**9. Practice implications**

Mental skill training for mental simulation should be incorporated into the surgical residency programme. Faculty members must be trained in the design and development of instructional videos and mental scripts. Every index procedure in procedural skill training should have the following:


*Edited by Wojciech Borek,*

*Tomasz Tański and Mariusz Król*

Cavitation erosion is one of the most popular phenomena of the destruction of engineering materials working in water conditions and various kinds of liquids. The cavitation effect is defined as a physical effect, induced by a variable field of liquid pressures, where bubbles or other voids (caverns)—containing steams of a given liquid, gas, or a steam–gas mixture—are formed, expanded, and disappear. A better understanding of all aspects related to cavitation wear will allow for more thoughtful analysis in the selection of innovative engineering materials additionally protected by various technologies or techniques in the field of surface engineering, and optimization of the design of constructional elements used in the cavitation environment. The novelty of this book is the presentation of extensive knowledge related to cavitation, erosion, and how to protect engineering materials against this phenomenon supported by the results of thorough research by the authors.

ISBN 978-1-78984-652-2

Cavitation - Selected Issues

Published in London, UK © 2018 IntechOpen © vale\_t / iStock


*2.1. Literature Survey*

The literature survey included a systematic four-step literature review where Scopus was used to locate the published literature.

In the first step, a combination of keywords was identified as follows: ("barriers" OR "opportunities") AND "PV". This combination was searched for in the abstracts, titles and keywords of the publications from 2012 to 2020 yielding 264 journal papers. Note that the search was not restricted to Kenya but yielded results from analyses worldwide to capture barriers and opportunities more generally.

In the second step, each publication was evaluated for its relevance to the integration of PV systems in the electricity generation mix, based on the abstract, title and keywords. If a publication had relevance, it was eligible for inclusion in the third step. This resulted in 102 journal papers.

In the third step, the full texts were evaluated in detail for their relevance to the barriers and opportunities for integration of PV technology in Kenya's electricity generation mix. This procedure ensured that no relevant information was missed from the publications. If a study addressed any kind of opportunity or barrier to the diffusion, it was included for analysis in the fourth step. Consequently, this resulted in 46 journal papers.


*Treatment of Uncertainties in Probabilistic Risk Assessment DOI: http://dx.doi.org/10.5772/intechopen.83541*

are not exactly known because of the lack of data, variability of plants,

• Modeling uncertainty—inadequacy of conceptual, mathematical, numerical,

• Uncertainty about completeness—systematic expert reviewing can minimize

The main focus of this work is the treatment of uncertainties regarding numerical values of the parameters used in fault and event trees in the scope of PRA and their propagation in these models. If a probability density function (pdf) is provided for the basic events (e.g., normal, log-normal, or triangular), a pdf or confidence bounds can be obtained for an FT top event or an ET scenario sequence.

There are several available methods for propagating uncertainties such as analytical methods (method of moments and Fenton-Wilkinson (FW) method), Monte Carlo simulation, Wilks method (order statistic), and fuzzy set theory. They are different from each other, in terms of characterizing the input parameter uncertainty and how they propagate from parameter level to output level [16].

The analytical methods consist in obtaining the distribution of the output of a model (e.g., fault or event trees) starting from probability distribution of input parameters. An exact analytical distribution of the output however can be derived

The method of moments is another kind of analytical method where the calculations of the mean, variance, and higher order moments are based on approximate models (generally using Taylor series). As the method is only an approximation, when the variance in the input data are large, higher order terms in the Taylor expansion have to be included. This introduces much more complexity in the analytical model, especially for complex original models, as in the case of PRAs [19]. The Monte Carlo simulation estimates the output parameter (e.g., probability of the top event of an FT) by simulating the real process and its random behavior in a computer model. It estimates the output occurrence by counting the number of times an event occurs in simulated time, starting to sample the pdf from the input

The fuzzy set theory is used when empirical information for input data are limited and probability theory is insufficient for representing all type of uncertainties. In this case, the so-called possibility distributions are subjectively assigned to input data, and fuzzy arithmetic is carried out. For uncertainty analysis in FTAs, instead of assuming the input parameter as a random variable, it is considered as a

