistics profiles are presented in figure 1. Data from the present experiment are indicated with continuous lines and circle markers, while DNS data taken from Moser, Kim & Mansour (Reference Moser1999) at $\textit{Re}_\tau =395$ are indicated with dashed lines. Figure 1(a,b,c,d) shows the mean velocity profile, the streamwise Reynolds stresses, skewness and flatness, respectively.

Figure 1.

Channel flow statistics. Continuous lines with circle markers indicate the canonical case, dashed lines indicate DNS data statistics taken from Moser et al. (Reference Moser1999). (a) Mean velocity $\overline {U}^+$ , (b) streamwise component of the Reynolds stresses $\overline {uu}^+$ , (c) skewness $S(U)$ , (d) flatness $F(U)$ .

In the present experiment, two hot-wire probes were used, both connected to a Dantec 55M10 CTA standard bridge. The front probe, a Dantec 55P11, was positioned upstream of the jet orifice at $x^+ = -55$ and a wall-normal distance of $y^+ = 15$ , with the centre of the jet orifice serving as the origin of the reference system. The streamwise position of the front probe was selected following the approach taken in the experiments carried out by Rebbeck & Choi (Reference Rebbeck and Choi2001, Reference Rebbeck and Choi2006) to account for both the convective time and the delay time associated with the control system. It can be noted that, in the current experiment, the actuation delay time can be modulated through a microcontroller. The rear probe, a Dantec 55P15 boundary layer probe, was mounted on a two-axis movable stand to allow movements in the streamwise and wall-normal directions. The positional accuracy of the streamwise axis, achieved using the OptoSigma OSMS33-500(X) stage, is ${25}\,\mu {\textrm {m}}$ while the wall-normal axis, guided by the OptoSigma OSMS26-300(Z) stage, is ${40}\,\mu {\textrm {m}}$ . A schematic view of the probes’ positioning is shown in figure 2. Both hot-wire probes feature a sensitive tungsten wire measuring ${5}\,\mu {\textrm {m}}$ in diameter and ${1.25}\,\textrm {mm}$ in length and were calibrated in situ. Hot-wire calibration curves were fitted using the King’s law and signals were collected by a National Instruments PCI-MIO-16-XE-10 16-bit DAQ board at a sample rate of ${10}\,\textrm {KHz}$ $ ( f^+_{{HW}} = 6.1 )$ .

Figure 2.

Sketch of the real-time opposition control experimental set-up. The airflow proceeds from left to right. The front probe is positioned at $x^+ = -55$ and $y^+ =15$ . The position of the rear probe can be adjusted in both $x$ and $y$ directions.

The National Instrument acquisition board was connected to the PCI bus of a laboratory workstation. Data post-processing and the BO algorithm were executed on a laptop connected to the workstation via LAN. A server-based Python algorithm leveraging Python’s built-in socket library was loaded onto the workstation, while a client-based script was executed on the laptop. Typically, the client (laptop) initiates a query to the server (workstation), which may involve executing a measurement or modifying a control policy. Once the server processes the request, the client retrieves feedback or a data buffer if a signal has been acquired. The laptop then processes the raw signal data.

3. Detection technique and control hardware

Following the work of Rebbeck & Choi (Reference Rebbeck and Choi2006), sweep events were detected using the velocity gradient technique applied to the longitudinal component of the velocity, measured by the front probe. The detection scheme is illustrated in figure 3. The signal obtained from the front probe is differentiated through an analogue differentiator to compute its time derivative. Subsequently, a comparator device identifies sweep events and generates a transistor–transistor logic (TTL) signal whenever the time derivative exceeds a predefined threshold. This signal is subsequently delayed via a microcontroller to account for the convection time and the control actuator response time. In figure 4 the velocity signal sampled by the front probe is represented as a continuous blue line, while its time derivative is depicted as a continuous green line. The dashed red vertical lines indicate the instants at which events are detected. This technique allowed the sweep event detection to be carried out in real time. The comparator threshold level has been set to ensure that both the gradient technique and the variable-interval time-averaging (VITA) technique (Blackwelder & Kaplan Reference Blackwelder and Kaplan1976) detected a comparable number of events. For a fluctuating quantity $Q(x_i, t)$ , the variable-interval time average is defined as

