**4. Discussion**

High genetic variability observed for aflatoxin resistance accumulation was an indication of the presence of novel or favorable alleles for population improvement. Furtherance to this, genotypes identified with reduced aflatoxin accumulation could be exploited in the development of superior hybrids that combine resistance to aflatoxin accumulation and high yields as described previously by Warburton and Williams [6]. The observed significant phenotypic variation for the major, minor and across seasons and locations among the genotypes for aflatoxin accumulation reduction and other agronomic traits suggested that progress could be made in developing well adopted lines with good aflatoxin accumulation resistance.

The significant environmental and genotypic effects detected for aflatoxin accumulation resistance and other agronomic traits indicated variability among the genotypes under different environments. Also the significant genotype x environment interactions observed across the seasons and locations indicates the need for evaluation of genotypes across several environments in order to determine most stable genotypes for aflatoxin accumulation resistance and other agronomic traits. According to Comstock and Moll [15], genotype x environment interactions determined in multi-location trials implied reduced correlation between genotypic and phenotypic values. Zuber [16] identified significant environmental effects on aflatoxin accumulation among commercial hybrids and OPVs in the United States of America. It was not uncommon to observe G x E effects on the genotypes evaluated across contrasting environments in Ghana.

Broad sense heritability among traits ranged from moderate to very high estimates during the major season where adequate rains and less disease pressure was observed. However, significantly lower range of estimates were detected during the minor season (data not shown) confirming earlier reports by [17] who demonstrated significant environmental influence on heritability estimates in cashew. Moderate to high heritability estimates realized in this study, suggested that possible gains are achievable in hybrid maize development for high yields and aflatoxin accumulation resistance.

Further evaluation of the agronomic traits revealed a range of genotypic influence on several parameters studied. Significant among them were days to 50% pollen and silking which clearly categorized the genotypes into the three well defined and established classes of extra early, intermediate and late types as reported by Badu- Apraku [18] who categorized maize genotypes into the different maturity groups. Such information is critical and necessary to guide planting periods in breeding nurseries designed to cross among the maturity groups for trait introgression and further improvement for hybrid development.

The combined analysis showed that most genotypes belonged to the intermediate group while a few were extra early or late maturing. For instance, genotype MP715 has been reported in previous studies [19] as highly resistant to aflatoxin accumulation with delayed silking ranging between 70 and 80 days when grown in a temperate environment, however in this study it ranged between 62 and 67 days under tropical conditions in Ghana, where it is evidently adapted. On the other

hand, genotypes identified with delayed silking dates included MP719, TZI8, NC334, OBAATANPA, CML176, CML247, CML287, CML343 and CML5.

Aflatoxin accumulation levels during the major season were comparatively lower across environments although levels in Wenchi were slightly higher. Unlike the major season, the accumulation levels in the minor season were considerably higher across environments with Wenchi still ranking highest. This observation agrees with the findings of several authors [2, 6, 20, 21] who reported the existence of positive correlation of drought and heat on aflatoxin accumulation level. The Guinea savanna transition environment, which appears to be relatively drier, was conducive for aflatoxin production.

The ranking of top ten resistant genotypes across environments revealed a consistent set of genotypes (although in different ranking order of resistance per environment) during both major and minor seasons. Genotypes which consistently displayed stable resistance across the environments included MP715, NC298, MP705, MP719, CML287 and TZEEI- 24 while the rest appeared less stable. Two local extra early lines (TZEEI-24 and TZEEI-4) were identified as sources of potential resistance to aflatoxin but their level of resistance was not as good as the Mississippi lines specifically bred for resistance and that further evaluations of these two locally adapted lines may be required to confirm their levels of resistance to aflatoxin accumulation.

It was also obvious from this study that, majority of the inbred lines outperformed the OPVs and the populations' in-terms of reduced aflatoxin accumulation levels which was in agreement with the previous findings of Zuber [16] who reported superiority of hybrids (inbred combinations) over OPVs in-terms of measured aflatoxin accumulation resistance across locations and years in the United States.

The levels of total aflatoxin accumulated by the resistant genotypes in this study are comparable to the levels previously reported by William and Windham [5] and Brown [2] where a set of hybrids were evaluated for aflatoxin accumulation resistance. Information obtained from the total aflatoxin accumulation levels among the genotypes could therefore guide the selection of appropriate parental candidates for future aflatoxin resistance breeding in Ghana. Breeding for resistance involves several approaches of which trait correlations is paramount. Indirect selection of one trait simultaneously improves other traits that are significantly correlated.

Zuber [16] discovered strong significant correlation between insect damage and aflatoxin accumulation during evaluation of OPVs and released commercial hybrids in the United States of America. The correlation observed between insect damage and aflatoxin accumulation in this study was similar to that of Zuber [16] as well as the observations made by Williams [22] and Ni [23]. Significant positive correlations were also observed between aflatoxin accumulation levels and plant aspect and cob aspect whilst ears per plant showed a weak negative correlation. Stay-green and open- tip did not correlate with aflatoxin accumulation levels as recounted in other studies [24, 25].

The study of genetic relationship among genotypes which was based on significant agronomic traits assigned all genotypes into three main groups when 40% of the variation among the genotypes was explained. On the contrary, only two main groups were realized when 20% of the genotypic variation was explained by the significant traits used for the grouping. In the case of the two groups, all exotic genotypes were assigned into one group except Ki3, CML108 and NC340 which clustered together with the local genotypes. This observation was not surprising since most of the local genotypes were sourced from CIMMYT and may have similar pedigree or ancestry records.

It appears that the top resistant genotypes which also clustered in one common group perhaps originated from a common ancestry of Tuxpe˜no germplasm native to Mexico which exhibits tropical characteristics coupled with aflatoxin accumulation resistance [6].

Although the analysis of the multiple phenotypic traits assigned genotypes into distinct groups, it showed a low corroboration when compared to other molecular methods (data not shown). This is probably because the expression of most agronomic traits are influenced by the environment.


**3. Deteriorative effects of iron against NASH/NAFLD**

Iron overload is one of the important risk factors for diabetes. The relationship between iron and diabetes was first recognised in pathologic conditions − namely hereditary hemochromatosis and thalassemia − but high levels of dietary iron also enhance the risk of diabetes. It is generally recognised that iron plays a direct and causal role in diabetes pathogenesis, mediated both by β-cell failure and insulin resistance.

Iron is capable of generating hydroxyl radicals from peroxide and can also inhibit antioxidant defences such as SOD2 [55]. Highly elevated iron levels have been linked to oxidative damage to DNA, lipids and proteins that, in turn, have been implicated in cardiovascular disease, diabetes, atherosclerosis and neurological degeneration, as seen in Alzheimer's disease [56].

Iron homeostatic pathways are tightly associated with inflammatory stressors. Inflammation causes significant upregulation of hepcidin, largely through interleukin-6 (IL-6), and results in large increases in serum ferritin levels.

There is a greater prevalence of iron deficiency in obese (39%) and overweight (12%) children and adolescents than in normal-weight children, the prevalence of iron deficiency in whom is only 4% [28]. The association of iron deficiency with obesity has been confirmed in other populations, which include children and adults of both sexes [57]. The conceivable cases for causality, in turn, can be made in both directions: normal or high iron stores might be required to support higher rates of fatty acid oxidation so that iron-deficient individuals are less able to mobilise and use high fat, or, conversely, the inflammatory nature of obesity might trigger increased hepcidin levels, which limit the absorption of dietary iron.

In the progression of diabetes, ROS can cause both β-cell failure and insulin resistance. β-cells are particularly sensitive to ROS because of low expression of antioxidants such as catalase and SOD2, overexpression of which has been associated with increased β-cell viability [58]. ROS can cause β-cell dysfunction by multiple mechanisms including decreased insulin gene expression secondary to decreased expression of transcription factors necessary for β-cell differentiation, maintenance and insulin gene transcription.

