Ayan Kumar Makar

Keywords: Social media, regression analysis, communications technologies, customer engagement, independent variables, band reputation

Customers propinquity for the Social Media Marketing ( SMM )

Introduction :

The research in the humanities has begun into the 21st century with various digital resources, and new disciplines outside of academia need change in the field of digital humanities ( DH ) . The Internet and social media have empowered customers with better content, more interactions and more resources.Digital marketing implies trading using digital technologies such as websites , social media, mobile ads and applications, streaming video content, e-mail, blogs, and other digital platforms, which can be accessed anywhere, any time by the customers through computers, smartphones , laptops, Internet ready TVs and other digital appliances. Social networking sites are described as web-based platforms that empower individuals to create a public profile in a bounded environment, share the list of other registered users , review and mark their connections' list . The platforms of social networking emerging as a significant communication medium these days . As a result, many corporate companies assumed that marketing on social network platforms could be achieved because users can share the information about their goods and services with each other [START_REF] Barczyk | Social networking media as a tool for teaching business administration courses[END_REF] . While social-media apps seem to antagonise some, these platforms and their data make them a strong marketing and research instrument . With regard to the business -clients interaction , the ability to enhance consumer correlation is one feature that is common among social networking activities: Evidence indicates that social media can strengthen correspondence besides online security and maintaining privacy among parties [START_REF] Risius | Effectiveness of Corporate Social Media Activities to Increase Relational Outcomes[END_REF][START_REF] Shareef | Social media marketing: Comparative effect of advertisement sources[END_REF] .Even now, on Facebook ,Instagram and hundreds of other social networking sites the traffic is rising constantly. Social networking marketing, or SMM, is a platform to construct and distribute contents on social network in order to accomplish your marketing promotion and branding objectives.Social media marketing involves practises such as posting of images and text notifications, videos and other content, which lead to public interaction and paid advertisements on social media.Social media marketing involves reaching your target customers and clients besides socially interconnecting each other and your brand. It has also been observed that increasing the brand awareness has public impact which has helped the organisation to understand the prospective customers and effectively reach a targeted audience [START_REF] Barefoot | Friends with benefits: A social media-marketing handbook[END_REF] . To address how this study qualifies as a digital humanities research and not humanities or a technical project , we put it simple that social media marketing focussed on sentiment analysis of customers , as well as it involves the interlink digitized text , images and time based media with maps ,timelines , blogs , data and visualisation etc . that are common tools of digital humanities which can be presented in real time applications and are becoming even more critical within the field of Digital Marketing . Digital infrastructure and the community could establish a joint platform for project development and aggregation of materials thereby promoting local , regional and global collaboration which is under the scope of digital humanities .

Research Questions

The current study is based on following research questions : i.

What are you trying to accomplish through marketing on social media?

ii.

Who is the intended consumer for you?

iii.

Where'd the target consumer prefer to hang out and how far the social media is accessible by them ?

iv.

What kind of advertisements regarding social media marketing do you like to broadcast among the consumers ?

v.

When has current social media participation been identified?

vi.

Where the campaigns for social media marketing is going to held to increase exposure and brand awareness?

Problem Statement :

The problem statement has been designed on five Ws ( who , what , when , where and why ) of the problems associated with the social media marketing that the present research seek to address. The research problem is the increased difficulties in marketing new products over social media network.

This research will analyze and understand how market penetration, customer brand recognition and brand credibility have an effect on purchasing and purchasing behavior through social media marketing.Some of the major objectives of this study include : i.

To understand why would consumers prefer social media marketing over traditional marketing .

ii.

Appraise the effect of customer engagement on consumer purchasing behaviour.

iii. Determine and measure the effect of brand credibility on customer purchasing behaviour.

iv.

Investigate the effects of brand awareness on consumer purchasing behaviour

Conceptualisation + Operationalisation

Social media marketing ( SMM ) constituted of mix marketing strategies that are primarily based on marketing promotion and social media promotion, driven mostly by participants in various interactive platforms and communities.Acknowledging the mechanisms and advantages of social media marketing, several enterprises and multinationals are already running their ads and marketing techniques digitally, several organizations have started to conducting their marketing strategies online on multiple social networking sites such as Facebook, Twitter, Blogging, Google etc. introducing an innovative marketing channel at a whole new paradigm.These types of marketing successfully establish another marketing sphere namely communication and interaction.Never before have advertising been so interactive.Marketers are using these interactive models to encourage their end users and consumers to receive feedback. It helps them to gain the consumers' perspective of the company's products and services.It also assists in knowing and following pricing strategies,analysis of competitors, perception of the market, global and international enterprises and other factors involved in the creation of a business. Buying behaviour can be described as the choice of a customer, including his or her interests, attitude and loyalty to a specific brand/product or service on the market. Studying purchasing behavior enables psychologists, retailers, advertisers and other integrated campaign staff to perceive, evaluate and appreciate how the consumers' imaginations and behaviors work that encourage them to purchase the specific product in the market.Consumer buying behaviour has set an ever-changing pattern in the demand for many goods and services in the market . Studying purchasing behaviour is thus imperative for the marketers to grasp and analyze the dynamics of one's favourite brands on the market.Consumer purchasing behaviour in world differs significantly in regard to various groups, starting from age to social status and also owing to diverse demographics , the perception of marketing among consumers differs remarkably from each other .

