**1. Introduction**

Wine tourism has a special impact on rural economies (López-Guzmán et al. 2009) as it involves activities in wineries, events, as well as different hospitality activities (Carlsen and Charters 2006). Wine has gone from being a consumer product to favoring the establishment of a development model for the rural territory, which requires policies and actions that seek a change in the productive structure, with the objective of environmental sustainability, as well as the enhancement of the heritage and culture of villages and nations (Bruwer and Rueger-Muck 2019; Lourenço-Gomes et al. 2015).

The economic data on wine show the interest of this resource. In terms of production, in 2019 it reached 26,000 million liters, of which 24,400 were consumed. Italy (47.5 mhl), France (42.1 mhl) and Spain (33.5 mhl) represent 48% of the total production (OIV 2020). And if we consider the value of wine tourism, Italy was estimated at 2.5 billion euros with 14 million tourists (MTV 2020); France accumulated more than 10 million wine tourists who accounted for 5.2 billion euros for the sector (Saybus 2020).

**Citation:** Zamarreño-Aramendia, Gorka, Elena Cruz-Ruiz, and Elena Ruiz-Romero de la Cruz. 2021. Sustainable Economy and Development of the Rural Territory: Proposal of Wine Tourism Itineraries in La Axarquía of Malaga (Spain). *Economies* 9: 29. https://doi.org/ 10.3390/economies9010029

Academic Editor: Michał Roman

Received: 7 February 2021 Accepted: 25 February 2021 Published: 4 March 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/).

1

In Spain, the institution that channels this tourism in a regulated manner is ACEVIN (Spanish Association of Wine Cities). It is a body that has numerous objectives, among which stand out the promotion and collaboration with other European cities that traditionally produce wine and a proposal for responsible wine tourism that could be achieved through sustainability and competitiveness plans to apply the concept of Social Responsibility to the territorial, socioeconomic and cultural sphere of the Wine Routes (ACEVIN 2020).

In 2021 it integrates 30 routes, with more than 2000 associated companies that make up the wine tourism offer of the destinations that are members of the Wine Routes of Spain Club. A significant figure is the number of visits to wineries and museums of the Wine Routes in 2019, which amounted to 3,076,334, experiencing a growth over the previous year of 3.9% with an expenditure of just over 85 million euros per year, representing a growth of around 5.68%. Turnover reached 256 million euros, adding the part corresponding to the catering, hotel, business and leisure sectors (ACEVIN 2020).

These data are a true reflection of the interest of a sector that, linked to tourism, exerts a great power of attraction in certain destinations, as they have placed value on tourism formulas that have rural areas as protagonists (Khartishvili et al. 2019). It should be noted that wine routes in destinations with tourist saturation can diversify the offer by revitalizing the inland ( Díaz Armas 2008), as well as promote job creation and rural development by favoring the deseasonalization of demand, as stated by numerous authors ( Álpizar and Maldonado 2009; Álvarez García et al. 2014; López-Guzmán et al. 2009; Ramis Hernández 2010).

Enotourism is defined as the movement of certain travelers for a holiday focused on getting to know certain areas and landscapes where wine is produced and carrying out activities that increase knowledge about this product (Elias Pastor 2006). It is a consolidated activity that is increasingly popular in countries with a long tradition in the Old World such as Spain, Italy, France, Portugal, Greece, Romania, Germany or Serbia (Coros et al. 2019; Dougherty 2012; Festa et al. 2020; Khartishvili et al. 2019; Koch et al. 2013; Lourenço-Gomes et al. 2015; Triši´c et al. 2020; Vieira-Rodríguez et al. 2013; Wolikow 2014), implementing tourism strategies significantly in other places such as Australia, New Zealand, South Africa, Canada or the USA (Bruwer 2003; Hall et al. 2019a; Kirkman et al. 2013).

Wine routes are an opportunity for the promotion of cultural values, gastronomy and local products, with a special consideration for wine (Bessière et al. 2013; Etcheverria 2015). Thus, the aim of this work is to investigate the possibilities of La Axarquía to develop a wine route through itineraries that discover the tourist potential of the area. From an academic point of view, it is essential to analyze these routes with criteria of efficiency and profitability, since for the wine route to be an attractive destination, it is necessary to know the resources available in the territory and this is a particularly important factor, as it may be what initially motivates the tourist to visit the area (Gatti and Incerti 1997).

This study is located in a line of research that revolves around wine tourism and Málaga wine route (Ruiz-Romero de la Cruz et al. 2017), circumscribed in La Axarquía of Malaga as it is a place where the climate, landscape and culture add an important value to the traditional activity of making wines protected under the Certificates of Origin "Malaga", "Sierras de Malaga" and "Pasas de Malaga" (DDOMSPM). The conclusion of this research phase culminated in a publication that modelled the fundamental elements (Figure 1) that should be present in a wine route in general and specifically in La Axarquía (Cruz-Ruiz et al. 2020). The structure of this research is based on the knowledge of the potential of La Axarquía in Malaga (Spain), located in the southern Mediterranean. After a review of the literature, the methodology of the study is presented, consisting of a field study, an analysis of documentary sources and in-depth interviews with winemakers and agents involved in the sector. The results obtained made it possible to carry out a specific diagnosis of the territory by means of a SWOT analysis. On this basis, several proposals for wine tourism itineraries have been drawn up, outlined with economic criteria of profitability for the

geographical area analyzed and its surroundings. The study ends with a discussion section and the conclusions.

**Figure 1.** Key elements for the design of a wine route. Source: Cruz-Ruiz et al. (2020).

The research has raised the following questions:

Q1: Does the territory of La Axarquía have sufficient resources to structure an enotourist offer that benefits its development?

Q2: What is the diagnosis of the territory according to the stakeholders and winemakers? Q3: Do the existing wineries offer adequate services to contribute to the development of the rural territory?

Q4: Is it possible to design wine tourism itineraries in La Axarquía with the elements available?

#### **2. Theoretical Background**

The development of wine tourism has grown and in many countries it has been due to wine routes, which can be defined as a set of duly marked itineraries that pass through a specific geographical area with a wine tradition, an essential issue if we take into account that they can be the reason for choosing a destination (Michael Hall 2013).

The study of the wine tourism phenomenon can be studied from three perspectives, Getz and Brown (2006) highlight its interest for regional development and its strategies. The opinions of consumers is another point of view that should be taken into account (Alant and Bruwer 2004; Garibaldi et al. 2017; Ruiz-Romero de la Cruz et al. 2017) and, on the other hand, the perspective provided by the wineries and the opportunity they have to promote and sell their product directly to visitors is of great analytical value (Carlsen 2011; Hall et al. 2019b; Peters 2018; Festa et al. 2020).

The enhancement of the territory's heritage is an important incentive for tourists to make the decision to visit a destination. This includes aspects such as the natural landscape and environment, heritage, cities, architecture, artefacts, vineyards, wineries and wines (Getz 2000; Getz and Brown 2006; Sparks 2007). The sensory enjoyment and pleasure produced by the consumption of wine, as well as by the territories where wine routes are located as the main motivation for wine tourists (Pulpón and Ruiz 2019; De Uña-Álvarez and Villarino-Pérez 2019; Wolikow 2014), make them a more demanding traveller in terms of quality, personalization and differentiation (Alonso and Liu 2012; Carlsen and Boksberger 2015; Fountain 2018; Vasco Santos et al. 2019).

Characterizing wine tourists allows us to build an appropriate offer, and numerous studies have produced profiles that bring us closer to their reality (Famularo et al. 2010; Garibaldi et al. 2017; Marzo-Navarro and Pedraja-Iglesias 2009; Quintal et al. 2017; Wade et al. 2006). Comparative studies between different types of tourists are not very abundant, although they are a very useful tool for making strategic decisions that make it possible to redirect the flow of visitors in order to deseasonalize tourism activity (Díaz Armas 2008; Ruiz-Romero de la Cruz et al. 2019).

The economic development potential of certain regions is linked to their ability to develop interesting tourism segments that offer economically viable alternatives and generate income for the local population (Roman et al. 2020). In this regard, wine tourism has an interesting attraction, generating visitor flows that bring significant economic benefit (Carlsen 2004; Gammack 2009; Hall and Mitchell 2000), providing greater brand awareness and involvement (Charters and Ali-Knight 2002), increasing the number of subsequent visits and encouraging purchasing behavior (Johnson and Bruwer 2007; Mitchell and Hall 2006; O'Neill et al. 2002). In this way, wineries are able to progressively add value to the destination, invigorating the traditional agricultural sector and innovating wine products with an impact on local economies. Hashimoto and Telfer (2013) highlight the contribution of wine routes to the improvement of wine product marketing strategies, economic performance and the efficiency of wine producers, while Carmichael and Sense analyze the competitiveness and sustainability of wine destinations (Carmichael and Senese 2012).

