**1. Introduction**

Occupational stress, also named work stress, is a psychological and physiological phenomenon, generated as a response to various external factors [1]. Resulting from insufficient coping skills with stressors at the workplace, occupational stress is a negatively perceived quality and has negative consequences on mental and physical health. This means that, prior to showing stress symptoms, at first, individuals must perceive a stressor negatively and then they must display inadequate coping abilities. That is, if a source of stress is perceived as a challenge to overcome rather than a threat to avoid, no negative outcomes will appear on mental and physical health [2].

Findings from previous studies have showed associations between high levels of stress at work and a broad range of disturbances, such as chronic fatigue, eating disorders, increased blood pressure, and the risk of cardiovascular diseases. Regarding psychological symptoms, occupational stress has been linked to depression and anxiety, mood disturbance and emotional exhaustion, and a decrease in attention and concentration [3–7].

In addition, significant positive associations were also found between occupational stress and a variety of job-related outcomes, such as intention to leave the workplace or absenteeism [6,8], whereas inverse relationships were estimated with job satisfaction, job performance, job motivation, and organizational commitment [9].

Occupational stress is considered both as a "public concern" and a "personal trouble" [10], because both job-related and individual factors influence it. Regarding job-related factors, some studies have linked occupational stress to several aspects, such as heavy workload, role ambiguity, role conflict, problematic interactions with colleagues or supervisors, inadequate training, job insecurity, low salary, and lack of career prospects [8,11,12].

With regard to individual factors, several studies have revealed significant associations with gender, age, educational level [13–15], and coping styles [16].

Owing to the complexity and heterogeneity of occupational stress, consensus about its assessment is lacking. Though some authors, such as Mensah [17], used a single item simply asking people "*Do you experience stress at work?*", occupational stress is described as

**Citation:** Valenti, G.D.; Faraci, P.; Magnano, P. Emotional Intelligence and Social Support: Two Key Factors in Preventing Occupational Stress during COVID-19. *Int. J. Environ. Res. Public Health* **2021**, *18*, 6918. https://doi.org/10.3390/ ijerph18136918

Academic Editors: Paolo Roma, Merylin Monaro and Cristina Mazza

Received: 18 May 2021 Accepted: 22 June 2021 Published: 28 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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/).

a multidimensional construct, and overload, work relations, psychological symptoms and physical burdens, pay and benefits, lack of rewards, and organizational policies are among the most widely investigated indicators [8,18,19].

A relevant individual factor related to occupational stress is emotional intelligence (EI), defined as a personality predisposition associated with individuals' tendency to understand their own and others' emotions, to manage their own feelings and their relationships with others [20]. Understanding emotions helps people to be aware of their own and others' behaviors and motivations, whereas managing emotions allows the individuals to navigate their feelings constructively at work. In other words, EI is the individuals' ability to properly handle their own interpersonal and intrapersonal skills, which improves the competence in facing stressors and, consequently, enhances positive outcomes. In addition, Goleman [21] asserts that EI is twice as important as technical skills and more important than IQ in predicting positive outcomes at the workplace, suggesting that people should be judged not according to their own intelligence or professional competence, but rather by their own behaviors toward themselves and others. These premises stress the relevance of taking into account EI in working environments, both to increase productivity and efficiency and to improve workers' wellbeing, job motivation, and job satisfaction.

Indeed, recent studies [18,22–28] have reported that workers with higher EI are more productive at the workplace and can cope with stressors more efficiently. The inverse relationship between EI and occupational stress has been found in different working contexts and for different categories of workers, such as police officers [26], human service professionals [19], bank employees [18], managers [29], health care professionals [30], and college teachers [31]. These findings outline that EI negatively affects occupational stress, regardless of the specific working sector. Although there is wide agreement about the negative association between EI and stress at the workplace, some authors did not show any statistical relationships [32], suggesting that other variables, such as organizational support, are protective factors in stress management rather than EI.

Social support has long been identified as a crucial resource for mitigating threats and challenges [33,34]. It is defined as the extent to which people perceive others as attentive and responsive to their needs. Social support is considered as an important factor in maintaining wellbeing and coping with challenges [35]. It can be assessed as both a global and generalized perceived social support and by discriminating different sources, such as social support from family, friends, and significant others [36–39]. However, in the work context, work-related social support (social support from coworkers and/or supervisors) is mostly investigated because these individuals are considered as the main sources of social support for workers seeking to accomplish their goals and adjust to the workplace [40]. Actually, the results of the studies investigating the effects of work-related social support on the levels of occupational stress are incoherent and inconsistent, suggesting that the kind and the quality of interactions with coworkers and supervisors may function both as protective and risk factors [11,41]. Nevertheless, a limited number of studies examining the relationships between sources of social support and occupational stress outlined the beneficial role in mitigating the degree of stress at the workplace [42,43].

Individuals who are able to understand their own and others' feelings more likely search for support from others in challenging situations [44]. Specifically, they may need others to empathize with their situation, identify their emotional reactions, and provide social support or resources to deal with a stressful situation [45]. Social support is a key candidate to mediate EI and wellbeing. Some theorists suggested that emotional abilities contribute to acquiring social skills, thus enhancing both the quality of relationships and the availability of social support, which in turn leads to a richer sense of wellbeing [46]. Some evidence supported this hypothesis. For example, some authors showed that people with high EI reported greater social support, as well as higher levels of satisfaction and lower grades of psychological distress [36–39,47,48]. Nevertheless, the mediating role of social support in the relationship between EI and occupational stress has not yet been explored. This study aims to fill this gap.

The diffusion of the COVID-19 virus has considerably affected work conditions, leading to new job demands and pressures. Though some working sectors—such as health care professionals—are more vulnerable to occupational stress, given the higher risk of being infected and longer working hours, the current pandemic has greatly influenced each working sector without distinction. In fact, many workers have experienced—and are experiencing—different changes at work, involving an increase or a reduction of working hours, alterations in job tasks and shifts, and a transition toward smart working. In other words, many working sectors have reorganized their environments and structures to accommodate the emerging demands. All these factors may further influence how people feel in their workplaces and affect their level of occupational stress.

A large number of studies are currently examining how the pandemic is changing work conditions and affecting several job-related outcomes [17,49–51]. Among them, some authors have pointed out that both EI and social support have a strong impact in mitigating negative job-related outcomes. For example, Soto-Rubio et al. [52] have emphasized EI's key role in preventing burnout among health care professionals and in improving their levels of job satisfaction, whereas other authors [53] have stressed the influence social support has in enhancing job engagement and job retention intention.

In summary, the relationship between EI and stress has been widely studied, as well as the beneficial role of social support in maintaining health and wellbeing. Further, their protective role in decreasing the levels of stress at work is well documented. However, the joint contribution of EI and social support in reducing occupational stress has not been examined during the COVID-19 lockdown. Given the importance of EI and social support in preventing occupational stress, this study aims to analyze these relationships in the Italian context during the pandemic. Specifically, the goals of this work are (a) to examine the direct relationship between EI and occupational stress, and (b) to test the mediating role of social support (see Figure 1 for a visual representation of our hypotheses). We expect that individuals with higher levels of EI will perceive their work environment as less stressful and will experience less negative health consequences, and that social support can function as a buffer in the relationship between EI and occupational stress. Thus, we formulated the following hypotheses: (i) EI negatively affects occupational stress and (ii) social support mediates the association between EI and occupational stress. Although a similar mediation analysis has not been previously tested, the proposed model derives from the existing literature described above in which the associations between EI and social support, between social support and occupational stress, as well as between IE and occupational stress have been investigated [18,19,28–31,42–44,46].

**Figure 1.** Conceptual model. Path a = association between EI and social support; path b = association between social support and occupational stress; path c = total effect of EI on occupational stress; c = direct effect of EI on occupational stress.

The current study takes into account support from family, friends, and significant others—which are little investigated in this specific field of study—to explore how not work-related sources of support affect occupational stress. This latter is defined as a broad concept in which effects on health (both psychological and physical) and work stressors (job features, career prospects, managerial role, work relationships, work–home interface, and

organizational structure) are indicators. Figure 2 displays the hypothesized relationships among the investigated variables.

**Figure 2.** Hypothesized relationships among the investigated variables. Full lines indicate direct effects; dotted lines indicate indirect effects.

This research contributes to a better understanding of job-related outcomes in the current circumstances.

#### **2. Materials and Methods**


*Article* **On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads**

**Stylianos I. Pardalopoulos 1, Stavroula J. Pantazopoulou 2 and George D. Manolis 1,\***

**Abstract:** Brittle failure is often observed in older reinforced concrete (R/C) buildings that have been designed prior to the 1980s following an earthquake event. Since this has ramifications on any subsequent repair protocol, it is important to quantify the remaining strength capacity for this class of building to determine a retrofit strategy. Following along these lines, an analytical-numerical methodology is presented for use as a third-tier seismic assessment which is based on a previously developed second-tier strength assessment criterion coming from a procedure known as Rapid Seismic Assessment (RSA). The assessment framework is performance-based, aiming to determine whether estimated local drift demands can be tolerated without failure developing along the load resistance path of substandard R/C buildings. This enables the development of guidelines for modeling all possible strength mechanisms that occur in the structural system of substandard R/C buildings. An application example using data provided by a benchmark experiment involving a full-scale R/C building helps to illustrate and then validate the proposed modeling procedures and establish their accuracy and efficiency for use by practicing engineers.