(3.1) \begin{equation} \widehat {Q}(x_i, t, T) = \frac {1}{T} \int _{t-\frac {1}{2}T}^{{t+\frac {1}{2}T}} Q(x_i, s)\, {\rm d}s , \end{equation}

where $T$ is the averaging time. Sweep events detection, in the VITA technique, is defined as

(3.2) \begin{equation} D(t) = \begin{cases} 1, & \text{if } \quad \widehat {v\textit{ar}} \gt \textit{k u}_{\textit{rms}}^2\\ 0, & \text{otherwise} \end{cases}, \end{equation}

where the localised variance of streamwise velocity fluctuation $u$ is

(3.3) \begin{equation} \widehat {v\textit{ar}}(x_i, t, T) = \widehat {u^2}(x_i, t, T) - \left [ \widehat {u}(x_i, t, T) \right ]^2\!, \end{equation}

$k$ is the threshold level and $u_{\textit{rms}}$ is the root mean square of the fluctuating velocity for the whole recorded signal. The comparator threshold for the gradient technique was set to have a similar number of VITA events with $k = 1.0$ and $T^+ = 10$ . These values match those reported in Rebbeck & Choi (Reference Rebbeck and Choi2006). A burst frequency of the sweep events detected using the tuned gradient technique was found to be $f^+_{\textit{sweep}} = {3.05\times {10}^{-3}}$ .

Figure 3.

Sweep event detector system scheme. Inputs are the front probe signal and the delay time, $\Delta T$ , applied to the TTL signal. The comparator threshold is kept constant. The output is the delayed TTL signal.

Figure 4.

Visualisation of the sweep events detection technique. The continuous blue line is the longitudinal component of the front probe instantaneous velocity signal, $U$ , while the continuous green line represents its time derivative, $\dot {U}$ . Red dashed vertical lines show the trigger instant. The starting time is arbitrary.

It can be observed in figure 2 that the front probe represented in the sketch was left intentionally fully exposed to the flow to have maximum flexibility in its placement. This set-up produces some flow perturbations that should be taken into account. However, it can be noted that the probe intrusiveness is not such as to highly affect the flow structure in the inner region compared with the canonical case. To evaluate the intrusiveness of the front probe, in figure 5 is illustrated the normalised burst frequency of sweep events, $n^+$ , as a function of $T^+$ for a given VITA threshold level $k=1.0$ , measured using the rear probe positioned at $x^+=66$ and $y^+=15$ . The figure compares results for the canonical case (without the presence of the front probe) and the baseline case (with the front probe positioned at $x^+=-55$ and $y^+=15$ and the control actuator deactivated). A reasonable agreement between the canonical and the baseline case can be observed, representing that the number of events is not strongly affected by the presence of the front probe. Both results also agree with the DNS channel flow simulations carried out by Johansson, Alfredsson & Kim (Reference Johansson, Alfredsson and Kim1991) at $\textit{Re}_\tau =180$ . Figure 6(a) presents a comparison of the VITA conditionally averaged sweep events for the canonical and baseline flows. This analysis was applied to the velocity signal sampled by the rear probe positioned at $x^+ =66$ and $y^+=15$ using a threshold level $k=1.0$ and an averaging time $T^+=10$ . Canonical and baseline cases are respectively represented by continuous and dashed lines. The discrepancy between the canonical and baseline curves primarily arises from the slightly lower value of $u_{\textit{rms}}$ observed in the baseline case, where the rear probe is located in the wake of the upstream sensor. This reduction in $u_{\textit{rms}}$ is attributed to the intrusive effect of the upstream probe. Since the VITA detection threshold is defined as $k u_{\textit{rms}}$ , a lower $u_{\textit{rms}}$ results in a reduced threshold, leading to the identification of a greater number of events in the baseline case. This fact can explain why the burst frequency is slightly different between the canonical and the baseline curves of figure 5 and why the baseline VITA event shown in figure 6(a) presents a reduced amplitude around $t^+ = 10$ with respect to the canonical one. Differences up to $18\,\%$ between the canonical and the baseline case can be observed primarily in the positive and negative peaks of the VITA event shown in figure 6(a). Although this bias is non-negligible, it cannot be entirely removed given the current experimental set-up. It should be noted that this systematic bias affects both the baseline and controlled signals, as they are sampled under the same experimental configuration. Consequently, it does not compromise the direct comparison between the baseline and the controlled case. Figure 6(b) shows a comparison between the conditionally averaged sweep events detected using the VITA technique and the gradient technique, both sampled at $x^+=66$ from the rear probe velocity signal in the canonical case. In the VITA method, the trigger for conditional averaging, unlike in figure 6(a) where it was computed from the rear probe positioned at $x^+=66$ , is here obtained from the front probe located at $x^+ = -55$ . Similarly, in the gradient-based approach, the trigger is provided by the front probe signal at $x^+=-55$ through the detector system. As discussed in Rebbeck & Choi (Reference Rebbeck and Choi2006), the amplitude of the conditionally averaged sweep event detected by the VITA technique is slightly higher than that obtained with the gradient-based method, as the latter is more susceptible to false detections. Nevertheless, the overall agreement between the two techniques is satisfactory. A key advantage of the gradient-based method lies in its real-time applicability, in contrast to the VITA technique, which inherently introduces a delay of at least half the averaging time.