Wine routes are therefore an integrated strategy for a rural development (Ferreira and Hunter 2017; Northwood 2000; Williams and Kelly 2001). They are intimately linked to institutional decisions, as well as to the commitment and responsibilities acquired between the public and private spheres, a point at which noticeable divergences can arise (Ferreira and Hunter 2017; Northwood 2000; Williams and Kelly 2001). The design of an enotourism route must address different angles (Blum et al. 2014; Cruz-Ruiz et al. 2020; Getz et al. 2007; Getz and Brown 2006): gastronomic (Crespi-Vallbona and Mascarilla-Miró 2020; Millán Vázquez de la Torre and Pérez 2014), cultural (Arnáiz et al. 2019; Carrasco et al. 2019; Mitchell et al. 2012), natural heritage or terroir (Harvey et al. 2014; Holland et al. 2014) and formative (Buhalis and O'Connor 2005; Famularo et al. 2010; Wargenau and Che 2006).

Wine routes are defined by the vineyards, festivals, shows and especially the wineries of a given wine-producing region (Sigala 2014). All this in a geographical space where the exploitation of the vine and the wine-making takes place, where the wineries are located, where the interaction of the tourist with all the elements that make up the wine tourism route occurs (Cruz-Ruiz et al. 2020; Pulpón and Ruiz 2019), becoming, together with the terroir, basic elements in the conceptualization, design and management of wine routes (Brás et al. 2010; Pérez-Calderón et al. 2015) and being one of the primary resources in the wine business (Riera Palmero 2014; Yagüe Guillén and Jiménez 2002).

It is in this framework where wineries have a greater chance of creating an offer focused on the attraction of wine linked to the hedonistic experience (Bruwer and Alant 2009; Crespi-Vallbona and Mascarilla-Miró 2020). Collaboration between all the actors involved is decisive for generating value on the routes (López-Guzmán et al. 2009; Medina and Tresserras Juan 2008; Miranda Escolar and Fernández Morueco 2011; Vieira-Rodríguez et al. 2013; McGregor and Robinson 2019) and for the entire wine sector (Gomis et al. 2010). A collaboration that will be more productive if the possibilities of generating enotourism circuits in geographical areas that meet certain conditions are analyzed.

The study of the wine tourism offers and the needs of wine tourists has received contributions from the perspective of case studies (Chiodo et al. 2020; Holmes 2017; Ilie¸s et al. 2020; Triši´c et al. 2020; Triantafyllou et al. 2020); which have led academics and specialists to understand the dynamics of this sector being assumed by the wineries as well as the public and private agents involved (Cruz-Ruiz et al. 2020).

All of these arguments highlight the importance of wine tourism and the interest in designing sufficiently attractive itineraries for the development of a sustainable tourism model. This is a challenge that institutions will have to take on from a multidisciplinary perspective, in which geographers, sociologists and economists, among others, will have to intervene (Fernández Portela and Vidal Domínguez 2020). In this way, the process of shaping a wine route as a tourism product is considered a way of conserving and enhancing the cultural heritage that belongs to the identity of the local population (Carrasco et al. 2019; Pulpón and Ruiz 2019), as well as an opportunity for economic diversification (Northwood 2000; da Silva et al. 2018; Wolikow 2014).

#### **3. Territory of La Axarquía**

La Axarquía belongs to the easternmost part of the province of Malaga and has a total surface area of 1026.7 km2 (Figure 2). It is bordered by the Mediterranean Sea to the south, while to the north and east is the province of Granada and to the west it is bordered by the capital of Malaga and the regions of Antequera and Nororma (Lucena 2007). It has peculiar features, orography, farming systems and diversity of landscape and resources. The average altitude of the region is 391 m, reaching a maximum altitude of 2069 m, making it a territory with steep slopes alternating with open areas.

It has a Mediterranean-type climate, semi-tropical with mild winters and warm summers. In fact, Tejeda, Almijara and Alhama mountain ranges protect this territory from the cold north winds. Its subtropical latitude allows it to enjoy 3000 h of sunshine a year. Average temperatures in the coastal area range from an average of 10 ◦C in winter to 25 ◦C in summer, being somewhat more extreme in the inland villages, especially in those located above the 900 meter mark (Carrión-García 2015).

**Figure 2.** Location map of La Axarquía (Malaga, Spain). ETRS89 UTM 30S. Own elaboration.

The cultivation of vines in La Axarquía has certain peculiarities that make it attractive for wine tourism, including the grape harvest, which is one of the earliest in Europe that used traditional techniques for harvesting. The difficulty imposed by the physical environment on the tasks of maintaining the vines and harvesting the grapes, which have to be done by hand, means that this viticulture can be described as heroic (CERVIM 2020).

La Axarquía is currently made up of 31 municipalities and up to 67 districts. The total population in the last municipal census amounts to 214,323 inhabitants and, as shown in Table 1, Vélez-Málaga is the most populated urban center, with 81,643 inhabitants (IECA 2020), therefore it is part of the province of Malaga, but has a sufficient entity to be analyzed separately. It has its own bodies that identify it and work in a coordinated manner throughout the territory, such as the Association of Municipalities of La Axarquía (Mancomunidad de Municipios de la Axarquía) and the Centre for Rural Development of La Axarquía (Centro de Desarrollo Rural de la Axarquía, CEDER).

At present, the coast municipalities of La Axarquía have a much higher population density than those of the inland, which means a strong urban pressure on the coast strip (Almeida García and López Cano 2003). Table 1 shows the towns and their surface areas, with Vélez-Málaga, Rincón de la Victoria, Nerja, Torrox and Algarrobo standing out as the most densely populated. On the other hand, the least populated municipalities are those located inland, marked by a rugged terrain and more complicated accesses, which may influence their tourist potential, the latter being Salares, Árchez, Alfarnatejo, Macharaviaya, Sedella, C útar, Totalán and Canillas de Albaida.

**Table 1.** Population of La Axarquía.

Source: IECA (2020).

#### **4. Materials and Methods**

The research was carried out in three stages. The first consisted of a study of the wine production area of La Axarquía. The visits to this geographical area were made between April and November 2019, a method used by other researchers to learn about the reality of wine tourism in specific areas (Bruwer 2003; López-Guzmán et al. 2014). In this phase a vital issue for the structuring of the itineraries of the wine tourism route was analyzed, namely the resources and services offered.

The information obtained was completed by means of a documentary analysis using multiple sources (General Catalogue of Andalusian Historical Heritage, Catalogue of Protected Assets and Spaces of the Provincial Council of Malaga and tourist information available both in brochures and online).

The second stage consisted of an in-depth interview with winemakers and agents involved in the production of wine (Table 2), an appropriate tool for exploring the subject, as it allows for the evaluation of non-neutral knowledge (Gillis and Jackson 2002; Mason 2006; Pepper and Wildy 2009). The questionnaire was designed by a work team belonging to the SEJ 121 "Mediterráneo Económico" research group at the University of Malaga and was structured in a single section of XII questions. In order to eliminate problems of comprehension and subsequent interpretation of the data, a pilot experience was carried out by selecting four participants. The interview (Appendix A) invited participants to comment on what they believed to be the key strengths and weaknesses of the wine activity in terms of wine tourism. The authors of the responses have remained anonymous. The interview was implemented by all 100% of the winemakers, whose wineries are located in eight

municipalities in the region. Vélez Málaga and Cómpeta hosted two wineries and the rest were distributed in the nearby towns of Árchez, Colmenar, Moclinejo, Sayalonga, Sedeya, and Torrox. Ten responses were collected from institutional representatives, managers of public and private companies, and other entities, which represented 70% of the institutional sector present in the territory of La Axarquía.

**Table 2.** Fact sheet of the interview.

Source: own elaboration.

Once the interviews had been analyzed, a SWOT was structured to determine the real situation and define the implementation of possible wine tourism itineraries in the region of La Axarquía, a methodology already used in other studies on the development of strategies related to wine tourism (Carrà et al. 2016; de la Torre and Navarro 2008; Wilkins and Hall 2001). SWOT analysis is a multi-application tool that can be used to analyze different aspects of a strategic nature, given that it provides excellent information for decision-making. The benefit obtained with its application is the knowledge of the real conditions in which an organization finds itself, in order to assume risk and take advantage of the opportunities offered by the environment. It is important that the wine industry and the tourism industry identify and understand their key strengths, weaknesses, opportunities and threats, as well as how these factors interact, so that effective decisions can be made in terms of sustainable wine tourism development (Álvarez García et al. 2014; Millán 2012).

Thirdly, with the information available, we proceeded to make a proposal for wine tourism itineraries that take into account the needs indicated by the interviewees, as well as the heritage elements of the territory and the most necessary services for the development of the enotourism route, having in mind the findings made by the research group (Cruz-Ruiz et al. 2020), shown in Figure 1.

## **5. Results**

The study of heritage resources, both tangible and intangible, tourism services and wineries present in a geographical space is valued to the extent that they provide options for progress in the form of wine tourism itineraries, taking into account the peculiarities of the territory. In this case study and in researches applied to other wine-growing areas, where wine and tourism come together (Harvey et al. 2014), where the rural is perceived as

a space in which the land prevails as an element of production, the values, resources and culture itself promote products to discover and enjoy (Privitera 2010).

#### *5.1. Heritage and Services in La Axarquía*

Following the Table 3, we can observe that the material heritage has a great diversity in the region in the form of unique historical buildings, traditional architecture and monuments, representing elements that add value to the territory. Obviously, the richness of this matter is highly variable and does not necessarily correspond to the size of the municipality, hence the importance of the fieldwork carried out.