ROS have also been reported to directly affect circulating human insulin by hydroxylation of phenylalanine residues that result in lower affinity binding to the insulin receptor [59]. Finally, ROS can induce insulin resistance through multiple mechanisms; for example, through the activation of FOXO1, which prevents downregulation of gluconeogenesis even in the presence of insulin signalling [60]. Hypoxia-inducible factors 1 and 2 (HIF-1 and HIF-2) regulate cellular responses against low oxygen by upregulating transcription of a diverse set of proteins involved in angiogenesis, erythropoiesis and glycolytic flux [61]. HIFs also regulate iron metabolism, and under conditions of low iron levels, HIF-2 upregulates DMT-1 and DCYTB, whereas HIF-1 upregulates DMT-1 and decreases ferritin [62]. Conversely, cellular iron levels regulate HIF protein levels through the control of prolyl hydroxylase (PHD) activity [63].

Emerging data demonstrate that iron plays an important role in metabolic regulation and the pathophysiology of diabetes. Iron overload is common in T2DM [64, 65]. On the contrary, iron depletion seems to be protective for the development of diabetes. Rats with iron-deficiency anaemia are more insulin sensitive than controls [66], and phlebotomy improves the insulin sensitivity and glycemia, both in nondiabetic subjects [67] and T2DM subjects with high ferritin [68]. These studies suggest that iron plays an important role both in the development and improvement of diabetes. However, the precise molecular mechanisms of iron-associated diabetes are not well understood at present [69].


**6. Conclusions**

Inertial sensors can be used as a performance assessment tool in rowing. In the last decade, research into this field has gained momentum. Inertial sensors were used to measure performance features associated with stroke quality, metrics obtained from instrumented materials, indicators of the athlete's physicality and physiology and also general biofeedback. The review also assessed the properties of hardware that has been used in previous rowing research. Operational guidelines, based on this review, have been created and are proposed to assist future researchers with their methodology design and development. It is suggested that future research starts to incorporate more machine learning/neural network/AI algorithms and starts to focus on instrumenting the athlete rather than the equipment.

**Author Contributions:** Data retrieval, literature review design, review screening, and manuscript preparation, M.T.O.W.; literature review design, project supervision, and manuscript editing, H.G.E.; project supervision and manuscript editing, J.B.S. and D.V.T.

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

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


**6. Discussion**

The conclusions drawn in our study are supported by the quality of the research conducted. A key aspect of the quality of a Group Concept Mapping study is the number of participants per phase. Rosas and Kane [28] suggested a minimum range of 20–35 participants per phase. Our study included significantly larger participant groups (see **Table 1**), ensuring that the study's quality in this regard was adequately maintained. The clustering of statements resulted in the identification of seven distinct clusters, each representing a different theme. The different themes are in line with the work of Porter et al. [30], who emphasised the need for an institutional approach to blended education, going beyond course-level development. Such an approach requires strategic planning, structural changes, and adequate support at the university or college level. The nature of the statements may have been influenced by the timing of the data collection. The study was conducted during the midst of the pandemic, when teachers were grappling with

the transition from classroom-based lessons to online activities. It is highly likely that the statements were influenced by the daily experiences of both students and teachers. This transition can be characterised as substitution, where the content and pedagogical approaches remained unchanged, but the modality shifted from the classroom to the online environment. This aligns with the perspective of [9], that characterised the online education during the pandemic as a form of emergency remote teaching. We presume that as students and teachers become more proficient, leading to the implementation of advanced types of online learning and teaching, their perceptions regarding the benefits of online education will also be influenced.

In general, our findings suggest more moderate opportunities for educational change compared to the more transformative views expressed by [14], that consider the pandemic as a catalyst for significant educational change. Our study highlights the potential for a blended approach to teaching and learning, combining both classroombased and online modalities, with the classroom retaining its prominent role as the primary mode of instruction.

## **7. Limitations**

While we conducted our study among students and teachers at a single university of applied sciences, caution should be taken when generalising the findings. However, it is worth noting that during the pandemic the daily experiences of teachers and students of various institutes across Europe and beyond exhibited striking similarities [3, 11, 12]. Given that the collected statements were deeply rooted in their daily experiences, we assume that our findings hold relevance for other institutes in the field of vocational and professional education as well. One of the main advantages of Group Concept Mapping is its ability to gather statements from large groups of participants. However, it is important to acknowledge that there is no direct interaction between the researchers and the participants, as is the case with interviews, for example. Therefore, the thoughts, beliefs, concerns, and considerations of the participants that influenced the formulation of the statements, or the reasoning behind the sorting and rating of the statements, remain unknown in the context of Group Concept Mapping. When the objective is to gather more comprehensive background information, it is advisable to employ other methods, such as interviews.

### **8. Recommendations**

The different nature of the statements suggests the need to apply an integral approach at the institutional level for taking the next steps in developing online teaching and learning as part of blended education. An approach that includes strategy, structure and support [30]. The strategy focuses at the creation of an institutional definition of blended education, at the goals of blended education (e.g. enhanced pedagogy, increased access and flexibility, improved cost-effectiveness and resource use) and at the advocacy of blended education among management, administrators, teachers and other institutional personnel. The structure refers to the need for establishing the necessary technological infrastructure, the governance, and the systematic monitoring of the implementation to generate frequent feedback that enables evidence-informed further development of blended education. The support refers to the need for technical and pedagogical support, including the professional

#### *Perspective Chapter: Online Learning in Professional and Vocational Education – Seeking… DOI: http://dx.doi.org/10.5772/intechopen.112513*

development of teachers and other stakeholders, including students, since their ability and/or motivation to participate in online education may vary.

It is important that the institutional approach includes a view on the desired ambition level of blended education. Van der Klink and Brand-Gruwel [31] argue that the levels of ambitions of colleges and universities to implement blended education may vary and they distinguish three levels, ranging from Low Impact Blend, Medium Impact Blend to High Impact Blend, respectively (see also [32]). Low Impact Blend refers to adding extra technology-based activities to an existing classroom-based course. Characteristic for Medium Impact Blend is the replacement of classroombased teaching and learning by online activities. Finally, a High Impact Blend implies a full redesign of an existing classroom-based course. In general, most colleges and universities will presumably strive for a Medium Impact Blend. Though a Low Impact Blend requires less efforts, its benefits are modest as well. Moreover, there is a danger that the addition of activities may increase the workload of teachers and the study time of students [32]. In contrast, a Medium Impact Blend offers more benefits (e.g. more flexible course delivery) but requires also more investments to achieve the benefits. A Medium Impact Blend allows an incremental design in which teachers gradually replace course components, by experimenting with different approaches to learning and various tools.

It is very likely that the pandemic will eventually pave the way to a more prominent place of online learning in the repertoire of vocational and professional education. Based on our experiences in this study, we would like to recommend a careful and thoughtful approach to further developing online learning as part of a blended education. Blended education will definitely improve the flexibility of educational programmes to, for example, attract employees who want to upgrade their competencies or allow full-time students to combine their study with a job. But how high or modest our online ambitions may be, we always must remember to reflect the voices of teachers and (future) students in these ambitions. Here we would like to emphasise the need to involve students in our endeavours [33]. Students have the potential to inform the development of blended education in ways that other stakeholders could not. Therefore, methodologies that incorporate these voices, such as GCM, deserve our attention when it comes to designing and evaluating blended education.


**3. Study area**

Study based on Ba Be District, Bac Kan province, a mountainous area located in the northern of Vietnam. Ba Be has 68,412 hectares in total, mean annual temperature ranges from 21.98 to 23.61°C, total sunshine hours in a year is around 1283–1577 hours, annual precipitation is from 1151.3 to 1699.2 mm, and the annual humidity is 85–86%. In 2019, the total population of this district was 47,415 persons, with an approximate

**Figure 1.** *Ba Be district— The area covered in this study shown on a map of Vietnam.*

population density of 70 persons per km2 . There are four main ethnic groups living in this district: Tay, Dao, Kinh, and H'Mong groups. In comparison to other districts, Ba Be has slow economic growth, depends deeply on the agroforestry sector (taking 50% of total GDP), has a low annual income per capita (10 million VND per person), and high rate of poverty in comparison to the average rate of Vietnam (18.04% poor households in total) (**Figure 1**) [24].