The buying behavior of consumers in world therefore varies from one another that needs to be targeted separately.

. Sample ( + Populations ) :

In the sampling, an element is the object (or person) about which or from which the information is sought. In survey study, the element is typically the respondent . A population is the total of all the elements that share some common set of characteristics. Each marketing research project has a uniquely defined population that is described in terms of its parameters. The objective of most marketing research projects is to obtain information about the characteristics or parameters of a population. Sampling design begins by specifying the target population. The target population is the collection of elements or objects that possess the information the researcher is seeking.The present research involves studies conducted all across the world.The campaigns on social media marketing has been organised among various communities without any topographic restriction all across the globe,the outcomes of various studies have been presented in this research as data sets which have been analysed further. Therefore the samples of this research are essentially comprises of individuals,communities and organisations all across the world on which various studies regarding social media marketing have been conducted .

Data Collection :

When the data are collected to analyse a particular marketing problem, they are categorized as primary data. A researcher should bear in mind that the problem under study might not be unique until initiating primary data collection.Somebody else might have studied the same or related problem in marketing research.A quest for existing data may lead to relevant information.

Secondary data are any data collected for purposes other than the given problem. These data can be found easily and inexpensively in comparison to primary data collection . A brief comparison between primary and secondary data are tabulated below :

Fig.2 : A brief comparison of primary and secondary data

Besides secondary data are also useful in forecasting demand, tracking the economy, designing business intelligence systems, segmenting and targeting, and a myriad of other applications.

In view of these advantages and the use of secondary data, the basic rule employed in this research is as follows: First, analyse the available secondary data.Unless the secondary data sources have been exhausted or marginal returns have been produced this research should only focus on secondary data collection as analysis of secondary data will offer useful information and set the groundwork for more formal research, such as focus groups and surveys.The secondary data can be further classified into two categories internal data ( those are generated within the system where the studies have been conducted ) and external data ( those are conducted outside the system ) .

2.1 Sources of Data collection : Social media can be a source of both internal and external secondary data.Defining the target audience requires transforming the research problem into an accurate estimation of who should and should not be counted in the survey. To begin with , an attempt has been made to analyse the relevant data according to the research questions:

1. What are you trying to accomplish through marketing on social media?

Sol : Some of the goals to be accomplished through marketing on social media are :

i.

Increasing the sales ii.

Enhanching the target population

iii.

Improving the conversion rate iv.

Expanding the organic traffic v.

Reducing the bouncing rate

The major point of digital marketing just like any other marketing is to increase sales by driving more people towards the products and services. Digital marketing , in particular the social media marketing is considered as the one of the cost effective marketing method as it is affordable among more number of individuals with comparatively less cost. In this era of smartphones, personalised gadgets, high speed internet and the present covid-19 situation, social media marketing is acquiring the precedence over other marketing methods.The tracking of conversion rate to social media marketing can be achieved using services like Google analytics [ ⅰ] . These services track the marketing activities more effectively and thus digital marketing has an edge over conventional marketing .

According the following census

[ ⅰ -ⅱ ] .
 Customers of the new generation check their smart devices every 5.6 minutes.

 There are 220 Million users who are accessing digital services through their smartphones.

 In December 2016, the number of internet users in India was at 295.39 million.

 By 2017 the number of internet users in India has reached 437 million.

 The number of internet users by 2021 in India is estimated to reach 601 million.

 The number of users in India is growing at a very fast pace at 38%.  In 2016, 70 percent of Indian internet users were male while 30 percent were female users. This was estimated to change to 60 percent male users and 40 percent female users by 2020. According to a study the most popular social networks worldwide as of July 2020, ranked by number of active users(in millions) These advertisements are customised for every platforms and sites to make them more engaging .

Who

The images and audios for a particular site won't either be compatible with other sites, or deliver the same effect . Hence the customisation of ads are necessary . Every domains in the digital world that attracts the crowds can be turned into a digital marketplace .

According to a study [ ⅶ ] : Several sources suggest that customers worldwide make much of their purchases online from social media networks [START_REF] Jati | International Social Media Marketing : A Global Business Environment Perspective[END_REF] .Several customers, particularly those with increasing earnings , are motivated by the notions of others, most of which are posted on social media.Thus increased awareness is the most widely cited benefit of using social media for marketing purposes among global business professionals.



