**1. Introduction**

Human beings are social animals with an innate desire to conform to socially accepted norms and values. Over periods of time, some of these norms become standards that all members of the community are expected to adhere to. Deviance from these standards is seen as absurd, wrong, or frankly abnormal. However, many of these cultural mores have no scientific basis and, some of them actually promote behaviors with negative health consequences. While the health consequences of many of these practices may not be of public health significance, some have major short and long term impact on the health of individuals in the community. The more difficult ones to appreciate are those practices that do not immediately appear to have deleterious health consequences but, may have direct and indirect long term impact on the health of individuals, families and the community.

It must be appreciated that not all cultural practices are deleterious to health. Some are actually beneficial. For example, many communities in rural Africa forbid intimacy between a newly delivered mother and her partner for some months. This practice encourages child spacing and allows the mother to adequately breastfeed the new baby [1].

Cultural practices are varied across different contexts. They have usually been viewed as the normal way of life and may be actively encouraged in the communities.

This chapter is a review of literature on some cultural practices with overt health consequences. It seeks to highlight some of these practices in Africa as prototype and explore ways they can be addressed at public health level.


**Appendix C**

**Figure A1.** Macronutrient distribution according to FC group in females. Each macronutrient distribution of three FC groups was presented. The Very Low FC is represented in red; the Low FC and Optimal FC are represented in purple and blue, respectively. The gray background indicates Korean acceptable macronutrient distribution range (AMDR).


**2. Power over fiber**

This section presents the technical principles of PoF including a short history, the main elements (high‐power lasers, fibers, and photovoltaic converters (PVs)), and their main limitations (laser power, converter efficiency, and fiber‐fuse effect), circuits, topologies and networks, application on multimode (MM), single mode (SMF) and special fibers, and finally the future perspectives.

#### **2.1. Historical overview**

#### *2.1.1. Telecom*

The concept of PoF was born together with the first optical fiber developments. Optical fiber with low attenuation (less than 20 dB/km) was developed in 1970, and the first fiber optic link was installed in Chicago in 1976, USA. To the best of author's knowledge, DeLoach et al. [1] published the first work about PoF in 1978. They proposed to use PoF to operate a sound alert of a telephone remotely. Continuing the previous experiment, in 1979, Miller and Lawry [2] implemented a two‐way speech communication between an electrically powered station and an optically powered station, and in 1982, Miller et al. [3] demonstrated a bidirectional speech‐television communication over a single optical fiber, with emergency optical powering of the remote station telephone. A great result of those researches was the development of a highly efficient photovoltaic converter based on GaAlAs.

other words, beyond their classical applications, optical fibers can also be used to transport optical energy to powering electric or electronic devices remotely. This is the concept of PoF. Since that time in the 1970s, many applications have emerged for PoF mainly in two different

Why PoF is interesting? The reasons depend on the applications but they are associated to the

For telecom applications, the key factors are (i) PoF eliminates the necessity of batteries, solar panels, and long cupper feeder wires in the remote sites, improving the reliability and the security of the system; (ii) PoF permits the reduction of the space and the installation cost in

For electrical utilities, there are at least four key factors: (i) PoF uses optical fiber, which is made of nonconductive material. This characteristic is important because in most applications in electrical world, the sensors are placed in high voltage. Any conductance in high‐voltage elements can create current leaks; (ii) optical fiber is immune to electromagnetic interferences. The electrical world environment is polluted of electromagnetic interferences; therefore, optical fiber can transmit signals without quality degradation; (iii) the optical fiber eliminates the need to run conductive copper wire into a high‐ground potential rise (GPR) zone. GPR arises when lightning strikes occur in substations and can cause severe interference problems in electronic equipment and systems. Considering that the sensor using PoF has a complete galvanic isolation to the ground potential, it is practically immune to the GPR effects; and (iv) there are many low‐cost/low‐power/high‐efficiency electronic sensors available for transmission lines and substations monitoring that can be supplied by PoF without incurring in the

This chapter describes a revision of PoF, its technical principles, main elements, technologies,

This section presents the technical principles of PoF including a short history, the main elements (high‐power lasers, fibers, and photovoltaic converters (PVs)), and their main limitations (laser power, converter efficiency, and fiber‐fuse effect), circuits, topologies and networks, application on multimode (MM), single mode (SMF) and special fibers, and finally

The concept of PoF was born together with the first optical fiber developments. Optical fiber with low attenuation (less than 20 dB/km) was developed in 1970, and the first fiber optic

and the applications in telecom and in utilities, developed by the author's group.

areas: telecommunications and utilities.

remote sites, which is very important to telecom companies.

optical fiber characteristics.

256 Optical Fiber and Wireless Communications

described problems.

**2. Power over fiber**

the future perspectives.

**2.1. Historical overview**

*2.1.1. Telecom*

In 1993, Banwell et al. investigated the issues of PoF application in fiber‐in‐the‐loop (FITL) [4]. In this work, many technical and cost aspects have been considered in the analysis. Almost a decade after that, Miyakawa et al. [5–7] presented fiber optic power and signal transmission systems considering the application of DC (direct current) powering to information equipment such as personal computers.

Werthen and Cohen [8] in 2006 and 2008 [9] proposed the use of PoF for driving low‐power switches or actuators to assuring path diversity in upstream data delivery in passive optical network (PON) architectures and for providing battery backup power in case of power outages.

In 2007, Wake et al. [10] studied the combination of radio over fiber and PoF, and in [11], they described optically powered radio‐over‐fiber remote units designed and constructed for distributed antenna system applications.

Sato and Matsuura [12] and Matsuura and Sato [13] demonstrated in 2013 the transmission of RF signal and high‐power light using a double‐clad fiber (DCF). A DCF has a single‐mode core and a multimode inner clad. The RF signal and the optical powering signal travel, respectively, through core and in the inner clad of DCF.

In 2014, Penze et al. [14] proposed powering PON extenders using PoF. In this research, SOAs (semiconductor optical amplifier) were powered using PoF. The SOAs were used in a bidirectional amplification of signals of Gigabit PON (GPON) and 10 Gigabit PON (XGPON). In the same year, Ikeda [15] proposed a PoF instead of metal waveguides in order to protect microwave radio equipment from lightning.

Yan et al. [16], in 2015, developed a wireless sensor system based on PoF to realize a flexible distributed sensing over a middle distance, in environments of high voltage, strong magnetic field, flammable, and explosives. In the same year, Matsuura and Sato [17] demonstrated experimentally a bidirectional radio over fiber using a DCF for optically powered remote antenna units. The feasibility of the technique was demonstrated by bidirectional RoF transmission over a 100‐m DCF optically feeding with 4.0 W, and in [18], Sato et al. demonstrated a bidirectional radio‐over‐fiber transmission using a double‐clad fiber with 40‐W optical power feeding. In the same year, Lee et al. [19] described the concept of cloud radio access network (CRAN) based on PON exploiting PoF, andSuto et al. [20] detailed the challenges of QoE‐ guaranteed and power‐efficient network operation for CRAN based on PON exploiting PoF.

In 2016, Minamoto and Matsuura [21] and Matsuura and Minamoto [22] presented an optically controlled beam steering system using 60‐W PoF in the fiber to feed remote antenna units, and in [23], Yoneyama et al. demonstrated a 1.3‐μm dual‐channel radio‐over‐fiber system using a 300‐m double‐clad fiber feed with 30‐W optical power of a PoF system. In the same year, Umezawa et al. [24] reported a high‐conversion gain in a high‐speed optical receiver based on PoF supply and designed to work with radio over fiber at 100‐GHz region. In [25, 26], the same authors proposed the use of a multicore‐based radio and PoF in a transmission using a 100‐GHz photo receiver.

#### *2.1.2. Utilities and other industries*

In 1980, Caspers and Neumann [27] first described a PoF method used to supply active electronic circuits at high potential. In the experiment, they used four infrared light‐emitting diodes (LEDs) emitting at a wavelength of 940 nm which were connected in parallel and coupled to an uncladded glass rod of 40‐mm diameter and a length of 1 m with an attenuation smaller than 200 dB/km at a wavelength of 850 nm. Four square silica solar cells of 20 mm length were connected in series in this experiment.

Ohte et al., in 1984 [28], demonstrated a transducer with optical‐fiber data link to provide electrical isolation. A pulse‐position–modulated optical signal was used in transmitted signal by optical fiber from a remote converter to mainframe. Wavelength division multiplexing (WDM) was used to transmit the modulated signal and the optical feed power in the same optical fiber.

In 1988, Trisno and Wobschall [29] described a method for improving the efficiency of the conversion of pulsed optical power to electrical power by photovoltaic. The system required a pulsed power source with a storage capacitor to hold energy for a time after the optical power is turned off. In the same year, Bjork et al. [30] demonstrated the ability to provide data communication a variety of off‐the‐shelf electronic transducers in a single fiber with proper attention to the synchronization issues and in [31] Lenz and Bjork presented a comparative study of four concepts for standardizing and multiplexing of fiber optic sensors for aircraft applications and compared them with PoF.

Kirkham and Johnston [32] presented in 1989 an optical frequency–modulated (FM) data link whose remote electronic sensors were optically powered. An application to current measurement is described in a high‐voltage line by means of a linear coupler.

In 1991, Yamagata et al. [33] described a PoF system to measuring gas density of extra high‐ voltage substation gas‐insulated switchgear. This system employed a method of matching the impedances of load and photodiode by optical electrical conversion of pulsed light with a photodiode and boosting the voltage with a transformer. In [34], Sai presented an optimization of this method. In the same year, Nieuwkoop et al. [35] described an alternative system to increase the voltage to the remote sensor using a low‐cost coil.

Spillman and Crowne [36] presented in 1995 a throttle level angle (TLA)‐sensing system applied to aircrafts utilizing a capacitance‐based rotary position transducer which was powered and interrogated via light from a single MM optical fiber. The system used a unique GaAs device that served as both a power converter and optical data transmitter. In the same year, Tardy et al. [37] described a PoF system designed to measure current in high voltage; Pember et al. [38] demonstrated a PoF network concept; and Dubaniewicz and Chilton [39] described a PoF system to gas monitoring in mines.

In 1996, Werthen et al. [40] presented an optically powered current transducer based on shunt technology using PoF and detailed a practical use of this technique. Wang et al. [41] and Zhijing [42] detailed the use of PoF to measure the pressure of liquids in 1998. In 2005, Turán et al. [43] review the basic properties of PoF, their key elements, and its industrial applications.