**Keywords:** reinforced concrete; substandard buildings; brittle failure; earthquake loads; rapid seismic assessment

#### **1. Introduction**

Existing reinforced concrete (R/C) buildings encompass a variety of structures, ranging from cases that were designed and constructed according to modern forms of detailing (see ASCE/SEI 41-17 [1], EN1998-1 [2]) to structures that were built before the early 1980s under design code frameworks (summarized in the FIB Bulletin 24 [3]) that are now often characterized as substandard. The seismic vulnerability of existing R/C buildings, particularly that of substandard construction, is continuously demonstrated when strong earthquakes strike urban areas (e.g., Loma Prieta 1989, Northridge 1994, Kobe 1995, Kocaeli 1999, Athens 1999, Bhuj 2001, Port-au-Prince 2010, Gorkha 2015, and Mexico City 2017). Field observations have repeatedly suggested that most of the buildings that collapsed did not show signs of flexural yielding (such as densely spaced flexural cracks normal to the member axis), nor the development of any kind of global ductility prior to collapse. Rather, it appears that most of the collapsed structures had formed a brittle mechanism upon failure, marked by severe damage localization in a few areas with high shear demand, such as the disintegration of exterior frame joints, shear failure of severely unconfined captive columns, and soft-story damage in sway-frames.

Given the need for identifying among the vast inventory of existing R/C buildings those cases that are potentially vulnerable to collapse, thus representing a serious hazard to human safety in the event of a moderate or a strong earthquake, extensive research has been conducted over the past three decades and different assessment procedures have been developed. Analytical assessment procedures, also known as third-tier evaluation

**Citation:** Pardalopoulos, S.I.; Pantazopoulou, S.J.; Manolis, G.D. On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads. *Appl. Sci.* **2022**, *12*, 1602. https:// doi.org/10.3390/app12031602

Academic Editor: Maria Favvata

Received: 29 December 2021 Accepted: 31 January 2022 Published: 2 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**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/).

procedures (ASCE/SEI 41-17 [1], EN1998-3 [4], Greek Code of Structural Interventions [5], FEMA-356 [6], Vamvatsikos and Cornell [7]) include the mathematical simulation of the examined building using advanced numerical tools such as 3D finite element (FE) models combined with elastic and/or inelastic analysis methods. This category of assessment procedures enables the simulation of complex mechanisms throughout the structural system of buildings and evaluation of demand and supply in R/C structures in terms of deformation (either drift or ductility ratios at milestone performance points). Since they originate from design procedures that were developed for modern R/C structures, most of the analytical assessment procedures simulate the response of R/C members using nonlinear moment-rotation envelope curves associated with zones of inelasticity-spread, demonstrating a strain hardening, post-yielding plateau. However, in poorly detailed R/C members, strength and deformation capacity seems to be controlled by localization of the prevailing mode of failure which depends on the rate of degradation of the alternative strength mechanisms with increasing ductility demand and load history [8–27]. In order for the analysis results to be realistic, member resistance skeleton curves must necessarily reflect the brittle modes of failure that typically prevail in poorly reinforced members, a feature that leads to an unstable solution and lack of convergence with most Newton-Raphson type schemes used to perform nonlinear structural analysis. This also affects the post-processing of the numerical analysis results [28,29].

A new methodology for modeling member response of substandard R/C buildings for seismic evaluation is presented here. This is motivated by the need for analytical modeling tools that can effectively capture the seismic behavior of substandard R/C structural elements. The proposed methodology can be used for a third-tier seismic evaluation procedure, using commercial software that is easily accessible to practitioners. Concepts from the strength assessment criterion in the Rapid Seismic Assessment (RSA) procedure are adopted here (Pardalopoulos and Pantazopoulou [30], Pardalopoulos et al. [31,32]). A core objective of the method is to determine whether or not the local drift demands can be tolerated without failure along the load resistance path of substandard R/C buildings. Building on the aforementioned concepts, we provide guidelines for modeling all possible strength mechanisms that may develop in the various components of the structural system of substandard R/C buildings. In order to validate the introduced modeling procedures and to establish their accuracy and efficiency, an application example is presented, illustrating in practical terms the steps needed for evaluating the seismic response of a substandard, full-scale R/C test building.

#### **2. Procedures for Simulating Strength Mechanisms in Substandard R/C Buildings**

Contrary to analysis procedures used in the design of new R/C buildings that focus on the numerical simulation of ductile resistance mechanisms in structural members (under the proviso that all undesirable brittle failure modes will be capacity-designed and therefore suppressed) in the analytical seismic assessment of poorly reinforced R/C buildings, the potential prevalence of brittle-type mechanisms of resistance across the structural system must be examined. The typical layout of the structural system of R/C buildings constructed up to the early 1980s (at a time when construction details were still relatively primitive since their role in the seismic response was not yet fully understood) included poorly reinforced frames comprising columns of section sizes ranging between 250 mm and 500 mm, beams of a 150 mm to 250 mm width and 600 mm to 700 mm height (including the slab thickness), and slabs with a thickness ranging between 120 mm and 160 mm. Longitudinal reinforcement usually comprised relative low amounts of StI (*fy* = 220 MPa, *fu* = 340 MPa) to StIII (*fy* = 420 MPa, *fu* = 500 MPa) smooth bars, lap-spliced to arbitrary lengths and under poor confinement conditions. Column and beam stirrups were usually 6 mm to 8 mm, smooth, rectangular, StI bars (usually mild steel), with 90◦ hooks in the ends, spaced at 200 mm to 300 mm on center (o.c.). Beam-column joints were usually left without stirrups for the convenience of construction. Concrete quality was usually

Bn150 to Bn200 as per DIN 1045 [33], corresponding to C12/15 and C16/20 concrete grades according to EN1992-1-1 [34].

To address the need for an effective simulation of the seismic response of substandard R/C buildings, the present research introduces new procedures for modeling the mechanisms of resistance developing in old-type R/C structural elements. Based on the principles of the RSA System [30–32], emphasis is placed on numerical simulation procedures that are applicable to column lines of existing R/C buildings, non-conforming to modern standards of seismic design and detailing. These lines usually collapse in a brittle manner, forming a mechanism characterized by pronounced localization of damage in a few locations with a high shear demand before there is a chance for the development of any form of redistribution and ductility (see Lang and Marshall [35], Augenti and Parisi [36], Mehrabian and Haldar [37], Dogangun [38], Joeng and Elnashai [39], and Varum [40]).

The modeling procedures introduced here include the simulation of the following mechanisms: M1: non-linear flexural response of columns and beams; M2: shear failure of the column web; M3: anchorage failure of longitudinal reinforcement of columns; M4: attainment of the development capacity in column lap splices; and M5: beam-column joint shear failure. The proposed procedures for simulating the seismic response of substandard R/C buildings are summarized in Figure 1 and discussed in detail in the following sections. Note that simulation of mechanisms {M2–M5} along column lines of existing R/C building is meaningful only if they prevail over mechanism M1. According to the RSA system, this occurs when the corresponding resistance ratios (*r*) that represent the shear strength associated with the examined failure mode, normalized by the shearing force required in order to support flexural yielding in the column, are equal to or greater than 1.0.

**Figure 1.** Simulation of strength mechanisms that develop within the structural system of substandard R/C buildings. Hatched regions represent cross-sections of members extending normal to the plane of view (e.g., slab and transverse beams).

#### *2.1. Simulation of InelasticFlexural Response in Columns and Beams*

Flexural behavior of R/C structural elements is associated with ductile member response and materializes only if it can be supported by all other resistance mechanisms developing along the element length. The inelastic flexural response is linked with the formation of extensive cracking, perpendicular to the axis of bending of R/C elements, in regions where the longitudinal reinforcement yields in tension. In columns and beams subjected to earthquake loading, flexural cracking usually forms in both ends, in a length approximately equal to twice the elements' width. By way of contrast, in R/C beams subjected to excessive gravity loading, the yielding of longitudinal reinforcement occurs at locations of maximum values for the developing bending moment.

Simulation of the inelastic flexural response of R/C elements may be performed using different, alternative approaches that are documented in the international literature. The most preferable approach in simulating inelastic flexural response in R/C elements subjected to biaxial bending is the use of linear elements encompassing fiber discretization of their cross-section [41]. According to this approach, the reinforcing bars plus the confined and the unconfined concrete of an R/C structural element are all modeled as separate fibers, possessing stress-strain relationships that characterize their response under uniaxial loading (see Figure 2). Based on the assumption that plane sections remain plane during member deformation, member stresses and deformations in both section directions are calculated through the integration of the response of the fibers over the element section. For R/C beams under seismic excitation that are primarily subjected to uniaxial bending, an alternative simulation approach is through the use of a lumped plasticity approach which combines a linear element with non-linear hinges at the locations where beams connect with other structural members (columns and/or beams). Inelastic response in each hinge is then defined by appropriate force-deformation relations, derived from sectional analysis of the corresponding element and classical mechanics.

**Figure 2.** Simulation of the inelastic flexural response of R/C columns and beams using fiber discretization of cross-sections.

#### *2.2. Simulation of Shear Failure of the Column Web*

Shear failure of an R/C element web develops when the transverse reinforcement cannot provide adequate supporting shear resistance to displacement reversals beyond flexural yielding. In a third-tier seismic evaluation of existing R/C buildings, simulation of shear failure of the column web is essential, as this mechanism is linked to brittle member failure that can compromise the load-carrying capacity of columns and potentially lead to the collapse of the building.

The best approach to simulate the brittle response of R/C columns to shear failure of the web is to use a non-linear, zero-length element (the two end element nodes are distinct from each other but placed at the same location) at mid-height of the column's clear (deformable) length, *Hcl* (see Figure 1). Element response in each section direction is defined by the multilinear Moment–Rotation (*M*–*θ*) relationship illustrated in Figure 3, where *Mv* = *Vv* · (*Hcl*/2) is the bending moment associated with the shear strength *Vv*, of the column web in the examined direction. This *Vv* is calculated according to the RSA system from Equation (A4) in the Appendix A. Coefficient *rv* in Figure 3 is the resistance ratio to shear failure of the column web, *rv* = *Vv*/*Vflex*, where *Vflex* is calculated according to Equation (A3) in the Appendix A. Note that the column normalized axial load appearing in the expressions given in the Appendix A (denoted as *νd*) is obtained from static analysis of the examined R/C building to gravity loading and for the vertical component of the seismic load combination *Gk* + *ψE* · *Qk*, as perEN1998-1 [2].

**Figure 3.** Moment–Rotation (*M*–*θ*) relationship used in simulating the response of R/C columns to shear failure in the web.