Source: Own elaboration according to IECA (IECA 2020), as well as on elements and resources of La Axarquía in the General Catalogue of Andalusian Historical Heritage and the Catalogue of Protected Assets and Spaces of the Provincial Council of Malaga. The symbol "x" means that the element is present in the corresponding municipality.

With regard to the tasks related to viticulture, heritage elements have been preserved, in particular the grape drying sheds for the production of raisins must be mentioned due to their exceptional nature. As reported by the respondents, there is a worrying and progressive process of disappearance of agricultural heritage elements, wine presses, drying sheds and warehouses, due to the updating of wine-making work and the lack of valorization of these places until recently. Some of them are part of the history of certain wine-producing localities in the territory under study.

Therefore, this vast heritage is present, to a greater or lesser extent, in all the municipalities of La Axarquía in the form of historic buildings (churches, houses, old industries, archaeological remains). As far as museums are concerned, although there are several of these infrastructures, only one of them is entirely devoted to traditional wine making. It is located in the municipality of Cómpeta. In the rest we can find and recognize some elements related to wine production, as well as archaeological, artistic or anthropological ones that illustrate the historical and patrimonial richness of the region.

In this way, the itineraries to be designed will be determined by the local wine industry and the value of its culture, contributing to sustainable development and preserving the existing rich heritage, a casuistry observed in other territories (Carrasco et al. 2019) under the model of wine tourism product club in Spain (Gomis et al. 2010).

La Axarquía has a strong sense of identity reflected in the potential of its intangible heritage. Even today, in most of its municipalities you can still find examples of traditional trades, mainly those related to agriculture and in particular those related to wine-making.

Festivals are another attraction and a perfect complement to wine tourism visits (Getz 2019; López-Guzmán et al. 2019). The cultural and ethnographic variability endows La Axarquía with a complex festive framework developed throughout the year, be it the typical patron saint feasts or other festivities and events related to the traditional tasks of wine and gastronomy, which is an added motivation for the visitor. In fact, the prominence of wine and raisins is a central theme of certain festivals usually held in the summer months, when the grapes are harvested. The municipalities with the greatest wine-growing traditions, such as Cómpeta, Moclinejo and Colmenar, are the main protagonists, although raisins and grapes are also part of the popular culture in El Borge, Iznate and La Viñuela.

The wine landscape is the most outstanding natural and genetic heritage. The tourist resource of the landscape and the vineyard offer one of the most interesting options in a wine tourism route (González Morales et al. 2015). In this sense, the vineyards of La Axarquía make up a very characteristic landscape due to the unevenness of the terrain, which makes it necessary to use mules to harvest the grapes. In addition, it is considered an economic and heritage resource, due to its determining influence on productive activities of great relevance, among which is tourism and also residential development (Almeida García and Cortés Macías 2011).

As for services, these are concentrated in the municipalities with the largest number of inhabitants and in the centers characterized by their offer of sun and beach tourism activities, such as Rincón de la Victoria, Vélez Málaga, Torrox and Nerja. Leisure services and tourist service companies are present in the aforementioned municipalities, to which are annexed Periana and Arenas, where there are companies related to active tourism.

More than a third of the municipalities in the inland of the region, apart from those on the coast, have tourist information offices, which makes them interesting stop points on the route: Cómpeta, Frigiliana, Benamocarra, Alcaucín, La Viñuela, Comares, Alfarnate and Sedella. Restaurant and accommodation services are omnipresent in all the towns. The type of accommodation is varied, ranging from the large hotels located in the coastal towns of Vélez Málaga and Nerja to the small rural hotels in municipalities such as Arenas, as well as the tourist apartments that flourish in towns such as Frigiliana and Alcaucín. In the case of restaurants, all the towns except C útar have them and, even though the types are varied, local gastronomy is present in all of them.

#### *5.2. Diagnosis of the Territory: SWOT*

The information compiled through the interviews has allowed the elaboration of a diagnosis of La Axarquía by means of a SWOT, in which the strengths and weaknesses, threats and opportunities of wine tourism in the area are specified (Table 4).

The present offer of services is based mainly on tangible elements such as wine and wineries, but there are intangible elements that add attractiveness and interest such as the surrounding elements or the associated services. The geographical context has a major influence on the analysis. In the case of La Axarquía, it has recently been transformed into an area where agriculture has given way to tourism as a source of income, becoming just another zone of the metropolitan area of Malaga, which can generate conflicts of interests that can be overcome with proper planning (Almeida García 2011).

Furthermore, it is necessary to take into account the important role played by the different local, provincial and regional public administrations in the development of the initiatives related to the construction of a certified wine route, as they require active incentive policies, as well as elements to boost the necessary infrastructures and the promotion of the territory. SWOT shows the most relevant issues for outlining the actions that can be derived from public policies to support the development of the rural territory.

**Table 4.** SWOT matrix on the wine sector in La Axarquía.

from the coast.

Source: own elaboration.

#### *5.3. Characteristics of the Wineries and the Services Offered*

Wine tourism as an economic driver has its ultimate expression in the organization of routes and itineraries. A construction that requires institutional collaboration and the involvement of private initiatives that are channeled through the winemaking businesses in La Axarquía.

The research carried out in person in each of the wineries (Table 5) has allowed a rigorous study of their possibilities and a mapping of the characteristics of each one of them, which is essential for the elaboration of wine tourism itineraries. Table 5 shows the characteristics of the wineries in the area of La Axarquía, as well as the services they provide.

**Table 5.** Characteristics and services of the wineries of La Axarquía.

\* The typology indicates the ownership of the business and its structure, irrespective of the corporate form under which they are registered in the business and company registers. \*\* Languages in which the public is served for the marketing of the wineries' wines. The symbol "x" means that the element is present in the corresponding winerie. Source: Own elaboration.

> The predominant business structure is the family-run type, with the exception of UCOPAXA, a cooperative that brings together more than 700 farmers and which produces and markets 70% of Malaga's raisin production, making various types of wine. Most of the wineries have their own vineyards; only Bodegas Luis Picante purchases must from local producers to make its wines. With regard to wine production, the traditional production of sweet wines in the area has given way to red, rosé and white wines, which in the case of Bodegas Jorge Ordoñez are organically produced.

> In the case of the wineries, the dates on which they were founded are striking, with those that began their activity at the end of the 21st century dominating the scene in the heat of the growing interest in viticulture. However, we recognize the singularity of Bodegas A. Muñoz Cabrera, known as Dimobe, founded in 1927, whose business has continued uninterruptedly since then.

> Despite the fact that all the wineries are committed to wine tourism, the degree of development of services is uneven. Customer service is provided in Spanish and English, at least in most of them. Most of the wineries offer the possibility of wine tastings which can be accompanied by gastronomic menus, while visitors can buy the wines they produce directly. Wine-related events are only offered at three wineries, while vineyard tours are only available at three of the wineries.

#### **6. Organization of Wine Tourism Itineraries**

Tourist routes and itineraries are nowadays a matter of great interest for the competent tourist bodies in Spain. In the case of Malaga, their existence is promoted by the Public Company of Andalusian Tourism, the Provincial Council of Malaga, and in La Axarquía by La Axarquía Rural Development Group (Grupo de Desarrollo Rural de La Axarquía, CEDER).

The wine tourism itineraries proposed for La Axarquía highlight the importance of the existing heritage resources and services. The opinions gathered among the agents involved point to the existence of numerous routes of tourist interest which can be based on the attractions of the area. The interviewees acknowledged the existence of some institutional initiatives, although they have not had a significant impact on the localities along the routes.

With regard to an enotourism route or itinerary, it must have a layout that brings together specific resources and that meets the criteria of efficiency and economic profitability. Assuming these criteria in a geographical, cultural and historical context linked to wine, two different wine tourism route/itinerary options are proposed, taking into account environmental sustainability criteria, placing value on the tangible and intangible elements it possesses and combining the efforts of social and institutional agents, private companies, producers and consumers.

After having catalogued the elements present in the region of La Axarquía useful for the definition of a wine tourism route, having validated them through a field study and the interviews in the SWOT matrix, we believe that it is possible to propose two wine itineraries in La Axarquía. Logically, the role played by the wineries is fundamental, especially those that are more closely linked to the wine tradition or those that show a greater interest in being linked to the wine tourism route.

These itineraries try to create a coherent visit, in which the greatest number of heritage elements and services are present, taking into account the mandatory inclusion of the wineries, which work as a critical element and must necessarily be included in the itinerary. The density of heritage elements complicates the route, as almost any corner of the territory is worth a visit. Services are another of the keys to success. The restaurant offer covers almost all the municipalities, with interesting proposals that recover the local culinary heritage and modernize it, while the local wines have an important presence in bars, restaurants and in the few wine cellars in the area. There is a wide range of possibilities for overnight stays in the area, thanks to the large network of rural accommodation available in most of the municipalities.