Bottger et al. [44], in 2008, presented an optically powered video camera link that allows acquiring and communicating a 100‐Mb/s video stream over a distance of hundreds of meters. In [45], M. Roger demonstrated an optically powered sensor network with subscribers consuming less than 1‐μW average power, and an optically powered high‐speed video link transmitting data at a bit rate of 100 Mbit/s.

In 2010, Rosolem et al. [46] described the results of a PoF sensing system for monitoring partial discharges on hydro generators and de Nazaré and Werneck [47] proposed a monitoring system based on PoF to measure the temperature and current of transmission lines.

Audo et al. [48], in 2011, proposed PoF‐based architecture to extend multidisciplinary‐cabled networks or to create a dedicated submarine hydrophone or seismometer network, and in 2012, Lau et al. [49] reported a prototype optically remote‐powered subsea video monitoring system that provides an alternative approach to powering subsea video cameras. In the same year, Tanaka and Kurokawa [50] presented a review of fiber optic sensor network that employs PoF. A hybrid sensor network with wireless sensors is also achievable by introducing wireless/optical interface nodes.

In 2014, Rosolem et al. [51] presented a PoF system to long‐distance applications based on charge/discharge of super‐capacitors. The system was installed in a transmission line tower, and it was connected to the substation using an optical ground wire cable (OPWG), and in [52], Silva et al. proposed a new MM fiber optic cable to transmit optical energy for long reach in PoF systems.

Rosolem et al. [53], in 2015, presented the results of a PoF system to monitor high‐voltage switchgear using video cameras and free space optics (FSO), and in [54], Rosolem et al. proposed the use of PoF and FSO to measure current in high‐voltage transmission lines.

In 2016, Zhang et al. [55] proposed a 15‐kV silicon carbide (SiC) MOSFET gate drive using PoF and replaced the traditional design based on isolation transformer.

## **2.2. Technical principles of PoF**

units, and in [23], Yoneyama et al. demonstrated a 1.3‐μm dual‐channel radio‐over‐fiber system using a 300‐m double‐clad fiber feed with 30‐W optical power of a PoF system. In the same year, Umezawa et al. [24] reported a high‐conversion gain in a high‐speed optical receiver based on PoF supply and designed to work with radio over fiber at 100‐GHz region. In [25, 26], the same authors proposed the use of a multicore‐based radio and PoF in a trans-

In 1980, Caspers and Neumann [27] first described a PoF method used to supply active electronic circuits at high potential. In the experiment, they used four infrared light‐emitting diodes (LEDs) emitting at a wavelength of 940 nm which were connected in parallel and coupled to an uncladded glass rod of 40‐mm diameter and a length of 1 m with an attenuation smaller than 200 dB/km at a wavelength of 850 nm. Four square silica solar cells of 20 mm

Ohte et al., in 1984 [28], demonstrated a transducer with optical‐fiber data link to provide electrical isolation. A pulse‐position–modulated optical signal was used in transmitted signal by optical fiber from a remote converter to mainframe. Wavelength division multiplexing (WDM) was used to transmit the modulated signal and the optical feed power in the same optical fiber.

In 1988, Trisno and Wobschall [29] described a method for improving the efficiency of the conversion of pulsed optical power to electrical power by photovoltaic. The system required a pulsed power source with a storage capacitor to hold energy for a time after the optical power is turned off. In the same year, Bjork et al. [30] demonstrated the ability to provide data communication a variety of off‐the‐shelf electronic transducers in a single fiber with proper attention to the synchronization issues and in [31] Lenz and Bjork presented a comparative study of four concepts for standardizing and multiplexing of fiber optic sensors for aircraft

Kirkham and Johnston [32] presented in 1989 an optical frequency–modulated (FM) data link whose remote electronic sensors were optically powered. An application to current measure-

In 1991, Yamagata et al. [33] described a PoF system to measuring gas density of extra high‐ voltage substation gas‐insulated switchgear. This system employed a method of matching the impedances of load and photodiode by optical electrical conversion of pulsed light with a photodiode and boosting the voltage with a transformer. In [34], Sai presented an optimization of this method. In the same year, Nieuwkoop et al. [35] described an alternative system

Spillman and Crowne [36] presented in 1995 a throttle level angle (TLA)‐sensing system applied to aircrafts utilizing a capacitance‐based rotary position transducer which was powered and interrogated via light from a single MM optical fiber. The system used a unique GaAs device that served as both a power converter and optical data transmitter. In the same year, Tardy et al. [37] described a PoF system designed to measure current in high voltage;

ment is described in a high‐voltage line by means of a linear coupler.

to increase the voltage to the remote sensor using a low‐cost coil.

mission using a 100‐GHz photo receiver.

length were connected in series in this experiment.

applications and compared them with PoF.

*2.1.2. Utilities and other industries*

258 Optical Fiber and Wireless Communications

A generic PoF system is shown in **Figure 1**. In the left side, the control unit composed by the high‐power optical source (HPOS) unit together with the optical reception unit (ORU) is shown, which receives signals from the remote sensor unit, shown on the right side of **Figure 1**. Two optical fibers connect the local control unit to the remote unit. The optical fibers may be standard SMF optical fibers or MM fibers. In the remote unit, a photovoltaic converter

**Figure 1.** Generic PoF system diagram showing its main elements HPOS, OF, PV, LD, electronic circuit, and sensors.

detects the power transmitted by the HPOS. The electrical energy produced by the photovoltaic converter is used to power up a low‐threshold laser (LD), electronic circuits, and sensors of the remote unit. The optical fibers and the remote unit can be installed in a hazardous environment, such as high‐voltage substations, oil refineries, mines, oil tanks, water reservoirs, and sea depth.

The biggest challenge for a generic PoF system is to provide to a load the highest possible power, at the greatest possible distance, with the highest reliability. There are limits today to PoF applications and the limits are attributed to technological, physical, and cost aspects of PoF elements.

The amount of power that the PoF system can deliver is determined to a great extent by its components: laser, fiber, and photovoltaic cell. The following parameters can be used to evaluate the delivered electric power (*P*Load) to an electronic load: the maximum transmitted optical power without causing damages in the optical fiber (*P*MaxFiber); the optical power of the HPOS (*P*HPOS); the optical power in the PV input (*P*In); the total loss on the fiber (*α*Fiber); the total loss of the optical connectors (*α*Conn); the link distance (*L*); and the efficiency of the PV (*η*PV). The power delivered to the extender can be expressed by

$$P\_{\rm load} = P\_{\rm ln} \cdot \eta\_{\rm PV} \tag{1}$$

$$P\_{\rm ln} = P\_{\rm H^{\rm COS}} \dots \,\, a\_{\rm Hbar} \dots \,\, a\_{\rm Conn} \tag{2}$$

$$
\alpha\_{\text{Fhor}} = 10^{(-\ell.a\_{\text{two}}/10)} \tag{3}
$$

$$
\alpha\_{\text{Com}} = 10^{\left( -\alpha\_{\text{c.s.o.}}/10 \right)} \tag{4}
$$

where *α*FiberdB is the fiber attenuation in dB/km and *α*ConndB is the total connector loss in dB. Notice that

$$P\_{\text{HTCS}} \le P\_{\text{MaxFlow}} \tag{5}$$

In the following subsections, the main elements of PoF will be described, and **Figure 2** will be used as a reference for further discussion. **Figure 2** shows a qualitative graph of some parameters of the PoF elements, such as the loss of the optical fibers and the responsivity of PV cells. The main spectral bands for HPOS are also shown in **Figure 2**.

**Figure 2.** Qualitative graph of some PoF parameters.

#### **2.3. Main elements of PoF**

detects the power transmitted by the HPOS. The electrical energy produced by the photovoltaic converter is used to power up a low‐threshold laser (LD), electronic circuits, and sensors of the remote unit. The optical fibers and the remote unit can be installed in a hazardous environment, such as high‐voltage substations, oil refineries, mines, oil tanks, water reservoirs,

**Figure 1.** Generic PoF system diagram showing its main elements HPOS, OF, PV, LD, electronic circuit, and sensors.

The biggest challenge for a generic PoF system is to provide to a load the highest possible power, at the greatest possible distance, with the highest reliability. There are limits today to PoF applications and the limits are attributed to technological, physical, and cost aspects of

The amount of power that the PoF system can deliver is determined to a great extent by its components: laser, fiber, and photovoltaic cell. The following parameters can be used to evaluate the delivered electric power (*P*Load) to an electronic load: the maximum transmitted optical power without causing damages in the optical fiber (*P*MaxFiber); the optical power of the HPOS (*P*HPOS); the optical power in the PV input (*P*In); the total loss on the fiber (*α*Fiber); the total loss of the optical connectors (*α*Conn); the link distance (*L*); and the efficiency of the PV (*η*PV).

*P*Load = *P*In . *η*PV (1)

*P*In = *P*HPOS . *α*Fiber . *α*Conn (2)

*α*Fiber = 10(−*L*.*α*FiberdB/10) (3)

*α*Conn = 10(−*α*ConndB/10) (4)

where *α*FiberdB is the fiber attenuation in dB/km and *α*ConndB is the total connector loss in dB.

*P*HPOS ≤ *P*MaxFiber (5)

In the following subsections, the main elements of PoF will be described, and **Figure 2** will be used as a reference for further discussion. **Figure 2** shows a qualitative graph of some parameters of the PoF elements, such as the loss of the optical fibers and the responsivity of PV cells.

The power delivered to the extender can be expressed by

The main spectral bands for HPOS are also shown in **Figure 2**.

and sea depth.

260 Optical Fiber and Wireless Communications

PoF elements.

Notice that

#### *2.3.1. High‐power optical source*

**Figure 2** shows the main spectral bands of HPOS. There are four main bands: 800, 950, 1050, and 1480 nm. The HPOSs for these bands have applications in medicine, pumping, thermal printing, and industrial applications. The power of these HPOSs can reach from 2 to 10 W for TO220 packaging depending on the wavelength band and from 6 to 650 W for laser modules. The output fiber core diameter for these HPOSs ranges from 50 to 600 μm depending on the HPOS output power. These fibers are MM types. For SMF fibers, the output power changes from 0.2 to 1.0 W.