#### *2.3. Simulation of Anchorage and Lap-Splice Failure of Longitudinal Reinforcement in Columns*

Failure of anchorage and lap-splice of longitudinal bars limits the force developing in the bars to a value lower than their true axial strength and strain capacity. Both anchorage and lap-splice failures result from insufficient bond strength and are manifested with the formation of a single crack, perpendicular to the axis of the member. For columns, this occurs below the beam-column joint and above the base of the column in cases of anchorage and lap-splice failures, respectively.

In the framework of a third-tier seismic assessment of existing R/C buildings, anchorage and lap-splice failure of longitudinal reinforcement can be simulated with the use of two different zero-length elements, located at the top and the bottom of the clear length of an R/C column, as illustrated in Figure 1. The response of the zero-length elements is defined in each of the two-section directions by the *M*–*θ* trilinear relationships of Figure 4, where *Ma* = *Vv* · (*Hcl*/2), *Mlap* = *Vlap* · (*Hcl*/2). The column shear strengths against anchorage and lap-splice failure of the longitudinal reinforcement, *Va* and *Vlap*, respectively, are calculated using the closed-form expressions given in the Appendix A and their respective resistance ratios, *ra* = *Va*/*Vflex* and *rlap* = *Vlap*/*Vflex*.

**Figure 4.** Moment–Rotation (*M*-*θ*) relationship for simulating (**a**) anchorage and (**b**) lap-splice behavior of longitudinal reinforcement in substandard R/C columns.

#### *2.4. Simulation of Beam-Column Joint Behavior*

Shear failure of beam-column joints in R/C buildings during earthquakes is a pronounced brittle mode of failure that may cause excessive flexibility of the overall frame and a consequent loss of vertical load-carrying capacity [3]. The integrity of R/C beam-column joints is secured through the compressive stress field acting within the joint which enables the concrete to participate in the joint shear action and allows (through the development of high bond stresses) for steep force gradients along with the beam and column primary reinforcements. In R/C buildings designed and constructed under contemporary standards (ASCE/SEI 41-17 [1], EN1998-1 [2], etc.), beam-column joints are dimensioned so as to sustain the development of the flexural strengths of the adjacent frame elements at the joint faces without significant degradation of the bond along with beam and column primary reinforcement. In substandard R/C buildings, the absence of a limited number of stirrups within the beam-column joints does not provide sufficient confinement to support the formation of the diagonal strut mechanism that is essential for force transfer between adjacent members during earthquake excitations.

Simulation of R/C beam-column joint behavior in FE models of existing R/C buildings can be achieved through the use of zero-length elements placed above and below the intersection of the beam and column elements used for simulating the mechanical behavior within the joint (see Figure 1). The joint response in each of the building principal plan dimensions is defined by the multilinear *M*–*θ* relationship of Figure 5. In this figure, *Mj* = *Vj* · (*Hcl*/2) is the bending moment associated with the shear capacity *Vj* of an R/C beam-column joint according to the RSA (see Equations (A11) and (A12) in the Appendix A, for unreinforced and well-reinforced joints, respectively), whereas *rj* (= *Vj/Vflex*) is the resistance ratio to shear failure in the beam-column joints.

**Figure 5.** Moment–Rotation (*M*–*θ*) relationship representing the shear response of R/C beam-column joints in an intermediate floor of a building (the 0.5 factor for the moment is replaced by 1.0 for a roof joint in the building).

#### **3. Example Application of the Proposed Numerical Simulation Procedures**

The accuracy of the present numerical simulation methodology is investigated through the analytical evaluation of the seismic response of the SPEAR test building that was constructed and tested in the European Laboratory of Seismic Assessment (ELSA) at the Joint Research Center (JRC) in Ispra, Italy. This testing was conducted within the framework of the Seismic Performance Assessment and Rehabilitation (SPEAR) European research program (Fardis [42]; Negro et al. [43], Jeong and Elnashai [44]).

#### *3.1. Geometric and Loading Characteristics of the SPEAR Building*

The SPEAR building was a full-scale, three-story, 2 × 2 bay, torsionally sensitive R/C building which is considered representative of the structures that were designed and constructed throughout southern Europe from the 1950s until the mid-1980s (Figure 6). The building was designed for gravity loads alone, in addition to the self-weight of the R/C structural elements, as well as for 0.5 kN/m2 and 2.0 kN/m2 gravity loads on slabs accounting for finishing and live loads, respectively. All stories had an identical plan

configuration with external dimensions of 12.825 m × 10.75 m, comprising eight columns of a 250 mm rectangular cross-section and one strong column of 250 mm × 750 mm cross-section. The columns were connected to beams having 250 mm × 500 mm web cross-sectional dimensions. Slab thickness was 150 mm, while story height in all cases was 3.00 m o.c. The columns had longitudinal reinforcement ∅12 mm smooth bars (see Figure 2), which were lap-spliced over 400 mm at the base for all three levels with a hook formation at the end of the bars. All columns had ∅8 mm perimeter stirrups, spaced at 250 mm o.c. which did not continue in the beam-column joints. Longitudinal reinforcement at both ends of all beams was 4 ∅12 mm bars at the top and 2 ∅12 mm bars at the bottom. Exceptions were: (i) beam B4 with 4 ∅20 mm plus 2 ∅12 mm bars at the top and 3 ∅20 mm bars at the bottom of both ends; (ii) beam B8 that was reinforced with 2 ∅20 mm top bars plus 4 ∅12 mm top bars at the connection with column C4, 4 ∅12 mm bars at the connection with column C7 and 2 ∅12 mm bars at both ends; (iii) beam B10 at the top had 4 ∅20 mm plus 2 ∅12 mm bars at the connection with column C5, 2 ∅20 mm plus 2 ∅12 mm bars at the connection with column C8 and 2 ∅20 mm bars at both ends; and (iv) beam B12 had 3 ∅20 mm plus 2 ∅12 mm bars at the top and 2 ∅20 mm bars at the bottom of both ends. The mean concrete compressive strengths *fcm* obtained from tests on cylindrical core specimen taken from the building after completion of the experiment was found equal to 24.73 MPa, 26.70 MPa, and 25.32 MPa for the first, second, and third story columns, respectively. Finally, uniaxial tensile tests on steel bar coupons yielded stress of reinforcement *fy* that was equal to 479.45 MPa, 474.11 MPa, and 396.87 MPa in the cases of the ∅8 mm, the ∅12 mm and the ∅20 mm bars, respectively.

**Figure 6.** Typical story plan of the SPEAR test building at ELSA-JRC, Ispra, Italy (units in m).

The testing protocol at JRC consisted of a series of simulated ground motions of increasing intensity which were applied to the R/C structure through a pseudo-dynamic procedure. The basic accelerograms used were the two components of the Montenegro 1979 (Herceg Novi) ground motion, sequentially scaled upwards to 0.02 g, 0.15 g, and 0.20 g, labeled as the s10, s11, and s12 pseudo-dynamic tests. These accelerograms were applied in both the *X* and *Y* plan directions and were normalized with respect to the peak ground acceleration (*PGA*), as shown in Figure 7.

**Figure 7.** Time-histories of the two components of ground acceleration used in the testing of the SPEAR building at ELSA-JRC.

#### *3.2. Numerical Simulation and Analysis of the SPEAR Building*

In order to evaluate the seismic response of the SPEAR test building, the structural system was simulated as a 3D-FE model comprising linear and zero-length elements as described in Section 2, using the OpenSees platform [41].

At first, the flexural response of the columns was modeled using two equal-length nonlinear Beam-Column element objects with a longitudinal fiber section discretization along the column clear length *Hcl* (see Figure 1). The reinforcing steel material properties were represented by the uniaxial, bilinear stress-strain relationship with kinematic hardening (Steel01 Material) with an initial elastic modulus equal to 200 GPa and a strain-hardening ratio of 3.3‰ and 5.3‰ in the cases of the ∅12 mm and the ∅20 mm bars, respectively. The inelastic concrete behavior was modeled using the uniaxial Kent-Scott-Park stress-strain envelope with degrading unloading/reloading hysteresis loops and no tensile strength (Concrete01 Material). Specifically, the concrete had an initial tangent modulus of 2 · *fcm*/*εcy* (*εcy* = 0.0022) and an ultimate strength and deformation capacity of *fcu* = 0.2 · *fcm* and *εcu*= 0.0035 according to Park, Priestley, and Gill [45,46]. Details of the fiber discretization of the column cross-sections are depicted in Figure 2.

Next, the modeling of the flexural response of beams was similar to that of columns, using the nonlinear Beam-Column element objects with longitudinal fiber section discretization. The cross-section of beam elements was a T-shape for all beams with effective width equal to *bw* + 2 · *d* (*bw*: beam web width; *d*: beam static height), except for beams {B1, B2, B5, B6, B7, and B8} which had an L-shape cross-section with effective width equal to *bw* + *d*. Beam finite elements spanning areas within the beam-column joints were modeled as rigid zones (see Figure 1).

Finally, the brittle response mechanisms of column failure (shear failure of the column web, of the anchorage, and lap-splice failure of column longitudinal reinforcements) were all simulated using Zero-Length element objects in the locations shown in Figure 1. Mechanical properties of the Zero-Length elements were defined according to the discussion in Sections 2.2–2.4, further considering column shear strengths corresponding to the different

response mechanisms as calculated from Equations (A1)–(A6). The normalized average axial load *ν* in the columns that were used in Equations (A1)–(A6) was calculated from a static analysis of the FE building model under the self-weight of the structural elements and the additional gravity loads applied to the SPEAR building during the tests [42–44]. It is noted that the true axial load is variable, fluctuating about an average value due to overturning effects in the ground motion, with maximum values recorded in the columns that are furthest from the center of mass. Table 1 presents the normalized average axial load and the shear strengths of the SPEAR building columns corresponding to the mechanisms considered in the RSA system [30–32], whereas Table 2 presents the parameters defining the multilinear *M*–*θ* relationships used for simulating the responses of the zero-length elements parallel to the two principal plan directions.