#### • 1st Proposed Itinerary

The first itinerary aims to showcase the largest number of wineries in La Axarquía, as well as its heritage elements (Figure 3). It is a circular route that starts and ends in Vélez Málaga, which is the municipality where the visitor can find the largest offer of accommodation and which is easily accessible from the A-7 motorway, which connects with the city of Malaga in 30 min. Vélez Málaga is the head of the region of La Axarquía and is home to two wineries, Jorge Ordóñez & Co. and Ucopaxa, the latter also dedicated to the marketing of raisins.

There is a wide range of heritage and services on offer, and it is worth highlighting the heritage that is concentrated in the historic center. The direction of the route does not affect the visit, so the first point of interest is Bodegas Medina y Toro, located in Torrox, a municipality that is divided between the coastal strip and Almijara mountain range and that is organized along the axis marked by the river Torrox. This town has a historical and archaeological heritage that dates back to the time of the Roman colonization and includes important remains of industrial activities such as the San Rafael sugar factory. The next milestone on the route is the town of Cómpeta, which stretches along the southern slopes of Sierra Almijara to the Montes de Málaga, with a landscape of hills covered with vineyards, olive groves, almond trees and scrubland. The town is especially known for its wine-growing tradition and culture and is home to Bodegas Luis Picante and Bodegas Almijara. Numerous heritage elements can be found (the cemetery of San Sebastián and its historic quarter stand out), as well as popular festivals.

Traditional work has also been preserved, apart from the work of the vineyard, which is still practiced today, such as the lime industry and tinplate craftwork. The next point on the route is Árchez, a small town at the foot of Sierra Tejeda, surrounded by vines and olive trees and which preserves a minaret of Muslim origin. In this town you can visit the Hermanos López Martín winery, whose main interest lies in the surrounding landscape and ethnographic values.

The route can be extended to Sedella, a municipality of singular interest that treasures an interesting popular architecture and where traditional crafts such as imagery and esparto grass work are still preserved. Sedella Vinos winery is responsible for keeping alive the town's winemaking tradition, where the mountain landscape and the vineyards, olive and almond groves coexist. The return is from Cómpeta in the direction of Sayalonga on the A-7206. This small municipality of steep slopes is home to Bodegas Bentomiz, ending the route back in Vélez Málaga.

**Figure 3.** Own elaboration based on the Digital Cartography of Andalusia (IECA). Location map of Itinerary #1. La Axarquía (Malaga, Spain). ETRS89 UTM 30S.

•2nd Proposed Itinerary

The second itinerary takes in what is known as the Raisin Route, which has an interesting heritage value, both tangible and intangible (Figure 4). It highlights the vineyard landscape in a steeply sloping terroir that extends over the hills of the Montes de Málaga and where the traditional grape drying sheds are also located. The route can be followed in either direction, and if you take the possible extension to El Rincón de la Victoria, it is a circular route. The possibilities for overnight stays in the area are varied, especially in terms of rural accommodation.

**Figure 4.** Own elaboration based on the Digital Cartography of Andalusia (IECA). Location map of Itinerary #2. La Axarquía (Malaga, Spain). ETRS89 UTM 30S.

Starting from Moclinejo, it is there where you can visit Bodegas Muñoz Molina, the only establishment dedicated to the production of wine along the route. The next point of interest is Almáchar, situated on a hill located between the rivers El Borge and Almáchar and here, from the end of August, you can observe the process of drying the grapes to produce raisins. Other activities of interest are the festivals and popular celebrations around the livestock activity and the typical products of the area such as "ajoblanco". A short distance away is El Borge, a municipality that is clustered around the Ejido hill, on the banks of the river from which the town takes its name. The urban center is integrated into the landscape with a structure of winding streets adapted to the relief of the area. Of interest are several heritage elements such as the cemetery, the parish church and two old mills. The traditional activities of grape harvesting and processing are still common among the inhabitants. The route now heads towards the small town of Cútar, which spreads out on a hill of the same name, dominating the surrounding valley. It is worth mentioning some heritage elements linked to economic activities, such as mills and fountains. Apart from the wine-growing activity, traditional trades such as esparto and basket weaving are still preserved. The route continues to Benamargosa, which takes its name from the river that runs through it and which allows the development of orchards where citrus and avocado

trees are grown, blending in with the vineyard landscape. Comares is the next point on the route, located on the hill from which it takes its name. Its geographical conditions made it an excellent defence post, especially during the period of Moorish rule. It is around the fortifications of this period that the historic quarter is clustered, with its typical Moorish urban layout, which is completely pedestrianized due to the narrowness and steepness of the streets. There are numerous heritage elements, some of which are linked to the defensive function of the town or to religious worship, as well as those of a civil nature. Of particular note is the folkloric expression of the Verdiales, a style of fandango typical of the province of Malaga, which takes its name from this locality in one of its styles and which is danced in its popular festivals. The route ends in Totalán, a small municipality adjoining the town of Málaga, which adapts to the terrain and takes advantage of the waters of the stream of the same name that runs through the town. The urban layout denotes its Moorish origins, although the area has been inhabited since prehistoric times.


*Background–Development of an Affordable and Simple Cost Estimation Tool*

The development of the cost estimation tool was made based on an SME manufacturing company that produces machined parts, primarily by the milling process. The analyzed company followed a conventional cost estimation process, shown in Figure 1. However, due to the high variability and small series of requested parts, the created budgets had some errors, usually resulting in over-estimated production costs and, in some cases, underestimated production costs, which resulted in company revenue loss. This was the case, especially for more complex parts. Thus, there is an opportunity to develop a tool that can be useful for this sector but also provide the necessary knowledge to be adapted and adopted by other kinds of industries.

**Figure 1.** Schematic representation of the conventional budgeting process.

To speed up the budgeting process and reduce the errors associated with it, a cost estimation tool based on the analyzed company's resources and conditions, such as machines, workforce, and client requests, was developed. In the subsequent sections, the methodology used for the development and validation of this tool, and the results obtained from this validation, are going to be presented. Furthermore, a discussion of the obtained data is going to be made, analyzing the advantages/disadvantages of the developed tool.

#### **2. Materials and Methodology**

To develop the cost estimation tool, it was decided that an approach based on the calculation of machining times and founded on the final part's dimension would be the best choice. The calculations were developed for each of the milling machine types considered for validation of the model. The different milling machines that were considered can be observed in Table 1, where the different specifications of each machine are presented.

**Table 1.** Considered CNC milling machining centers.

As observed in Table 1, the main difference between machines is the workspace volume, the amount of axis, and the workpiece fixation method. These machines were considered as they are selected based on the requested final workpiece (size, tolerances, number of needed axes, etc. ... ). The machines with vacuum tables are mainly used for the machining of parts with small heights or thickness. In Figure 2, some parts being produced on the mentioned machined can be observed.

**Figure 2.** The part being machined in an M1 milling machine (**a**), and an M4 milling machine (**b**).

The developed tool's working principle is shown in Figure 3.

**Figure 3.** Schematic representation of the working principle of the developed tool, for the cost estimation of machined parts.

The inputs for the tool, as observed in Figure 2, are the part's material, the initial required material amount (based on the part's dimensions), machining strategy (parameters and operations), and required machines to obtain the workpiece, and part complexity level definition. Based on all this information, the tool performs the calculation of machining time, which can be used to estimate the overall production cost for the machined parts.

Total production time and, consequently, the total production cost are obtained by determining the operation time for the five production steps that each part undergoes, as follows:

(1) CAD (2D/3D): The 2D technical drawings are needed for part production; additionally, the 3D drawings can be used to perform the CAM software. If these are not provided, they need to be made.

These five steps are applied for every part that is produced in the milling machines; however, due to the existing variability from part to part in terms of geometry complexity and required details, the determination of the operation times is insufficient to provide an accurate prediction. Thus, a part complexity level was created to be applied to each of the parts that are being analyzed in terms of cost, which influences the estimated times for each of the production steps.

In the following subsections, the operation time calculation method for each of the five production steps is going to be presented. Furthermore, the working principle of the model will be described in more detail, including the determination of the part complexity level and its influence on the estimated times are going to be explained. Furthermore, the methodology adopted for the validation tests is going to be presented.


**6. Management of ocular surface disease in patient with Glaucoma: general perspective**

Currently there are numerous bak-free drugs, laser therapy and minimally Invasive Glaucoma Surgery (MIGS) that help us in the management of the ocular surface and also improve adherence to therapy. The adherence and persistence is a problem, between 30 to 70% of patients do not comply with the indications in the management of glaucoma [25], in large part it is due to the irritative symptoms that these eyedrops produce.

Gupta et al. in his study shows that 90% of patients do not instillate the Eye drop properly [26]. The new advances in glaucoma therapy are focused on improving adherence and persistence with the aim of preserving the ocular surface and slowing the progression of the disease.

The bak-free medicine maintains an antimicrobial environment in a multidose container while minimizing toxicity to the ocular surface. The major disadvantage of preservative-free therapy is its cost and the handling of these containers, is often difficult for patients squeze the bottle, many of them have double chambers that avoid microbial contamination.

Selective laser trabeculoplasty (SLT) reduces intraocular pressure by increasing aqueous outflow through the trabecular meshwork with a single, painless outpatient laser procedure, minimal recovery time, and good safety profile. The Light study found that 74% of patients randomized to initial SLT remained drop-free at 36 months, suggesting that SLT is a particularly effective treatment in treatmentnaïve patients [27].