Ba Be district has a large forest area of 68,412 hectares with forest coverage reaching 65%, especially in the district with Ba Be National Park which has high biodiversity and conservation value, so Ba Be receives interest and support from the State and many NGOs for forest conservation and development. Currently, in the district, there are many projects being implemented such as 3PAD, REDD+, UN-REDD, and so on. Since 2013, the PFES program has been implemented in Bac Kan province in general and in Ba Be district between Na Hang and Chiem Hoa hydropower plants and forest owners in Ba Be district. With the above conditions, it can be seen that the Ba Be district is an appropriate place to conduct research to evaluate the actual effectiveness of the PFES program in Vietnam.

### **4. Study methods**

#### **4.1 Study data sources**

The data used to evaluate the integrated effectiveness and analyze the actual impacts of the PFES program in Ba Be were collected from two specific sources as follows:

#### **4.2 Criteria for evaluating the effectiveness of the PFES program**

Vietnam's PFES policy toward sustainable development of three pillars in the forestry sector: economic, social and environmental fields [25]. On that basis, we have built a set of criteria to evaluate the combined effectiveness of PFES program with 15 indicators. In which the economic aspect was evaluated based on four indicators (symbols Ec1, Ec2, Ec3, and Ec4), the social aspect was evaluated through six indicators (symbols So1, So2, So3, So4, So5, and So6) and the environmental aspect was assessed in five indicators (symbol En1, En2, En3, En4, and En5) **(Table 1)**.

All these 15 criteria were synthesized and selected from the reality of the evaluation of PFES programs in the world and Vietnam. Specifically, four economic criteria (Ec1, Ec2, Ec3, and Ec4), 5 environmental criteria (En1, En2, En3, En4, and En5), and three social criteria (So1, So2, and So4) were used by the Vietnam Administration of Forestry during the evaluation of PFES programs [25]. Meanwhile, the remaining three social criteria (So3, So5, and So6) have been mentioned by scientists around the world when considering and evaluating PFES programs [26–28].

*Integrated Effect of the Payment for Forest Environmental Services (PFES) in Vietnam DOI: http://dx.doi.org/10.5772/intechopen.112900*

#### **Table 1.**

*Criteria for evaluating the effectiveness of PFES program.*

#### **4.3 Evaluation of the integrated effectiveness the of PFES program**

#### *4.3.1 Scoring method*

The combined effectiveness of the PFES program was evaluated by the weighted scoring method. The efficiency of the PFES program will be divided into seven levels according to a 10-point scale, specifically as shown in **Table 2**.

The Integrated Effectiveness Score (IES) was calculated on the basis of three economic, social, and environmental dimensions according to the following formula:

$$\text{IES} = \text{EcS}^\* \,\text{W}\_{\text{Ec}} + \text{SoS}^\* \,\text{W}\_{\text{So}} + \text{EnS}^\* \,\text{W}\_{\text{En}} \tag{1}$$

In which:

The weights of economic, social, and environmental sectors are taken according to the following three scenarios:

**Table 2.**

*Integrated effectiveness rating scale of the PFES program.*

### *Integrated Effect of the Payment for Forest Environmental Services (PFES) in Vietnam DOI: http://dx.doi.org/10.5772/intechopen.112900*

Analysis of scenarios contributes to the change in the overall effectiveness of the PFES program. On that basis, to flexibly adjust the activities of the PFES programs to suit the actual situation of the locality. This has important implications when applying the integrated efficiency assessment system of the PFES program in other localities in the future.

### *4.3.2 Calculation method for the EcS, SoS, and EnS*

Scores for each economic, social, and environmental aspect were calculated based on the evaluation indicator. The score of each aspect was divided equally among the evaluation indicators with equal weight. Specifically, the economic aspect has four indicators, so the maximum score for each indicator was 2.5 points; the social aspect has eight indicators so the maximum score of each indicator was 1.25 points; the environmental aspect has five indicators so the maximum score of each indicator was 2.0 points. The scoring of the indicators was based on the classification of the people and the actual results obtained from the PFES program (**Table 3**).

The basis for evaluating scores for each criterion was described in detail in **Table 4**.

#### **Table 3.**

*Scoring scale to assess the effectiveness of the PFES program.*

#### **Table 4.**

*Detailed description of the basis of classification of evaluation indicator.*

*Integrated Effect of the Payment for Forest Environmental Services (PFES) in Vietnam DOI: http://dx.doi.org/10.5772/intechopen.112900*


**1. Introduction**

As a unique type of structural and functional material, a porous structure has unique advantages in fields including filtration and separation [1], energy absorption [2], heat exchange [3], electromagnetic shielding [4], and artificial implants [5], and is widely used in aerospace, automotive, chemical, and biological medical industries. Depending on the demand, the porous structure can be manufactured from materials including metal [6,7], ceramics [8], and polymers [9]. With the deepening of their application, porous structures with function-oriented design have been widely developed to obtain precise and complex structures, such as porous implants [10]. However, it is difficult to fabricate such structures using the traditional processing method. Additive manufacturing (AM) techniques are attracting increasing attention due to their impressive capability to produce precise parts with a controlled architecture [11]. Using a layer-wise building approach and a direct link with a

computer-aided design (CAD) model, AM has been described as a crucial production technique to achieve a more controlled porous structure [12–15]. A recently developed AM technique, the laser powder bed fusion process (LPBF), usually called selective laser melting (SLM), can directly create a functional and complex metal part, like a Ti-based porous scaffold for bone tissue engineering, bringing a high degree of freedom to design [16,17]. Most researchers have focused on evaluating the function or forming quality of as-designed porous samples fabricated by LPBF using a set of universal process parameters embedded in the commercial equipment [6,18–22]. However, a porous structure is composed of the struts or walls, which usually have small geometric characteristic size, so a set of process parameters with a universal nature may not be optimal for manufacturing porous structures. A small number of researchers have focused on the impact of process parameters on the forming quality of LPBF-built porous structures. For example, Liu et al. [23] investigated the effect of the scan speed on the forming defects, precision, and mechanical properties of biomedical titanium alloy scaffolds fabricated by LPBF. Ahmadi et al. [24] studied the effects of laser power on features including the surface roughness, strut diameter, relative density, hardness, and elastic modulus of the porous structures. In addition, Jamshidinia and Kovacevic found that the thin wall achieved more heat accumulation during the LPBF process, affecting the forming quality [25]. These findings indicate that the small geometric characteristic size may be a factor affecting the forming quality of LPBF-built porous structures.

On the basis of the above statement, the effect of the geometric characteristic size of the objective part on the forming quality of the solid strut is discussed in this work. The energy density was introduced to reveal the combined action of scan speed, laser power, hatching space, and layer thickness [26], which represented the thermal input during the LPBF process. As the most commonly used material in metal implant fields, Ti–6Al–4V alloy powder was selected for the experiment. Taking the geometric characteristic size into consideration, the influence rule of the factor on the forming quality of solid struts fabricated via LPBF using different scan speeds was investigated from the perspective of thermal transmission. The entire experiment was made up of two steps. Firstly, struts with different geometric characteristic size were fabricated using different combined process parameters. Secondly, porous structures with two strut sizes were fabricated with two scan speeds to verify the analysis in the first step.

## **2. Materials and Methods**


*Article* **A Regional Application of Bayesian Modeling for Coastal Erosion and Sand Nourishment Management**

**Alessio Giardino 1,\*, Eleni Diamantidou 2, Stuart Pearson 1,3, Giorgio Santinelli 1 and Kees den Heijer 1,3**

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +31-(0)-6-1582-1874

Received: 26 September 2018; Accepted: 22 December 2018; Published: 1 January 2019

**Abstract:** This paper presents an application of the Bayesian belief network for coastal erosion management at the regional scale. A "Bayesian ERosion Management Network" (BERM-N) is developed and trained based on yearly cross-shore profile data available along the Holland coast. Profiles collected for over 50 years and at 604 locations were combined with information on different sand nourishment types (i.e., beach, dune, and shoreface) and volumes implemented during the analyzed time period. The network was used to assess the effectiveness of nourishments in mitigating coastal erosion. The effectiveness of nourishments was verified using two coastal state indicators, namely the momentary coastline position and the dune foot position. The network shows how the current nourishment policy is effective in mitigating the past erosive trends. While the effect of beach nourishment was immediately visible after implementation, the effect of shoreface nourishment reached its maximum only 5–10 years after implementation of the nourishments. The network can also be used as a predictive tool to estimate the required nourishment volume in order to achieve a predefined coastal erosion management objective. The network is interactive and flexible and can be trained with any data type derived from measurements as well as numerical models.