Regarding the building mass needed for conducting a dynamic analysis, the numerical simulations used lumped masses defined at the centroid of each structural element (i.e., the slabs, the clear length of columns and beams, and the beam-column joints). Lumped masses were also added at individual nodes which were inserted at locations on the building floors where water tanks were placed during the tests for simulating the operational loads. For more information on the location of these tanks in the SPEAR building see References [42–44].

Diaphragm action at the floor levels was simulated by slaving the translational and rotational degrees of freedom acting parallel to the floor plane of all nodes located at the mid thickness of the building's slabs. This was done by employing the rigid-Diaphragm multi-point constraint object at each floor level, in order to connect all intersected column nodes, all nodes located at the centroid of the corresponding R/C slabs, and all nodes simulating the aforementioned water tanks representing the SPEAR building operational loads. Furthermore, gravity loads associated with the SPEAR building and used for static analysis of the FE model were simulated as uniformly distributed loads along with the frame elements of the model.

The first step was to investigate the accuracy of the numerical simulation procedures proposed in this research. To this end, the SPEAR building FE model was subjected to timehistory dynamic analyses for the cases of the s10 (*PGA* = 0.02 g), the s11 (*PGA* = 0.15 g), and the s12 (*PGA* = 0.20 g) earthquake records. Damping in the FE model during the dynamic analyses was represented by Rayleigh damping coefficients using the principal translational mode with the greatest period of vibration and the first torsional period of vibration in the *X*–*Y* plane. These were computed from a modal analysis of the FE building model, to which the standard 5% viscous damping was applied.

#### *3.3. Evaluation of the Analyses Results*

In order to evaluate the accuracy of the results obtained from a third-tier seismic assessment of substandard R/C buildings simulated according to the proposed modeling procedures, the computed response of the FE building model of the SPEAR building is compared to the actual response recorded at ELSA–JRC during the testing. To demonstrate the significance of simulating the brittle mechanisms of failure in substandard R/C buildings, these comparisons considered modifications in the structural response as follows: (i) a first FE building model of the SPEAR building accounted only for the inelastic flexural response of the R/C structural elements, while (ii) in a second FE building model, zero-length elements simulating mechanism {M2–M5} along column lines according to Section 2 were also included.

Figures 8–13 present a comparison between the computed time histories of the horizontal displacements along with the *X* and *Y* plan directions, *UX* and *UY*, versus those recorded at ELSA–JRC during the s10, s11, and s12 pseudo-dynamic tests (black lines). Specifically, the numerical responses obtained from the time-history dynamic analyses of the FE building model using the proposed simulation procedure (dark grey lines) and those of the FE building model, accounting only for an inelastic flexural response, are plotted concurrently (light gray lines). These displacements correspond to the vibration of the center of mass

(*CM*) of the three floors of the SPEAR building. Note that the overestimation of flexural stiffness leads to very low estimates of displacements and a stiffer overall structure, i.e., a lower natural period leading to unconservative results for the displacement demands and the anticipated damage. In the s11 earthquake case, the displacement demands estimated from analysis of the FE building model accounting only for inelastic flexural response are downgraded by 24% to 58% in the *X* plan direction and by 16% to 37% in the *Y* plan direction as compared to the response of the test building. In the case of the s12 earthquake case, the estimated displacement demands according to the analysis results of the same FE building model are downgraded by 32% to 61% and by 51% to 57% in the *X* and *Y* plan directions, respectively, as compared to the actual building response. On the other hand, the addition of the zero-length elements seem to have lengthened the natural period, leading to convergence of the displacement response and damage as compared to the response of the test building. Decisions made based on these two bounding estimates respectively would lead to little or no retrofit in the former case, and excessive and invasive retrofit in the latter case. It is also noted that as the intensity of shaking and damage accumulation from previous shaking increases in the structure, the waveforms of the more compliant model where all mechanism formations have been activated converge to the experimental response. This primarily occurs during the duration of the response pulses, which suggests convergence in the fundamental period computation.

**Table 1.** Normalized average axial load and shear strengths of the SPEAR building columns calculated according to the RSA system [30–32].

**Table 2.** Moment-Rotation relationships used in the zero-length elements of the SPEAR FE building model. Note: Symbols (-) indicate that brittle fracture was not considered and (;) separate values between the X and Y directions.

Table 3 summarizes the peak displacement values obtained from the sequence of analyses for the center of mass of the three floors to the different intensity ground motions. Relative lateral drift ratios were obtained by dividing the relative floor displacement values by the clear floor height. Peak values, as well as the time instant of their occurrence, are also given in Table 3.

It is observed that the results of the flexural analysis (Fiber Model), where all the other premature local failure mechanisms were omitted in the model, fail to reproduce the salient characteristics of the response including the intensity of the drift demands by systematically underestimating them. In the s11 case, the analysis results of the fiber model lead to an underestimation of the actual drift demands by 24% in the first and by 69% in the second and third story with regards to the vibration in the *X* plan direction. These numbers respectively are 16%, 40%, and 53% in the first, second, and third stories in reference to the vibrations in the *Y* plan direction. In the s12 case, the drift demands obtained from analysis of the fiber FE model in the first, second, and third stories were underestimated by 32%, 73%, and 75% in the *X* plan direction and by 51%, 63%, and 64% in the *Y* plan direction as compared to the drift demands recorded during the testing of the SPEAR building. On the

contrary, the complete model where local mechanism formation was enabled showed an increased rate of convergence with the experimental values as the intensity of the shaking and damage accumulation increased. In the s11 earthquake case, the results obtained from analysis of the complete model deviate by {+17%; −5%; +9%} in the *X* plan direction and by {+37%; +25%; +43%} in the *Y* plan direction with regards to the drift demands recorded at the first, the second, and the third story of the SPEAR building. Furthermore, in the case of the s12 pseudo-dynamic testing, the corresponding deviations of the analytical and experimental results were {−18%; −46%; +27%} in the *X* plan direction and {−43%; −32%; +35%} in the *Y* plan direction.

**Figure 8.** Comparison of the horizontal displacements in the *X*-plan direction measured at the SPEAR building during the s10 earthquake case and the corresponding response estimated from a dynamic analysis using two different FE building models.

**Figure 9.** Comparison of the horizontal displacements in the *Y*-plan direction measured at the SPEAR building during the s10 earthquake case and the corresponding response estimated from a dynamic analysis using two different FE building models.

In reference to the instant of maximum horizontal translation of the centers of mass of the three floors, the analysis results converged to the experimental values in the longitudinal (*X*) direction (both in terms of the instant of time of occurrence as well as in terms of the magnitude). There was, however, a deviation in the transverse (*Y*) direction, particularly in the higher intensity earthquake motions s11 and s12. This deviation in the convergence of the estimated responses of both FE building models with the responses recorded at the SPEAR building in the *Y* direction is mainly due to the degree of accuracy prescribed in simulating the flexural response of the columns of the SPEAR building through fiber discretization. A discretization of the core of the building columns that is finer than the one used in the two FE building models (Figure 2), combined with the use of more advanced stress-strain relationships from the OpenSees library for simulating the inelastic response of steel and concrete materials, would most probably result in a better convergence between the analytically and experimentally obtained responses. However, such fine-tuning of the flexural behavior of the FE building models would have not affected the degree of influence that the simulated brittle mechanisms of response along the column lines of the SPEAR building have on the overall seismic response of the FE building models.

**Figure 11.** Comparison of the horizontal displacements in the *Y*-plan direction measured at the SPEAR building during the s11 earthquake case and the corresponding response estimated from a dynamic analysis using two different FE building models.

Finally, with regards to the additional computational cost incurred from implementing the present analytical-numerical methodology for simulating the brittle mechanisms of response along the column lines of sub-standard R/C buildings, the conclusion is as follows: No significant difference was observed in terms of convergence rate and time requirements by either simulating the brittle mechanisms of failure in the FE building models according to the proposed methodology or by simulating only the nonlinear flexural response of the same buildings.

**Figure 12.** Comparison of the horizontal displacements in the *X*-plan direction measured at the SPEAR building during the s12 earthquake case and the corresponding response estimated from a dynamic analysis using two different FE building models.

**Figure 13.** Comparison of the horizontal displacements in the *Y*-plan direction measured at the SPEAR building during the s12 earthquake case and the corresponding responses estimated from a dynamic analysis using two different FE building models.

**Table 3.** Peak floor displacements and inter-story drifts in the two plan directions of the SPEAR building were obtained from the test and the analyses (ID = Inter-story drift; FD = Floor Displacement).

#### **4. Conclusions**

This work investigates the validity of a proposed methodology for the performance assessment of older, substandard moment-resisting R/C frame buildings following an earthquake event. The classification 'sub-standard' comes from the fact that R/C construction prior to the mid-1980s did not benefit from the findings of subsequent research regarding pertinent seismic detailing of R/C structures which has now filtered into contemporary building codes. The proposed methodology is based on the earlier work by two of the authors leading to the development of a procedure known as Rapid Seismic Assessment (RSA) which hinges on whether or not the local drift demands can be tolerated without failure along the load resistance path. Guidelines are provided here for modeling all brittle localized strength mechanisms that may occur in the load path of frame structures under lateral loading which is manifested in substandard R/C buildings subjected to seismic loads. An application example using test data from a well-documented experimental program helps to clarify the importance of these mechanisms in a realistic evaluation of the seismic response for this category of buildings.

**Author Contributions:** Conceptualization, S.I.P., S.J.P. and G.D.M.; methodology, S.I.P. and S.J.P.; software, S.I.P.; validation, S.I.P.; formal analysis, S.I.P., S.J.P. and G.D.M.; investigation, S.J.P.; resources, G.D.M.; data curation, S.I.P.; writing—original draft preparation, S.I.P.; writing—review and editing, G.D.M. and S.J.P.; critical review, G.D.M.; project administration, G.D.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data generated by the FE numerical simulations of the SPEAR testing building carried out for the purposes of this work are available in the form of text files by directly contacting the first author (SIP).