MIGS have been developed as safer and less traumatic surgical interventions for patients with mild to moderate glaucoma or who are intolerant to standard medical therapy. It is an excellent option to avoid the use of topical medications. The problem of the MIGS continues to be accessibility; the high costs make them often prohibitive as a therapeutic option in developing countries.

Intense pulsed light therapy (IPL) is a promising complementary treatment for dry eye disease, specifically when dry eye syndrome is associated with skin disorders. Recent studies demonstrated in patients suffering from meibomian gland dysfunction (MGD), IPL therapy also reduces signs and symptoms of ocular surface disease [28]. The biological basis of this process is not well understood. The mechanism of action is by photomodulation that induces intracellular changes at the ducts of meibomian glands. There are no conclusive studies of its exact utility in patients with dry eye and glaucoma, however it may be a tool to consider [29].

## **6.1 Management of ocular surface disease in patient with Glaucoma**

The classic management of glaucoma must be relationated with the Ocular surface evaluation. It's known the low % of glaucoma eye drops adherence. Recognize and make objective evaluations of the ocular surface can provide vital information about our patients. It can help to stratify the initial baseline therapy, and propose a double objective. Achieve the target IOP and the best Ocular surface condition in all patients.

There are two complementary forms of evaluate the ocular surface condition; Subjective, using validated questionnaires. These test evaluate the symptoms and how the patients confront the environment with the disease. Objective methods, is a standardized test to evaluate the cornea and conjunctival epithelium, and the tear film osmolarity.

• Subjective evaluation

Validated questionaries

	- a.Ocular vital tinctions
	- b.Osmolarity
		- Tearlab
		- Ipen
	- c.Inflamation marker
	- d.No contact measurements
		- Lacrydiag
		- Keratograph


2.2.1 Calculating the thermoelectric couple open-circuit voltage Voc

According to [8], if we consider the thermoelectric couple in Figure 3 (a), and assume that no other heat arrives at the cold side Tc other than through the two thermoelectric legs, the thermoelectric couple open-circuit voltage Voc can be found by:

$$V\_{\alpha\varepsilon} = \left(\mathbf{a}\_p - \mathbf{a}\_n\right) \left(T\_h - T\_c\right) \text{ measured in volts} \tag{1}$$

where αp and αn is the Seebeck coefficient of the p-type and n-type pellets of the thermoelectric couple respectively, and may be found quoted in manufacturer literature or obtained by practical measurement. Typical values for Bi2Te3 thermoelectric couples are αp of around 230 � 10�6 V/K and αn of around �195 � 10�6 V/K [9]. Th is the surface temperature of the hot side of the thermoelectric couple, and Tc is the surface temperature of the cold side of the thermoelectric couple, measured in Kelvin.


*Editorial* **What Do We Know about Suicide Bereavement, and What We Can Do to Help Suicide-Loss Survivors?**

**Yossi Levi-Belz 1,\*, Karolina Krysinska 2 and Karl Andriessen 2**

"*Suicide is not only the end of life for the deceased but also the beginning of a highly challenging life for those left behind*". While most efforts and scientific studies concerning suicide focus on prevention [1], these touching words of Edwin Shneidman remind us that the societal toll of suicide reaches well beyond human loss. Recent studies [2–4] noted that each suicide affects, on average, five family members and up to 135 community members. Considering that approximately 700,000 people worldwide die by suicide annually [5], estimates are that 60 million people are added to the suicide-loss survivors' population each year. These numbers alone underscore the importance of understanding how we can help those bereaved by suicide in their psychosocial journey of dealing with their grief.

A large body of data has found that suicide-loss survivors are at greater risk than other bereaved individuals and the general population for many severe psychological and health problems. Research has revealed that suicide-loss survivors present higher levels of depression, and suicidal ideation and behavior [6,7] than other bereaved individuals. Moreover, those bereaved by suicide can experience adverse grief reactions such as prolonged grief disorder symptoms [8,9] which can persist even several years following the loss.

Suicide loss has also been associated with other deleterious psychosocial consequences. The turmoil of guilt, shame, anger, and embarrassment that follow the suicide of a loved one (e.g., [10]) seems to facilitate social withdrawal and efforts to conceal the cause of the significant other's death [11,12]. These behaviors, along with low self-disclosure [13], low perceived social support [14], and high levels of thwarted belongingness [15], have all been found to characterize suicide-loss survivors. Together, these features can be viewed as a call to action to devise ways to help those bereaved by suicide.

We have co-edited a Special Issue which focuses on suicide bereavement and postvention, with the aim to highlight the current knowledge and advances in the research, practices, and policies regarding suicide bereavement. The Special Issue includes 19 papers which cover a wide range of topics, including (a) the impact of suicide on individuals and communities, and adverse grief reactions, (b) the impact of suicide on health professionals, and (c) coping and support for those bereaved by suicide. The findings of these studies are an important step forward in our understanding of additional approaches to support those bereaved by suicide in their healing journey.

### **1. Impact of Suicide and Adverse Grief Reactions**

Macdonald and colleagues [16] conducted a qualitative study with participants who had lost a male family member by suicide. The participants reported on their perception of the suicide and their struggles with meaning making and finding closure. Mathieu and colleagues [17] compared bereavement after different modes of death six months after the loss and did not find a difference in coping styles. However, having a previous mental health diagnosis was associated with increased avoidant and problem-focused coping, and stigma and shame were associated with increased avoidant coping. Women were more

**Citation:** Levi-Belz, Y.; Krysinska, K.; Andriessen, K. What Do We Know about Suicide Bereavement, and What We Can Do to Help Suicide-Loss Survivors? *Int. J. Environ. Res. Public Health* **2023**, *20*, 5577. https://doi.org/10.3390/ ijerph20085577

Received: 31 March 2023 Accepted: 18 April 2023 Published: 19 April 2023

**Copyright:** © 2023 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/).

likely to report using adaptive coping than men. Goodall and colleagues [18] conducted a systematic review on continuing bonds in suicide bereavement and found that continuing bonds can be experienced in various ways and that most people bereaved by suicide tended to perceive it primarily as a positive experience that may help with coping and meaning making.

Little is known about suicide bereavement in later life, and to address this gap Hafford-Letchfield and colleagues [19] explored how suicide loss can intersect with ageing and what supports are needed for this population. Interestingly, several participants had guided their social network to receive the necessary support. In another important study, Tiech Fire and colleagues [20] focused on school staff, with the aim of understanding the impact of student suicides on post-trauma and grief symptoms among teachers, counsellors, and school principals. The authors found that homeroom teachers suffered more from complicated grief and post-traumatic stress disorder (PTSD) compared to psychologists and counsellors and, as such, should receive more preparatory training. Additionally, in the context of schools, Khalid and colleagues [21] found encouraging results from a training program that increased preparedness and skills in school staff to respond to student suicides. Rivant and colleagues [22] focused on suicide bereavement among ethnic minority groups. They found that this population suffers from a lack of support and high prevalence of stigma in the aftermath of suicide loss. These preliminary results broaden our understanding of a minority population which requires special attention, more visibility, and better access to support services.

Andriessen and colleagues [23] examined the experiences of adolescents who participate in qualitative research interviews about suicide-related experiences, as there is a perception of risk regarding asking young people about these topics. Importantly, the findings indicated that bereaved adolescents, as well as parents and clinicians, could safely participate in research interviews regarding their experiences of grief after suicide, and they highly valued this opportunity to share their experiences. These findings can be used to build future study designs to help us to better understand the processes of grief after suicide among adolescents.

Several studies in our Special Issue examined deleterious and long-term effects of suicide bereavement. In a latent class analysis, Grafiadeli and colleagues [24] found that about half of the examined population showed elevated prolonged grief disorder symptoms, and one-third of the sample also showed PTSD symptoms. In a six-year longitudinal study, Levi-Belz and Brinbaum [15] highlighted that suicide bereavement facilitated higher levels of depression and suicide ideation. Other studies also emphasized the moderators of these negative outcomes. Levi-Belz and Brinbaum [15] found that the sense of belongingness can serve as a buffer against depression, as suicide-loss survivors with higher levels of belongingness were less vulnerable to depression at later assessments. Levi-Belz and Ben-Yaish [9] highlighted interpersonal factors, such as social support and self-disclosure, that serve as moderators of prolonged grief symptoms following suicide bereavement. Pitman and colleagues [25] examined whether bereavement by various causes had a deterrent effect on alcohol and drug use in bereaved individuals. They found no group differences regarding reduced alcohol use, but a significantly greater proportion of people bereaved by sudden unnatural causes, including suicide, reduced/stopped drug use post-bereavement compared to people bereaved by sudden natural causes.

### **2. Impact of Suicide on Mental Health Professionals**

Both health and mental health professionals are at risk of losing a client or a colleague to suicide. The integrated review of 17 articles conducted by Causer and colleagues [26] emphasized the impact that a suicide by a colleague may have on workers in healthcare and other settings. They found that the perceptions of grief are complicated by professional identities and workplace cultures. Tamworth and colleagues [27] revealed that losing a patient to suicide can be a profoundly traumatic experience for psychiatrists. Peer support was key in processing their grief.  These authors examined the relationships between attitudes toward (client) suicide and the psychological impact of client suicide as perceived by the therapists. It was found that those who believe that "suicide can and should be prevented" reported a higher impact in the form of short-term emotional and long-term professional impacts. Together, these studies indicate a need for systemic postvention, enhanced peer support, and promotion of self-care among mental health professionals.