Normally, an SMA (Sub‐Miniature A) high‐power type with metal ferrule is used in the HPOS output optical fiber. This metal ferrule is used for thermal dissipation in the HPOS connection to the fiber link. The high‐power SMA connector utilizes air‐gap‐ferrule technology that eliminates the materials near the fiber end face that absorbs energy (e.g., epoxy). This absorption can damage the connector end face [56].

HPOS can also transmit information to the remote unit. The information signal is modulated in the continuous optical power generated by the HPOS. In general, this signal transmits commands to be executed in the remote unit, such as requesting the sensor parameters transmission, switching the sensor, and so on.

The most common modulation formats used to modulate the HPOS are on‐off keying (OOK), pulse‐width modulation (PWM), or frequency modulation. The extinction ratio of this signal can be high (100%) for few milliseconds like burst signals or low (less than 5%) during all the time of optical power sending. The extinction ratio is the ratio of the power used to transmit a logic level "1," to the power used to transmit a logic level "0." **Figure 3** shows an oscilloscope trace (voltage vs. time) of a telecommand signal transmitted over the optical supply power.

The main HPOS parameters required for a PoF project are maximum output power (*P*HPOS), the operation wavelength (*λ*op), the output fiber core diameter (*D*core), the numerical aperture of the fiber (NA), and connector loss *α*ConndB.

#### *2.3.2. Optical fiber*

The next element in the PoF system after the HPOS is the optical fiber, which is responsible to send the optical power from the HPOS to the PV. The fiber has two main parameters in the PoF system design: its attenuation and its limit of transmitted optical power.

The attenuation in modern optical fiber is basically caused by the intrinsic loss due to Rayleigh backscattering. Silica fibers are glasses that have materials with microscopic variations of density and refractive index. This effect gives rise to energy losses due to the scattered light. The loss due to the Rayleigh backscattering has high dependence with the operation wavelength (*1/λop 4* ). The typical loss in the HPOS bands is 2.8 (800 nm), 1.8 (950 nm), 1.4 (1050 nm), and 0.25 dB (1480 nm).

The loss of optical fiber is not a big problem for the major PoF applications that has dozens of meters of fibers. It can be a problem for distances longer than 1 km. The major problem is regarding the maximum transmitted optical power. Next, the physical mechanism that limits the power in optical fiber will be detailed. After this limit, a degradation of the fiber core and the fiber coating occurs.

**Figure 3.** Oscilloscope trace showing a telecommand signal transmitted over the optical supply power.

Optical fibers when subjected to reduced diameter curvatures exhibit further attenuation of the optical signal. This attenuation may be significant when the bending diameter reaches a critical value. The attenuation of the optical signal in the bending zone of the fiber is related to the leakage of the fiber core region signal to the cladding region. The material of the outer‐ coating layer of the optical fiber absorbs the signal lost to the cladding region. When a high‐ power optical signal is propagated in the fiber, the energy absorbed by the coating in the zone of curvature is high, generating a local increase in temperature in the coating [56].

logic level "1," to the power used to transmit a logic level "0." **Figure 3** shows an oscilloscope trace (voltage vs. time) of a telecommand signal transmitted over the optical supply power.

The main HPOS parameters required for a PoF project are maximum output power (*P*HPOS), the operation wavelength (*λ*op), the output fiber core diameter (*D*core), the numerical aperture

The next element in the PoF system after the HPOS is the optical fiber, which is responsible to send the optical power from the HPOS to the PV. The fiber has two main parameters in the

The attenuation in modern optical fiber is basically caused by the intrinsic loss due to Rayleigh backscattering. Silica fibers are glasses that have materials with microscopic variations of density and refractive index. This effect gives rise to energy losses due to the scattered light. The loss due to the Rayleigh backscattering has high dependence with the

The loss of optical fiber is not a big problem for the major PoF applications that has dozens of meters of fibers. It can be a problem for distances longer than 1 km. The major problem is regarding the maximum transmitted optical power. Next, the physical mechanism that limits the power in optical fiber will be detailed. After this limit, a degradation of the fiber core and

). The typical loss in the HPOS bands is 2.8 (800 nm), 1.8 (950

PoF system design: its attenuation and its limit of transmitted optical power.

**Figure 3.** Oscilloscope trace showing a telecommand signal transmitted over the optical supply power.

of the fiber (NA), and connector loss *α*ConndB.

*4*

nm), 1.4 (1050 nm), and 0.25 dB (1480 nm).

*2.3.2. Optical fiber*

262 Optical Fiber and Wireless Communications

operation wavelength (*1/λop*

the fiber coating occurs.

The heating of the coating of the optical fiber leads to its degradation, implying a consequent reduction of the useful life of the fiber. This degradation of the optical fiber is related to the reduction of the volume of the coating in the zone of curvature.

The second problem resulting from the propagation of high‐power signals is the occurrence of the "fiber‐fuse" effect on the optical fibers. This phenomenon was first observed in 1987 in a standard SMF fiber with optical intensity exceeding 5 MW/cm2 at 1064 nm [57]. The fiber‐fuse effect was initiated at a point of the fiber with a high‐temperature value, then propagating toward the optical source with a velocity of about 1 m/s and emitting an optical signal in the spectral region of the visible. The propagation of this high‐temperature zone is similar to the burning of a wick, which gave rise to the name of the "fiber‐fuse" effect. After propagation of the fiber‐fuse effect, the optical‐fiber core presents a periodic bubble chain (see **Figure 4**) and is permanently destroyed, being unable to guide an optical signal.

Currently, the most accepted general explanation for the fiber‐fuse effect relates to the ignition of this effect with the increase of fiber optic absorption at a point with a high‐temperature value [56]. In turn, the increase in optical signal absorption is responsible for the catastrophic temperature increase in the fiber core, reaching values higher than the vaporization temperature of the silica. Through the thermal diffusion mechanism, this high‐temperature zone is transmitted to neighboring regions and the process evolves toward the optical source. Thus, the "fiber‐fuse" effect is related to the increase in fiber optic absorption and the thermal diffusion process.

**Figure 4.** Schematic of a fiber‐fuse effect and a photo of an optical fiber core presenting a periodic bubble chain due to fiber‐fuse effect.

It should be noted that ignition and propagation of the fiber‐fuse effect occurs only if the power of the optical signal in the fiber is maintained above a threshold value. According to [56], this threshold is proportional to the diameter of the fiber modal field (MDF) and dependent on the wavelength of the optical signal. A typical SMF fiber (MDF = 7.8 μm) presents a threshold of 1.5 W at 1467 nm. In other study [58], it was observed that an SMF fiber type 28F (MDF = 7.8 μm) presents a threshold of 1.0 W, and an MM fiber of 62.5‐μm core (MDF = 12.0 μm) presents a threshold of 4.0 W at 1060 nm.

In order to increase the optical power in SMF fibers, many efforts have been made to transmit the high power by the cladding of the SMF fiber. In [21, 22], an optically controlled beam steering system using 60 W transmitted in the cladding of the fiber to feed remote antenna units is presented.

The propagation of signals with optical power exceeding the threshold required for ignition and propagation of the fiber‐fuse effect is not sufficient to trigger it, and an ignition point characterized by having a high‐temperature value is also required. This point of ignition occurs in contaminated and/or degraded connectors or in optical fibers subject to tight bending. As described previously, in optical fibers subjected to curvatures of reduced diameters, an additional attenuation of the optical signal occurs, which in combination with high‐power signals generates a considerable localized heating.

Optical connectors can be easily contaminated with dust or organic particles that are common in outdoor environments. This additional attenuation in the connectors, contaminated and/or degraded, may be considerable and when associated with high‐power signals also generate localized heating.

PoF is generally used in hazardous environment requiring rugged optical cables for this kind of environment. It is desirable that such cables containing fiber from 100‐ to 1000‐μm core diameter be available on the market, since PoF requires fibers with large core diameter. The development of a rugged PoF optical cable using 100‐μm fiber core for long‐distance applications is described in [52].

The main OF parameters required for a PoF project are maximum transmitted optical power without causing damages (*P*MaxFiber), fiber attenuation (*α*FiberdB) in dB/km at the operation wavelength (*λ*op), the fiber core diameter (*D*core), and the numerical aperture of the fiber (NA).

#### *2.3.3. Photovoltaic converter*

A photovoltaic power converter is the element where the light will be finally transformed in electricity to supply the control unit and the sensors. PV is one (or more) photodiode that operates in photovoltaic mode. When the supply optical power reaches the PV, electron‐hole pairs (carriers) are generated creating a photocurrent. The total current is the photocurrent produced by the supply optical power minus the dark current, which is related to the reverse saturation current. This photocurrent (*I* ph) is proportional to the incident supply optical power according to Eq. (6)

$$I\_{ph} = P\_{\rm ln} \cdot R(\lambda\_{\rm op}) \tag{6}$$

*R*(*λ*op) is the spectral responsivity of the cell, which is dependent on the HPOS operation wavelength (**Figure 2**).

It should be noted that ignition and propagation of the fiber‐fuse effect occurs only if the power of the optical signal in the fiber is maintained above a threshold value. According to [56], this threshold is proportional to the diameter of the fiber modal field (MDF) and dependent on the wavelength of the optical signal. A typical SMF fiber (MDF = 7.8 μm) presents a threshold of 1.5 W at 1467 nm. In other study [58], it was observed that an SMF fiber type 28F (MDF = 7.8 μm) presents a threshold of 1.0 W, and an MM fiber of 62.5‐μm core (MDF = 12.0

In order to increase the optical power in SMF fibers, many efforts have been made to transmit the high power by the cladding of the SMF fiber. In [21, 22], an optically controlled beam steering system using 60 W transmitted in the cladding of the fiber to feed remote antenna

The propagation of signals with optical power exceeding the threshold required for ignition and propagation of the fiber‐fuse effect is not sufficient to trigger it, and an ignition point characterized by having a high‐temperature value is also required. This point of ignition occurs in contaminated and/or degraded connectors or in optical fibers subject to tight bending. As described previously, in optical fibers subjected to curvatures of reduced diameters, an additional attenuation of the optical signal occurs, which in combination with high‐power

Optical connectors can be easily contaminated with dust or organic particles that are common in outdoor environments. This additional attenuation in the connectors, contaminated and/or degraded, may be considerable and when associated with high‐power signals also generate

PoF is generally used in hazardous environment requiring rugged optical cables for this kind of environment. It is desirable that such cables containing fiber from 100‐ to 1000‐μm core diameter be available on the market, since PoF requires fibers with large core diameter. The development of a rugged PoF optical cable using 100‐μm fiber core for long‐distance applica-

The main OF parameters required for a PoF project are maximum transmitted optical power without causing damages (*P*MaxFiber), fiber attenuation (*α*FiberdB) in dB/km at the operation wavelength (*λ*op), the fiber core diameter (*D*core), and the numerical aperture of the fiber (NA).