**Keywords:** BERM-N; coastal erosion; sea level rise; sand nourishments; Bayesian belief network; JarKus data; coastal state indicators; dune foot; momentary coastline; Holland coast

#### **1. Introduction**

Coastline retreat is a worldwide phenomenon caused by an imbalance between sediment supply and demand. The authors of [1] showed that 24% of the world's sandy beaches are eroding, with erosion rates exceeding 0.5 m/year, while 28% are accreting and 48% are stable. Causes of erosion may be either anthropogenic (e.g., construction of river dams, ports or coastal protection works, sediment mining) or natural (e.g., natural gradients in alongshore sediment transport, storms, presence of submarine canyons near the coastline) [2]. Additionally, coastal retreat can be exacerbated by the effects of sea level rise and soil subsidence. The Holland coast is a typical example of an erosive coastline, along which coastal erosion is managed by applying sand nourishments.

The management of coastal erosion relies on the continuous development of new and flexible solutions and tools, which can account for changes in natural hazard conditions and anthropogenic interventions and which are based on long-term observations [3,4]. Coastal erosion is, however, a process characterized by high temporal and spatial variability. Several examples are available of small-scale data or numerical modeling studies with long-term datasets (e.g., [5–7]). However, the use of data analysis or numerical modeling at the local scale often provides information which is site-dependent and only reliable for a short time period for which they are validated. This may not

be sufficient for decision makers and coastal managers to assess the effectiveness of coastal erosion strategies at larger spatial and temporal scales.

The use of a Bayesian belief network (BBN) can provide a very powerful tool to bridge the existing gap between the needs of coastal managers and the currently available data and numerical models [8]. BBN is a method of reasoning using probabilistic relationships between causes and effects. Bayesian statistics have been applied to very diverse fields. In the field of coastal engineering, they have been used for predicting coastal dune and beach erosion and overwash [9–13], assessing wave height evolution in the surf zone [14], and estimating offshore wave heights and depth given limited offshore information [15]. Recent studied have used BBN to evaluate the coastal vulnerability due to sea level rise [16], the relationships between observed damages and multiple hazard indicators due to hurricanes [17], and the estimation of flooding hazards at coral reef islands [18]. They have also been used to assess the applicability of parametric morphodynamic classification of beach states [19]. BBN can also be an effective tool for data mining where large datasets are available [20,21].

The studies in which BBN was applied to evaluate the effectiveness of disaster risk reduction (DRR) measures are still rather limited in number and are restricted to local study cases. The authors of [22] applied BBN to assess the effectiveness of coastal protection measures (i.e., a seawall) and vulnerability reduction strategies at a small town in North Norfolk (UK). The effectiveness of exposure reduction strategies (i.e., partial house removal) and beach replenishment, at one coastal sector in South Portugal was also assessed using BBN [23]. The authors of [24] applied BBN to assess the effectiveness of measures against sea-level rise (i.e., salt marsh restoration and beach nourishments) in a lagoon in northeast Italy.

This paper describes the implementation and application of a "Bayesian ERosion Management Network" (BERM-N) to be used for coastal erosion management at a larger (regional) scale. The network is based on data collected over more than 50 years along the entire Holland coast, one of the most data-rich environments in the world. The large data availability allows to capture the spatial and temporal variability related to coastal erosion processes and human interventions. BERM-N is used in this manuscript to assess the effectiveness of different adaptation solutions in the form of beach and shoreface nourishments, and also as a predictive tool to achieve a predefined coastal erosion management objective.

#### **2. Bayesian Modeling for Coastal Erosion Management**

A Bayesian network is a method of reasoning using probabilities, where the nodes of the network represent variables and the arrows indicate the cause–effect relationships between the nodes. The advantage of using this approach is that by combining the information from multiple variables, it makes it possible to make robust data-driven or model-driven forecasts.

At the heart of Bayesian networks lies the Bayes rule, generally expressed as:

$$p(F\_i|O\_j) = p(O\_j|F\_i)p(F\_i)/p(O\_j),\tag{1}$$

where the left-hand term is the updated conditional probability (or 'posterior probability') of a forecast *Fi*, given a particular set of observations, *Oj* (Pearl, 1988). The first term on the right-hand side is the likelihood of observations *Oj* given that the forecast *Fi* is true. The second term on the right is the prior probability distribution of *Fi* (e.g., the probability of a given forecast based on the entire training dataset, in the absence of any additional observations). The denominator on the right side is the prior probability distribution of *Oj*.

In this specific case, the posterior probability is described by the distribution of a chosen coastal state indicator (e.g., changes in shoreline or dune foot position), in response to a nourishment strategy (e.g., nourishment type or nourishment volume), representing the observations. Constructing a network first involves defining the variables which best describe the process to be studied. In this study, the main variables are selected through the identification of measurable indicators describing the coastal erosion

process and the relation between adaptation measures and coastal response. The selected variables are represented by nodes in the BBN. The states of these nodes must be mutually exclusive and collectively exhaustive. A BBN is a directed acyclic graph, where the direct cause–effect relationship between two variables in a BBN is illustrated by an arrow. The feeding of information into the Bayesian network in order to construct the conditional probability tables is called "training".

An advantage of BBN is that it is interactive and fast to operate. Once the network is trained, it can be used to carry out quick simulations based on the data included in the network. Moreover, being a probabilistic method, it can account for uncertainties by specifying probability distributions for input variables and generating such distributions as output.

### **3. Study Area**

The Holland coast is a sandy, microtidal, wave-dominated coast located in the central part of the Netherlands (Figure 1). The region is divided in three subregions: Noord-Holland, Rijnland, and Delfland. The coastline is bounded in the north by a tidal inlet named the Marsdiep, connecting the Wadden Sea to the North Sea, and in the south by the long jetty near Hook of Holland, which allows ships to access the Port of Rotterdam. The coastal defense mainly consists of a sandy dune system 117 km long.

**Figure 1.** Map of Holland, the Netherlands, including the three subregions considered in this study: Delfland, Rijnland, and North Holland. Net yearly alongshore sediment transport rates are also shown [25].

A detailed sediment budget analysis for the entire country has been presented by several authors (see for example: [25,26]). Net alongshore sediment transport is mostly northward directed, with yearly rates ranging approximately between 200,000 and 500,000 m3/year (Figure 1). In general, the natural supply of sediment to the coast is very limited and, consequently, the coastline is retreating [4,27].

Protection against flooding is traditionally the primary objective of coastal policy in the Netherlands. However, since 1990, additional objectives have been included: the sustainable preservation of safety against flooding and of values and functions in the dune area [28]. To fulfill these objectives, the yearly volume of sand for nourishments along the entire Dutch coast was first increased from about 3 million m3 to 6 million m3 of sand in 1990, and then to 12 million m3 in 2001 [29]. Even higher volumes might be necessary in the future to cope with the more severe predicted sea level rise scenarios. The total nourishment volumes implemented along the Holland Coast between 1965–1990, 1991–2000, and 2001–2016, and divided for different nourishment types (beach nourishments, shoreface nourishments, dune nourishments, and others), are shown in Figure 2. Beach and dune nourishments are generally implemented directly on the beach or dunes. Shoreface nourishments are implemented in proximity of the breaker bars (≈3 to 5 m water depth). As shown in Figure 2, the total volume of shoreface nourishments has been increasing since 1990, due to their lower cost (relative to beach nourishments) and lower interference with the coastal environment.

**Figure 2.** Nourishment volumes (millions m3/year) at the Holland coast for the three periods: 1965–1990, 1991–2000, and 2001–2016. Note that the North Holland coast is ≈55 km long, Rijnland ≈41 km, and Delfland ≈21 km.

As a result of these large nourishment works, the generally erosive trends which characterized the shoreline before 1990 have changed into generally accretive trends. This was confirmed for example by analyzing volume changes within different water depths (−8 ÷ −3 m NAP and −3 ÷ +3 m NAP) for different time periods [30].