### **3. Coping and Support for Those Bereaved by Suicide**

Agniete˙ Cepulien ˇ e and Skruibis [ ˙ 29] conducted a qualitative interview study and analyzed the data using reflexive thematic analysis. They found that spirituality can function as a resource after a loved one's suicide and can even contribute to post-traumatic growth after the loss, while spirituality-related issues, such as stigmatization and a lack of personally meaningful traditions, can contribute to higher distress among suicide-loss survivors. In a scoping review, Higgins and colleagues [30] indicated the potential effectiveness of peer-led suicide bereavement support, but also highlighted a need for rigorous design and evaluation of peer-led interventions in this field. Hybholt and colleagues [31] explored the experiences of members of peer-led support groups in Denmark and Ireland. Although some participants found it difficult to participate in a peer support group, most participants described them as safe and supportive spaces that aided in their grief process. Griffin and colleagues [32] surveyed participants of peer-led support groups and found a significant improvement in wellbeing and grief reactions, adjusting for time since bereavement. The participants reported that the groups provided a sense of belonging and hope. This study underscored the enduring mental health challenges for those bereaved by suicide and the need for the ongoing availability of peer-led support in postvention.

In conclusion, the studies included in this Special Issue emphasize the short- and long-term impact of suicide loss, the needs of those bereaved by suicide, and appropriate interventions in the aftermath of suicide loss. The included studies showed that suicide bereavement impact various populations, far beyond the nuclear family of the deceased. Moreover, these studies highlight the risk of long-term mental health challenges and adverse grief reactions among those bereaved by suicide. Health professionals, often involved in suicide prevention, should not be overlooked with regard to support after a loss by suicide.

### **4. Public Health Approach to Postvention**

As individuals and population groups may experience suicide loss differently, and their needs for support may evolve over time, various support options must be available. A recent review of the literature indicates that adjusting the support to the level of the impact of the bereavement, and focusing the support on the grief rather than on other outcomes are key characteristics of effective suicide bereavement support [33]. As indicated by studies on peer-led support in this Special Issue, the involvement of trained peers who may serve as role models or community members enhancing the social support network, may contribute to the effectiveness of suicide bereavement support [33].

According to the public health model, universal interventions target those who experience little impact from a death by suicide. Such interventions may include, for example, leaflets, fact sheets, or online information about suicide bereavement for wide audiences. Selective interventions target people with moderate grief reactions and include support groups, community and educational support, and training for health professionals. Indicated interventions, focusing on people with adverse grief and mental health reactions, may include specific grief therapy, and psychological and psychiatric support [33]. Adopting a public health approach to postvention can help to better tailor service delivery to the needs of the bereaved individuals and to align postvention with suicide prevention programs, which are also often based on this public health model. The training of service providers, including peers, volunteers, and health professionals, is paramount. Further evaluation

and research will strengthen the evidence of effectiveness of the interventions and service delivery in this important field.

**Author Contributions:** Conceptualization, Y.L.-B. and K.A.; investigation, Y.L.-B., K.A. and K.K. writing—original draft preparation, Y.L.-B., K.A. and K.K.; writing—review and editing, Y.L.-B., K.A. and K.K. All authors have read and agreed to the published version of the manuscript.

**Conflicts of Interest:** The author declares no conflict of interest.

### **References**

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.


**4.1 A blueprint for an organizational culture**

The establishment of a new institution created an opportunity for devising a professionspecific, independent system of shared values and beliefs implying and reinforcing a collective identity centered on the mission of the biomedical engineer. Our aims exceeded "standard faculty" programs, providing students with government-designed minimum curricula. Our main objective is for MSIB to become a leading research and educational center (Augustyniak et al. 2010). Despite a relatively short history of only five years, the School has undoubtedly earned high marks in Poland and has become well-recognized abroad. This was possible due to:

Fig. 8. Professor Zbigniew Kakol, Rector of AGH-UST, confers an Engineering Diploma (2010).

The organizational culture of the MSIB is based on a deeply motivated concept of a highquality teaching and learning institution, aiming at the education of marketable BME professionals (Gordon & DiTomaso, 1992). The School is student-friendly and supports students' educational initiatives in various fields of activity. What is expected and/or requested from the staff and students are well-defined goals to achieve. In this spirit, thanks to the common sense of responsibility, the internal atmosphere in the School supports cooperation rather than competition.

To make common attitudes and values more popular and generally recognized, the organizational culture of the MSIB offers the following:

• Leadership and promotion of common activities, exchanges, encouragement of staff

• Dissemination of knowledge and participation of staff members in international conferences and their activity in commissions and other opinion-forming bodies.

Fig. 8. Professor Zbigniew Kakol, Rector of AGH-UST, confers an Engineering Diploma

The organizational culture of the MSIB is based on a deeply motivated concept of a highquality teaching and learning institution, aiming at the education of marketable BME professionals (Gordon & DiTomaso, 1992). The School is student-friendly and supports students' educational initiatives in various fields of activity. What is expected and/or requested from the staff and students are well-defined goals to achieve. In this spirit, thanks to the common sense of responsibility, the internal atmosphere in the School supports

To make common attitudes and values more popular and generally recognized, the

• Ceremonies (matriculation, the Dean's address at the New Year, summarizing

• Corporate design (a well-recognized logo, a precisely defined color, organizational

• Outstanding personalities - undoubtedly this honor goes to Professor Ryszard Tadeusiewicz, the founder of the School and former Rector of AGH-UST, a pioneer in

• Common recreational activities (mountain trekking, sailing, skiing, student sports teams in various disciplines, volunteer-based events in hospitals and hospices, initiatives on behalf of the handicapped, extramural students' organizations and

biomedicine and author of several BME-related books since the mid-70s;

and students' mobility, additional lectures etc.;

(2010).

cooperation rather than competition.

forums).

organizational culture of the MSIB offers the following:

achievements challenges, and future plans, etc.);

badges for Board members, corporate T-shirts for students);

The corporate culture is built on selected values and behavioral norms that influence both the employees and students through the internal and external institutional policy. The commonly accepted standards constitute the internal ambience and friendliness of the School, but as a long-term investment become everyday habits. We easily observe teachers transferring these standards to their own departments, which justifies the belief that in the future the graduates will also promote such standards in their workplaces.

Fig. 9. Informal mountain trekking of MSIB students and the Dean (first from the left).


**4. Conclusion**

Occupational therapy is a rehabilitation specialty that facilitates the development of functional skills in children with ASD. Occupational therapists often work as part of an interdisciplinary treatment team. In this capacity, it is important for therapists to communicate across disciplines to be sure that treatment is carried over from one area to another.

There are many therapeutic approaches that occupational therapists can use to encourage growth and development in children with ASD. These treatment approaches have varying levels of evidence supporting their efficacy. Clinicians need to be mindful of the current evidence and use their knowledge of the child and the treatment, along with their clinical judgment, to create effective interventions.


Percentiles of RUL at 9 cycles

During MCMC sampling, the number of samples Ns is set to 5000 (line 12). Since the sampling process takes many iterations to converge, the initial 20% of the samples are discarded in calculating the posterior distribution by command burnIn = 0.2 (line 13). In order to keep 5000 samples, Ns/(1-burnIn) = 6250 samples (line 21) are

and upper-bounds of the distribution.

DOI: http://dx.doi.org/10.5772/intechopen.82781

Following is the sample output from BM.m:

(line 62–64):

end

17

for j=1:size(param,1)

b = param(1,:); s = param(2,:);

given time t (line 66).

eval([ParamName(j,:) '=param(j,:);']);

is used for calculating the acceptance ratio (line 23).

time and model parameters can be an array of samples.

3.2 Bayesian parameter estimation with MCMC (lines 16–31)

In the case of the battery example, this command is equivalent to.

It is expected that the MATLAB script is saved as a file with the name of 'BM.m', which has two input arguments, para0 and weigh (line 1). The first argument, para0, is the initial sample of model parameters, and weigh is the width w of the proposal distribution in Eq. (12). The size of each array should be the same as the number of model parameters. The following is an example of calling the code in the command window of MATLAB:

#### samplResul=BM([0.011 0.02]', [0.001 0.003]');

In the above MATLAB command, para0 = [0.011 0.02]' is the initial sample of b and s, and weigh = [0.001 0.003]' is the width of proposal distribution of b and s. Since the convergence and accuracy depend on these two variables, it is suggested to try with different values. Since the users know the prior distribution of the model parameters, it is a good practice to start with the mean of the prior distribution as an initial sample. If the code ran successfully, it will return the samples of model parameters in the samplResul array and will generate two plots. The first plot is the trace of MCMC samples, and the second plot is the histogram of the RUL.