A photovoltaic power converter is the element where the light will be finally transformed in electricity to supply the control unit and the sensors. PV is one (or more) photodiode that operates in photovoltaic mode. When the supply optical power reaches the PV, electron‐hole pairs (carriers) are generated creating a photocurrent. The total current is the photocurrent produced by the supply optical power minus the dark current, which is related to the reverse

ph) is proportional to the incident supply optical power

ph = *P*In . *R*(*λ*op ) (6)

μm) presents a threshold of 4.0 W at 1060 nm.

signals generates a considerable localized heating.

units is presented.

264 Optical Fiber and Wireless Communications

localized heating.

tions is described in [52].

*2.3.3. Photovoltaic converter*

according to Eq. (6)

saturation current. This photocurrent (*I*

*I*

The most important photovoltaic parameter is the conversion efficiency (*η*). It is defined as the maximum electric power produced by the PV (*P*elecmax) divided by the incident light power under standard light conditions or as defined by Eq. (7):

$$\eta = P\_{\text{obcmax}} / P\_{\text{Pn}} = (\text{V}\_{\text{OC}} \dots \text{I}\_{\text{SC}} \text{ FF}) / (P\_{\text{Pn}}) \tag{7}$$

where *V*oc is the open‐circuit voltage, *I*SC is the short circuit current, and FF is the fill factor of PV.

Many PV types are actually made of micro‐PV arrays [59, 60]. In this way, connecting the micro‐PVs in parallel to the output voltage can reach an adequate level. **Figure 5** shows a schematic arrangement of a commercial PV array with four elements compared with 100‐μm‐core optical‐fiber diameter. This type of fiber is normally used in fiber‐packaged PVs.

The fill factor is the parameter that evaluates the junction quality and series resistance of the PV array. The fill factor is the ratio of the maximum electric output power to the product of VOC and ISC.

A comparative study of PV efficiency for the materials Si, GaAs, and Ge is founded in [61]. PV devices made of Si or GaAs proper for PoF uses can be founded in market. Unfortunately, these devices operate in the spectrum region where the fiber does not have the minimum attenuation (**Figure 2**). For operation in 1310 or 1550 nm, the PV arrays can be obtained easily connecting many InGaAs or Ge photodiodes in series or in parallel using an optical splitter. This is a topic for the next section.

The main PV parameters required for a PoF project are the maximum output electric power (*P*elecmax), the maximum optical input power without damaging the PV (*P*Inmax), the operation spectral band (*λ*op), the efficiency (*η*), open‐circuit voltage (*V*oc), and the short‐circuit current (*I* SC).

**Figure 5.** Schematic arrangement of a commercial PV array with four elements compared with 100‐μm‐core optical fiber diameter.

#### *2.3.4. Basic remote unit circuits*

The electronic circuits of unit control including LD driver and sensors need to work in a specific voltage (*V*cc), and they consume an electrical current (*I* load). To provide the required voltage and current, some basic circuits can be designed. The most basic circuits use just one PV and a DC‐DC converter to stabilize the voltage, as shown in **Figure 6(a)**. In this case, the PV should be an array type to provide voltage higher than 3 V, although there are many integrated circuits that work below 3 V. If the PV chosen has low‐output voltage (lower than 2V), the circuit shown in **Figure 6(b)** can be used. In this circuit, the DC‐DC converter was substituted by a step‐up converter, which elevates the PV output voltage to the voltage required by the circuit. Other possibility to elevate the voltage is using an optical splitter (with *n* output ports) connected to the optical fiber and the PVs (or photodetectors) connected in series (**Figure 6(c)**). Typically, splitters with *n* = 4–8 have been used, to provide *V*cc ranging from 2.4 to 4.8 V. Each splitter output port is connected to one PV. This is an easy solution to use in spectral bands where there is no commercial PV array available, such as in 1310 and 1550 nm. **Figure 6(d)** shows a different version of **Figure 6(c)** circuit. In this case, the association of the PVs is made in parallel in order to increase the current available to the circuit. Certainly, the association of PVs can be made simultaneously in parallel and in series.

**Figure 6.** Some types of circuits used in the design of PoF remote units, (a) direct conversion, (b) conversion using a step‐up converter, (c) PVs connected in series, (d) PVs connected in parallel, and (e) charging circuit using a capacitor.

**Figure 6(e)** shows a charging circuit type. This type of circuit is used to supply loads in long‐distance PoF links where the available input optical power level in the PV is not enough to provide a necessary electric power. In this circuit, when the capacitor C connected in the PV output is charged in the maximum PV voltage output, an analog switch connects the capacitor to a DC‐ DC converter that stabilizes its output voltage for the load for a specific time period. This type of circuit should be used only if the sensors do not require measuring their parameters all the time.

#### **2.4. PoF topologies**

*2.3.4. Basic remote unit circuits*

266 Optical Fiber and Wireless Communications

The electronic circuits of unit control including LD driver and sensors need to work in a

voltage and current, some basic circuits can be designed. The most basic circuits use just one PV and a DC‐DC converter to stabilize the voltage, as shown in **Figure 6(a)**. In this case, the PV should be an array type to provide voltage higher than 3 V, although there are many integrated circuits that work below 3 V. If the PV chosen has low‐output voltage (lower than 2V), the circuit shown in **Figure 6(b)** can be used. In this circuit, the DC‐DC converter was substituted by a step‐up converter, which elevates the PV output voltage to the voltage required by the circuit. Other possibility to elevate the voltage is using an optical splitter (with *n* output ports) connected to the optical fiber and the PVs (or photodetectors) connected in series (**Figure 6(c)**). Typically, splitters with *n* = 4–8 have been used, to provide *V*cc ranging from 2.4 to 4.8 V. Each splitter output port is connected to one PV. This is an easy solution to use in spectral bands where there is no commercial PV array available, such as in 1310 and 1550 nm. **Figure 6(d)** shows a different version of **Figure 6(c)** circuit. In this case, the association of the PVs is made in parallel in order to increase the current available to the circuit. Certainly, the

**Figure 6.** Some types of circuits used in the design of PoF remote units, (a) direct conversion, (b) conversion using a step‐up converter, (c) PVs connected in series, (d) PVs connected in parallel, and (e) charging circuit using a capacitor.

load). To provide the required

specific voltage (*V*cc), and they consume an electrical current (*I*

association of PVs can be made simultaneously in parallel and in series.

The connection between the control units and remote units in PoF systems is usually made in the same way of telecommunications links. **Figure 7(a)** shows a typical PoF link using two fibers. However, in some cases the quantity of fibers is a limiting factor in specific application. WDM can be used to multiply the supply optical power transmitted by the HPOS and the sensor signal transmitted by the LD in the remote unit. The WDM device must support the high power of the HPOS. WDM devices for high‐power applications can support around 2 W of handling power. The wavelength pairs used in a WDM PoF system as the one shown in **Figure 7(b)** are as follows:

**Figure 7.** Illustrations of some topologies for PoF systems, (a) two fibers topology, (b) bidirectional WDM topology, and (c) tree topology.

PoF networks have also been reported. A typical tree topology (**Figure 7(c)**) permits the connection of a single control unit to many remote units. This type of network works in a similar way as a passive optical network used in telecommunications.

### **2.5. Example of PoF link calculations**

Using Eqs. (1)–(5), it is possible to calculate the maximum PoF link for two cases, using SMF and MM fibers. **Table 1** shows the parameters used in this calculation.

**Figure 8** shows a plot of the delivered power (*P*Load) to an electronic load as a function of link distance. It can be observed that MM fiber option is better until 2.2 km. After this distance, the SMF option is better.

**Table 1.** Parameters used to calculate the maximum PoF link distance.

In utilities, the major applications of PoF occur in the substations, which the maximum internal distances are less than 0.2 km. For telecommunications, the distances in the major application are longer than 2 km.

**Figure 8.** Plot of the delivered power to an electronic load as a function of link distance.

### **2.6. PoF applications developed at CPqD**

PoF networks have also been reported. A typical tree topology (**Figure 7(c)**) permits the connection of a single control unit to many remote units. This type of network works in a similar

Using Eqs. (1)–(5), it is possible to calculate the maximum PoF link for two cases, using SMF

**Figure 8** shows a plot of the delivered power (*P*Load) to an electronic load as a function of link distance. It can be observed that MM fiber option is better until 2.2 km. After this distance, the

In utilities, the major applications of PoF occur in the substations, which the maximum internal distances are less than 0.2 km. For telecommunications, the distances in the major applica-

way as a passive optical network used in telecommunications.

**Parameter/fiber SMF MM** HPOS optical power 1.0 W 2.0 W Wavelength 1480 nm 830 nm Total connectors attenuation 1.0 dB 1.0 dB Fiber attenuation 0.25 dB/km 3.0 dB/km

PV efficiency 0.2 0.4 PV material InGaAs GaAs

**Table 1.** Parameters used to calculate the maximum PoF link distance.

**Figure 8.** Plot of the delivered power to an electronic load as a function of link distance.

and MM fibers. **Table 1** shows the parameters used in this calculation.

**2.5. Example of PoF link calculations**

268 Optical Fiber and Wireless Communications

SMF option is better.

tion are longer than 2 km.

This section presents some PoF systems and sensors developed by the author's group for telecommunications and for utilities applications. Most PoF systems for utilities have been tested in field trials.

#### *2.6.1. PoF applications in telecommunications*

In telecommunication, we developed a new approach to powering PON extenders using PoF [14]. PON extenders are elements that recover the downstream and upstream signals. These signals are highly attenuated by the splitters and by link length in any PON. However, the use of extenders in PON modifies its passive characteristic since extenders require electrical supply to work. Using PoF to supply, the extenders turns them virtually passives.