The Wilks method is an efficient sampling approach, based on order statistics,

which can be used to find upper bounds to specified percentiles of the output

fuzzy number, and the uncertainty is propagated to the top event [21].

only for specific models such as normal or log-normal distributions [17]. The Fenton-Wilkinson (FW) method is a kind of analytical technique of approximating a distribution using log-normal distribution with the same moments. It is a moment-matching method for obtaining an exact analytical distribution for the output (closed form). This kind of closed form is helpful, when more detailed uncertainty analyses are required, for instance, in parametric studies involving uncertainty importance assessments, which require re-estimating the overall

the difficulties in assessing or quantifying this type of uncertainty.

processes or components, and inadequate assumptions.

**3. Methods of uncertainty propagation used in PRA**

and computational models.

*Reliability and Maintenance - An Overview of Cases*

uncertainty distribution many times [18].

data [20].

**130**

distribution. Order statistics are statistics based on the order of magnitudes and do not need assumptions about the shape of input or output distributions. According to the authors' knowledge, this method has been of little use in the field of reliability modeling and PRA, although it is used in other aspects of NPP safety, such as uncertainty in input parameters associated with the loss-of-coolant accident (LOCA) phenomena [22].

The mentioned methods for uncertainty propagation have many differences and similarities, advantages and disadvantages, as well as benefits and limitations. **Table 1** summarizes a comparison of these methods.

A brief discussion about the comparison of the mentioned methods is given as follows.

The method of moments is an efficient technique that does not require the specification of the probabilistic distributions of the basic event probabilities. It is difficult to be applied to complex fault trees with many replicated events [23]. This can be solved with the use of computer codes that automatically get the minimal cut sets (MCSs) of the fault trees. It is a simple method, easily explainable and suited for screening studies, due to inherent conservatism and simplicity [24].

The Monte Carlo simulation is computationally intensive for large and complex systems and requires pdf of input data. It has the disadvantage of not readily revealing the dominant contributors to the uncertainties. With current computer technology and availability of user-friendly software for Monte Carlo simulation, computational cost is no longer a limitation.

The fuzzy set theory does not need detailed empirical information like the shape of distribution, dependencies, and correlations. Fuzzy numbers are a good representation of uncertainty when empirical information is very scarce. It is inherently conservative because the inputs are treated as fully correlated [25].

The Fenton-Wilkinson (FW) method improves the understanding of the contributions to the uncertainty distribution and reduces the computational costs involved, for instance, in conventional Monte Carlo simulation for uncertainty

#### **Table 1.**

*Comparison of methods for uncertainty propagation.*

estimation. It is applicable only when the uncertainties in the basic events of the model are log-normally distributed. FW estimates are most accurate in the central range, and the tails of the distributions are poorly represented. The Wilks method requires relatively few samples and is computationally inexpensive. It is useful for providing an upper bound (conservative) for the percentiles of the uncertainty distribution. However, its calculated values are less accurate than the FW estimates over practically the entire range of the distribution. For both Wilks and FW methods, the greatest errors are found in the low tails of the distributions, but in almost all reliability applications the high tails are of more interest than the low tails [26].

*C*0 *i* ¼ *si* 1 � *Pi*

given by Eq. (8):

"AND" gate.

event tree.

**133**

(15), respectively:

where *si* denotes the standard deviations of ith (i = 1, 2, 3, …*, n*) input, *n* is the number of input events, and *sor* is the standard deviation of the output of "OR" gate. For an "AND" gate of a fault tree, the probability of output event, *Pand*, is

*Pand* ¼ Y*n*

where *Pi* denotes the probability of ith (i = 1, 2, 3, …, *n*) independent events

The uncertainty propagation through the "AND" gate is given by Eq. (9). It calculates the coefficient of variation of output, *Cand*, as function of the coefficients