Methods of data collection :

Considering the scope of qualitative analysis, a range of data collection methods are adaptable for exploratory analyses of business problems in which the case studies are focused on numerous data sources derived from triangulation. This is the benefit of case studies because it allows a combination of various types of data, such as interviews, documentation , records and findings.The benefit of these data soucerces can be maximised under the account of following principles :

i.

Usage of various information sources

ii.

Establishing a case study repository iii.

Preserving a chain of evidence

The purpose of this research proposal , however, is not to elaborate in depth on these principles , but to enhance these multiple forms of data collection:

interviews ,reports ,documents,archives and observation.

Interviews :

The most often used source of evidence for evidence collection and case studies are the interviews that are mostly unstructured, unlike structured surveys where one participant asks questions, and the other provides answers. In common parlance, the word "interview" refers to a one-on-one conversation between an interviewer and an interviewee. These methods are widely accepted for any types of social research such that calculation or measurement techniques should be objective, accurate and reliable as far as possible.

3. Data Analysis : After the researcher has established the research questions , devised an appropriate research design , carried out fieldwork, and derived an appropriate solution ; the researcher can move on to next step that is the interpretation and analysis of the data.

Methodology :

Differences exist between qualitative and quantitative data analysis. In qualitative research using interviews, focus groups, tests, etc. , the interpretation and analysis of data involves recognizing and objectively evaluating common trends within the responses in order to achieve research goals and objectives. On the other hand the data analysis for quantitative research includes critical analysis and assessment of figures and statistics, and seeks to figure the reason behind the appearance of main findings. The present study involves both Quantitative (numerical) and qualitative (descriptive ) forms of data to analyse the trends of social media marketing worldwide and its benefit in human society . Thus it fulfil the objective of using the basic tools of digital humanities in the field of digital marketing and welfare of the human society .

Data Visualisation :

The regression analysis of the data of social media marketing has been performed with NCSS software on the basis of statistical analysis ; the analysis of Facebook and youtube are depicted below : From these figures ( Fig. 3 and Fig . 4 ) ; it can be concluded that there is a positive correlations between the independent and dependent variables that means the sales and advertisements bear a positive relationship .

The analysis of the term ' Social Media Marketing ' using Google Ngram Viewer that charts the frequency of this term from a large corpus of books that were printed between 1500 and 2019 in Google's text corpora In global context , there are variety of reasons why global business professionals prefer social media marketing ( SMM ) over any other business platforms , some of them are followed:

i. Social media platforms enable to measure return on investment ( ROI ) :

Investment Return (ROI) is the relation between payback and investment that induces surplus and is typically used to evaluate the profitability on the investment. In view of this the managers must always have to consider trade-offs between rival strategic marketing innovatives and therefore their decision making is primarily focused on the maximisation of revenues.ROI thus satisfies the company's expectation for a tangible financial gain from an investment . However, when it comes to social media marketing, a range of new metrics are expected to be taken into account. The social network marketing differs from conventional marketing in a number of ways . Social media / digital marketing, for instance , could allow faster and easier marketing strategies to be created, faster and greater reach across a larger audience and enables easier assessment of the success of a campaign by virtue of analytics.Therefore, a clear emphasis and different approach are needed to be created for a more optimistic brand image and loyalty. Efforts have been made to assess the success of social media platform by using ratings ,shares, tweets, likes , scores, views and shifts in market share.However, several analysts argue that managers should begin by understanding user incentives to use social media and then assess social media investments made by consumers as they engage with marketers' products [7][START_REF] Appel | The future of social media in marketing[END_REF] .Therefore, ROI is not often financially tangible rather it is customers' activities (consumer investment), related to a certain social media platform which can be assessed with sentiment analysis .

ii.

Increase Brand Awareness :Social networking is one of the cheapest digital marketing tools for content syndication and to enhance the exposure of any company .Implementing a social media campaign would dramatically increase your brand visibility, while you reach a widespread audience which has the ability to further strengthen the image of your brand.Indeed, social media has been shown to raise awareness of the brand by boosting engagement.Social commitment involves aspects such as tweets, views, shares and postings.Social networking platforms also enable you to boost recognition of your brand by driving traffic to your website.It is obvious that your company will benefit from a social media platform that will have a larger reach among audiences and ultimately enhancing the popularity of the brand .

iii.

Foster Customer engagement/relationship : Customer engagement is characterised as frequent experiences of appreciation between customer and the company.Customer interaction strengthens a customer's personal relationship with an organisation, product or brand.Customer participation plays an significant role in forecasting company success and growing revenue. There is no denying that organizations ought to ensure better partnerships with their prospective customers. In order to measure participation, it is important to analyse the ratio of preferences (number of likes / number of total followers), responses (number of comments / number of total followers) and reposts (number of reposts / number of total followers).

iv.