Using PoF to eliminate the batteries located at telecom remote sites, the reliability and the security of the system are improved. Furthermore, PoF can reduce the copper cables theft, used to power the extenders in many cases. We demonstrated the performance of a fiber‐powered extender using semiconductor optical amplifiers in a 10‐gigabit passive optical network system and a gigabit passive optical network system (G‐PON) setup using a 1:32 splitter and 50‐km reach. The extender was powered from a remote site placed in the access area using a 62.5‐**μ**m MM fiber at 830 nm. **Figure 9** shows a schematic of the PON using the fiber‐powered extender and the photo of the extender.

#### *2.6.2. PoF applications in utilities*

In utilities, we developed applications for monitoring hydrogenerators, power transformers, switchgears, and for transmission lines.

**Figure 9.** Schematic of a PON using extender powered by a PoF system and the extender photo.

**Figure 10** shows the applications for partial discharges monitoring in hydrogenerators [46] and for 500‐kV power transformers [62]. Partial discharges on high‐voltage equipment insulation are a symptom of fragility of the dielectric capacity. The growing of partial discharges can cause serious consequences for the equipment and the electrical system. Partial discharges generate some physical effects, such as conducted and radiated electromagnetic pulses, light, acoustic noise, localized temperature variation, and chemical reactions. In the developed PoF‐monitoring systems, we used a powered antenna to detect the radiated electromagnetic pulses of discharges.

For hydrogenerator monitoring (**Figure 10(a)**), the sensor is composed by one dipole meander antenna, one photovoltaic converter, and one semiconductor laser. Some passive components such as resistors, capacitors, and inductors are omitted in the schematic of sensor circuit to simplification. This system was installed in the Eletrobrás' Coaracy Nunes power plant, which is located in Amapá state, in the north of Brazil.

The sensor for monitoring the high‐voltage power transformers (**Figure 10(b)**) is composed by one monopole antenna, one photovoltaic converter, one field‐effect transistor (FET) amplifier, and one semiconductor laser. The FET was used in this sensor to increase the sensitivity of the sensor in this particular application. This system was installed in the Cemig's Neves substation, which is located in Minas Gerais state, in the southeast of Brazil.

**Figure 10** shows the schematic circuit and sensor photo of antenna powered by fiber for partial discharges monitoring in (a) hydrogenerators and (b) high‐voltage power transformers.

**Figure 10.** Schematic circuit and sensor photo of antenna powered by fiber for partial discharges monitoring in (a) hydrogenerators and (b) high‐voltage power transformers.

**Figure 11** shows some applications using more complex electronic circuits with PoF. **Figure 11(a)** shows a 138‐kV switchgear‐monitoring application using fiber‐powered video cameras to inspect the quality contact of the switchgear [53]. In this application, the three phases of 138‐kV switchgear were monitored using three sensors. The connection of the sensors to the control unit used the tree topology shown in **Figure 7(c)**. This system was installed in the Cemig's Bonsucesso substation, which is located in Minas Gerais state, in the southeast of Brazil.

**Figure 11(b)** shows a fiber‐powered camera installed in a 138‐kV transmission line tower [51]. The camera was used to monitor possible invasions in the security area of transmission line. The circuit of the camera works in a noncontinuous regime (circuit of **Figure 6(e)**) since the power transmission was done using an SMF fiber embedded in an optical ground wire cable. This system was installed in the Cemig's Bonsucesso/Gutierrez transmission line, which is located in Minas Gerais state, in the southeast of Brazil.

Remembering that for electrical utilities, there are key factors to use PoF. Optical fiber is made of nonconductive material. In high‐voltage environment, any conductance can

**Figure 11.** PoF applications with fiber‐powered video cameras, (a) 138‐kV switchgear sensor shown in the circle (above) and a sensor image (below) and (b) 138‐kV transmission line sensor shown in the circle (above) and a sensor image (below).

**Figure 10.** Schematic circuit and sensor photo of antenna powered by fiber for partial discharges monitoring in (a)

**Figure 10** shows the applications for partial discharges monitoring in hydrogenerators [46] and for 500‐kV power transformers [62]. Partial discharges on high‐voltage equipment insulation are a symptom of fragility of the dielectric capacity. The growing of partial discharges can cause serious consequences for the equipment and the electrical system. Partial discharges generate some physical effects, such as conducted and radiated electromagnetic pulses, light, acoustic noise, localized temperature variation, and chemical reactions. In the developed PoF‐monitoring systems, we used a powered antenna to detect the radiated electromagnetic

For hydrogenerator monitoring (**Figure 10(a)**), the sensor is composed by one dipole meander antenna, one photovoltaic converter, and one semiconductor laser. Some passive components such as resistors, capacitors, and inductors are omitted in the schematic of sensor circuit to simplification. This system was installed in the Eletrobrás' Coaracy Nunes power plant,

The sensor for monitoring the high‐voltage power transformers (**Figure 10(b)**) is composed by one monopole antenna, one photovoltaic converter, one field‐effect transistor (FET) amplifier, and one semiconductor laser. The FET was used in this sensor to increase the sensitivity of the sensor in this particular application. This system was installed in the Cemig's Neves

**Figure 10** shows the schematic circuit and sensor photo of antenna powered by fiber for partial discharges monitoring in (a) hydrogenerators and (b) high‐voltage power transformers.

substation, which is located in Minas Gerais state, in the southeast of Brazil.

hydrogenerators and (b) high‐voltage power transformers.

pulses of discharges.

270 Optical Fiber and Wireless Communications

which is located in Amapá state, in the north of Brazil.

create current leaks. Optical fiber is immune to electromagnetic interferences. The electrical world environment is polluted of electromagnetic interferences; therefore, optical fiber can transmit signals without quality degradation. The optical fiber eliminates the need to run conductive copper wire into a GPR zone. GPR arises when lightning strikes occur in substations and can cause severe interference problems in electronic equipment and systems. PoF sensors have a complete galvanic isolation to the ground potential, then they are practically immune to the GPR effects and finally, as we show, there are many low‐cost/ low‐power/high‐efficiency electronic sensors available for transmission lines and substations monitoring that can be supplied by PoF increasing the monitoring capacity for utilities companies.


*3.1.  Generally, a simple ANN model consists of an input layer, one or two hidden layers, and an output layer. There are several neurons in each layer of ANN, where the number of neurons in the input layer and output layer depends on the number of input parameters and output parameters, respectively. In this paper, the number of neurons in the input layer and output layer can be seen in Table 1, which equals 6 and 1, respectively.

Except for the output layer, the neurons of each layer needs to be activated by activation function. In ANN, generally, the sigmoid function is used as activation function [51], which expression can be written as:

$$\mathbf{g}(z) = \frac{1}{1 + \mathbf{e}^{-z}} \tag{2}$$

$$z = w^\mathrm{T} \mathbf{x}^\* + b \tag{3}$$

where *b* is the bias unit; *w* denotes the weight vector of sample. According to Rumelhart et al. [52] described, when ANN is used for regression forecasting, the cost function of model as follows:

$$J(w, b) \;= \frac{1}{m} \sum\_{i=1}^{m} \left( y\_{\text{pred}}^{(i)} - y^{(i)} \right)^2 + \frac{\mathcal{C}}{2m} ||w||^2 \tag{4}$$

where *y*pred denotes the predicted value of machine learning; *C* is the regularization coefficient.

Since the cost function represents the error between the actual value and the predicted value, to improve the accuracy of predicted result, a method similar to gradient descent, in order to decrease the value of cost function, is required. The gradient descent is expressed as:

$$\begin{cases} w\_{\rangle} := \; w\_{\rangle} - \alpha \frac{\partial}{\partial w\_{\rangle}} I(w, b) \\\ b := \; b - \alpha \frac{\partial}{\partial b} I(w, b) \end{cases} \tag{5}$$

where *α* is learning rate.

Before starting the training procedure, there are some values of hyper-parameters need to be set. For neuron number of hidden layer, Shen et al. [53] mentioned a method to determine their value range, which method as follows:

$$\begin{cases} \sum\_{i=0}^{X} \mathbf{C}\_{H}^{i} > m\\ H = \sqrt{X + O} + a\\ H = \log\_{2} X \end{cases} \tag{6}$$

where *X* is the number of neurons in the input layer; *H* is the number of neurons in the hidden layer; *O* is the number of neurons in the output layer; *a* is the constant between 1 to 10. According to the Equation (6), it can be ascertained that the range of neurons in hidden layer ranges from 7 to 13.

In order to better compare the performance of models which have different neuron numbers in the hidden layer, 3 indicators are introduced, which names root mean squared error (RMSE), mean absolute error (MAE) and coefficient of determination (R2 ), which are, respectively, defined as:

$$\text{RMSE} = \sqrt{\frac{1}{m} \sum\_{i=1}^{m} \left( y\_{\text{pred}}^{(i)} - y^{(i)} \right)^2} \tag{7}$$

$$\text{MAE} = \frac{1}{m} \sum\_{i=1}^{m} \left| y\_{\text{pred}}^{(i)} - y^{(i)} \right| \tag{8}$$

$$\mathbf{R}^2 = 1 - \frac{\sum\_{i=1}^{m} \left( \mathcal{Y}\_{\text{pred}}^{(i)} - \mathcal{Y}^{(i)} \right)^2}{\sum\_{i=1}^{m} \left( \mathcal{Y}^{(i)} - \frac{1}{m} \sum\_{i=1}^{m} \mathcal{Y}^{(i)} \right)^2} \tag{9}$$

The performance of ANN which have different neuron numbers in hidden layer is shown as Table 2. According to the comparative results, the number of neurons in the hidden layer *H* is determined as 8. In addition, the values of other hyper-parameters confirmed by manual adjustment are: the number of hidden layers equal 1; the training times equal 5000; the learning rate *α* equals 5 × 10−5 ; the regularization coefficient *C* equals 20.