Figure 5.

Sweep events burst frequency, $n^+$ , as a function of the averaging time, $T^+$ , for the canonical and baseline case. The rear probe is positioned at $x^+= 66$ and $y^+=15$ . Solid square: DNS data from Johansson et al. (Reference Johansson, Alfredsson and Kim1991) at $\textit{Re}_\tau =180$ . The VITA threshold level is $k=1.0$ .

Figure 6.

Conditionally averaged sweep event sampled at $x^+= 66$ and $y^+= 15$ . (a) Comparison between canonical and baseline cases employing the VITA technique with threshold $k=1.0$ and averaging time $T^+=10$ . Detection is performed at $x^+=66$ using the rear probe velocity signal. (b) Comparison between the VITA technique and the gradient technique, both applied to the baseline case. Detection is performed at $x^+=-55$ using the front probe velocity signal. The VITA parameters are the same as in (a), while the gradient technique employs the detector system sketched in figure 3.

A detected sweep event triggers a TTL signal that is sent to an Arduino Uno Rev3 microcontroller, introducing with the latter a delay to account for the convection time and the actuator response. The microcontroller has been programmed with a circular buffer of a sufficiently large number of elements so that no events are missed. The connection through the USB serial interface with the workstation allows the delay time to be changed once requested by the optimisation algorithm, as can be seen in figure 7 where the control system scheme is represented. The delayed TTL signal triggers a signal generator (Agilent 33120A) to produce a single-period sine wave, $\mathcal{F}(f, \hat {A}, \Delta T)$ , which is a function of frequency ( $f$ ), voltage amplitude ( $\hat {A}$ ) and delay time ( $\Delta T$ ). The signal is subsequently amplified by an amplifier (Kenwood KAC-5205) to drive a loudspeaker. The latter emits a jet through an orifice with a diameter of ${1}\,\textrm {mm}$ , equivalent to $10$ viscous units. Figure 8 depicts the wall-normal velocity $V^+$ of the jet as a function of the time sampled at $y^+=5$ (red curve) and $y^+=15$ (blue curve) in still air for an actuation frequency of ${60}\,\textrm {Hz}$ and a voltage amplitude of ${60}\,\textrm {mV}_{\textit{pp}}$ . After a quick velocity increase, the maximum velocity reached in that condition was $V_{\textit{max}}^+ = 10.2$ for $y^+=5$ and $V_{\textit{max}}^+ = 9.0$ for $y^+=15$ . The suction phase can be observed only in the case of $y^+=5$ since $y^+=15$ is above the height where the saddle point is formed.

Figure 7.

Schematic of the control system. The signal from the upstream probe is used to trigger the actuation. The signal coming from the downstream probe allows the optimisation of the control strategy.

Figure 8.

Jet wall-normal velocity in still air as a function of the viscous time at $y^+ = 5$ (red curve) and $y^+ = 15$ (blue curve). Actuation parameters: frequency ${60}\,\textrm {Hz}$ , voltage amplitude ${60}\,\textrm {mV}_{\textit{pp}}$ . The figures are temporally aligned such that the onset of the velocity increase occurs at the same viscous time in both cases.