Helps to Learn From Competitors : Social media are a good way to keep the rivals on record -whether this applies to their social media strategies, the goods they advertise, the promotions they are carrying out or their degree of engagement with followers.Social networking enables you to track what does and does not succeed with your competition, and allows you to determine what may or may not change your approach towards your business.Finally , the review of the rivals' social media accounts will help you to ensure that your content is exclusive to your company.

v.

Better Satisfaction among Customers : -Social media is an interaction and collaboration medium. It is essential to maintain the voice for your business through these medium to humanize your business.Customers would prefer that they receive a personalised message, rather than an automated response, when they share their comments on your site.To be able to identify any feedback implies that you are aware of the needs of your customers and are committed to fulfil these with best experiences.

Each consumer engagement with your company's social media platforms is a chance to exhibit your empathy for them . If a question or grievance is raised by the user, social media enables you to resolve the issue through interpersonal communication. Any brand that takes time to write personal letters, is regarded as intrinsically favourable ,even though a consumer's complaint is responded.

Conclusions

Fig . 1 :

 1 Fig .1 : The above figure illustrates the conceptual framework of the research ; customer engagement ,band reputation and customer brand attitudes are considered as independent variables affecting the buying behaviour of the customers which is considered as an dependent variable that helps to determine the success of social media marketing over purchasing behaviour of the consumers .

3 .

 3 Where'd the target consumer prefer to hangout and how far the social media is accessible by them? Sol : The primary domains in the digital world where large crowds visit are the search engines, social media, email sites, blogs and websites. Major search engines are google and Bing. Some of the most used social media are Facebook and Instagram. This varies from country to country from time to time. Email sites like Gmail and Yahoo are currently leading the market. There are plenty of popular blogs and sites that attracts large crowds as well .The digital marketers make use of these platforms depending upon the targeted groups and audiences .

2. 2 . 2

 22 Documents , reports and archieves : Secondary data and archives are a very rich source of data that are seldomly exploited in other analysis methods. These kinds of data include newspapers , articles and memos . Archive reports are also a valuable source of information, and examples include the outcome of customers' survey , databases of customers' accounts , online messages or events and charts. The documents and archives used in this research proposal were statistics and reports of customers collected from online .

3. 2

 2 Methods of data analysis : The data has been analyzed using regression model with the help of NCSS software which has a full array of powerful software tools for regression analysis. The MLR (Multi linear regression) model has been employed as the study focuses on three independent variables that are customer engagement,band reputation and customer brand attitudes while the buying behaviour of the customers is considered as an single dependent variable that helps to determine the success of social media marketing over purchasing behaviour of the consumers . Besides we have employed Google Ngram which is an online search engine that charts the frequencies of any set of search strings using a yearly count of n-grams found in sources printed between 1500 and 2019 in Google's text corpora. TwXplorer that helps one understand what people are talking about some topic on Twitter and Voyant Tools which is an open-source, web-based application for performing text analysis. It supports scholarly reading and interpretation of texts or corpus, particularly by scholars in the digital humanities, but also by students and the general public.

Fig. 3 :Fig . 4 :

 34 Fig.3 : The regression analysis of Facebook

Fig . 5 :

 5 Fig .5 : Google Ngram analysis of the term ' Social Media Marketing ' .

Fig . 6 :

 6 Fig .6 : The analysis of the term ' Social Media Marketing ' using Twxplorer .

Fig . 7 : 4 .

 74 Fig .7 : An analysis of collected data using Voyant Tools

:

  The influence of social media has gained greater significance with the emerging communication technologies. The social media platforms are important to describe what we think, how we perceive things around us and to speak about the different issues in our society . Social media has greatly influenced various facets of society, such as cultural , spiritual, social , economic , political and religious issues and has impacted the way people think , feel, and respond to specific issues. Social networking in a way spreads awareness and had provided the medium for advertisers to sell their products online. This research analyses and acknowledges the influence of Social Media and its role in marketing by comprehensive analysis of existing research.The benefits of social media marketing in global context are discussed in the current study as well.

's the intended consumer for you? Sol :

  Target group changes from people to people. It depends upon the types of services or products the business is offering. While targeting, factors like race, ethnicity, gender, age, education, profession, income, marital status, hobbies buying behaviour and habits, values, access to technology etc. are to be considered. This would help the effective execution of the marketing problem. Technology is not only a young person's game. According to recent statistics [ ⅳ ] , people in the 55+ age group worldwide are flocking towards Facebook. Besides that, among four in ten seniors now own smartphones.  85% of the people in the 55+ age group have a cell phone; 46% have a smartphone  67% of the people in the 55+ age group have internet at home (84% of those age between 65-69, number reduces for older seniors beyond age 69 )  62% of the people in the 55+ age group use Facebook and 20% use LinkedIn  Very few (less than 10%) of the people in the 55+ age group use other popular social networks (Instagram, Twitter, SnapChat etc . ) Around 54 percent of the Indian internet base users was between 20 and 39 years old in early 2019. People over the age of 40 formed the lowest share, while youngsters in the age group of 12 to 15 years made up a good 14 percent share of the total internet user base. India had over 560 million internet users that year, ranking second in the world in terms of the number of people with internet access.