**Table 2.** Performance and ranking of ANN which have different neuron numbers in hidden layer.

### *3.2. Support Vector Machine*

Support vector machine (SVM) was originated from statistical learning theory, and it was firstly proposed by Cortes and Vapnik [54] in 1995. When SVM is used for regression analysis, it can also be called support vector regression (SVR). The predicted method of SVR maps the data to high-dimensional space and use hyperplane for fitting, and these data are generally hard to fit into low-dimensional space [55]. The expression of SVR reflect the relation between input factors and predicted value [56], it can be written as:

$$y\_{\text{pred}} = w^{\text{T}} \phi(\mathbf{x}) + b \tag{10}$$

where *φ*(*x*) means feature vector after mapping. With the same as ANN, SVR also has the cost function to represents the performance of model. The cost function can be written as:

$$J(w, b, \mathfrak{f}\_{l}, \mathfrak{f}\_{l}^{\*}) = \frac{1}{2} \left\| w \right\|^{2} + \mathbb{C} \sum\_{i=1}^{m} \left( \mathfrak{f}\_{i} + \mathfrak{f}\_{l}^{\*} \right) \tag{11}$$

where *ξ* and *ξ* \* are the slack variables, they represent the errors of the sample exceeding the lower and upper bounds of the hyperplane, respectively.

To minimize the value of cost function, Lagrange multiplier method is used for transforming the original problem to its dual problem. The Lagrange multiplier method is formulated in the following form:

$$\begin{aligned} L(w, b, \lambda, \lambda^\*, \mathfrak{f}, \mathfrak{f}^\*, \mathfrak{f}, \mu^\*) &= \frac{1}{2} \|w\|^2 + \mathbb{C} \sum\_{i=1}^m \left(\mathfrak{z}\_i + \mathfrak{f}\_i^\*\right) - \sum\_{i=1}^m \mu\_i \mathfrak{z}\_i - \sum\_{i=1}^m \mu\_i^\* \mathfrak{z}\_i^\* \\ + \sum\_{i=1}^m \lambda\_i \left(y\_{\text{pred}}^{(i)} - y^{(i)} - \varepsilon - \mathfrak{z}\_i\right) + \sum\_{i=1}^m \lambda\_i^\* \left(y^{(i)} - y\_{\text{pred}}^{(i)} - \varepsilon - \mathfrak{z}\_i^\*\right) \end{aligned} \tag{12}$$

where *µ*, *µ* \* , *λ*, *λ* \* denote the Lagrange multiplier; *ε* is the maximum allowable error. After transforming, the expression of dual problem as follows:

$$\text{Maximise } \sum\_{i=1}^{m} y^{(i)} (\lambda\_i^\* - \lambda\_i) - \varepsilon (\lambda\_i^\* + \lambda\_i) - \frac{1}{2} \sum\_{i=1}^{m} \sum\_{j=1}^{m} (\lambda\_i^\* - \lambda\_i) \left(\lambda\_j^\* - \lambda\_j\right) \mathbf{x}\_i^{\mathrm{T}} \mathbf{x}\_j \tag{13}$$

subjected to *m* ∑ *i* = 1 *λ* ∗ *i* − *λi* = 0, 0 ≤ *λi* , *λ* ∗ *i* ≤ *C*.

The Karush-Kuhn-Tucker (KKT) conditions need to be met for Equation (13), which can be written as:

$$\begin{cases} \lambda\_i \left( y^{(i)}\_{\text{pred}} - y^{(i)} - \varepsilon - \mathfrak{f}\_i \right) = \ 0, \\\ \lambda\_i^\* \left( y^{(i)} - y^{(i)}\_{\text{pred}} - \varepsilon - \mathfrak{f}\_i^\* \right) = \ 0, \\\ \lambda\_i \lambda\_i^\* = 0, \mathfrak{f}\_i \mathfrak{f}\_i^\* = 0, \\\ (\mathbb{C} - \lambda\_i) \mathfrak{f}\_i = \ 0, \{\mathbb{C} - \lambda\_i^\*\} \mathfrak{f}\_i^\* = \ 0. \end{cases} \tag{14}$$

According to Equations (13) and (14), the weight vector *w* and bias unit *b* can be acquired. Finally, the expression of SVR as follows:

$$y\_{\text{pred}} = \sum\_{i=1}^{m} (\lambda\_i^\* - \lambda\_i) \kappa(\mathbf{x}, \mathbf{x}\_i) + b \tag{15}$$

$$\kappa(\mathbf{x}\_{i\prime}\mathbf{x}\_{j\prime}) = \phi(\mathbf{x}\_{i\prime})^{\mathrm{T}}\phi(\mathbf{x}\_{j\prime}) \tag{16}$$

where *κ*(*xi , xj* ) denotes kernel function, which can used to express the inner product of eigenvectors in high-dimensional space. The kernel function has many types, and the radial basis function (RBF) kernel function is selected in this paper, which can be expressed as:

$$\kappa(\mathbf{x}\_{i}, \mathbf{x}\_{j}) \;=\; \exp\left(-\gamma \|\mathbf{x}\_{i} - \mathbf{x}\_{j}\|^{2}\right) \tag{17}$$

where *γ* > 0 is the coefficient of RBF kernel function, which is a hyper-parameter. Except that, in this paper, the values of other hyper-parameters in SVR need to be determined: the maximum allowable error *ε*, the regularization coefficient *C*. There are many methods which can be used for numerical adjustment of hyper-parameters, in this paper we have selected particle swarm optimization.

Particle swarm optimization (PSO) is an optimized algorithm inspired by the foraging behavior of bird flock [57,58]. On account of the fact that PSO has a large number of advantages, such as being easily comprehendible and containing, it is usually used for hyper-parameter adjustment in SVM [59,60]. For every particle in PSO, there is two parameters to determine the search result, which are position *p* and velocity *v,* respectively. These 2 parameters are defined as [58]:

$$v\_{d^\*}^{t+1} = Wv\_{d^\*}^t + r\_1 \mathbb{C}\_1(P\_{d^\*}^t - p\_{d^\*}^t) + r\_2 \mathbb{C}\_2(\mathbb{G}\_{d^\*}^t - p\_{d^\*}^t) \tag{18}$$

$$p\_{d^\*}^{t+1} = \ p\_{d^\*}^t + v\_{d^\*}^{t+1} \tag{19}$$

where *t* is the number of iterations; *d* \* denotes the dimension of search space; *W* is the inertial coefficient; *C*1 and *C*2 are the self-learning factor and the global learning factor; *r*1 and *r*2 are random number between (0, 1); *P* is the location with the best fitness among all the visited locations of each particle; *G* is the location with the best fitness among all the visited locations of all the particles.

In this paper, some hyper-parameters in Equations (18) and (19) have been confirmed: the maximum of iteration equals 150; the dimension of search space *d* \* equals 3; the inertial coefficient *W* equals 0.8; the total number of particles equals 40; the self-learning factor *C*1 and global learning factor *C*2 are all equal to 2. The hybrid machine learning approach consists of PSO and SVR can be called PSO-SVR, whose best value of hyperparameters also can be determined by calculating: the maximum allowable error *ε* equals 10; the regularization coefficient *C* equals 4238.58; the coefficient of RBF kernel function *γ* equals 2.88.

### *3.3. Decision Tree*

Decision tree (DT) served as a supervised learning algorithm that is proposed by Quinlan [61]. In the beginning, DT only could be used for conducting the classification forecasting, and its types less such as iterative dichotomiser 3 (ID3) and classifier 4.5 (C4.5). In this paper, classification and regression tree (CART) [62] is selected to make a study of regression prediction. The dividing evidence of CART is the variance of samples, which can be written as:

$$\text{Minimise}\left[\sum\_{\mathbf{x}\_{i}\in\mathcal{R}\_{1}}\left(\mathbf{y}^{(i)}-\mathbf{c}\_{1}\right)^{2}+\sum\_{\mathbf{x}\_{i}\in\mathcal{R}\_{2}}\left(\mathbf{y}^{(i)}-\mathbf{c}\_{2}\right)^{2}\right] \tag{20}$$

where *R*1 and *R*2 denote the sample set after dividing; *c*1 and *c*2 are mean of samples in *R*1 and *R*2, respectively. With the division of sample set, gradually, the purity of leaf nodes will improve.

Pruning is a method to avoid the over-fitting in DT, and it contains two basic methods: pre-pruning and post-pruning [63,64]. In this paper, the specific way of pruning is to adjust the maximum of depth, which equals 5.

### *3.4. Adaptive Boosting*

Adaptive boosting (AdaBoost) is one of the ensemble learning algorithms that can combine multiple weak learners into strong learner [65]. To be distinct from aforementioned machine learning algorithms, each sample in AdaBoost has a subsampling weight which will constantly adjust [66]. At the beginning of the training process, the weights of samples need to be initialized [67], which can be written as:

$$w\_{ki}^{\*} = \frac{1}{m} \tag{21}$$

where *w* \* *ki* denotes the weight of the *i*-th sample in the *k*-th weak learner. The largest error of the *k*-th weak learner on the training set as follows:

$$E\_k = \max \left| y^{(i)} - G\_k(x\_i) \right| \tag{22}$$

where *Gk* (*xi* ) denotes the predicted value of the *i*-th sample in the *k*-th weak learner. The relative error *eki* of each sample and the error ratio *ek* of the *k*-th weak learner can be written as:

$$e\_{ki} = \frac{\left(y^{(i)} - G\_k(x\_i)\right)^2}{E\_k^2} \tag{23}$$

$$e\_k = \sum\_{i=1}^{m} w\_{ki} e\_{ki} \tag{24}$$

After that, the weight *βk* of the *k*-th weak learner can be calculated, the value of which will increase as the error ratio *ek* decreases. The weight *βk* can be defined as:

$$
\beta\_k = \frac{e\_k}{1 - e\_k} \tag{25}
$$

Afterwards, the error ratio of the next weak learner can be reckoned, and the weights of samples need to be updated:

$$w\_{k+1,i}^{\*} = \frac{w\_{ki}^{\*}}{Z\_k} \beta\_k^{1-\varepsilon\_{ki}} \tag{26}$$

$$Z\_k = \sum\_{i=1}^{m} w\_{ki} \boldsymbol{\beta}\_k^{1-\varepsilon\_{ki}} \tag{27}$$

where *Zk* is the normalization factor. Finally, the expression of the strong learner can be written as:

$$f(\mathbf{x}) = \sum\_{k=1}^{K} \left( \ln \frac{1}{\beta\_k} \right) g(\mathbf{x}) \tag{28}$$

where *K* is the total number of weak learners; *g*(*x*) is the median of all the *βkGk* (*x*). The algorithm of the weak learner needs to be confirmed, and PSO-SVR is chosen in this paper.