### **4. Material and Methods**

#### *4.1. Data Availability*

Two main data types were used to build BERM-N: (a) Information on nourishment types and volumes and (b) changes in coastal state indicators to quantify the coastal erosion processes and the effects of different nourishment schemes.

The nourishment database supplied by Rijkswaterstaat (Ministry of Transport, Public Works, and Water Management) was used, which includes information on nourishment type, year and month when construction started/ended, location, and volume. For simplicity, the nourishment volumes were converted to m3 of sand nourishment per linear meter of coastal length where the nourishment was built.

The coastal state indicators were derived based on the JarKus profiles. The JarKus ("Jaarlijkse Kustmeting", Annual Coastal Measurement) program was started in 1963 by Rijkswaterstaat. Coastal elevation profiles are measured yearly, during spring, with a longshore spacing of 250 m. Measurements above land were carried out until the 1990s using a differential GPS (dGPS), while measurements are currently carried out using LIDAR. Measurements below water are carried out using multibeam surveying techniques.

Thus, in total, coastal indicators were derived from 31,408 cross-shore profile measurements (604 transects × 52 years). In the cross-shore direction, measurements begin at approximately the first dune row and continue until the −8 m ≈ −12 m contour with respect to MSL (mean sea level), depending on the transect and the year. The cross-shore resolution of the measurements increases from 20 m offshore up to 5 m at the coast. An example of a series of JarKus profile measurements at a single location is given in Figure 3.

**Figure 3.** Example of the morphological development of a single cross-shore JarKus profile (transect 11,301) located at Delfland, between 1965 and 2015.

The authors of [31] defined suitable coastal indicators to assess the morphological development of the Holland coastline due to natural and anthropogenic pressure factors. In particular, the following indicators were used for setting up BERM-N:

### *4.2. Bayesian Network*

To construct the Bayesian belief network, the Netica software package [33] was chosen. Netica uses the probabilistic inference algorithms of Reference [34], and it is widely used for coastal applications (e.g., [12,14,18,20]). The standard network construction and updating procedures outlined in [33] were followed to create BERM-N.

BERM-N, after construction and training in Netica, is shown in Figure 5. In the network, nodes have been grouped in three categories, namely:

These are discussed in greater detail below.

**Figure 4.** Computation of the momentary coastline (MCL) volume for a given JarKus transect. *A* is the area used to compute the Momentary Coastline position. *A* is delimited by an upper boundary, corresponding to the dune foot position, and a lower boundary, at a distance equal to 2 x *H* from the dune foot position. *H* is defined as the distance between the dune foot position and the mean low water line. RSP is the reference point from which distances are computed ("rijksstrandpalen"). Therefore, the MCL position can be estimated as MCL = (A/2H) + x, with x being the distance between the RSP line and the dune foot position.

**Figure 5.** Visualization of BERM-N. Nodes have been grouped in three categories according to the color. Yellow is used for the nodes describing the spatial characterization of the study area and the time interval; purple for the nodes describing the nourishment types and volumes; and green for the nodes describing the effects on the morphological indicators. At each node, the first column indicates the chosen discretization intervals, while the second column (adjacent to the histogram) is the percentage of the prior distribution in each bin. The last line indicates the mean of the prior distribution ± one standard deviation.

4.2.1. Time Interval and Spatial Characterization of the Study Area

It includes the following nodes:

It includes the following nodes:

#### 4.2.3. Effects on the Morphological Indicators

#### **5. Results**

In this section, a number of possible applications of BERM-N and results are described. The predictive skill of the network was evaluated by means of confusion matrixes (similarly to References [12,18]). This resulted in predictive skills of 77% and 87%, respectively, for MCL and DF changes.

#### *5.1. Prior Probability Distributions*

The prior probability distribution describes the baseline situation, in which no node is constrained, and the network is trained based on all data from all the available 604 transects at the 52 years in which measurements were available (Figure 5). Some relevant information can be depicted from this baseline situation.

First of all, the node "Area" shows that most of the observations are available for the North Holland coastal section, in view of its wider extension, considering that JarKus transects are almost equally spaced.

Of all data, 92.4% fall in the category no nourishment, meaning that when considering all the transects for all the years, 92.4% of them do not contain a nourishment at a given year (see node "Nourishment Type"). Of all data, 4.42% include a beach or a dune nourishment, 2.52% a shoreface nourishment and only 0.72% more than one nourishment type per year. As a consequence, most of the data indicate a nourishment volume equal to 0 (see node "Nourishment Volume").

The nodes "MCL change" and "dune foot change" show that the indicators MCL and dune foot, based on all data, tend to move, in average, seaward 1.8 m/year and 0.6 m/year, respectively. This also suggests that beaches are becoming wider since the MCL position is moving seaward at a faster rate than the dune foot position, as a result of the volume of sediments in the nearshore zone.

The fact that most of the data show a seaward migration is confirmed by the nodes "percentage of transects in which MCL moves" and "percentage of transects in which DF moves". In particular, 52.4% of data show a seaward migration of MCL and 56.0% of the data a seaward migration of DF. Nevertheless, there is also a consistent percentage of transects which are characterized by a landward trend (i.e., erosion).

#### *5.2. Assessment of the Effectiveness of Sand Nourishments Against Erosion*

This section illustrates the effectiveness of past nourishments in addressing the coastal erosion along the Holland coast. In order to do so, the node "Nourishment" was constrained to a "No" then to a "Yes" value, to consider, respectively, transects which have not been nourished and transects which have been nourished (see Figure 6). The nodes: "Percentage of transects in which MCL moves" and "percentage of transects in which DF moves" show, respectively, the percentages of transects in which an erosive and accretive trend has to be expected. In particular, in case of no nourishment, about half of the cases are characterized by an erosive trend (i.e., 49.3% if considering MCL and 45.2% if considering the dune foot position as coastal indicator). The effect of nourishment is to decrease the number of erosive transects to 26.6%, when considering MCL as indicator, and 29.5% when considering dune foot as indicator.

**Figure 6.** BERM-N application to assess the effectiveness of sand nourishments. Panel above (**a**): BERM-N constrained in order to consider only transects which have not been nourished (see red box). Panel below (**b**): BERM-N constrained in order to consider only transects which have been nourished (see red box).

#### *5.3. Assessment of the Effectiveness of Different Nourishment Designs*

In this section, the effectiveness of the two most common nourishment designs in the Netherlands (i.e., beach and shoreface nourishments) has been assessed using BERM-N. In order to do so, the node "nourishment type" was constrained first to "beach or dune" and then to "shoreface". To facilitate the visualization, the resulting changes in MCL and DF position (i.e., landward or seaward) are shown using a pie chart in Figure 7.

**Figure 7.** Effects of no nourishments, shoreface, and beach nourishments on MCL (**upper panel**) and dune foot (DF) (**lower panel**) indicators. The red color represents the probability of a landward displacement of the indicator, whereas a green color represents the probability of a seaward displacement. Values indicate the mean values of the distributions.

The figure confirms the positive effect of nourishments on counteracting coastal erosion on both indicators of MCL and DF position, as indicated by the green color (i.e., seaward displacement). Among the two types of nourishments, the effect of beach nourishments appears more pronounced than the effect of shoreface nourishments.

To shed light on the effect of different nourishment type in time, after implementation of a nourishment, the same network was trained with three different datasets. These three datasets were derived considering the effects on the indicators, respectively, one year, five years, and ten years after implementation of a nourishment. In case of multiple nourishments taking place within the considered time window, only the first nourishment was taken into account.

The results are shown in Figure 8, respectively, for the MCL indicator (upper panel) and DF indicator (lower panel). A first, important observation which can be derived from the figure is that even in the case of no nourishment, the percentage of transects characterized by indicators experiencing a landward trend (erosion) decreases when moving from a one-year time window to a five- or ten-year time window. This is the result of the large nourishment volumes implemented along the entire Holland coast. As nourished sand tends to move in an alongshore direction (Figure 1), even transects which have not been nourished tend to benefit from the sand nourished at neighboring transects.