4. Optimisation algorithm

An open-loop control logic was implemented through a BO algorithm. Bayesian optimisation is well suited for minimising functions that are expensive to evaluate and for handling stochastic noise in the function evaluation. The algorithm is constituted of two main components: a Bayesian statistical model to build a surrogate for the objective function and an acquisition function to determine the next point to sample.

The statistical model, a Gaussian process (GP), provides a Bayesian posterior distribution for potential values of the cost function $\mathcal{J(\psi )}$ at any candidate point $\psi$ , which is updated with each new observation of $\mathcal{J}$ . A GP represents a distribution over functions, with the smoothness of these functions determined by a covariance function, which is calculated using a kernel. The kernel $\varSigma _0(\psi _i, \psi _j)$ is designed such that input points ( $\psi _i, \psi _j$ ) that are closer together in the input space have a stronger positive correlation.

The acquisition function assesses the value that would be generated by evaluating the objective function at a new point $\psi _{n+1}=\psi$ , leveraging the posterior distribution that is formed after observing $n$ data points. Let $\boldsymbol{\psi _t} := \{ \psi _i \}_{i=1}^n$ a set of $n$ tested points and $\boldsymbol{\mathcal{J}_t} := \{ \mathcal{J}(\psi _i)\}_{i=1}^n$ the associated cost function values. The acquisition function drives the selection of the next sampling point by balancing exploration and exploitation. The balance is achieved by considering both the exploration of regions with high posterior variance and the exploitation of areas where the posterior mean is low. This strategy guides the sampling process to effectively minimise the objective function while also reducing uncertainty. Finally, the cost function for this new point is evaluated and the algorithm is repeated for all further iterations in the same way.

According to Rasmussen & Williams (Reference Rasmussen and Williams2008) and Frazier (Reference Frazier2018) the posterior probability distribution is defined as

(4.1) \begin{equation} \mathcal{J}\left (\psi \right ) | \boldsymbol{\mathcal{J}_t} \sim \mathcal{N} \big ( \mu _n (\psi ), \sigma _n^2 (\psi ) \big ), \end{equation}

in which

(4.2) \begin{equation} \mu _n(\psi ) = \varSigma _0\left (\psi , \boldsymbol{\psi _t}\right ) \varSigma _0^{-1}\left (\boldsymbol{\psi _t}, \boldsymbol{\psi _t}\right ) \big (\boldsymbol{\mathcal{J}_t} - \mu _0\left (\boldsymbol{\psi _t}\right )\big ) + \mu _0(\psi )\end{equation}

and

(4.3) \begin{equation} \sigma _n^2(\psi ) = \varSigma _0(\psi , \psi )- \varSigma _0\left (\psi , \boldsymbol{\psi _t}\right ) \varSigma _0^{-1}\left (\boldsymbol{\psi _t}, \boldsymbol{\psi _t}\right ) \varSigma _0\left (\boldsymbol{\psi _t}, \psi \right )\!, \end{equation}

where $\mu _n(\psi )$ is the posterior mean that is a weighted average of the prior mean $\mu _0(\psi )$ and an estimate derived from the prior explored cost function values $\boldsymbol{\mathcal{J}_t}$ having the weights dependent on the kernel; $\sigma ^2_n(\psi )$ is the posterior variance that is equal to the prior covariance $\varSigma _0(\psi ,\psi )$ minus a term representing the variance reduction from observing $\boldsymbol{\mathcal{J}_t}$ .