#### 3.1 Problem definition (lines 2–15, 65–67)

The problem definition means defining the degradation equation using model parameters and time/cycle. All known parameters, as well as the initial estimate of unknown parameters, parameter names, and model data, need to be defined. The problem definition consists of two parts: parameter definition and model definition. For parameter definition (lines 2–15), 'Battery' is used as a WorkName (line 3). The capacity is measured every week, so TimeUnit is 'weeks' (line 4). In line 5, time is an array of discrete times in the units of TimeUnit. Measurements and predictions will be done at these times. The relative C/1 capacity data is stored as measuData (lines 6–7), which has 10 weeks of measurement; that is, Ndata ¼ 10 (k1 in line 18). These data correspond to the first 10 times in time array. Since time starts from 0, the 10th time corresponds to 9 weeks, which is the current time; that is, tCUR ¼ 9week. The degradation will be predicted for future times that are from 10 to 50 weeks. The measurement data are generated using the MATLAB script in Section 2.1. It is noted that due to random noise, the users may experience different realizations of measurement data.

In line 8, the degradation threshold ythreshold is defined using variable 'thres' with the value of 0.7. ParamName in line 9 is the name of model parameters: model parameter 'b' and standard deviation of noise 's'. Since the parameter name will actually be used in the model, it is important to use the actual name of variables here. The number of parameters is stored in the variable 'p' in line 17. It is noted that the last parameter should be the standard deviation of noise 's'. prioDisPar stores the information of the prior distribution of model parameters, as given in

Prognostics 102: Efficient Bayesian-Based Prognostics Algorithm in MATLAB DOI: http://dx.doi.org/10.5772/intechopen.82781

Eq. (9). When a uniform prior distribution is used, each row contains the lowerand upper-bounds of the distribution.

During MCMC sampling, the number of samples Ns is set to 5000 (line 12). Since the sampling process takes many iterations to converge, the initial 20% of the samples are discarded in calculating the posterior distribution by command burnIn = 0.2 (line 13). In order to keep 5000 samples, Ns/(1-burnIn) = 6250 samples (line 21) are generated first, and then, nBurn = 1250 samples (line 30) are discarded.

Since the RUL is represented by Ns samples, the confidence interval or the prediction interval is often used to support the decision-making process. signiLevel (line 14) is the significance level of this interval in percentage. When signiLevel = 5, the code will return the lower 5 percentile, median, and the upper 5 percentile. Following is the sample output from BM.m:

> # Percentiles of RUL at 9 cycles 5prct: 18.7182, median: 20.381, 95prct: 22.1576

For the model definition, the degradation model ~y tð Þ ; b in Eq. (1) is defined in lines 65–67. In this equation, t is the time of measurement, and b is the model parameter as defined in line 9. The model equation needs to be defined in such a way that component-by-component operations are possible. This is because the time and model parameters can be an array of samples.

#### 3.2 Bayesian parameter estimation with MCMC (lines 16–31)

In the Bayesian parameter estimation process, the posterior distribution is expressed in terms of the product of the prior distribution and the likelihoods of all measured data. In the MATLAB code BM.m, the degradation model and the posterior distribution are calculated in the function BMappl (lines 60–76). First, the parameter samples in param are assigned to the variables using the eval function (line 62–64):

for j=1:size(param,1) eval([ParamName(j,:) '=param(j,:);']); end

In the case of the battery example, this command is equivalent to.

b = param(1,:);

3. MATLAB implementation

Fault Detection, Diagnosis and Prognosis

command window of MATLAB:

3.1 Problem definition (lines 2–15, 65–67)

realizations of measurement data.

16

quent sections with an example of battery degradation.

In this section, MATLAB implementation of prognostics using the Bayesian method is discussed. In the following explanation, 'line' or 'lines' in a parenthesis indicated the number of the line of the code in Appendix. The code is divided into three parts: (1) Problem Definition (lines 2–15, 65–67) (2) Bayesian parameter estimation and MCMC sampling (lines 16–29, 60–76) (3) Post-processing for displaying results (lines 40–57). Only the Problem Definition part needs to be changed for different applications. Detailed explanations are given in the subse-

It is expected that the MATLAB script is saved as a file with the name of 'BM.m',

which has two input arguments, para0 and weigh (line 1). The first argument, para0, is the initial sample of model parameters, and weigh is the width w of the proposal distribution in Eq. (12). The size of each array should be the same as the number of model parameters. The following is an example of calling the code in the

samplResul=BM([0.011 0.02]', [0.001 0.003]');

trace of MCMC samples, and the second plot is the histogram of the RUL.

In the above MATLAB command, para0 = [0.011 0.02]' is the initial sample of b and s, and weigh = [0.001 0.003]' is the width of proposal distribution of b and s. Since the convergence and accuracy depend on these two variables, it is suggested to try with different values. Since the users know the prior distribution of the model parameters, it is a good practice to start with the mean of the prior distribution as an initial sample. If the code ran successfully, it will return the samples of model parameters in the samplResul array and will generate two plots. The first plot is the

The problem definition means defining the degradation equation using model parameters and time/cycle. All known parameters, as well as the initial estimate of unknown parameters, parameter names, and model data, need to be defined. The problem definition consists of two parts: parameter definition and model definition. For parameter definition (lines 2–15), 'Battery' is used as a WorkName (line 3). The capacity is measured every week, so TimeUnit is 'weeks' (line 4). In line 5, time is an array of discrete times in the units of TimeUnit. Measurements and predictions will be done at these times. The relative C/1 capacity data is stored as measuData (lines 6–7), which has 10 weeks of measurement; that is, Ndata ¼ 10 (k1 in line 18). These data correspond to the first 10 times in time array. Since time starts from 0, the 10th time corresponds to 9 weeks, which is the current time; that is, tCUR ¼ 9week. The degradation will be predicted for future times that are from 10 to 50 weeks. The measurement data are generated using the MATLAB script in Section 2.1. It is noted that due to random noise, the users may experience different

In line 8, the degradation threshold ythreshold is defined using variable 'thres' with

the value of 0.7. ParamName in line 9 is the name of model parameters: model parameter 'b' and standard deviation of noise 's'. Since the parameter name will actually be used in the model, it is important to use the actual name of variables here. The number of parameters is stored in the variable 'p' in line 17. It is noted that the last parameter should be the standard deviation of noise 's'. prioDisPar stores the information of the prior distribution of model parameters, as given in

```
s = param(2,:);
```
This is why the ParamName in line 9 must have the same name with the actual variable. Then, these parameters are used to calculate the degradation model with given time t (line 66).

If measurement data (measuData) is empty, then BMappl only calculates the degradation model with given parameter samples at a given time t. This corresponds to propagating the degradation model using parameter samples to the future time for prognostics. If measurement data are provided (lines 71–74), then BMappl calculates the values of the posterior distribution at the parameter samples. In this case, the time should be given as an array of Ndata components from the start time to the current time. The posterior distribution in Eq. (11) (line 74) is the multiplication of the prior distribution (line 71) in Eq. (9) with the likelihood of all measured data (lines 72–73) in Eq. (10). The calculated posterior distribution from BMappl is used for calculating the acceptance ratio (line 23).

MCMC sampling using the MH algorithm starts with the initial sample that is provided by the users (line 19) and the value of the posterior PDF (line 20). In the loop of MCMC sampling (lines 21–29), a candidate sample is randomly generated from a uniform distribution, centered at the current sample and the width of �w (line 22). The value of posterior PDF for the candidate sample is also calculated (line 23). If the acceptance ratio in Eq. (13) is greater than a randomly generated number u, then the candidate sample is accepted as a new sample (lines 25–26). Otherwise, the current sample and its posterior PDF are kept as a new sample and PDF. Once the MCMC sampling loop is over, the first 20% of the samples are discarded as a burn-in process (line 31). At the end of Bayesian parameter estimation, samplResul array contains Ns samples of model parameters.

### 3.3 Remaining useful life prediction (lines 32–39)

Once the samples of model parameters are obtained based on the posterior distribution, they can be used to find the RUL, which is the time when the degradation prediction reaches the threshold. First, for all samples in samplResul, the degradation is predicted in the future times between tCUR ¼ k1 and tend.

for k=1:length(time(k1:end)) [degrPreCon(k,:),�]=BMappl(samplResul,ParamName,time(k1-1+k),[],[]); end

Once the degradations in the future times are calculated, MATLAB function interp1 is used to find the time when ~y tð Þ¼ EOL; b ythreshold. Once tEOL is found, the RUL can be calculated using Eq. (3).

```
for i=1:Ns
 RUL(i)=interp1(degrPreCon(:,i),time(k1:end),thres,'pchip') - time(k1);
end
```
The option 'pchip' in interp1 uses a shape-preserving piecewise cubic interpolation, which preserves C1 -continuity.

### 3.4 Postprocessing (lines 40–58)

In the postprocessing stage, the results given in samples are interpreted in terms of statistical quantities or in the form of graphs. First, in the RUL array, those components that have an infinite life should be removed (line 41). Then, the confidence intervals of [5%, median, 95%] are calculated from the RUL array and stored in rulPerce (line 42–43).