Some of the studies

[ⅲ]

suggest that : 

What kind of advertisements regarding social media marketing do you like to broadcast among the consumers? Sol

	11. 5.	QZone amazon.com	[ⅴ ]	517 492,468,801
	S. No. 12. 6.	Social media platform Snapchat yelp.com	Number of active users in millions 433 189,284,057
	1 . 13. 7.	Facebook Reddit reddit.com		2,701 430 184,283,420
	2. 8.	YouTube imdb.com		2,000 168,686,113
	3. 9.	WhatsApp fandom.com		2,000 168,358,254
	4. 10.	Facebook Messenger pinterest.com	1,300 160,008,934
	-Most visited websites by search traffic(US,2020) [ ⅵ ]
	5. Site/monthly traffic Weixin / WeChat		1,206
	4.
	6. S. No.	Instagram Website		1,158 Monthly Traffic
	7. 1 .	TikTok youtube.com		689 1,625,928,544
	8. 2.	QQ en.wikipedia.org		648 1,032,257,682
	9. 3.	Douyin twitter.com		600 535,672,329
	10. 4.	Sina Weibo facebook.com		523 512,517,207

: The major types of advertisements in digital marketing are image, gifs, video and audio.

Where the campaigns for social media marketing is going to held to increase exposure and brand awareness?

  Email marketing is also very effective because users are tied to their emails for both professional and personal uses.Content marketing is referred to the delivering of relevant and consistent content to attract and retain a defined audience among potential consumers.Search engine optimization dictates the search engine results which does great favor for marketing.Pay per click ads are literally the digital version of the billboards, that companies pay the owners of the websites to put up their advertisements on websites. Affiliate marketing is a type of referral to products or services in return for commissions.The following report indicates the social media users worldwide based on a study performed on October 2018 and the reports are compiled from Statista [ Xi -Xiii ; 5 ] :

	 91% of all social media users access social channels via mobile devices. Likewise, almost iii. Email marketing 69.7
	iv.	80% of total time spent on social media sites occurs on mobile platforms (Lyfemarketing, Content marketing
	v.	2018). SEO
	vi.	Pay per click
	 Only 15% of people watch Facebook videos with the sound on. Thus while creating a vii. Affiliate marketing
		video on Facebook, it is emphasized to use the subtitles or make the video more
	comprehensive in the absence of audio . Otherwise, the majority of the views could be Statistics indicate that average users have about eight social media accounts and spend an
	wasted! If you scroll through your newsfeed, you'll likely notice that most viral videos average of 2 hours and 22 minutes per day on them. Brands partnering with influencers in the
	are capable of getting the targeted views without sound. (Lyfemarketing, 2019) digital spaces are common. Celebrities endorsing a product or service would build trust among Social Media Platforms No. of users (in millions )
	5. When has current social media participation been identified? Facebook YouTube WhatsApp Facebook Messenger WeChat Instagram Tencent QQ QZone Douyin / TikTok SinaWeibo Twitter Reddit the customers. • Google ad revenue [ⅹ] LinkedIn	2.2 1.9 1.5 1.3 1.0 1.0 0.803 0.548 0.500 0.431 0.335 0.330 0.303
	BaiduTieba		0.300
	Skype			0.300
	S.No. Snapchat	Year	USD ( in billions ) 0.291
	Viber			0.260
	Pinterest		0.250
	LINE	1.	2015	0.203	67.39
	Telegram		0.200
	 worldwide revenue of digital market 2. 2019		134.82
	 2019-335.5 billion USD
	• 2024 -estimating 460.65 billion USD • Facebook ad revenue [ⅹ]
	S.No. 6. Sol : Major platforms in digital marketing are: Year 1. 2015	USD ( in billions ) 17.93
	i.	Social media
	ii.	Influencer marketing

video ads are shared 1200% more than texts and links combined  The following social media statistic shows us the number of daily active Instagram users, which has increased from 150 million in January 2017 to 500 million in January 2019 (Statista, 2019 ).