One of the most commonly used acquisition functions is the expected improvement (EI). By setting $\mathcal{J}_{\textit{min}} = \text{min}_{m \leqslant n} \mathcal{J}(\psi _m)$ as the best function value, the EI function can be written as

(4.4) \begin{equation} \text{EI}(\psi ) \equiv \mathbb{E}_n \left [ I(\psi ) \right ] = \int _{-\infty }^{+\infty } I(\psi ) \phi (Z)\, {\rm d}Z, \end{equation}

where $\mathbb{E}_n [\boldsymbol{\cdot }] = \mathbb{E} [\boldsymbol{\cdot }| \boldsymbol{\psi _t}]$ is the expectation taken under the posterior distribution of (4.1) (Frazier Reference Frazier2018), $\phi (Z)$ is the probability density function (PDF) of a standard Gaussian and $I(\psi ) = \text{max} ( \mathcal{J}_{\textit{min}} - \mathcal{J}(\psi ) )$ is the improvement. Integrating by parts, EI can be written as (Jones et al. Reference Jones, Schonlau and Welch1998)

(4.5) \begin{align} \text{EI}(\psi ) = \left (\mathcal{J}_{\textit{min}} - \mu _n(\psi ) - \xi \right ) \varPhi \left (\frac {\mathcal{J}_{\textit{min}} - \mu _n(\psi )}{\sigma _n(\psi ) - \xi }\right )+\sigma _n(\psi ) \phi \left (\frac {\mathcal{J}_{\textit{min}} - \mu _n(\psi ) - \xi }{\sigma _n(\psi )}\right )\!, \end{align}

with $\varPhi (\boldsymbol{\cdot })$ the cumulative distribution function and $\xi$ a hyperparameter to tune how much exploration versus exploitation is needed. Equation (4.5) highlights the balance between exploitation by sampling in regions in which $\mu _n(\psi )$ is smaller than $\mathcal{J}_{\textit{min}}$ and exploration by sampling in regions where $\sigma _n(\psi )$ is high. Increasing the value of $\xi$ can be seen as reducing the current minimum value and, thus, the need for lower $\mu _n(\psi )$ . Therefore, this increases the BO algorithm exploration.

Finally, the optimisation algorithm requires the choice of a kernel function. Kernels have the property that points close to each other in the input space are strongly correlated, i.e. if three generic points are defined as $\psi _i$ , $\psi _j$ and $\psi _k$ and $|| \psi _i - \psi _j || \lt || \psi _i - \psi _k ||$ for some norm $|| \boldsymbol{\cdot }||$ then $\varSigma _0(\psi _i, \psi _j) \gt \varSigma _0(\psi _i, \psi _k)$ (Frazier Reference Frazier2018). Kernels also require to be positive semi-definite functions. One of the most commonly used kernel functions is the Màtern kernel that is a stationary kernel and a generalisation of the radial basis function (RBF) kernel (Rasmussen & Williams Reference Rasmussen and Williams2008). It includes an additional parameter that governs the smoothness of the resulting function, $\eta$ , and is also defined with a length scale parameter, $l$ . The following equation defines the Màtern kernel:

(4.6) \begin{equation} \varSigma _0(\psi _i, \psi _j)=\frac {2^{1-\eta }}{\varGamma (\eta )}\left (\frac {\sqrt {2 \eta } || \psi _i - \psi _j ||}{l}\right )^\eta K_\eta\! \left (\frac {\sqrt {2 \eta } || \psi _i - \psi _j ||}{l}\right )\!. \end{equation}

Here $K_\eta (\boldsymbol{\cdot })$ is the modified Bessel function and $\varGamma (\boldsymbol{\cdot })$ is the Gamma function (Abramowitz & Stegun Reference Abramowitz and Stegun1988). The Màtern kernel converges to the RBF kernel if $\eta \to \infty$ . In the present study, both $\eta = 3/2$ and $\eta = 5/2$ were tested, with $\eta = 5/2$ ultimately selected to achieve an optimal balance. Lower values led to a rough process, while higher values produced an overly smooth process.

The Màtern kernel in the case of $\eta = 5/2$ is written as

(4.7) \begin{equation} \varSigma _0(\psi _i, \psi _j)=\left (1+\frac {\sqrt {5}}{l} || \psi _i - \psi _j ||+\frac {5}{3 l^2} || \psi _i - \psi _j ||^2\right ) \exp\! \left (-\frac {\sqrt {5}}{l} || \psi _i - \psi _j ||\right )\!. \end{equation}

A constant term was multiplied to the Màtern kernel to better model the amplitude of the function to be approximated. Subsequently, a white noise kernel was added to the resulting kernel to account for noise due to the measurement.