**Acknowledgments:** The Civil Engineering department of Aristotle University is acknowledged for providing a post-doctoral appointment to the first author (SIP) for the period 2017–2021.

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

#### **Appendix A**

The individual strength terms of an R/C column for an RSA are calculated using closed form expressions which lend themselves to easy spreadsheet calculations. These expressions represent the current state-of-the-art information in the field and may be subject to revisions as the knowledge base in R/C leads to improved models for the individual resistance mechanisms.

The first step towards the calculation of the individual strength terms of an R/C column is the determination of the normalized depth of the compression zone, *ξ* = *x*/*d*, at the ultimate limit state, which is estimated for a specified axial load ratio *ν* = *N*/(*Ac* · *fc*) from the following interpolations:

$$\text{if } \upsilon\_{\text{bal}} < \upsilon < \upsilon\_{\text{max}}, \,\, \mathfrak{J} = \mathfrak{J}\_{\text{bal},u} + \,\, (1 - \mathfrak{J}\_{\text{bal},u}) \cdot \frac{\upsilon - \upsilon\_{\text{bal}}}{\upsilon\_{\text{max}} - \upsilon\_{\text{bal}}} \tag{A1}$$

$$\text{if } \upsilon\_{\min} < \upsilon \le \upsilon\_{\text{bal}}, \,\, \xi = \delta\_2 + \, (\xi\_{\text{bal},u} - \delta\_2) \cdot \frac{\upsilon - \upsilon\_{\min}}{\upsilon\_{\text{bal}} - \upsilon\_{\min}} \tag{A2}$$

The values of *νmin*, *νbal*, and *νmax* correspond to characteristic values of the depth of compression zone *x*, for *εcu* = 0.005, and are given as follows:

$$\text{for } \mathbf{x} = d\_2 \Rightarrow \xi\_2 = \delta\_2, \ \frac{v\_{\min}}{A\_\varepsilon \cdot f\_\varepsilon} = 0.72 \cdot \delta\_2 - \frac{f\_y}{(1 - a) \cdot f\_\varepsilon} \cdot \left[\rho\_{s1} + \rho\_v \cdot (1 - 2 \cdot \delta\_2)\right] \tag{A3}$$

$$\text{for } \mathbf{x} = \mathbf{x}\_{\text{ball}} \Rightarrow \mathbf{j}\_{\text{ball},u} = 0.64, \; \frac{v\_{\text{ball}}}{A\_{\text{c}} \cdot f\_{\text{c}}} = (\rho\_{\text{s2}} - \rho\_{\text{s1}}) \cdot \frac{f\_{\text{y}}}{f\_{\text{c}}} + 0.462 + 0.275 \cdot \rho\_{\text{v}} \cdot \frac{f\_{\text{y}}}{f\_{\text{c}}} \tag{A4}$$

$$\text{for } \mathbf{x} = d \Rightarrow \zeta\_d = 1, \,\frac{v\_{\text{max}}}{A\_c \cdot f\_c} = 0.85^2 + \frac{f\_y}{f\_c} \cdot (\rho\_{s2} + 0.8 \cdot \rho\_v) \tag{A5}$$

With the interpolated value of *ξ*, the following strength terms are now determined: Flexural shear demand:

$$V\_{flex} = \left[\rho\_{\ell,tot} \cdot \frac{f\_y}{f\_c} \cdot (1 - 0.4 \cdot \xi) \right.\\ \left. + \left. v \cdot \left(\frac{h}{d} - 0.8 \cdot \xi\right) \right] \cdot \frac{b \cdot d^2 \cdot f\_c}{H\_{cl}} \tag{A6}$$

Exhaustion of shear strength:

$$\text{If } v < 0.10: V\_v = A\_{tr} \cdot f\_{st} \cdot \frac{d \cdot (1 - 0.4 \cdot \xi)}{s} \cdot \cot \theta\_v \tag{A7}$$

$$\text{If } v \ge 0.10: V\_v = v \cdot b \cdot d \cdot f\_c \cdot \tan \alpha + A\_{tr} \cdot f\_{st} \cdot \frac{d \cdot (1 - 0.4 \cdot \frac{\pi}{b})}{s} \cdot \cot \theta\_v \tag{A8}$$

Anchorage failure of longitudinal reinforcement:

$$V\_a = \left[ \rho\_{\ell, \text{tot}} \cdot \frac{\min \left\{ \begin{array}{ll} \frac{4 \cdot L\_a \cdot f\_b}{D\_b} + a\_{\text{hol}} \cdot 50 \cdot f\_b & ; & f\_y \\ \end{array} \right\}}{f\_\varepsilon} \cdot (1 - 0.4 \cdot \xi) + v \cdot \left( \frac{h}{d} - 0.8 \cdot \xi \right) \right] \cdot \frac{b \cdot d^2 \cdot f\_\varepsilon}{H\_{\varepsilon l}} \tag{A9}$$

#### Lap failure of longitudinal reinforcement:

$$V\_{lap} = \frac{\begin{bmatrix} \min\left\{ & \left( \mu\_{fr} \cdot L\_{lap} \cdot \left[ \frac{A\_{lr}}{s} \cdot f\_{rl} + a\_{b} \cdot (b - N\_{b} \cdot D\_{b}) \cdot f\_{l} \right] + \right.\\ & + a\_{hok} \cdot 50 \cdot N\_{b} \cdot A\_{b} \cdot f\_{b} \end{bmatrix} + \\\ \begin{array}{l} \text{;} \quad N\_{b} \cdot A\_{b} \cdot f\_{y} \end{array} \right\} \cdot d \cdot (1 - 0.4 \cdot \xi) + \\\ \begin{array}{l} \text{;} \quad N\_{b} \cdot \mu\_{r} \cdot L\_{b} \cdot f\_{r} \end{array} \left( \begin{array}{l} \text{;} \quad (1 - 0.4 \cdot \xi) + \\ \text{;} \quad (1 - 0.4 \cdot \xi) \end{array} \right) \end{array} \tag{A10}$$

Shear capacity of joints:

$$\text{Unreinfored or lightly reinforcement joints}:\\V\_{\circ} = \gamma\_{\circ} \cdot 0.5 \cdot \sqrt{f\_c} \cdot \sqrt{1 + \frac{v\_{\circ} \cdot f\_c}{0.5 \cdot \sqrt{f\_c}}} \cdot \frac{b\_{\circ} \cdot d \cdot d\_{bam}}{H\_{cl}} \tag{A11}$$

Well reinforced joints :*Vj* = *γj*·0.5· *fc*· \$ 1 + *vj*· *fc* 0.5· *fc* · *bj*·*d*·*dbeam Hcl* · \$ 1 + *ρj*,*horiz*· *fst ft*

In the above expressions, the following terms appear:

• *ρ*-*,tot* = *As,tot*/(*b* · *d)* is the total longitudinal reinforcement ratio of a column with external dimensions *h* × *b*,

(A12)

#### **References**


**1. Introduction**

Considering that buildings account for 40% of the primary energy consumption (EC) in the European Union [1], reducing the EC of buildings has become a necessity. The European Union, considering the increasing urbanization and climate change trends, defined the objective to reduce EC by 32.5% until 2030, from the baseline year of 2007, as a key priority in the EU's strategy and Green deal [2] to increase EE and decrease the energy performance (EP) of existing buildings [2–4]. This goal is aligned with the United Nations' seventh Sustainable Development Goal (SDG): "Ensure access to affordable, reliable, sustainable and modern energy for all" [5].

Buildings are responsible for the second largest portion of the final EC in the European Union [1,6,7], with households on 26.3% and public buildings on 28.8%, just after the transport sector (with 30.9%). Their refurbishment and energy-efficient retrofitting is a priority for many countries to reduce EC and decrease the EP of existing buildings as part of the EU Green deal [2,8]. In the current state of the art, data science and machine learning are available to analyze, predict and improve energy efficiency (EE) in buildings in meaningful ways. Such computer science approaches can be used to forecast and minimize energy consumption, design energy-efficient buildings, define strategies for mitigating

**Citation:** Anastasiadou, M.; Santos, V.; Dias, M.S. Machine Learning Techniques Focusing on the Energy Performance of Buildings: A Dimensions and Methods Analysis. *Buildings* **2022**, *12*, 28. https:// doi.org/10.3390/buildings12010028

Academic Editors: Roberto Alonso González-Lezcano, Francesco Nocera and Rosa Giuseppina Caponetto

Received: 3 December 2021 Accepted: 23 December 2021 Published: 31 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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/).

impacts on the environment and climate, and predict and propose useful and cost-effective retrofit measures to increase the EE of buildings to provide a comfortable indoor living environment [9,10]. By measuring, monitoring, and improving the EE in buildings, we can reduce the amount of energy consumed while maintaining or even enhancing the quality of services provided by those buildings, a "double the global rate of improvement in EE"—SDG7.8 [5,11].

This paper proposes a conceptual and theoretical framework applicable in the analysis of literature papers that tackle the problem of the EPB with machine learning or statistical methods. In more detail, this work aims to add to the improvement of the EP of existing buildings, one of the core goals of the EU Green deal [2], by identifying and analyzing the latest and most appropriate machine learning or statistical techniques, as a baseline for future research by building a conceptual and theoretical framework based on a systematic literature review using PRISMA guidelines. Our approach helps the researcher find which methods are most used and more appropriate for analyzing the EP of different types of buildings.

Moreover, our framework addresses the dimensions and factors extracted from available data sources such as building energy certification data, EC data, wheatear and climate data, and others. Our proposal will help the community foster innovation on enhanced buildings' energy performance (EP) and predict energy-efficient retrofit measures (EERM).

In this context, our study adopts a well-established systematic literature review (SLR) method, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA [12]), to identify the most relevant literature contributions to the energy performance of buildings (EPB) and the prediction of EERM, using machine learning (ML) or statistical methods. Furthermore, we used a visualization bibliometric tool, VOSviewer [13], to find the most used terms in the literature related to the EPB with machine learning or statistical methods.