Sol : Digital marketing started during the 1990s. The advent of companies like Yahoo and google after the internet boom, paved way for this. During this period, the general public were consumers of the internet. After the advent of social media like Facebook, the common people also started actively participating in contributing contents over internet which made internet more popular and engaging among the crowds. Cookies were introduced that would track the browsing habits of users that has helped the digital marketers to a great extent.According to a study

[ ⅷ -ⅸ ]

 The digital advertising industry across India had a market size of around 160 billion Indian rupees in the financial year 2019, up from just 47 billion Indian rupees in financial year 2015. This was projected to go up to around 539 billion rupees by financial year 2024, indicating a big growth in the industry segment.

References :

Journals :


Mohammad Ali Mir

Malakoutian

Pooria Mostafapoor

Yas Malakoutian

Statistic and Probabilistic Variations and Trends of Rainfall Data of TRNC

Rainfall, TRNC, T-test, F-test, Wet or dry spells

Introduction

The Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC-AR4) indicates significant summer warming in south-eastern Europe and the Mediterranean, while downward trends are associated with the mean annual rainfall [START_REF] Jerin | Climate change effects on potential evapotranspiration in Bangladesh[END_REF][START_REF] Lemke | Meta-learning for time series forecasting and forecast combination[END_REF]. The combined effect of high temperatures and low rainfall poses challenges to many economic sectors as well as significant threat on desertification [START_REF] Ginoux | Long-term simulation of global dust distribution with the GOCART model: correlation with North Atlantic Oscillation[END_REF][START_REF] Gao | Increased aridity in the Mediterranean region under greenhouse gas forcing estimated from high resolution simulations with a regional climate model[END_REF]. For instance, the IPCC-AR4 highlights that, water stress will increase in southern Europe, and hence agriculture will have to cope with increasing water demand for irrigation. In addition, the observed climate changes are likely to enhance the frequency and intensity of extreme events' occurrence, such as heatwaves and droughts [START_REF] Meehl | Global climate projections[END_REF] which may critically affect the society and economy of small island countries, like Cyprus. There is therefore a need for more accurate climate model predictions that will provide meteorological information on national level and enable relevant climate change impact studies to assist adaptation strategies.

Weather forecasting plays an important role in our daily life. Especially in engineering, it shows itself more significantly. Among meteorological data, mainly the rainfall variations are the subject that the researchers are interested a lot [START_REF] Neshaei | Investigation of Cross Shore Sediment Transport Using Physical and Numerical Methods[END_REF][START_REF] Sotoudeh | Reduction the risk of cavitation phenomenon in dam spillway with controlling the cavitation index[END_REF]. Although rainfall has a high positive effect on ecological sustainability of the living organisms, but can cause disasters like flooding or drying up of the existing reservoirs due to global warming. Hence, estimating the daily, monthly, seasonally and even the yearly amount of rainfall values for different locations may guide the researchers to some extent, for their future strategies [START_REF] Movahhed | The Effect of Rain on Pedestrians Crossing Speed[END_REF][START_REF] Bargegol | The effect of rainy weather on walking speed of pedestrians on sidewalks, Buletin Teknol[END_REF].

Data is an information (observation or experimental result or numerical figure or evidence) that is gathered for examining (or using during the decision making process) from which conclusions can be obtained. The topic of statistics involves the study of how to gather, sum up, and interpret any existing data since such conclusions are essential for the decision making processes Bowerman and Oconnell, 1997. Any properly classified collection of objects about which a statistical investigation is being created is a population. So the number of individuals in any population is the size of that population which can be finite or infinite. A finite set of items taken from the population with a specific plan is called a sample. The total number of individuals in a sample is called the sample size. Generally, if the data are less than or equal to 30, in statistics is referred as sample.

From the available literature, it was observed that, not too many studies have been carried out on the rainfall distribution patterns of North Cyprus. Ismail and Goymen (1985) discussed the general outlook of rainfall in North Cyprus whereas [START_REF] Kypris | Diachronic changes of rainfall and the water resources in Cyprus[END_REF], only studied the rainfall data of South Cyprus, and attempted to find monthly base diachronic changes. Biyikoglu 1995, analyse the rainfall data of TRNC to some extent. Altunc 1995 and 1997, published two conference papers for the water problems of TRNC based on the basic meteorological parameters. Tayanc 1997, studied the opportunity of making cloud seeding over Cyprus. Altan and Sen 2000, studied the rainfall analysis of TRNC where Pashiardis 2003, studied the records of rainfall of South Cyprus to some extent, for agricultural planning needs [START_REF] Kypris | Diachronic changes of rainfall and the water resources in Cyprus[END_REF]. Kimyaci 2004, examined the extreme rainfall data and established the intensity-duration and frequency curves for North Cyprus [START_REF] Kimyacι | M Sc Thesis: Rainfall data, establishment of intensity duration -frequency curves for Cyprus[END_REF]. Sharifi 2006, studied in detail, the basic hydro-climatological variations and trends of N. Cyprus but his studied time period was pretty short [START_REF] Sharifi | Hydro-Climatological Variations and Trend in TRNC[END_REF].