In the present study, the control triplet $\psi$ is a three-dimensional array composed of a frequency, a voltage amplitude and a delay time. A measure of control effectiveness in terms of sweep events intensity can be obtained through the difference between area of the baseline case, $A_{{b}}$ , and the area of the controlled case, $A_{{c}}$ . For a generic triplet $\psi _i$ , the difference in areas is depicted in figure 9 and the corresponding cost function can be written as

(4.8) \begin{equation} \mathcal{J}(\psi _i) = -\frac {A_{{b}} - A_{{c}}(\psi _i)}{A_{{b}}}, \end{equation}

where the generic area in either baseline or controlled cases is

(4.9) \begin{equation} A_{(\boldsymbol{\cdot })} = \int _{t_m}^{t_w} u^+ \, {\rm d}t, \end{equation}

where $u^+$ is the fluctuating component of the streamwise velocity in wall units, $t_m$ is the time in correspondence of the first minimum peak and $t_w$ is the window ending time that was selected to ensure the robustness of the cost function. The negative sign in (4.8) was introduced since the difference in areas between the baseline and controlled case should be as large as possible but the cost function needs to be minimised. Regarding the definition of the cost function adopted in this study, it should be pointed out that it is specifically tailored to the definition of event intensity proposed in Rebbeck & Choi (Reference Rebbeck and Choi2001). A relatively high uncertainty (about $1\,\%$ ) characterises the velocities of the conditionally averaged sweep event. This level of uncertainty arises from the real-time nature of the control and the limited number of sweep events taken into account for conditional averaging, as only the most intense sweep events were considered. Moreover, the velocity signal exhibits long-period fluctuations attributed to the slowly varying operating conditions during the experiment. In practice, this uncertainty does not allow the optimisation process to be successfully completed. It is therefore necessary to realign the velocity minimum of the baseline conditionally averaged sweep event with the first minimum observed in the controlled case. This realignment is justified under the assumption that the velocity signal characterising the conditionally averaged sweep event in the controlled case remains unchanged with respect to the baseline case until the effect of the control begins. This strategy enabled the definition of a cost function robust enough to drive the optimisation process. It should be noted that the realignment of the velocity minima limits the lower bound of the feasible delay time imposed by the microcontroller. This is because the velocity reduction induced by the control should necessarily start after $t_m$ .

Figure 9.

Conditionally averaged sweep events in the baseline (uncontrolled) case and the controlled case for a generic triplet $\psi _i$ . The area difference is highlighted in grey.

The cost function was evaluated at the end of each episode whose length was set to 120 s. The episode duration was adjusted to ensure approximately 600 events for statistical analysis. Frequency, voltage amplitude and delay time were kept constant all over each episode.

The optimisation bounds imposed on the BO are shown in table 1. They were chosen for both equipment limitations and operational reasons. Instrumentation limitations set a lower bound on the amplitude at ${50}\,\textrm {mV}_{pp}$ as the function generator used could not generate a lower value for the output signal. The amplifier gain was set as its minimum value. Additionally, the minimum achievable frequency was constrained to prevent damage to the speaker. Moreover, operational limitations emerged, as using actuation parameters outside these ranges led to ineffective control, characterised by excessively high delay or amplitude.

Table 1.

Bayesian optimisation algorithm bounds imposed.

An initial exploration phase was conducted prior to optimisation, during which 32 points were sampled using the Sobol’ sequence (Sobol’ Reference Sobol’1967), a quasi-random low-discrepancy method. In summary, for each optimisation iteration, the posterior mean and variance are computed based on the outcomes of previous cost function evaluations; see (4.1). The acquisition function is then used to determine which triplet to sample in the current iteration according to (4.5). Once the selected triplet is identified, the actuation parameters are automatically adjusted. The function generator, which controls frequency and voltage amplitude, is controlled through a Python routine by using the PyVISA library. All the queries to the function generator are written with the rules and conventions of SCPI (standard commands for programmable instruments) language. Additionally, the BO interacts with the Arduino microcontroller to adjust the delay time, through a USB serial port. As well as for the signal generator, a Python routine was written to change the delay of the microcontroller. At the end of the iteration the cost function is evaluated (see (4.8)) and the next iteration is started. A further description, step-by-step, of the algorithm can be found in Appendix A.