Some literature review papers tackle similar problems, mostly related to EC [14–18]. The main innovation and novelty of the study is how we present and group the data, focusing on the building types and addressing the dimensions and methods for each type. We believe that our study will help the community foster innovation on the enhanced EPB and predict energy-efficient retrofit measures. We present and visualize our results using the bibliometric network software tool VOSviewer. This tool allows creating and visualizing bibliometric networks based on text data and keyword co-occurrence, and authors' co-authorship networks of terms. This allows us to visualize and identify the most important terms and authors co-authorship respective relations for quantitative analysis.

Considering the stated intentions of this paper, we raised the following research questions:

The research questions focus on two objectives (1) automatic clustering—classification of the EPC of a building, and (2) prediction of energy-efficient retrofit measures, using ML and EPC data. Additionally, as mentioned, our approach brings a clear contribution to the EU Green deal and SDG7 of the United Nations [5].

Our paper is organized as follows. Section 2 presents the adopted systematic literature review technique (PRISMA) and our overall methodology. Section 3 describes the application of PRISMA and details the collected data from the survey, whereas in Section 4, we present and analyze such results using the visualization and bibliometric tool. Section 5 discusses our findings, aligned with our research questions, while in Section 6, we present our conclusions.

#### **2. Methodology**

The SLR analysis was performed by adopting a well-established systematic literature review and meta-analysis method (PRISMA). In our methodology, we combined this method with data visualization techniques, ending up with 4 main phases: (1) data selection, (2) results and analysis: survey results, categorization and dimensions analysis, visualization and bibliometric analysis, (3) discussion, (4) conclusions [19], as depicted in Figure 1.

**Figure 1.** Methodology.

Phase 1—Data Collection: Following PRISMA guidelines [12], we conducted an evidence-based systematic review to select the best basis for reporting systematic reviews. Our adoption of PRISMA follows the literature trend of using such a method as a basis for reporting systematic reviews, especially evaluations of interventions [12]. The PRISMA guidelines consist of a flow diagram and a checklist. The flow diagram of conducting a PRISMA survey has four phases: identification, screening, eligibility, and inclusion, as depicted in Figure 2. The checklist proposes a pre-defined structure for a survey with different sections. In addition, there are precise guidelines to be followed and described in more detail in Section 3 [12]. As mentioned, we focused our analysis on ML or statistical approaches using the public build, residential, and office buildings.

Phase 2—Results and Analysis: In this phase, we present the analysis of our PRISMA results. We analyze the main journals and conferences, the keyword co-occurrence, and the authors' co-authorship. We present and visualize our results using the bibliometric network software tool VOSviewer. This tool allows creating and visualizing bibliometric networks based on text data, particularly keyword co-occurrence and authors' co-authorship networks of terms. This analysis illustrates the relationships and connections between the network's elements (nodes), corresponding to the most used terms, allowing the identification of networks characteristics, such as node and cluster centrality. VOSviewer calculates the node links and weight, demonstrating each node's importance in the network. This allows us to visualize and detect the most important terms and authors' co-authorship individual relations for quantitative analysis. The size of nodes presents the degree of centrality: the larger the node, the more times it is reported in the text data. The thickness of edges presents the number of times two linked nodes are reported, showing their significance; by default, the networks are allocated from the largest to the smallest [13]. With this approach, we could summarize and critically analyze the most used dimensions, clustering and classification techniques, EP retrofitting prediction techniques, and the most used building types in each study. This method allowed us to find, accurately and efficiently, the best literature modeling practices and techniques for achieving enhanced EP.

Phase 3—Discussion: In this phase, we discuss the previous phases' findings by following the research questions. We specifically address the identified knowledge gaps and our study limitations.

Phase 4—Conclusion: We sum up and present the conclusion of our study.

**Figure 2.** PRISMA Flowchart.


**3. Single user selection criteria**

In this section, we derive user selection criteria depending on the type of actually employed MIMO detector, where a single user is selected to transmit signals to a BS at a time. Suppose that user *k* is chosen, the system model in (1) is simplified as

$$\mathbf{Y}\_k = \mathbf{H}\_k \mathbf{S}\_k + \mathbf{N} \tag{8}$$

For detection method, the ML detector and two suboptimal detectors will be considered: one is the linear detector and the other is the SIC detector. As for the two suboptimal detectors, the LR is applied for better performance [6][7].

#### **3.1. ML detector**

4 Recent Trends in Multiuser MIMO Communications

where the complexity grows exponentially with *MP*.

where **W** is a linear filter that is given by **W** =

For the sake of convenience, we omit the index set K. The ML detection is given by

Alternatively, an estimate of **s** can be obtained by a linear transformation as follows:

corresponds to the zero-forcing (ZF) detector, while the minimum mean square error (MMSE) detector is obtained if *c* = *N*0/*Es*. Here, *Es* is the symbol energy and it is assumed that

To improve the performance of the detector, the LR is performed in the LR-based detection. A complex valued matrix can be converted into a real valued matrix for the LR as in [7]. Alternatively, the LR can be directly performed with a complex valued matrix as in [6], [8]. For convenience, in this chapter, we assume that the LR is performed with complex valued

where **U** is an (complex) integer unimodular matrix and **G** is a matrix whose column vectors

Under the MMSE criteria, the linear filter of LR-based MMSE linear detector is given by

An SIC detector is not a linear detector due to its cancellation operation. In [7], the LR-based SIC detectors are proposed. To generalize the LR-based SIC detector, define the extended

where **U**ex is a complex integer unimodular matrix and **G**ex is a matrix whose column vectors

are nearly orthogonal. If the LR basis is not used, **U**ex = **I** (i.e., **G**ex = **H**ex).

T. The LR basis can be found as

For a given channel matrix **H**, the LR basis can be found as follows:

are nearly orthogonal. The received signal can be rewritten as

**H**H**H** + *c***I**

**s**ˆml = arg min **s**∈S *MP* �**y** − **Hs**�2 , (2)

**s**ˆ = **Wy**, (3)

**H** = **GU**, (4)

**y** = **Hs** + **n** = **Gc** + **n**, (5)

**H**ex = **G**ex**U**ex, (6)

−1 **H**. If *c* = 0, the linear detector

*2.2.1. ML and linear detection*

**E**

matrices.

**W** =

**G**H**G** + *N*0

*2.2.2. SIC detection*

*Es* **U**H**U**

channel matrix as **H**ex = [**H**T √*c***I**]

−1 **G**H.

**ss**H = *Es***I**.

Assuming that user *k* is selected, we omit the user index *k* for the sake of simplicity. To derive the selection criterion, we can consider the pairwise error probability (PEP). Suppose that **s**(1) is transmitted, while **s**(2) is erroneously detected. Then, the PEP is given by

$$P\left(\mathbf{s}\_{(1)} \rightarrow \mathbf{s}\_{(2)}\right) = \Pr\left(\left\|\mathbf{y} - \mathbf{H}\mathbf{s}\_{(2)}\right\|^2 \leq \left\|\mathbf{y} - \mathbf{H}\mathbf{s}\_{(1)}\right\|^2\right)$$

$$= \mathcal{Q}\left(\sqrt{\frac{\left\|\mathbf{H}\mathbf{A}\right\|}{2N\_0}}\right). \tag{9}$$

where Q(*x*) = � ∞ *x* √ 1 2*π ez*2/2d*z* and **∆** = **s**(1) − **s**(2). Then, the following upper bound can be obtained as

$$P\left(\mathbf{s}\_{(1)} \to \mathbf{s}\_{(2)}\right) \le \mathcal{Q}\left(\sqrt{\frac{\|\mathbf{H}\bar{\mathbf{d}}\|^2}{2\mathbf{N}\_0}}\right),\tag{10}$$

where

$$\bar{\mathbf{d}} = \arg\min\_{\mathbf{d}\in\mathcal{D}, \mathbf{d}\neq\mathbf{0}} ||\mathbf{H}\mathbf{d}||^2. \tag{11}$$

10.5772/57128

, (16)

http://dx.doi.org/10.5772/57130

, (17)

*p*,*p* denote the (*p*, *p*)th element of **R**

. (18)

*λ*min(**H**H**H**).

165

because Q(·) is a decreasing function and **∆**H(**H**H**H**)−1**∆** ≤ *λ*max(**H**H**H**)−1�**∆**�2 = �**∆**�2

It is important to note that this ME criterion is valid for the LR-based linear detectors [6], [7].

*λ*min �

where **G***k* is the reduced basis from **H***k*. This ME criterion is the same as that in (14) except

As the LR is performed, the column vectors of **G**ex would be nearly orthogonal. In other words, the upper off-diagonal elements of **R** would be small. Thus the SIC detection performance would mainly depend on the diagonal elements of **R**. For convenience, let

from the *k*th user's channel **H***k*. Then, ignoring the interference terms (as they are canceled when the detection of the lower layers is successfully carried out with no error), the SNR of

> � min *p* � � � *r* (*k*) *p*,*p* � � � �

The MD criterion is also closely related to the minimum error probability criterion when the

Let *np* denote the *p*th element of **n**. Then, the LR-based SIC detection at the *P*th layer does

**G**H *k* **G***k* �

**G**H**G**�

2*N*0

(*k*)

*N*0 . From this, the selection criterion can be given by

**x** = **Rc** + **n**. (19)

4 . Thus, the LR-based SIC detection would have no

4 , for all *p*. The probability of no error can be lower

�**∆U**�2

. From (16), the selection criterion becomes

Lattice Reduction-Based User Selection in Multiuser MIMO Systems

Therefore, the ME criterion in (14) can be used for the user selection criterion.

� ≤ Q � *λ*min �

�

*k*∗ = arg max*k*

**s**(1) − **s**(2)

Let **c**(*i*) = **Us**(*i*), *i* = 1, 2. Then, from (15), the PEP is bounded as

**s**(1) → **s**(2)

�

that the channel matrix **H***k* is replaced by its reduced one **G***k*.