The engineering problems in general and the hydrologic cycle especially contain quantity of events such as rainfall, runoff, infiltration, evaporation, etc. that can be explained through above mentioned approach where the time component as well interferes. Usually, the number of available data in engineering are small in size, so the sample statistics are used during analyses.

Methodology

Study Area

After the peace operation in 1974, TRNC was established in 1983, as a separate unilateral state on the northern one third of the island, where the remaining part is under the control of so called Cyprus Government. Its capital is Nicosia (Lefkoşa) being the unique divided capital in the world. The population of the whole island based on recent census in 2000 was 748000 of which 68 percent is Greek, 27 percent is Turkish and the remaining 5 percent belongs to various minorities [START_REF] Kimyacι | M Sc Thesis: Rainfall data, establishment of intensity duration -frequency curves for Cyprus[END_REF].

Island of Cyprus intense Mediterranean climate with a typical seasonal rhythm strongly marked with respect to temperature, rainfall and weather in general. Winters, rather changeable are mild, with some rain and snow on Troodos Mountain, are from November to mid-March and separated by short autumn and spring seasons of rapid change in weather conditions. In summer, the extension of the summer Asian Thermal Low is evident throughout the eastern Mediterranean in all seasonal circulation patterns [START_REF] Kostopoulou | Comprehensive analysis of the climate variability in the eastern Mediterranean, Part I: Map pattern classification[END_REF][START_REF] Kostopoulou | Comprehensive analysis of the climate variability in the eastern Mediterranean, part II: relationships between atmospheric circulation patterns and surface climatic elements[END_REF], associated with high temperatures and abundant sunshine with hot dry summers from mid-May to mid-September. Hence, in summer, the island is mainly under the influence of a shallow through of low pressure extending from the great continental depression cantered over southwest Asia. It is a season of high temperatures with almost cloudless sky. Rainfall is almost negligible but isolated thunderstorms sometimes occur which give rainfall amounting to less than 5% of the total in the average year. In winter, Cyprus is near the track of fairly small depression that cross the Mediterranean Sea from west to east between the continental anticyclone of Eurasia and the generally low-pressure belt of North Africa. These depressions give periods of disturbed weather usually lasting from one to three days and produce most of the annual rainfall.

The wet season extends from November to March, with most of the rain falling between December and February (approximately 60% of the annual total). Rainfall is generally associated with the movement of moist maritime flows to the North, occurring particularly over areas of high elevation [START_REF] Kostopoulou | Comprehensive analysis of the climate variability in the eastern Mediterranean, Part I: Map pattern classification[END_REF][START_REF] Kostopoulou | Comprehensive analysis of the climate variability in the eastern Mediterranean, part II: relationships between atmospheric circulation patterns and surface climatic elements[END_REF]. Winter rainfall is closely related to cyclogenesis in the region [START_REF] Pinto | Assessment of winter cyclone activity in a transient ECHAM4-OPYC3 GHG experiment[END_REF]. Nevertheless, it is not uncommon for isolated summer thunderstorms to occur, which however contribute to less than 5% to the total annual rainfall amount.

In this study, amending 10 more recent years monthly based regional rainfall data of North Cyprus to the previously studied rainfall data by [START_REF] Sharifi | Hydro-Climatological Variations and Trend in TRNC[END_REF], is re-examined so as to establish the most appropriate statistically acceptable probability function(s) and model(s) through which the near future occurrences could be forecasted [START_REF] Sharifi | Hydro-Climatological Variations and Trend in TRNC[END_REF]. Since the exact hydrologic model for any data is never known, among the popular models existing in literature, some of them were selected for this study.

Island of Cyprus is meteorologically grouped into 14 main geographical regions as shown in Figure 1, but due to political reasons, no official communication based on exchanging, sharing or using the gathered relevant data of any documents is possible hence, for this small island, the southern part excludes the northern part in any study including hydro-meteorological studies so as the northern part.

Statistical analysis methods 2.2.1. Homogeneity Test

Homogeneity and its opposite, heterogeneity, relate the statistical properties of any one part of an overall data are the same as any other part. Homogeneity can be studied to several degrees of complexity among them homoscedasticity examines how much the variability of data-values changes throughout a data [START_REF] Gilani | Estimation delay variation and probability of occurrence of different level of services based on random variations of vehicles entering signalized intersections[END_REF]. It is used to determine whether frequency counts are distributed identically across different data subset groups. A test of homogeneity compares the proportions of responses from Fixing the degree of freedom and confidence interval and referring to table of t-distribution, allowable (critical) value of t is found. Compare the t value with critical t, if the calculated value is smaller, test is acceptable and correlation exists otherwise the two sets of data are not correlated [START_REF] Ziari | Investigation of the Effect of Crumb Rubber Powder and Warm Additives on Moisture Resistance of SMA Mixtures[END_REF][START_REF] Bargegol | Estimating delay of vehicles in nearside legs of the signalized intersections under expectation method in under-saturation conditions for isolated intersection[END_REF]