**Figure 8.** Effects of no nourishments, shoreface, and beach nourishments on MCL (**upper panel**) and DF (**lower panel**) indicators. The effects are shown in three different columns, to indicate the effects one year, five years and ten years after implementation of a nourishment.

The effect of nourishments is to further decrease the number of transects experiencing erosion with a similar qualitative effect on both indicators. When comparing the effect of shoreface and beach nourishments on the two indicators, one can see that the effect of shoreface nourishments is less evident than that of beach nourishments one year after construction. In the case of shoreface nourishments, 35% of the transects at which MCL was computed still experience a landward trend one year after implementation of the nourishment, compared with 23% in the case of beach nourishments. Similarly, for the DF position, 38% of the cases show a landward trend one year after implementation of a shoreface nourishment, against just 27% in case of a beach nourishment. However, the positive effect of shoreface nourishments on the indicators continues in time and becomes more noticeable 5 years after implementation of the nourishment, with a similar (i.e., for DF indicator) or even higher (i.e., for MCL indicator) impact than for beach nourishments.

The comparison of the effect of beach and shoreface nourishment after 10 years requires careful interpretation. In particular, the figure seems to suggest that the effectiveness of beach nourishments starts increasing again 10 years after implementation of the nourishments, after a drop at 5 years. In particular, the number of cases receiving a positive effect from beach nourishments after 10 years is 80% for both MCL and DF indicators, and only 66% for MCL and 71% for DF after 5 years. This is, however, rather due to the effect of sand coming from neighboring transects than the result of sand from the nourished transects. Beach nourishments have lifetimes in the order of 1–5 years, depending on the size of the nourishment and the local wave climate [30]. The effect of shoreface nourishments 10 years after implementation is consistent with the observation at 5 years, with a larger effect of shoreface nourishments on the indicators compared to that of beach nourishments.

#### *5.4. Application of BERM-N as Predictive Tool to Achieve a Predefined Coastal Management Objective*

In this last application, BERM-N was used as predictive tool to quantify the sand volumes required in order to reach a specific objective. The objective which is tested in this example is a coastline at which any erosion trend (i.e., described by the MCL and DF indicators) is stopped and replaced by accretive trends over the entire region. In order to do so, the two nodes ("% of transects in which MCL/DF moves") are constrained to a value equal to "seaward".

Figure 9 shows that in order to achieve this objective, an average nourishment volume of 161 m3/m/year would be required, distributed over 13.7% of the transects. Considering a total length of the coastline equal to 117 km, this would correspond to a yearly volume of about 2.5 million m3 of sand/year (i.e., 161 m3/m/year × 117,000 m × 0.137). This is less than the current nourishment volume applied along the Holland coast, which currently results in an average accreting coastline as a result of the large nourishment volumes applied yearly. These nourishments are applied not just to preserve the current position of the coastline, but to maintain the entire coastal foundation in future sea level rise scenarios, as well as to provide the boundary conditions for the developments of additional functions, such as wide beach and dunes for nature and recreation (Section 3).

**Figure 9.** BERM-N application as predictive tool to assess the required nourishment volume in order to reach a predefined coastal erosion management objective: Reduce to zero the erosion over the entire coastline, only allowing for accretion. The red boxes show the two nodes constrained to a condition of "seaward" movement at the two coastline indicators.

#### **6. Discussions**

For clarity, discussion points have been grouped under three main topics.

#### *6.1. General Assumptions Related to the Construction of the BERM-N*

In order to develop BERM-N, a number of general assumptions have been adopted. First of all, the indicators chosen to describe the morphological development of the region (i.e., MCL and DF positions) are arbitrary. In principle, other indicators could also be selected, such as beach width (i.e., useful for recreational purposes) or the probability of dune breaching (i.e., important for safety). However, we have given preference to these indicators, as they are widely used for similar studies in the region [31,32] as well as by the local government.

The choice of processes to be included in the network is also arbitrary. In this paper, we have chosen to focus on the effects of anthropogenic forcing (i.e., nourishments) as the major driver for coastal development along the Holland coast. On the other hand, natural forcing has been omitted from the network. This choice is due to the fact that the large-scale and multi-year development of this coastline in the recent years are mainly the result of the large nourishment volumes which have been applied to manage coastal erosion. However, this is not the case at most coastlines around the world, where the effect of natural forcing is dominant. Another assumption relates to the discretization (i.e., number of bins and size of each bin) [35] of the continuous variables such as MCL change. We followed the guidance of the authors of [15], who suggest that each bin should be as wide as

possible to limit the computational expense and capture multiple data points, but narrow enough to give meaningful forecasts and resolve uncertainty. Hence, node discretization presents a tradeoff between the precision and accuracy of predictions. In this study, the bin width was chosen in such a way that each bin would contain a sufficient number of data points, so we have avoided using bins with a very small size. Similarly, there should be a sufficient number of bins in order to properly describe the statistical distribution of the variable under consideration. BBN cannot extrapolate, only interpolate within the bounds of the data with which they have been trained, so the extremes of the training dataset determine the upper and lower limits of each node.

A final assumption relates to how to account for the effects of multiple nourishments in subsequent years, when considering time windows of several years (i.e., 5 or 10), and specifically at the transects where multiple nourishments occurred. This effect is currently included in BERM-N by only looking at the first nourishment within the considered time window. Although other options may be possible and were explored while setting up the network (i.e., adding the total volumes or correcting volumes with functions which would account for the exact timing when a nourishment occurred), it should be recognized that each of these approaches contains a bias. It was finally decided to adopt the approach used in the paper, because of its simplicity and because it provided the highest predictive skill.

#### *6.2. Alongshore Effects of Sand Nourishments*

The analysis as presented in this study fully relies on data measured at cross-shore transects along the entire region (i.e., nourishment volumes, types and spatial displacement of the indicators resulting from the nourishments). The basic assumption is that the effect of nourishments can be described by cross-shore processes and that a nourishment will only affect the coastal indicators at the transect in which it has been applied. In reality, sand nourishments, and in particular shoreface nourishments, also have an alongshore effect, as discussed in Section 5.3. This is a simplification, as it is not straightforward to link the displacement of a coastal indicator resulting from a sand nourishment applied at a different location.

This alongshore effect is also visible as a background signal in the displacements of the coastal indicators. For example, Figures 7 and 8 show that, even without nourishments, the coastal indicators are characterized by accretive trends, which is most likely related to the positive effect of sand nourishments applied at neighboring transects.

#### *6.3. BERM-N Tool for Coastal Erosion Management of Past and Future Conditions*

BERM-N, as presented in this study, is fully trained based on data from past observations, collected over more than 50 years. This means that the response and outcome of the network is derived based on these past observations. This further implies that in case of future changes to the physical system (e.g., accelerated sea level rise) or development of new anthropogenic interventions which may interfere with the coastal systems, the model may have insufficient data on which to base its predictions. Bayesian networks can interpolate but not extrapolate beyond the data with which they have been trained. A possibility to overcome this is by complementing and retraining the BERM-N with data derived from numerical modeling simulations (e.g., [36]), which may also include information on possible future scenarios.

Similarly, the network has been trained with data from all past nourishment projects carried out in the region, i.e., one of the most nourished region in the world, per kilometer length of coastline (see, e.g., [37]). This is a very extensive database, including nourishments with different sizes and volumes. Nevertheless, this also means that the network can only be used as a predictive tool to simulate cases which are included within the statistical distribution of these past nourishment projects. In case, for example, the effects of a very different type of nourishment should be simulated (e.g., much larger in size than the ones included in the database), it may be required to extend the database with data derived from numerical modeling simulations, which include these new nourishments as synthetic cases.

#### **7. Conclusions**

In this study, an application of Bayesian statistics for coastal erosion management at the regional scale has been presented. A tool based on the use of a Bayesian network (BERM-N) was constructed using measured data collected along the entire Holland coast for a period of over 50 years at 604 cross-shore transects. The effects of different sand nourishment designs on two pre-identified coastal indicators (i.e., dune foot and momentary coastline position) were assessed at these transects.