### *3.5. Predicted Results*

The result comparison between ANN, PSO-SVR, DT and AdaBoost are provided in Table 3. The four machine learning models shows high predicted accuracy reflected in R2 . Especially AdaBoost and PSO-SVR, the predicted accuracy of the former is highest among these four AI models in training set, and the latter is in test set. It is noted that although the forecasting performance of ANN for the test set is better than DT and just slightly lower than PSO-SVR and AdaBoost, the performance for training set is much lower than the other three models.

**Table 3.** Result comparison between machine learning algorithms.

Figures 4–7 depict the scatter distribution of predicted results for each machine learning model. In Figure 4, it can be found that the fitting condition of ANN is not very

suitable when the true value is larger than 1400 kN. Maybe this situation is related to insufficient data of punching shear strength larger than 1400 kN. Therefore, it is noted that if we want to use this ANN model for predicting the punching shear strength of FRP reinforced concrete slabs, the value range of the predicted object should be restrained under 1400 kN. In addition, from the figure, it can be seen that ANN focuses more on fitting samples which are located in the interval with dense sample distribution. Consequently, a way to improve the overall predicted accuracy of ANN is to ensure that the samples are evenly distributed. It is demonstrated in Figure 5 that PSO-SVR shows the good predicted performance. Although there some predicted values have a relatively larger error between the actual values, the overall predicted accuracy is higher than ANN and DT. Figure 6 depicts the predictions of DT on the dataset; there doubt that the predicted result of DT for the test set is worse than ANN and PSO-SVR. In training set, the predictions of DT are almost no error with the punching shear strength is larger than 1200 kN, it is related to the predicted mechanism of DT [68]. Moreover, the situation also can be seen from the predicted results of DT on punching shear strength less than 1200 kN, the predicted value of which is same when the punching strength is in the identical range. Meanwhile, in test set, DT has a low predicted accuracy for samples with punching shear strength of around 1200 kN, i.e., the DT model proposed in this paper has the risk of over-fitting when the punching shear strength larger than 1200 kN. Obviously, no matter ANN or DT, the predicted accuracy of them is closely related to the number of samples in each value range. Furthermore, in this paper, it can be concluded that neither ANN nor DT has mined the true intrinsic connection between the data. Figure 7 shows the predicted results of AdaBoost for the training set and the test set, it can be seen that all of the dots are closely distributed around the best fitting line. Since PSO-SVR is chosen as the weak learner of AdaBoost, some wildly inaccurate predicted values are improved, and some comparatively accurate predicted values are retained. Moreover, compare Figure 4 to Figure 7, it is no hard to see that the fitting situation of AdaBoost reveals the best predicting performance.

**Figure 5.** The predictions of PSO-SVR for data set. (**a**) Training set; (**b**) Test set.

### *3.6. Comparison with Traditional Empirical Models*

In order to reflect the accuracy of the machine learning calculation results, this paper introduces design specifications and empirical models proposed by researchers. In this study, 3 punching shear strength models are selected from design codes and reviewed: GB 50010-2010 (2015) [14], ACI 318-19 [69] and BS 8110-97 [70]. Most design codes adopt the same function for both FRP slabs and reinforced concrete slabs. The punching shear strength of slabs as a function of the concrete compressive strength. Some design codes also take the reinforcement ratio, size effect, depth of the slab and so on into consideration. Three design specifications and three empirical models are adopted in comparative analysis between calculations. The formulas of selected traditional empirical model are shown in Table 4.

**Figure 6.** The predictions of DT for data set. (**a**) Training set; (**b**) Test set.

**Figure 7.** The predictions of AdaBoost for data set. (**a**) Training set; (**b**) Test set.

**Table 4.** Calculation formulas of traditional empirical model.

*β*h is the sectional depth influence coefficient; *f* t is the design value of tensile strength; *b*0,0.5*d* is the the perimeter of the critical section for slabs and footings at a distance of *d*/2 away from the column face; *β*s is the ratio of the long side to the short side of the sectional shape under local load or concentrated reaction force; *α*s is the influence coefficient of column type; *f* cu is the compressive strength of concrete cube; *b*0,1.5*d* is the perimeter of the critical section for slabs and footings at a distance of 1.5*d*/2 away from the loaded area; *E*s is the Young's modulus of steel bar.

Table 5 summaries experimental results of machine learning models and traditional models. Obviously, the predicted performance of AdaBoost is better than other predicted models reflected in RMSE, MAE and R2 . ANN, DT and PSO-SVR, the other three AI models, although their predicted results are not best, they show a better performance compared with traditional empirical models. Among these traditional models, Formula (1) (GB 50010-2010 (2015)) has the highest predicted accuracy, the RMSE, MAE and R2 of which are 150.41, 98.48 and 0.73, respectively. Notably, the predictions between Formulas (1) and (2) only has a little error; perhaps it is related to the fact that they are both derived from the eccentric shear stress model [14,69]. In addition, the forecasting performance of the model proposed by El-Ghandour et al. is better than the other traditional models proposed by other researchers. In brief, the RMSE and MAE of traditional empirical models are generally greater than 100, and the R2 of them ranged from 0.6 to 0.8. However, the RMSE and MAE of machine learning models are less than 100, and the R2 of them are generally greater than 0.9 and even close to 1.0. Consequently, it can be said that the difference in the predicted accuracy between traditional empirical models and machine learning models is obvious.

**Table 5.** Result comparison between machine learning and traditional empirical models.

Figure 8 shows the predicted results of traditional empirical models and machine learning models for the whole data set. To facilitate comparison between different types of models in these figures, the red dots are used to represent the predicted result of national codes. Afterwards, the blue and purple dots are used to represent the predicted results of traditional models proposed by researchers and machine learning models, respectively. It can be found that the predicted error of traditional models is relatively large, and the machine learning models reach the opposite conclusion. The forecasting result of Figure 8a is similar to Figure 8b, and this conclusion is also reflected in Table 5. In addition, although the predicted accuracy of Formulas (1) and (2) is better than other traditional empirical models, their predicted results are still unsafe. On the contrary, the predicted results of Formula (3) to Formula (6) tend to be conservative even though they do not have the best predicted performance. From the predicted performance of the machine learning models for the complete database, it can be found that the predicted results of ANN and PSO-SVR are likely to be unsafe when the punching shear strength smaller than 200 kN. On the side, when the punching shear strength larger than 1200 kN, the forecasting result of ANN is conservative. Furthermore, except formula 4, the predicted accuracy of all the empirical models are better than ANN when the punching strength larger than 1400 kN. Consequently, it can be concluded that ANN is very dependent on samples.

**Figure 8.** *Cont*.

**Figure 8.** The predictions of models for the whole data set. (**a**) Formula (1); (**b**) Formula (2); (**c**) Formula (3); (**d**) Formula (4); (**e**) Formula (5); (**f**) Formula (6); (**g**) ANN; (**h**) PSO-SVR; (**i**) DT; (**j**) AdaBoost.

### **4. Model Interpretations**

### *4.1. Shapley Additive Explanation*

In this study, SHapley Additive exPlanation (SHAP) is applied to explain the predicting results given by the AdaBoost model. SHAP originates from game theory and is an

additive model, i.e., the output of the model is a linear addition of the input variables [71]. The expression of SHAP can be defined as:

$$y\_{\text{pred}}^{(i)} = y\_{\text{base}} + \sum\_{j=1}^{n} f(x\_{ij}) \tag{29}$$

where *y*base is the baseline value of model; *n* is the total number of input variables; *f*(*xij*) is the SHAP value of the *xij*.

According to Equation (29), it can be concluded that the predicted value of each sample depends on the SHAP value of each feature in the sample. In other words, each feature is a contributor for final predicted value. The SHAP value can be positive or negative, depending on the influence trend of each feature to predicted result. SHAP contains several explainers, in current machine learning papers it often uses the tree explainer to illustrate its models, which is only suitable for a part of machine learning algorithms. Consequently, the kernel explainer will be used to illustrate the machine learning model which has the best predicted performance in this paper.

### *4.2. Global Interpretations*

According to the experimental results obtained above, the predicted results of AdaBoost, which has the best predicted performance, was explained. The predicted results of AdaBoost can be interpreted by SHAP in different ways. Firstly, the feature importance analysis of input parameters is shown in Figure 9a. It can be seen that the importance of each input parameter is non-negligible, that is each input parameter will have a different degree of influence on the predicted results. This is consistent with the existing experimental conclusions [4,72]. According to the analysis results, it can be understood that the SHAP value of each parameter are *x*1 equals 53.45, *x*2 equals 44.50, *x*3 equals 126.36, *x*4 equals 21.57, *x*5 equals 17.23, *x*6 equals 52.96, respectively. Obviously, the slab's effective depth (*x*3) has the most critical influence on the punching shear capacity, more than twice as much as types of column section (*x*1). Moreover, though the Young's modulus of FRP reinforcement (*x*5) has the least importance on the predicted results, sometimes ignoring this feature will cause unnecessary errors in the predicted results of model. Consequently, using these 6 features as the input parameters of machine learning algorithm is reasonable.

**Figure 9.** Global interpretations of PSO-SVR model by SHAP values. (**a**) SHAP feature importance; (**b**) SHAP summary plot.

Figure 9b is a SHAP summary plot of the features, which displays the distribution of the SHAP values of each input variable in each sample and demonstrates the overall influence trends. In the figure, the x-axis is the SHAP value of input parameters, the y-axis is the input parameters, ranked by importance. The points in the figure represent the samples in the dataset and their colors represent the feature value, for which color from blue to red represents the value from small to large. From the figure, it can be seen that a few of SHAP values of samples in *x*3 are very high, which are around 600. It can be said that in these samples, the value of *x*3 has decisive effect on the predicted results. In these input variables, the slab's effective depth (*x*3), types of column section (*x*1), reinforcement ratio (*x*6), cross-section area of column (*x*2), Young's modulus of FRP reinforcement (*x*5) all have the positive influence on the punching shear strength. However, the influence trend of the compressive strength of concrete (*x*4) on the predicted results is hard to definite, which is very complex.