*and* ¼ Y*n*

*i*¼1

*Cand* ¼ *sand Pand*

> *Ci* ¼ *si Pi*

where *si* denotes the standard deviations of ith (i = 1, 2, 3, …, *n*) input, *n* is the number of input events, and *sand* is the standard deviation of output of the

Uncertainty propagation in an event tree is similar (or analogous) to uncertainty propagation of an "AND" gate of a fault tree. The frequency of occurrence of each

*i*¼1

*Fseq* ¼ *λ* � Y*n*

where λ is the frequency of occurrence of the initiating event and *Pi* denotes the probabilities of ith (i = 1, 2, 3, …, *n*) subsequent independent events leading to the accident scenario and *n* is the number of input events. These values can be obtained from fault trees constructed for each ith event or system failure of the

The uncertainty propagation through the accident sequence is given by Eq. (13) that provides the coefficient of variation of accident sequence, *Cseq*, as function of the coefficients of variation of subsequent events, *Ci*, according to Eqs. (14) and

> 1 þ *C*2 *i*

1 þ *C*2

*seq* ¼ Y*n i*¼1

*Cseq* ¼ *sseq Fseq*

1 þ *C*2 *i*

(or basic events) and *n* is the number of input events.

*Treatment of Uncertainties in Probabilistic Risk Assessment*

*DOI: http://dx.doi.org/10.5772/intechopen.83541*

**4.2 Method of moments applied to ETA**

accident scenario, *Fseq*, is given by Eq. (12),

of variation of inputs, *Ci*, according to Eqs. (10) and (11) [29]:

1 þ *C*2

*i*¼1

*,* (7)

*Pi,* (8)

� �*,* (9)

*,* (10)

*,* (11)

*Pi,* (12)

� �*,* (13)

*,* (14)


**1. Introduction**

The significant increase in energy requirements and the depletion of fossil fuels have caused researchers to develop energy harvesting from renewable energy resources [1,2]. The use of solar-driven photovoltaic technologies and heterogeneous photocatalysis offers an appealing solution to the current global energy crisis and environmental remediation [3–5]. In terms of solar energy conversion technologies, dye-sensitized solar cells (DSSC) and heterogeneous photocatalytic dye degradation are the most attractive and promising areas of research to address energy and environmental concerns [6,7]. Semiconducting titanium dioxide (TiO2) nanostructures are typically potential candidates as photoanode materials in DSSC devices and photocatalysts for the heterogenous photodegradation of toxic dyes due to their unique physicochemical properties [8–10]. However, the wide bandgap of the TiO2 nanostructures (3.2–3.3 eV) has the absorption region below 4% in the entire solar spectrum compared to that of the visible region (43% solar energy) [11]. As a result, inefficient use of the visible light spectral portion and the fast recombination of electron-hole pairs (TiO2) are significant constraints in the large-scale development of

**Citation:** Athithya, S.; Manikandan, V.S.; Harish, S.K.; Silambarasan, K.; Gopalakrishnan, S.; Ikeda, H.; Navaneethan, M.; Archana, J. Plasmon Effect of Ag Nanoparticles on TiO2/rGO Nanostructures for Enhanced Energy Harvesting and Environmental Remediation. *Nanomaterials* **2023**, *13*, 65. https:// doi.org/10.3390/nano13010065

Academic Editor: Muralidharan Paramsothy

Received: 22 October 2022 Revised: 10 December 2022 Accepted: 11 December 2022 Published: 23 December 2022

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

efficient photoanodes for DSSC devices and photocatalysts [12–14]. To overcome these constraints, different TiO2 nanostructure composites with two-dimensional (2D) carbon materials have been employed as an effective strategy in recent decades. In nature, 2D-single molecular layered structures with sp2 hybrid carbon atoms, i.e., graphene, possesses high surface area (ca. 2600 m2/g), electron mobility (ca. 15,000 m2/V.s at room temperature) and unrestricted movement of electrons in the crystal lattice [2,15,16]. During the formation of the nanocomposite, TiO2 nanostructures are bonded with the graphene surface due to the presence of intermolecular forces. This increases the number of electron spots and electron bridges, which promotes electron transport with a suppressed recombination rate at the interface [17]. Moreover, reduced graphene oxide (rGO) nanosheet composites with TiO2 nanostructures offer enhanced active surface area, good electrical conductivity and a lower recombination rate of photon-induced-charge carriers for photovoltaic and photocatalytic performance [18]. Manikandan et al. reported TiO2 along with rGO not only enhanced the surface area but also influenced the short-circuit current (*JSC*) in a device due to the high carrier mobility behavior of the rGO [19].