Different applications of BERM-N have been described. A first application was used to quantify the issue of coastal erosion along the Holland coast region. Additionally, the tool has shown how sand nourishments have been effective in counteracting this issue. In a second application, the tool was used to assess the effectiveness of different nourishment designs (i.e., shoreface vs. beach nourishments) in counteracting coastal erosion. The results have shown how beach nourishments have an immediate effect on the chosen indicators. On the other hand, shoreface nourishments become more effective with time, reaching a similar effect to the one of beach nourishments after about five years. For coastal managers, this is important, as beach nourishments may be more suitable for achieving short-term safety objectives (≈months/years), whereas shoreface nourishment may be more appropriate to counteract erosion at medium- and long-term (≈decades) temporal scale. In a last application, the tool was used as a predictive tool to assess the nourishment volumes required in order to achieve a specific coastal management objective (e.g., extending the coastline in seaward direction of a given value).

The advantage of the tool is that it is flexible, fast, and interactive and can accommodate the use of measured data (i.e., as shown in this study) as well as synthetic data derived from numerical modeling simulations. This makes it suitable for discussions with policy makers and other stakeholders, following a collaborative modeling approach [38].

**Author Contributions:** A.G. and E.D. conceptualized the research; E.D. implemented the methodology; E.D. and G.S. contributed to data analyses and figures; A.G. prepared the original draft of the manuscript and contributed to further revisions; S.P. and K.d.H. supervised the research; S.P. reviewed and edited the original manuscript and further revisions.

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

**Acknowledgments:** We would like to thank Dirk Knipping, who has helped developing the first setup of the Bayesian network. We are also thankful to Matthijs Kok, Saskia van Vuren, and Sierd de Vries for their suggestions in developing this research. Finally, we would like to thank Björn Röbke for his help in preparing Figure 1.

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

#### **References**

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).


**1. Introduction**

Complexity of the control synthesis problems for autonomous robots which must perform the assigned tasks and achieve the set goal, led to new ideas in the control theory. Now, to create a control system for an autonomous robot, this system needs to be trained [1,2], instead of obtaining it by solving some known optimization problems.

To formulate the real problem of mobile robot control, it is needed to describe a large number of different phase constraints. These can be walls, doors between the rooms, windows, columns and other obstacles. For example, a robot has to avoid a column, not to hit on a wall and to get in a door. Now, when control systems for mobile robots are being created, programmers imagine the problems that this robot must face and decide how it should overcome them. Quite a laborious process, but it is quite justified in conditions when control systems were developed on an individual basis for single technical objects, such as spacecraft. However, modern automation and robotization is reaching a broader level and becoming ubiquitous. This trend requires the development of new universal and even automatic approaches to the development of control systems.

Application of symbolic regression methods allows to automatically receive mathematical expressions for control functions. Such mathematical expressions describe how the robot should optimally reach the goal avoiding the obstacles.

Only symbolic regression methods can search structure and parameters of mathematical expression. Other methods, and even artificial neural networks, search only parameters.

**Citation:** Diveev, A.; Konstantinov, S.; Shmalko, E.; Dong, G. Machine Learning Control Based on Approximation of Optimal Trajectories. *Mathematics* **2021**, *9*, 265. https://doi.org/10.3390/ math9030265

Academic Editor: Mikhail Posypkin Received: 30 December 2020 Accepted: 26 January 2021 Published: 29 January 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/).

The searching of control function structure in the control synthesis problem is called machine learning control [1]. This is a new technology in the development of control systems and it has not yet been proposed a rigorous mathematical formulation that defines this approach. In this paper, we propose some mathematical formalization of the machine learning problem (Section 2) and, on the basis of the proposed definitions, we single out a special area of machine learning—machine learning control (Section 3).

One of the main problems of machine learning control is the problem of control synthesis. The paper first presents the general mathematical formulation of the control synthesis problem, and then proposes its numerical formulation, since according to the methodology of machine learning control, the synthesis problem must be solved numerically using symbolic regression methods.

Further in the work in Section 4, we present our approach to solving the problem of machine learning control based on approximation of optimal trajectories. According to the technique of learning firstly it is necessary to create a training set in order to show to learning object what we want of it. For this purpose initially the optimal control problem is solved with the same quality criterion as for the synthesis problem from some different initial conditions. Obtained optimal trajectories are templates for learning. They show what forms of plots for variables must be obtained in the result of control synthesis problem solution and what values of functional must give these solutions. Then, obtained optimal trajectories for different initial conditions are approximated by a numerical method of symbolic regression. The proposed approach of machine learning based on approximation of optimal trajectories is demonstrated in the computational example of general synthesis of optimal control for a spacecraft landing on the surface of the Moon (Section 5).


*3.1. Data Collection*

Original data were collected for both modern and MIS 5e coastal boulder deposits at two localities (Prainha and Ponta do Castelo, Figure 1b) and only MIS 5e from one locality (Ponta do Cedro, Figure 1b). Measurements from modern deposits were performed at mean sea level, while Pleistocene deposit heights varied from ~2.5 m and as much as ~9.0 m above mean sea level (amsl) at five localities, all on the southern and eastern shores of Santa Maria Island. The definition for a boulder adapted to this exercise is that of Wentworth [35] for an erosional clast equal or greater than 256 mm and less than 4096 mm in diameter, with cobbles defined as clasts pertaining to the class 64-256 mm in maximum diameter. For each data set, 25 of the largest available clasts were selected along a transect line parallel to the shore spaced no more than one meter apart. Each clast required three measurements along principle axes (long *a*, intermediate *b*, and short *c*). The initial calculation for volume was simply a multiplication of the long, intermediate, and short-axis values. In all cases, this resulted in a cubical to a rectangular shape that did not take into account the rounding of the boulders by erosion; therefore, a final adjustment to 75% was made, regarding the volume estimates for each boulder, in accordance with previous works [18,19]. Triangular plots were employed to demonstrate variations in boulder shape, following the practice of Sneed and Folk for river pebbles [36]. Data regarding the maximum and intermediate lengths perpendicular to one another from individual boulders were plotted in bar

graphs to show potential shifts in size from one transect to the next. A brief description of the fossil fauna in each site was also provided. This was important information, as, together with the geological data, the presence of the characteristic MIS 5e thermophilic taxa [4] attested to the age of the deposit, which was not possible to date due to the absence of suitable biogenic material (e.g., corals).

#### *3.2. Hydraulic Model*

With the determination of specific gravity based on the standard density value for oceanic basalt at 3.0 g/cm3, a hydraulic model might be applied to predict the energy needed to transfer larger basalt blocks from rocky shoreline to an adjacent coastal boulder deposit as a function of wave impact. Basalt is a volcanic rock that forms from surface flows with variable thicknesses and a propensity to develop vertical fractures. These factors regulate the size and general shape of blocks loosened in the cliff face [6]. Herein, we used two different formulas to estimate the magnitude of storm waves applied to joint-bounded boulders derived, respectively, from Equation (36) in the work of Nott [37] (Equation (1)) and from a recent formula of Pepe et al. [38] that used the velocity equations of Nandasena et al. [39] to estimate wave heights (Equation (2)):

$$H\_S = \frac{\left(\frac{\rho\_s - \rho\_w}{\rho\_w}\right)a}{\mathcal{C}\_l} \tag{1}$$

$$H\_S = \frac{\left(\frac{\left(\frac{\rho\_s - \rho\_W}{\rho\_l}\right)}{\zeta\_l}\right) \cdot \varepsilon \left(\frac{\cos \theta + \mu\_s \times \sin \theta}{\zeta\_l}\right)}{100} \tag{2}$$

where *Hs* is the height of the storm wave at breaking point; ρ*s* is the density of the boulder (3 tons/m3 or 3 g/cm3); ρ*w* is the density of water at 1.02 g/cm3; *a* is the length of the boulder on long axis in cm; *c* is the length of the boulder on short axis in cm; θ is the angle of the bed slope at the pre-transport location (1◦ for joint-bounded boulders); μ*s* is the coefficient of static friction (=0.7); *C*l is the lift coefficient (=0.178). Equation (1) was more sensitive to the length of a boulder at the long axis, whereas Equation (2) was more sensitive to the length of a boulder on the short axis. Therefore, some differences were expected in the estimates of *HS*.