*c* = 0 (this is the case when *N*0 → 0 or high SNR). Let *r*

*p* = |*r* (*k*) *p*,*p* | 2

SNR is high. For convenience, let **x** = **Q**H**y**. Then, (18) is rewritten as

2 < |*rP*,*P*| 2

2 < |*rp*,*p* | 2

*k*∗ = arg max*k*

This selection criterion is referred to as the max-min diagonal term (MD) criterion.

*P* �

where **∆U** = **c**(1) − **c**(2) = **U**

**3.3. SIC detectors**

not have error if |*nP*|

|*rP*,*P*| < 1

error across all the layers if |*np*|

2 or |*nP*|

the *p*th layer of **H***k* becomes *γ*(*k*)

Here, D = � **d** = **s** − **s**′ � � � **s**, **s**′ ∈ S*P* � ⊂ **Z***P* + *j***Z***P*. For convenience, denote by *S*(**H**) the length of the shortest non-zero vector of the lattice generated by **H**. Then, we can see that *S*(**H**) = �**Hd**¯ �. From (10), if the ML detector is employed, the user selection criterion to minimize the error probability becomes

$$k^\* = \arg\max\_k S(\mathbf{H}\_k). \tag{12}$$

Throughout this chapter, the user selection criterion in (12) is referred to as the max-min distance (MDist) criterion as *S*(**H**) is the minimum distance of the lattice generated by **H**.

The problem to find a non-zero shortest vector in a lattice is called the shortest vector problem (SVP) and known to be NP-hard. For an approximation, the LLL algorithm in [4], which has a polynomial time complexity, can be used.

Another approximation can be considered by relaxing the constraint on **∆**. We have

$$\|\|\mathbf{H}\Delta\|\|^2 = \Delta^\mathbf{H}\mathbf{H}^\mathbf{H}\mathbf{H}\Delta \ge \|\|\Delta\|^2 \lambda\_{\text{min}}\left(\mathbf{H}^\mathbf{H}\mathbf{H}\right),\tag{13}$$

where *λ*min(**A**) stands for the minimum eigenvalue of **A**. This shows that the selection criterion can be based on the minimum eigenvalue of the channel matrix, i.e.,

$$k^\* = \arg\max\_k \lambda\_{\min} \left( \mathbf{H}\_k^H \mathbf{H}\_k \right). \tag{14}$$

Thus, each user can feed back its minimum eigenvalue of the channel matrix and the user who has the maximum *λ*min � **H**H *k* **H***k* � can be selected to access the channel. This selection criterion is referred to as the max-min eigenvalue (ME) criterion throughout this chapter.

#### **3.2. Linear detectors**

As the SNR increases, we have *c* → 0 (in this case, the MMSE detector becomes the ZF detector) and the PEP has the following upper bound:

$$\begin{split}P\left(\mathbf{s}\_{(1)}\rightarrow\mathbf{s}\_{(2)}\right) &= \mathcal{Q}\left(\frac{\|\mathbf{A}\|^2}{\sqrt{2N\_0\mathbf{A}^\mathbf{H}(\mathbf{H}^\mathbf{H}\mathbf{H})^{-1}\mathbf{A}}}\right) \\ &\leq \mathcal{Q}\left(\sqrt{\frac{\lambda\_{\text{min}}(\mathbf{H}^\mathbf{H}\mathbf{H})}{2N\_0}\|\mathbf{A}\|^2}\right),\end{split}\tag{15}$$

because Q(·) is a decreasing function and **∆**H(**H**H**H**)−1**∆** ≤ *λ*max(**H**H**H**)−1�**∆**�2 = �**∆**�2 *λ*min(**H**H**H**). Therefore, the ME criterion in (14) can be used for the user selection criterion.

It is important to note that this ME criterion is valid for the LR-based linear detectors [6], [7]. Let **c**(*i*) = **Us**(*i*), *i* = 1, 2. Then, from (15), the PEP is bounded as

$$P\left(\mathbf{s}\_{(1)} \to \mathbf{s}\_{(2)}\right) \le \mathcal{Q}\left(\sqrt{\frac{\lambda\_{\text{min}}\left(\mathbf{G}^{\text{H}}\mathbf{G}\right) \|\mathbf{A}\_{\text{U}}\|^2}{2N\_0}}\right) \tag{16}$$

where **∆U** = **c**(1) − **c**(2) = **U** � **s**(1) − **s**(2) � . From (16), the selection criterion becomes

$$k^\* = \arg\max\_k \lambda\_{\min} \left( \mathbf{G}\_k^H \mathbf{G}\_k \right),\tag{17}$$

where **G***k* is the reduced basis from **H***k*. This ME criterion is the same as that in (14) except that the channel matrix **H***k* is replaced by its reduced one **G***k*.

#### **3.3. SIC detectors**

6 Recent Trends in Multiuser MIMO Communications

**d**¯ = arg min **d**∈D,**d**�=**0**

*k*∗ = arg max*k*

Another approximation can be considered by relaxing the constraint on **∆**. We have

�**H∆**�2 = **∆**H**H**H**H∆** ≥ �**∆**�2*λ*min

criterion can be based on the minimum eigenvalue of the channel matrix, i.e.,

*k*∗ = arg max*k*

� **H**H *k* **H***k*

detector) and the PEP has the following upper bound:

**s**(1) → **s**(2)

� = Q �

> ≤ Q �

*P* �

of the shortest non-zero vector of the lattice generated by **H**. Then, we can see that *S*(**H**) = �**Hd**¯ �. From (10), if the ML detector is employed, the user selection criterion to minimize the

Throughout this chapter, the user selection criterion in (12) is referred to as the max-min distance (MDist) criterion as *S*(**H**) is the minimum distance of the lattice generated by **H**.

The problem to find a non-zero shortest vector in a lattice is called the shortest vector problem (SVP) and known to be NP-hard. For an approximation, the LLL algorithm in [4], which has

where *λ*min(**A**) stands for the minimum eigenvalue of **A**. This shows that the selection

*λ*min � **H**H *k* **H***k* �

Thus, each user can feed back its minimum eigenvalue of the channel matrix and the user

As the SNR increases, we have *c* → 0 (in this case, the MMSE detector becomes the ZF

�**∆**�2 �2*N*0**∆**H(**H**H**H**)−1**∆**

> *λ*min(**H**H**H**) 2*N*0

criterion is referred to as the max-min eigenvalue (ME) criterion throughout this chapter.

�**Hd**�2. (11)

*S*(**H***k*). (12)

, (13)

. (14)

, (15)

⊂ **Z***P* + *j***Z***P*. For convenience, denote by *S*(**H**) the length

� **H**H**H** �

� can be selected to access the channel. This selection

�

�**∆**�2

where

Here, D =

�

error probability becomes

who has the maximum *λ*min

**3.2. Linear detectors**

**d** = **s** − **s**′

� � �

a polynomial time complexity, can be used.

**s**, **s**′ ∈ S*P*

�

As the LR is performed, the column vectors of **G**ex would be nearly orthogonal. In other words, the upper off-diagonal elements of **R** would be small. Thus the SIC detection performance would mainly depend on the diagonal elements of **R**. For convenience, let *c* = 0 (this is the case when *N*0 → 0 or high SNR). Let *r* (*k*) *p*,*p* denote the (*p*, *p*)th element of **R** from the *k*th user's channel **H***k*. Then, ignoring the interference terms (as they are canceled when the detection of the lower layers is successfully carried out with no error), the SNR of the *p*th layer of **H***k* becomes *γ*(*k*) *p* = |*r* (*k*) *p*,*p* | 2 *N*0 . From this, the selection criterion can be given by

$$k^\* = \arg\max\_k \left\{ \min\_p \left| r\_{p,p}^{(k)} \right| \right\}. \tag{18}$$

This selection criterion is referred to as the max-min diagonal term (MD) criterion.

The MD criterion is also closely related to the minimum error probability criterion when the SNR is high. For convenience, let **x** = **Q**H**y**. Then, (18) is rewritten as

$$\mathbf{x} = \mathbf{R}\mathbf{c} + \mathbf{n}.\tag{19}$$

Let *np* denote the *p*th element of **n**. Then, the LR-based SIC detection at the *P*th layer does not have error if |*nP*| |*rP*,*P*| < 1 2 or |*nP*| 2 < |*rP*,*P*| 2 4 . Thus, the LR-based SIC detection would have no error across all the layers if |*np*| 2 < |*rp*,*p* | 2 4 , for all *p*. The probability of no error can be lower bounded as

$$\Pr(\text{no error}) \ge \Pr\left( |n\_p|^2 < \frac{|r\_{p,1}|^2}{4}, \forall p \right)$$

$$= \prod\_{p=1}^{P} \Pr\left( |n\_p|^2 < \frac{|r\_{p,p}|^2}{4} \right). \tag{20}$$

10.5772/57128

167

http://dx.doi.org/10.5772/57130

Lattice Reduction-Based User Selection in Multiuser MIMO Systems

(24)

. (25)

*i*=0 (*K* − *i*) possible user index sets.

, (26)

**4.2. LR-based MMSE and MMSE-SIC selection criteria**

compared to *P* in the case of *M* = 1.

can be extended to the case with *M* > 1 as follows:

In this subsection, the user selection criteria with LR-based detectors in Section 3 are extended to the case of *M* > 1, where the number of transmit layers are extended to *MP*,

The MD criterion derived in Section 3, with *M* = 1 for the LR-based MMSE-SIC detection,

 min *q r* (K) *q*,*q*

*λ*min

The user selection based on (22), (23), (24), and (25) is called the combinatorial user selection,

The computational complexity of the user selection under the criteria derived in Section 4 grows rapidly with *M* or *K* as they are all combinatorial optimization problems. Thus, it is desirable to derive low complexity approaches for the user selection. In this section, we propose low complexity greedy approaches for the user selection. Note that we focus on the greedy user selection with a LR-based MIMO detector only as its performance is comparable to that of the ML detector and, more importantly, we can derive a computationally efficient

The user selection approaches in Section 4 have the complexity that becomes prohibitively

For each user index set, an LR of an *N* × *MP* complex channel matrix is to be performed. For example, when *K* = 10, *M* = *N* = 4 and *P* = 1, 10 × 9 × 8 × 7 = 5040 LRs of 4 × 4

To reduce the computational complexity in the user selection, we consider a greedy approach when a LR-based MIMO detector is employed. The resulting approach is called the LR-based greedy (LRG) user selection, which is of course suboptimal. The LRG user selection

1. Let *m* = 1 and K¯ = {1, . . . , *K*}. In order to select the first user, we can use any criterion.

**G**H *k* **G***k*

*k*(1) = arg max *k*∈K¯ *λ*min

**G**H K**G**K

KMD = arg max K

and the ME criterion for the LR-based MMSE detection can also be modified as

KME = arg max K

because the users have to be selected by combinatorial (or exhaustive) search.