### *4.3. Individual Interpretations*

Except the global interpretations, SHAP also can provides the individual interpretation for each sample in the dataset. In this study, 2 samples are selected, the predicted process of which are illustrated as Figure 10. In the figure, the gray line represents the baseline value, which equals 403.62, and the colorful lines represents the decisive process of each feature. In Figure 10, it can be seen that from the baseline value, every feature will change the value to a different degree, and finally predicted values 419.27 and 501.00, respectively, will be obtained. In the predicted process of the 2 samples, types of column section (*x*1), slab's effective depth (*x*3), the compressive strength of concrete (*x*4) have negative influence on predicted results; whereas, the cross-section area of column (*x*2), Young's modulus of FRP reinforcement (*x*5), reinforcement ratio (*x*6) have positive influence on it. Furthermore, reinforcement ratio (*x*6) acts as determinant in forecasting process of sample 1, and the cross-section area of column (*x*2) plays an essential role in sample 2. In summary, both the global interpretations and the individual interpretations give a detailed insight into the process by which each input feature affects the final predicted value.

**Figure 10.** Individual interpretations for selected samples. (**a**) Sample 1: Specimen G(1.6)30/20; (**b**) Sample 2: Specimen G(1.6)45/20-B.

## *4.4. Feature Dependency*

In addition to explaining the predicted mechanism of model, SHAP can also reveal the interaction between the specific feature and its most closely related feature, which is shown in Figure 11. It can be seen from the Figure that with the values increasing of *x*1, *x*2, *x*3, *x*6, their SHAP values will also be increasing, but the relationships between *x*4, *x*5 and their SHAP values are complicated and nonlinear. As the values of *x*4, *x*5 increase, the SHAP values of them will increase or decrease; thus, it is difficult to describe the concrete relationships. However, the one that interacts most closely with *x*1, *x*2, *x*5, *x*6 is *x*3, the features most closely related to *x*3 and *x*4 are *x*2 and *x*6, respectively. According to the results of feature dependency, further experiments can be carried out to analyze the relationship between the two variables that interact most closely, and analyze the collaborative impact of these two variables to output. It might be helpful to improve the punching shear resistance of FRP reinforced concrete slab-column connections, and the traditional empirical models

cannot accomplish this because the traditional models, relatively, have the worse predicted performance.

**Figure 11.** Feature dependence plots. (**a**) *x*1 ; (**b**) *x*2 ; (**c**) *x*3 ; (**d**) *x*4 ; (**e**) *x*5 ; (**f**) *x*6 .

## **5. Conclusions**

In this paper, several machine learning algorithms, ANN, SVR, DT and AdaBoost, are adopted for punching shear strength of FRP reinforced concrete slabs. A total of 121 groups of experimental tests are collected and the test variables are divided into 6 inputs (types of column section, cross-section area of column, slab's effective depth, compressive strength of concrete, Young's modulus of FRP reinforcement, reinforcement ratio) and 1 output (punching shear strength). Random subsets of 80% and 20% of the data were used for training and testing, respectively, and 10% of the data in training set were used for validating. In addition, 3 indicators (RMSE, MAE, R2 ) are introduced to assist the predicted

performance. For improving the predicted performance, the empirical method and PSO are utilized for adjusting the values of hyper-parameters in ANN and SVR, respectively. After tuning, both ANN and SVR display the good predicted performance. According to the experimental results, the best performance model is AdaBoost, the RMSE, MAE, R2 of which are 29.83, 23.00, 0.99, respectively. The predicted performance of ANN, DT and PSO-SVR are worse than AdaBoost, but they are all better than the 6 traditional empirical models introduced in this paper. The predicted result of ANN for training set has a relatively large deviation when the punching shear strength exceeding 1400 kN, but DT has almost no error. Among these traditional models, GB 50010-2010 (2015) has the least deviation reflected in RMSE and R2 , the values of them are 150.41 and 0.73, respectively. Moreover, the model proposed by El-Ghandour et al. (1999) has the best forecasting performance among three traditional models proposed by researchers.

SHAP is used to interpret the predicted process of AdaBoost with the best performance in this study. On the basis of the result of global interpretations, it can be known that every input variable has the different degrees of influence on predicted results, which demonstrates the rationality of input variables selection. Furthermore, the slab's effective depth has the highest impact factor on the predicted results, equaling 126.36, more than twice as much as types of column section, which equals 53.45. In addition, the Young's modulus of FRP reinforcement has the lowest impact factor, equaling 17.23. From the SHAP summary plot, it can be understood that all input variables have positive influence on predicted results except the compressive strength of concrete, it is because its influence trend is relatively fuzzy. According to the individual interpretations, the forecasting process of single sample is shown, which can help researchers to understand the predicted process of model roundly. In addition, SHAP also provides the results of feature dependency, which is helpful to researchers in understanding the relationship between the specific feature and its most closely related feature. According to the analysis results of SHAP, the relationship between material properties and punching shear strength may really be revealed.

**Author Contributions:** Conceptualization, Y.S. and S.L.; software, Y.S. and J.S.; validation, Y.S. and S.L.; formal analysis, S.L.; writing—original draft preparation, Y.S.; writing—review and editing, S.L.; visualization, Y.S.; supervision, S.L.; project administration, S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Science Foundation of Zhejiang Province of China, grant number LY22E080016; National Science Foundation of China, grant number 51808499.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This study is supported by the Engineering Research Centre of Precast Concrete of Zhejiang Province. The help of all members of the Engineering Research Centre is sincerely appreciated. We would also like to express our sincere appreciation to the anonymous referee for valuable suggestions and corrections.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A Test Data of FRP Reinforced Concrete Slabs**

The sources of the database and the specific material properties are listed in Table A1. The input variables are the types of column section *x*1, cross-section area of column *x*2 (*A*/cm2 ), slab's effective depth *x*3 (*d*/mm), compressive strength of concrete *x*4 (*f'*c/MPa), Young's modulus of FRP reinforcement *x*5 (*E*f/GPa), and reinforcement ratio *x*6 (*ρ*f/%), respectively. The output variable is the experimental value of punching shear strength *y* (*V*/kN). The column section has three types: square (*x*1 = 1), circle (*x*1 = 2), rectangle (*x*1 = 3). In order to use the experimental data for comparative analysis between models, the concrete compressive strength of columns with different cross-section types (cylinder

and cube) was unified. Furthermore, to prevent errors caused by different data precision, retain two significant digits to the decimal point for input parameters except for column section type *x*1.

**Table A1.** Database of punching shear strength for FRP reinforced concrete slabs.


4.11.3. Confirmation of CCK-2R Membrane Expression by Flow Cytometry

Cells of the selected line (A549) were detached with 5 mM EDTA then stained with 100 µL of phosphate buffer saline (PBS) containing 0.1% Live–Dead Fixable Dead Cell Stain near-IR-fluorescent reactive dye (Molecular Probes) on ice for 30 min to exclude dead cells from the analysis. After washing with PBS added to 1% heat-inactivated FBS (PBS/FBS), cells were incubated on ice for 30 min with 50 µL of PBS/FBS containing 20 µg/mL of anti-CCK-2R-phycoerythrin antibodies (clone E-3, sc-166690, Santa Cruz Biotechnology), 40 µg/mL of anti-CCK-2R-Dy488 antibodies (LS-C756504, LSBio), or 40 µg/mL of CCK-8 peptide (Asp-Tyr-Met-Gly-Trp-Met-Asp-Phe) labelled with FAM supplied by GenScript Biotech (Piscataway, New Jersey, USA). Isotype control antibodies labelled with phycoerythrin (20 µg/mL, Santa Cruz Biotechnology) were used to check nonspecific binding. After washing with PBS/FBS, cells were analyzed with the FACSCantoII flow cytometer (BD).


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**Author details**

*Models and Technologies for Smart, Sustainable and Safe Transportation Systems*

be achieved is not clear.

ity and of the provided information.

**5.2 Remarks on the Hypermode paradigm**

the MaaS.

of the service.

mode choices.

behaviour, respectively.

on a wide variety of data.

same market place does not suffice to guarantee intermodality: who chooses the service/services to offer to the users? Instead, the literature agrees that if MaaS is developed according to a purely commercial approach, there is a serious risk to dis-incentivize sustainable trips, encouraging instead a shift towards car use. Hence, the literature also agrees on the need of regional authorities to lead MaaS development through new models of governance. However, the way this result can

Consistently with these premises, one of the main necessary research perspective is to investigate and identify possible regulatory frameworks, MaaS schemes and approaches for bidding/tendering the services enabling the public entity to rule

In addition, the way MaaS should work is clear in the literature, but models and methodologies enabling such working are very complex and largely new with respect to the approaches currently used in transportation system modelling.

From the demand side, new approaches are needed to profile users coupling with MaaS requirements and involving also psychological and social science. Moreover, new approaches are needed for the modelling of individual choices, considering the intrinsic dynamicity of the MaaS system and including the effect of service reliabil-

From the supply side, new modelling framework are needed to integrate continuous and discontinuous services, to deal with diffused/distributed inter-modality and with dynamically changing conditions and unpredicted temporary disruptions

The widespread of real-time travel information combined with the presence of a variety of travel modes available in dense urban areas could lead travellers to reconsider their planned mode choices based on real-time events, such as realtime passenger information, transport disruptions, overcrowdings, and weather. However, most existing mode choice studies analyse the decision process as planned behaviour, and hence do not capture the influence of these real-time events on

This paper aims to address this limitation by presenting an innovative approach to interpret mode choice, which captures an adaptive behaviour of travellers. The underpinning assumption is that the traveller first identifies a set of feasible modes that connect his/her origin to the destination; then he/she evaluates the real-time situation in order to select a specific mode of transport from the feasible set. This novel behaviour paradigm is referred to as hypermode in this paper, in analogous to the hyperpath concept used extensively in transit assignment. A two-level decisionmaking process is illustrated, which rests on planned and adaptive model choice

A survey has been undertaken to test the proposed approach; it demonstrates the validity of the underlying assumption of hypermode, and serves as a proof of concept. As the next step of this research, we will explore different modelling approaches (e.g. Nested/Mixed Logit and discrete choice model with endogenous attribute threshold/cut-off) along with calibration and validation methods based

For future research, the hypermode concept could be explored alongside dynamic assignment of the multimodal network, which provides feedback to mode choice models in the form of real-time events. For example, the dynamic re-distribution of shared bikes, as a result of multimodal traffic assignment, could affect the availability of bikes at docking stations and hence travellers' mode choices.

**18**

Stefano de Luca1 \* and Margherita Mascia2

1 Department of Civil Engineering, University of Salerno, Salerno, Italy

2 ITS Counsult, Bari, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.