The MATLAB code plots two figures. The first figure plots the trace of MCMC samples (lines 45–50) as shown in Figure 6(a). This trace shows the quality of MCMC samples. If samples are distributed randomly and symmetrically around the mean with a constant bound, then it means that the samples are stabilized and well represent the posterior distribution. If the trace of samples shows an irregular behavior as shown in Figure 6(b), the samples may not represent the posterior PDF properly. This can happen when the initial sample was far away from the mean and when the width of the proposal distribution is too narrow or too wide.

The second plot is the histogram of RUL (lines 51–53) as shown in Figure 7. At the end of the code, the confidence intervals of [5%, median, 95%] are printed on the command window (lines 54–56). All variables are saved in the computer file so that they can be loaded to the memory for further analysis (line 57). The name of the saved database is "WorkName at tCUR.mat". For example, in the battery case, the saved database name is "Battery at 9.mat".

Although the MATLAB code plots two figures, it is possible that the users can plot different figures using the saved database. After calling the BM.m function, the saved database has to be loaded to the memory using the following commands:

Trace of samples from MCMC sampling (a) proper samples and (b) improper samples.

Prognostics 102: Efficient Bayesian-Based Prognostics Algorithm in MATLAB

DOI: http://dx.doi.org/10.5772/intechopen.82781

clear; clc; load('Battery at 9.mat')

Histogram of the remaining useful life.

Figure 6.

Figure 7.

19

Prognostics 102: Efficient Bayesian-Based Prognostics Algorithm in MATLAB DOI: http://dx.doi.org/10.5772/intechopen.82781

Figure 6.

loop of MCMC sampling (lines 21–29), a candidate sample is randomly generated from a uniform distribution, centered at the current sample and the width of �w (line 22). The value of posterior PDF for the candidate sample is also calculated (line 23). If the acceptance ratio in Eq. (13) is greater than a randomly generated number u, then the candidate sample is accepted as a new sample (lines 25–26). Otherwise, the current sample and its posterior PDF are kept as a new sample and PDF. Once the MCMC sampling loop is over, the first 20% of the samples are discarded as a burn-in process (line 31). At the end of Bayesian parameter estimation, samplResul

Once the samples of model parameters are obtained based on the posterior distribution, they can be used to find the RUL, which is the time when the degradation prediction reaches the threshold. First, for all samples in samplResul, the

[degrPreCon(k,:),�]=BMappl(samplResul,ParamName,time(k1-1+k),[],[]);

Once the degradations in the future times are calculated, MATLAB function interp1 is used to find the time when ~y tð Þ¼ EOL; b ythreshold. Once tEOL is found, the

RUL(i)=interp1(degrPreCon(:,i),time(k1:end),thres,'pchip') - time(k1);

The option 'pchip' in interp1 uses a shape-preserving piecewise cubic interpola-

In the postprocessing stage, the results given in samples are interpreted in terms

of statistical quantities or in the form of graphs. First, in the RUL array, those components that have an infinite life should be removed (line 41). Then, the confidence intervals of [5%, median, 95%] are calculated from the RUL array and

The MATLAB code plots two figures. The first figure plots the trace of MCMC samples (lines 45–50) as shown in Figure 6(a). This trace shows the quality of MCMC samples. If samples are distributed randomly and symmetrically around the mean with a constant bound, then it means that the samples are stabilized and well represent the posterior distribution. If the trace of samples shows an irregular behavior as shown in Figure 6(b), the samples may not

represent the posterior PDF properly. This can happen when the initial sample was far away from the mean and when the width of the proposal distribution is too

The second plot is the histogram of RUL (lines 51–53) as shown in Figure 7. At the end of the code, the confidence intervals of [5%, median, 95%] are printed on the command window (lines 54–56). All variables are saved in the computer file so that they can be loaded to the memory for further analysis (line 57). The name of the saved database is "WorkName at tCUR.mat". For example, in the battery case,

degradation is predicted in the future times between tCUR ¼ k1 and tend.

array contains Ns samples of model parameters.

for k=1:length(time(k1:end))

Fault Detection, Diagnosis and Prognosis

RUL can be calculated using Eq. (3).

3.4 Postprocessing (lines 40–58)

stored in rulPerce (line 42–43).

the saved database name is "Battery at 9.mat".

narrow or too wide.

18

end

end

for i=1:Ns

tion, which preserves C1

3.3 Remaining useful life prediction (lines 32–39)

Trace of samples from MCMC sampling (a) proper samples and (b) improper samples.

Figure 7. Histogram of the remaining useful life.

Although the MATLAB code plots two figures, it is possible that the users can plot different figures using the saved database. After calling the BM.m function, the saved database has to be loaded to the memory using the following commands:

clear; clc; load('Battery at 9.mat')

In addition to the trace of samples shown in Figure 6, it is possible to plot the histogram of model parameters using the same samples. The following commands plot the histograms of all model parameters.

20.38 weeks, which is close to the true RUL. In addition, the 90% confidence interval is about 3.4 weeks; that is, the uncertainty in the prediction is about 17%.

Prognostics 102: Efficient Bayesian-Based Prognostics Algorithm in MATLAB

The code can be modified easily by the users for various applications. In this section, an example of crack growth is used to explain how the MATLAB code BM.m

In fatigue crack growth, the failure criterion is given in terms of the crack size. Therefore, it would be appropriate to use the size of crack as a degradation feature. In this case, the degradation feature monotonically increases, while it was monotonically decreased for the battery example. Assuming that a through-the-thickness center crack exists in an infinite plate under mode-I loading condition, the rate of

dN ¼ Cð Þ ΔK m (16)

1�m 2 0

2 ð Þ, s ¼ 0:0005m to the true crack sizes. The

2�m

(17)

πa p is the range of stress intensity factor, and Δσ is the stress

π � � p m þ a

h i 2

fatigue crack growth can be expressed using the Paris-Erdogan model as

da

where a is the half crack size, N is the number of cycles, m and C are model

range. It is assumed that time is the number of fatigue loading cycles. For the consistent notation, the crack size and cycles are replaced with ~y ¼ a and t ¼ N in the following explanation. Since the degradation model requires the crack size as a function of time and model parameters, Eq. (16) can be integrated to obtain the

> 2 � � Δσ ffiffiffi

mtrue ¼ 3:8 and Ctrue ¼ 1:5 � 10�10. The measured crack size data are then generated

θ ¼ f g m; ln ð Þ C ; s . In the Paris-Erdogan model, the y-intercept C is very small but changes its magnitude by several orders. Therefore, it would be better to identify logarithm of C. For RUL calculation, the critical crack size is determined as 0.043 m. For the Bayesian method, it is necessary to define the prior distribution and the

likelihood function. In the battery example, it was assumed that noise in data follows a normal distribution. However, when the distribution type of measurement noise is unknown, it is possible that the likelihood function might be different from the true noise distribution. The same is true for the prior/initial distribution. Therefore, it would be a good exercise to study the effect of different distribution types by changing the MATLAB codes. In this example, the lognormal distribution

the true crack size data are generated at every 50 cycles using Eq. (17) with

measured crack size data are used to identify three model parameters,

The system is under fatigue loading with the range of stress being Δσ ¼ 75MPa at each cycle. It is assumed that the health monitoring is performed every 50 cycles to measure the crack size yk until the current time tCUR ¼ 1, 200 cycles, and the initial size of the crack is a0 ¼ 0:01m. Similar to the battery degradation example, the measurement data are simulated by adding random noise to the true crack size. First,

~y tð Þ¼ ; m;C tC 1 � m

4. Application to crack growth prognostics

DOI: http://dx.doi.org/10.5772/intechopen.82781

4.1 Model definition: crack growth

parameters, ΔK ¼ Δσ ffiffiffiffiffi

following degradation model:

by adding Gaussian noise ε � N 0; s

is employed for the likelihood function as:

21

can be modified.

```
figure; % histogram of parameters
for j=1:p;
 subplot(1,p,j);
 hist(samplResul(j,:),30);
end
```
When the true degradation model is known, it is possible to compare the predicted degradation with the true one. The following MATLAB script plots the median and confidence intervals of the predicted degradation along with the true degradation and the threshold.

```
figure;
degraTrue=exp(-0.012.*time);
degraPI=prctile(degraPredi',perceValue)';
plot(time,degraTrue,'k'); hold on;
plot(time(1:k1),measuData,'*b');
plot(time(k1:end),degraPI(:,1),'–r');
plot(time(k1:end),degraPI(:,2:3),':r');
plot([0 time(end)],[thres thres],'g');
xlabel('weeks'); ylabel('Relative C/1 capacity');
```
The degradation curves up to 50 weeks are shown in Figure 8 for the battery example. The true degradation with b ¼ 0:012 is shown with the black curve. The red curves show 5, 50 (median) and 95 percentiles of the predicted degradation, which are caused by signiLevel = 5 (line 14). The plot also shows the threshold (green line) and measurement data (blue asterisk marks). Based on the true model, the end of life of the battery is tEOL ¼ 29:72 weeks, and thus, the true RUL should be tRUL ¼ 20:72 weeks. The prediction shows that the median of RUL is

Figure 8. Comparison of the predicted degradation with the true degradation.

20.38 weeks, which is close to the true RUL. In addition, the 90% confidence interval is about 3.4 weeks; that is, the uncertainty in the prediction is about 17%.