#### **4. Results**

#### *4.1. Prainha on the South Shore*

Located 3.5 km east of the harbor at Vila do Porto (Figure 1b), Prainha's area presented well-developed modern CBD, at heights of ~0.5 m amsl (Figure 2), as well as exposed Pleistocene marine sequences, deposited on top of volcaniclastic rocks at an elevation of ~3 m amsl [40] (Figure 3). Although CBDs were present all-year-round at Prainha, the location of this site (south coast of the island) combined with the fact that Prainha was found within a bay, and taking into consideration the wave regime, it resulted that, in some cases, the modern CBD was covered by sand. Raw data on clast size in three dimensions collected from the two parallel transects at this locality are present in Tables 1 and 2.

Data points representing individual boulders grouped by transect were plotted on a set of Sneed-Folk triangular diagrams (Figure 4a,b), showing shape variations. Those points clustered nearest to the core of the diagrams were most faithful to an average value with somewhat equidimensional axes in three directions. Only rarely any points fell into the upper-most triangle, which signified a cube-shaped endpoint.

The majority of points from both sets fell within the central part of the two tiers beneath the top triangle. However, the overall trend shared between the two sets traced a similar pattern angled toward the lower right corner of the diagrams. The modern CBD at Prainha (Figures 2 and 4a) demonstrated a greater tendency to elongate shapes represented by the endpoint for bar-shaped clasts. No points appeared in the lower-left tier of either diagram, which represented an endpoint reserved

for plate-shaped clasts. Although the general trend in slope was similar between the modern and Pleistocene CBDs, the plots had no bearing on actual variations in clast size.

Variations in boulder size as a function of maximum and intermediate axis length were plotted using bar graphs (Figure 5), based on raw data drawn from Table 1. The greatest number of boulders in the sample measured from the modern CBD fell within a maximum diameter size range between 26 and 35 cm (Figure 5a), which qualified as small boulders in the Wentworth scheme [35]. The largest boulders encountered at Prainha were few in number but ranged in size between 46 and 55 cm. The tendency towards an elongated shape among these clasts was shown by a marked shift in the dominant bin-size for the intermediate axis, within an interval of 16 to 25 cm (Figure 5b).

**Figure 2.** Modern coastal boulder deposit (CBD) eroded from adjacent basalt sea cliffs at Prainha (site 1). Note that some boulders on the far inland end of the littoral boulder cordon were embedded within the sand.

**Figure 3.** Pleistocene (MIS 5e, Marine Isotope Substage 5e) marine sequence, 2.5 m above the modern CBD at Prainha (site 2). Note that, as modern CBD, Pleistocene boulders were covered by Pleistocene fossiliferous sands.

**Table 1.** Quantification of boulder size, volume, and estimated weight from the modern coastal boulder deposit at site 1 at Prainha, on the southern coast of Santa Maria Island (see Figure 1b). The standard density of basalt at 3.0 gm/cm3 was applied uniformly in order to calculate wave height for each boulder. EWH: estimated wave height (in meters), calculated according to equations from Nott [37] and Pepe et al. [38]. See the methods Section 3.2. (hydraulic model).

**Table 2.** Quantification of boulder size, volume, and estimated weight from the Pleistocene (MIS 5e, Marine Isotope Substage 5e) coastal conglomerate at site 2 at Prainha, on the southern coast of Santa Maria Island (see Figure 1b). The standard density of basalt at 3.0 gm/cm3 was applied uniformly in order to calculate wave height for each boulder. EWH: estimated wave height (in meters), calculated according to equations from Nott [37] and Pepe et al. [38]. See the methods Section 3.2. (hydraulic model).

**Figure 4.** Set of triangular Sneed-Folk diagrams used to show variations in boulder and cobble shapes compared between modern and Pleistocene (MIS 5e) deposits. (**a**,**b**): Prainha. (**c**,**d**): Ponta do Castelo. (**e**–**g**): Ponta do Cedro. (**a**,**c**): modern CBD at Prainha and Ponta do Castelo, respectively. (**b**,**d**), (**e**–**g**): Pleistocene (MIS 5e) CBD at Prainha, Ponta do Castelo, and Ponta do Cedro, respectively.

In strong contrast, all clasts encountered from the Pleistocene (MIS 5e) conglomerate fell into the category of cobbles as defined in the Wentworth scheme [35]. By far, the largest number of clasts within the sample fell into the size range between 6 and 15 cm in maximum diameter (Figure 5c), also replicated by the same frequency for the intermediate axis (Figure 5d). However, a subsample of

smaller clasts in the size range of pebbles to small cobbles appeared in the sample measured for the intermediate axis. Comparing the modern CBD at Prainha (Figure 2) with the general contents of the Pleistocene conglomerate at the same locality, it was clear that wave conditions on the modern shore eroded significantly larger clasts from the parent basalt rocky shore.

**Figure 5.** Bar graphs used to appraise variations in the long and intermediate axes on basalt clasts from modern and Pleistocene CBDs at Prainha; (**a**) Long-axis length from clasts in the modern CBD; (**b**) Intermediate-axis length from clasts in the modern CBD; (**c**) Long-axis length from clasts in the Pleistocene CBD; (**d**) Intermediate-axis length from clasts in the Pleistocene CBD.

### *4.2. Context of the Pleistocene Fauna at Prainha*

Prainha is one of the six Pleistocene (MIS 5e) fossiliferous outcrops described for Santa Maria Island. MIS 5e CBDs are known from Prainha, Ponta do Castelo, Ponta do Cedro, and Pedra-que-pica, but do not occur at Lagoinhas nor at Vinha Velha.

Prainha is the best-studied outcrop from Santa Maria Island, and its fossils being first reported by Portuguese geologists [41,42]. After these pioneer works, Santa Maria outcrops' and their fossiliferous remains have been systematically described, with a total of 148 fossil marine-specific taxa presently reported from the Santa Maria Last Interglacial deposits [4]. The most biodiverse invertebrate group is, by far, the marine mollusks, with a total of 138 taxa (114 Gastropoda and 24 Bivalvia) [41,43–45] reported for all MIS 5e deposits in the island (of these, 100 gastropods and 20 bivalve taxa are reported from Prainha). It is followed by the Echinodermata (three taxa) and Cnidaria Anthozoa (one coral taxa) [40,46,47]. Four species of coralline red algae have also been reported from the MIS 5e of Prainha [48]. Finally, rare vertebrate remains have been described from the MIS 5e sedimentary sequences in Santa Maria: one bony fish species, *Sparisoma cretense* (Linnaeus, 1758) reported from the MIS 5e of Vinha Velha [49], and one undetermined Balaenopteridae species (a baleen whale) reported

from the MIS 5e of Prainha [50]. As a result of its high palaeobiodiversity, a high number of scientific studies, education and touristic potential, and the presence of extremely rare vertebrate cetacean remains, Prainha is considered as a high-relevance, national geosite [15,16].


Control over Antigen Orientation

From the early years of VLP research, the importance of ordered antigen display has been noted [80]. Since then, there has been a further appreciation of the benefits of unidirectional display, which can be achieved with the Tag/Catcher-AP205 technology. This was demonstrated by a study comparing different platforms presenting the malaria Pfs25 antigen with varying degrees of antigen organization [55]. The unidirectional display, obtained by the Tag/Catcher-AP205 technology, induced antibodies of higher biological efficacy, compared to when the antigen was presented in several different orientations, as the result of chemical cross-linking [55]. On that basis, it was hypothesized that unidirectional antigen display can enable induction of a more focused antibody response. Moreover, unidirectional presentation may also be exploited to mask certain regions of an antigen. In a recent study by Escolano et al., a Spy-tagged HIV envelope protein was displayed on SpyCatcher-AP205 CLPs [72]. Here, the dense unidirectional antigen display promoted induction of broadly neutralizing antibodies (bNAb), while masking dominant non-neutralizing epitopes, present near the CLP surface. An additional benefit of the Tag/Catcher conjugation technology is the small size of the SpyTag (13 amino

acids), which allows its incorporation into internal antigen positions (e.g., in flexible loops) [81,82]. This provides further opportunities to optimize antigen orientation on the CLP surface.