In recent decades, the localized surface plasmon resonance (LSPR) phenomenon of noble metal nanoparticles has played a dual role as potential visible sensitizers and electron sinks in the degradation of pollutant dyes and in DSSC device performance. It is a wellknown strategy to trap electrons and harvest maximum light for the development of high-efficiency photovoltaic devices. Amine-functionalized TiO2 composites with GO and Ag nanoparticles exhibited high current density due to the improved electron transfer at the photoanode/electrolyte interface, as reported by Kandasamy et al. [20]. The incorporation of Ag nanoparticles (NPs) into TiO2-carbon nanotube (CNT) nanocomposites exhibited a photocatalytic activity of 66% for methylene blue (MB) degradation under visible light due to the presence of the CNTs and Ag NPs, as reported by Zhao et al. [21]. MB is a well-known, highly carcinogenic thiazine pollutant that has been manufactured and used in a variety of industries for various purposes. Therefore, it is strongly recommended to remove such a persistent contaminant from any given aqueous solution [22].

Moreover, the introduction of Ag NPs onto a TiO2 nanocomposite improved the absorption-coefficient of the organic dye and eventually enhanced the optical absorption in the visible-light region [23,24]. It is similarly promising to achieve superior electrical conductivity with a prolonged lifetime of the photogenerated charge carriers for rGO/TiO2 nanocomposites [25]. For example, Huan et al. prepared a flower-shaped nanosheet rGO/TiO2 composite material that exhibited a photocatalytic efficiency of 92.3% under UV–visible light irradiation for the degradation of a rhodamine B (RhB) solution [26]. Duygu et al. reported the development of rGO-TiO2-CdO-ZnO-Ag based composites that exhibited an excellent degradation rate of methylene blue (MB) dye (15 min) with 91% photocatalytic efficiency under UV light irradiation [27]. Similarly, Zohreh et al. reported the influence of surface plasmon resonance on the photovoltaic characteristics of Ag/TiO2 in a photoanode-based DSSC device with a power conversion efficiency (PCE) of 6.5% under 1 sun simulated solar irradiation [28]. As a result, the combination of the LSPR influence of Ag NPs and the conductivity of rGO nanosheets with the reduced recombination rate of the TiO2/rGO/Ag hybrid nanostructures is advantageous for long-term dye degradation photocatalysts and photoanodes for DSSC devices.

In the present work, we report the in situ growth synthesis of mesosphere TiO2/rGO nanosheets/Ag NPs as a plasmonic hybrid nanostructures for visible-light-responsive DSSCs and photocatalytic applications. The prepared hybrid nanostructures are further examined with respect to their structural, morphological and optical properties using various advanced characterization techniques. The influence of the LSPR properties on a constructed DSSC device with the visible-light-driven photoanode and photocatalyst dye (MB) degradation is systematically investigated with an appropriate mechanism.

#### **2. Experimental Section**

#### *2.1. Materials and Reagents*

Titanium tetra-isopropoxide (TTIP), ethylene glycol (C3H6O2), acetone (C3H6O), ethanol (C2H6O), graphite powder, sodium nitrate (NaNO3), sulfuric acid (H2SO4), potassium permanganate (KMnO4), hydrochloric acid (HCI), hydrogen peroxide (H2O2), isopropyl alcohol (IPA), 1,4-benzoquinone (BQ), ethylenediaminetetraacetic acid (EDTA) and silver nitrate (AgNO3) were purchased from SRL Co., Mumbai, India. All the purchased chemicals were analytical grade and used in the synthesis without further purification.