**5. LR-based greedy user selection using an updating method**

LR updating method in conjunction with greedy user selection.

high as *M* or *K* increases, because there are *U* = ∏*M*−1

complex-valued channel matrices should be carried out.

For example, if the ME criterion is used, we have

**5.1. LR-based greedy user selection**

algorithm is summarized as follows:

Since |*np*| 2 is a chi-square random variable with 2 degrees of freedom (or an exponential random variable), we have Pr |*np*| 2 < |*rp*,*p* | 2 4 = 1 − exp −|*rp*,*p* | 2 4*N*0 . Thus, from (20), the probability of error can be given by

$$\Pr(\text{error}) \le 1 - \prod\_{p=1}^{Q} \left( 1 - \exp\left(\frac{|r\_{p,p}|^2}{4N\_0}\right) \right)$$

$$\simeq \exp\left(-\min\_p \frac{|r\_{p,p}|^2}{4N\_0}\right) \text{ as } N\_0 \to 0. \tag{21}$$

Therefore, to minimize the probability of error, the user who has the maximum min*p* |*rp*,*p*| can be selected.


**3.2 The properties and applications of BNNSs**

hBN has attracted many attentions due to its low density, high thermal conductivity, electrical insulation, high resistance to oxidation, low chemical efficiency, and low refractive index. BNNSs also inherit these properties, and in addition, they also have special properties due to high surface area.

### *3.2.1 Optical properties of BNNSs*

BNNSs have not any absorption in the visible region but have absorption spectroscopy in the ultraviolet region [62]. Its commercial powders are white and its single crystal is transparent. Thin films obtained from chemical exfoliation or CVD also have high transparency [39, 40]. BNNS dispersion is often transparent at low concentrations and shows the Tyndall effect (the path of visible light inside the dispersion with laser light); at higher concentrations, the laser light is diffracted; and the dispersion is seen milky because of the lateral dimensions of nanosheets that are larger than the wavelength of laser light. Due to diffraction, there is any peak in the visible area. The measured extinction coefficient for absorption and diffraction of nanosheets is much smaller than that of graphene. The smaller lateral dimensions and more defects often influence on the optical bandgap, which is attributed to the absorption of the small distribution bandgap at the fermi surfaces and is produced due to the presence of defects [57]. However, hBN has two peaks in the 4 and 5.7 eVs: the first one related to the bandgap energy of BN, as a direct-gap semiconductor, and the latter is related to impurities and vacancy defects [63]. The lateral dimensions and number of layers affect the bandgap energy of nanosheets. For example, Rafiei-Sarmazdeh et al. [58] reported the absorption spectra of as-obtained BNNSs (2-nm-thick layer) at 204 nm (6.08 eV) that are related to the intrinsic excitement of BN structure and which is consistent with the reported results in other previous literatures [64, 65] and is also close to the bandgap energy predicted by theoretical calculus (6.0 eV) [66].

#### *3.2.2 Thermal conductivity*

The thermal conductivity for BNNSs is in range 300–2000 W/mK, which is comparable to graphene (1500–2500 W/mK). The difference in the conductivity may be due to the soft phonon modes of carbon sheets and the mass difference between boron and nitrogen [67]. Single BN layers have higher conductivity than multilayers, as the number of layer decreases and the phonon diffraction between layers reduces. As the number of layers increases, the conductivity decreases and converges to the conductivity of hBN. Although hBN has high conductivity and thermal capacity, recent studies have shown that its strong phonon diffraction leads to lower thermal conductivity than graphite. Therefore, the reduction of diffraction in BNNS leads to a significant increase in the conductivity (at room temperature > 600 W/mK) [68].

### *3.2.3 Mechanical properties*

The hardness for BNNS and graphene is 267 and 335 TPa, respectively [69]. Hence, BNNSs can be used as reinforcement for polymer composites. It has been shown that modulus and tensile strength for nanosheets (thickness of 1–2 nm) are in the range of 220–510 and 8–16 TPa [39]. For multilayer, it is expected that the main values are somewhat less than these values.

#### *3.2.4 Lubricant properties*

Another interesting case with BN materials is frictional properties. hBN and graphite are used as lubricants for many years. The lubricating properties result from the application of the external shear force on the weak forces between the layers and sliding. At the level of atomic layers, friction force microscopy (FFM) studies show that the friction properties of these nanosheets depend on their thickness.

**29**

*Two-Dimensional Nanomaterials*

used as lubricating additive.

*3.2.5 The neutron absorption*

**4.1 The synthesis of TMD**

**4.2 The application of TMD**

hydrogen evolution reactions (HER).

nanomaterials [75].

**5. Future outlook**

*DOI: http://dx.doi.org/10.5772/intechopen.85263*

Thin nanosheets show more friction due to increased out-of-plane deformation. More studies have shown that reversible dynamic wrinkling on the top surface of most layers is created by frictional force [70]. Then, BNNSs and graphene could be

Boron is introduced as one of the most important neutron absorbers due to its high neutron absorption cross section. The compounds containing of boron are good neutron absorber. In the middle, hBN and, of course, BNNSs are better absorbers due to layer structure and larger surface area that is exposed to neutron beam than other BN structures (such as nanotube, nanoparticle, etc.). They are

In recent years, metal dichalcogenides (MX2) have attracted a lot of attention, like other 2D materials where M is transition metals and Xs are S, Se, and Te such as WSe2, molybdenum disulfide (MoS2), tellurium disulfide (TeS2), etc. MX2 can be a semiconductor or metal depending on the oxidation state of their metal atoms. As graphene-like compounds, they have similarities to graphene, resulting in new opportunities for detecting and building sensors, lithium batteries, optoelectronics, and energy storage. Many researchers have shown that the exfoliated layers of MX2 have large energy of bandgap and are semiconductors. In addition, they have the

There are currently only a limited number of reports on single-layer and fewlayer group IV–VI and III–VI layered compounds. Therefore, the 2D properties of these materials are largely unknown. However, MX2 shows a variety of electrical and optical properties that are suitable for catalysts, nanotribology, optoelectronics, and lithium-ion batteries. These materials are expected to exhibit extraordinary

The synthesis routes to MX2 are similar to other 2D nanomaterials that are based on two top-down and bottom-up approaches. Methods such as chemical synthesis, CVD, mechanical cleavage, and liquid exfoliation are performed to produce of these

These layered compounds, like other 2D nanomaterials, have interesting optical, electrical, photovoltaic, and catalytic properties. These compounds are considered as the next generation of flexible and ultrathin photoelectric devices. Also, MX2 has a suitable photovoltaic response to laser excitation and also used as catalyst in the

One of the major problems with 2D nanostructures is to achieve a large-scale synthesis method for producing high quality, large surface area, high crystallinity,

properties after reaching a thickness to single layer or multilayer [74].

used in nuclear shielding [71] and boron neutron therapy [72].

**4. Introduction of metal dichalcogenides**

properties of fluorescence and photoluminescence [73].

Thin nanosheets show more friction due to increased out-of-plane deformation. More studies have shown that reversible dynamic wrinkling on the top surface of most layers is created by frictional force [70]. Then, BNNSs and graphene could be used as lubricating additive.


**4. Conclusions**

In this research, we focused on the assessment of phthalate compounds in beverages, products whose consumption has grown dramatically in Vietnam, and thus the phthalate contamination factor for non-alcoholic drink was not exactly reflected the exposure level. Phthalate exposure in daily life possibly originates from different sources such as air [31–33], food [28,34], beverages [35,36] as well as cosmetics [37]. As a consequence, in this study, we solely concentrated on evaluating phthalate in beverage drinks, products which are consumed in huge quantities in Vietnam.

Liquid–liquid extraction and the GC-MS/MS analysis technique were optimized and conducted successfully in determining 10 phthalate compounds in different kinds of non-alcoholic drinks. The good recoveries (70–120%), RSDs of all the analysis samples and matrices were lower than 15% and low LOQ (0.5 ng/L) was confirmed. This method was utilized to analyze 10 phthalate substances in 148 non-alcoholic drink samples. The result showed that 100% of the samples were contaminated by DEHP and DEP, and almost all samples were polluted by phthalates. The result of phthalate contamination in this study did not reflect accurately the exposure of phthalates in beverage drinks because of other influencing factors. Therefore, it is necessary to implement more in-depth research to assess properly phthalate contamination during the production process, storage conditions, and when the human body is exposed to these products.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2305-6304/6/4/69/s1, Table S1: Identifying, quantifying ions, retention time, and collision energy of 13 phthalates.

**Author Contributions:** All authors have equivalent contributions in this study.

**Funding:** This research is financially supported by the project VAST.TĐ.TP.03/16.

**Acknowledgments:** Thanks to the Vietnam Academy of Science and Technology for financial support.

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


Acknowledgements

The authors sincerely thank M/s Coal India Limited, DGMS, Govt. of India and IIT (ISM) Dhanbad for providing the necessary resources and extending cooperation during the field experiments.


# **Power System Dynamic and Stability Issues in Modern Power Systems Facing Energy Transition**

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## **Power System Dynamic and Stability Issues in Modern Power Systems Facing Energy Transition**