*2.2. Water Flow Velocity Measurement*

Figure 1 presents the signal processing setup for water flow velocity measurement, where **y***v* = [*yv*,1, ... , *yv*,*Nv* ] is the sampled version of the received signal *y*(*t*) at a sampling rate of *fv* and window size of *Nv*-point. The envelope of the received signal **y***v* is computed to outline the characteristics of the signal. Let the Hilbert transform of **y***v* be **~ y***v* = [-*yv*,1, ... ,-*yv*,*Nv* ]. The envelope of the received signal **y***v* can be expressed as

$$\mathfrak{F}\_v = [\mathfrak{H}\_{v,1}, \dots, \mathfrak{H}\_{v,N\_v}] \tag{5}$$

in which *y*ˆ*i* = %*y*2 *<sup>v</sup>*,*i* + *y*2 *<sup>v</sup>*,*i* , *i* = 1, ... , *Nv*. The frequency of the envelope from the received signal can be obtained as

$$\mathbf{y}\_F = [y\_{F,1}, \dots, y\_{F,N\_v}] = \mathfrak{d}(\mathfrak{y}\_v) \tag{6}$$

where (•) describes the Fourier transform operation. Herein, only half of **y***F* is considered due to the symmetric property of the frequency response (i.e., *yF*,1, ... ,*yF*,*Nv*/2 ). To remove the direct current (DC), the system applies a frequency-domain DC-block filter with the coe fficients

$$\mathbf{h}\_{\rm DC} = \begin{bmatrix} h\_1, \dots, h\_{\rm N\_v/2} \end{bmatrix} \tag{7}$$

where *hi* = & 1, *i* ≥ *pcut* 0, *i* ≤ *pcut* , *i* = 1, ... , *Nv*/2.

In Equation (7), *pcut* = [(*fv*/2 + *fcut*)( *Nv* − 1)/ *fv*+<sup>1</sup>] − *Nv*/2, and *fcut* represents the DC-block filter of the desired cuto ff frequency. The DC-block filter provides

$$\mathbf{y}\_{\rm DC} = \begin{bmatrix} y\_{\rm DC,1}, \dots, y\_{\rm DC,N\_v/2} \end{bmatrix} \tag{8}$$

in which *yDC*,*<sup>i</sup>* = *yF*,*<sup>i</sup>hi*, *i* = 1, ... , *Nv*/2.

> The Gaussian smoothing filter is applied to smooth the frequency response **y***DC*

$$\mathbf{y}\_G = \mathbf{y}\_{DC} \otimes \mathbf{g} \tag{9}$$

where **g** = [g1, ... , g*L* shows the *L*-point filter coe fficients and g*i* = *e* (− 1 <sup>2</sup>σ<sup>2</sup> )[(2/*L*−<sup>1</sup>)(*<sup>i</sup>*−<sup>1</sup>)−<sup>1</sup>] 2 , *i* = 1, 2 ... *L*, herein, the σ contains the variance of the Gaussian coe fficients. In the proposed system, the flowing velocity is measured from the frequency response in Equation (9).

Figure 2 depicts the experimental system for the water turbidity and water flow velocity measurement processes. The water flow was generated by a pump driven by a 1/6-hp motor in a 0.35 m wide and 2 m long flume. Four release holes were established at the end of the water channel to control the amount of water released. The sluice has been applied to the water flow channel to steadily control the water level of the flowing water. The turbidity of the flowing water was slight adding fine sand to the water. Sieving sediments of uniform sand with a diameter of 0.88 mm were used in this experiment. A 0.2 × 0.2 m pier made by a transparent acrylic column with VLC sensors was placed in the middle of the flume.

**Figure 2.** Experimental setup consisting of **A**: VLC sensor (Tx & Rx); **B**, **C**, **D**: waveform signal generator; **E**: input waveform signal monitoring; **F**: sensor signal response monitoring.

#### *2.3. Experimental Setup for Water Turbidity Measurement*

A sinusoidal signal with the frequency of 1 MHz was generated from the arbitrary waveform generator (AWG) in this turbidity measurement and stayed an amplitude of 0.2 V. The received signal was then obtained from the oscilloscope at a sampling rate of *ft* = 1.024 Ghz with a window size of *Nt* = 10, 240. From Equations (3) and (4), Δ*RMS* values were computed. In this experiment, signal measurements were conducted at water turbidity levels of 0, 200, 400, 600, 800, 1000, and 1200 ppm and at two water flow velocities of 83.14*q* and 136.40*q*, where *q* = (Liter)/(second × meter<sup>2</sup>).

#### *2.4. Experimental Setup for Water Flow Velocity Measurement*

As mentioned, the sinusoidal signal was generated from the AWG. Signals were captured on the oscilloscope using a sampling rate of *fv* = 50 hz with a window size of *Nv* = 500 to estimate the flowing velocity. The envelope of the received signal **y**ˆ *v* was then calculated using Equation (5) and the DC-blocked frequency of the received signal **y***DC* has computed from Equations (6)–(8). Finally, the Gaussian smoothing filter with a variance of σ = 1.8 and a window size of *L* = 45 was substituted into the smoothed frequency **y***G* in Equation (9). The flowing velocities were set to be 25.98*q*, 83.14*q*, and 136.40*q* in the experiments.

Figure 3a shows the received signals at turbidity levels of 0, 200, 600, and 1000 ppm and at a water flow velocity of 83.14*q*. The attenuation of the amplitude of the received signals increased in accordance with the water turbidity levels. Figure 3b illustrates the relationship between Δ*RMS* values and water turbidity levels at the water flow velocities of 83.14*q* and 136.40*q*. It seems that a linear relationship was observed between the Δ*RMS* values and trifling water turbidity levels. Furthermore, Δ*RMS* values computed at different flowing velocities were approximately the same. It shows that Δ*RMS* is independent of the flowing velocity in the experiment.

**Figure 3.** (**a**) Received signals at turbidity levels of 0, 200, 600, and 1000 ppm and at water a flow velocity of 83.14*q*; (**b**) water turbidity levels versus Δ*RMS* values.

Figure 4 shows the turbidity effect in nephelometric units (NTU) of the output voltage value for VLC, blue LED, and infrared LED (IR LED). VLC turbidity data was tested in the flowing flume with suspension particles distribution while the blue LED and IR LED turbidity data is obtained from the standard specimen. As shown in Figure 4, the VLC data have a slightly variated than the blue LED and IR LED, this variation is because the flowing suspension particles of the scattering, attenuation, and absorption effects have a significant influence on the measurement in the water. It is well-known that the on-line resolution of the experiment progress is highly dependent on the measurement angle of the sensor between the transmitter and the receiver. In addition, the ambient indoor light would be a noise resource which affects the performance of VLC during the experiment progress. Despite the influence of these factors, the nonlinear nature of turbidity which actually responds in exponential form to the light intensity was obviously obtained from the VLC monitoring system.

**Figure 4.** Turbidity effect in nephelometric units (NTU).

According to the results of the underwater turbidity and water flow velocity experiments in Section 2, we see that the communication light path of the VLC modules can be sensitively affected by turbulent movement of particles in water. In the following sections, the study further examines the

effects of this notable phenomenon on real-time scour measurement by conducting real-time scour measurement and Hilbert transform analysis.