F-test

This test is based on comparing the standard deviations. The procedure is to determine the standard deviations of two set sx and sy. Obtain the deviation of smaller value over the larger value. As the F-test formula implies [START_REF] Rahman | Parkinson's Disease Detection Based on Signal Processing Algorithms and Machine Learning[END_REF][START_REF] Mobtahej | Evaluation of Innovation Maturity Model (IMM) Framework on Assessment of Software Development Projects[END_REF][START_REF] Mirmozaffari | New Combined Parametric and Non-parametric Operation Research Models[END_REF][START_REF] Mirmozaffari | A novel artificial intelligent approach: comparison of machine learning tools and algorithms based on optimization DEA Malmquist productivity index for eco-efficiency evaluation[END_REF][START_REF] Mirmozaffari | Machine Learning Algorithms Based on an Optimization Model Preprints[END_REF] s 2 two or more populations. In other word homogeneity tests determine if within the time series data there is a specific time period at which a change within the data occurs.

F = x 2 y (2)
Knowing that, the climate change studies based on long climate records where the homogeneity testing is inevitable. One type of non-homogeneity in long meteorological time series is the sudden shifts of the mean level compared with surrounding sites. Such unrepresentative shifts are often related to relocations of the station but also may be caused by changes in observing schedules and practices, changes in instrument exposure or abrupt changes in the immediate environment. Changes in the surroundings also may be more gradual in the case of an urban influence, which affects mainly temperature data thus needs homogeneity testing [START_REF] Ashraf | Multibiometric Sustainable approach for human Appellative[END_REF][START_REF] Hosseinian | Analysis of factors affecting urban road accidents in rasht metropolis[END_REF]

ANOVA

In order to check the homogeneity, correlation and comparison of any two sets of, a common method called Analysis of Variances 'ANOVA' is used. Student's t-test and Fisher's F-test are mostly used distributions for this purpose. The formulations of these tests are given as below; beside the formulation, the determined answers from the equations should be checked by appropriate tables of t-test and F-test given in appendix, based on the degrees of freedom and the interested confidence intervals. If the obtained value is less than the calculated critical value, the test proves the homogeneity and the test is hence assumed to be acceptable. In fact t-test is comparing the means and F-test is comparing the standard deviations of the datas .]19,20[

T-test

The means of the two sets x and y were found. The standard deviations of the two sets sx and sy were determined. Then the formula ]21[ Like t-test, considering the confidence level and degree of freedom, the allowable F value would be read from the appropriate table. The obtained F value and the allowable F value were compared and if the calculated F is smaller than allowable F, a correlation between two sets exists. Otherwise there is no correlation between two sets. The important note in F-test is that, the smaller value of the standard deviation should also be at the numerator and the larger value should be at denominator [START_REF] Golilarz | Optimized wavelet-based satellite image de-noising with multipopulation differential evolution-assisted harris hawks optimization algorithm[END_REF][START_REF] Yazdani | Improving construction and demolition waste collection service in an urban area using a simheuristic approach: A case study in Sydney, Australia[END_REF][START_REF] Mirmozaffari | A novel machine learning approach combined with optimization models for eco-efficiency evaluation[END_REF][START_REF] Malakoutian | SBM model based productivity evaluation[END_REF][START_REF] Mirmozaffari | Ranking of Heart Hospitals Using cross-efficiency and two-stage DEA[END_REF][START_REF] Mirmozaffari | A Cloud Theory-based Simulated Annealing for Discovering Process Model from Event Logs[END_REF]

Result and Discussion

The minimum number of required data for any statistical study depends on the range of the available data, its average, and the expected degree of acceptable level of deviation. For this statistical study, to determine the minimum number of required data nmin, an empirical method that bases on two simple tests was performed and the minimum value nmin, which satisfies these tests, is supposed to be the answer of the above mentioned problem. Figure 2 shows the required number of sample size for Central Mesaria regions' rainfall data, based on the percentage deviations of the mean values. The tests are a kind of altering average tests. The test starts from number of two data (the value of n=1 and n+1=2) and compares the mean deviation of the averages and standard deviations of these n and n+1 values with the subsequently verified mean and standard deviation value that was computed founded on one less than number of data, i.e. If the variation of the average is less than 2 and standard deviation is less than 5 percent, the minimum required number of the data, based on average and standard deviation is then obtained.

As it can be seen through the graph of Figure 2, minimum number of data for Central Mesaria region is 28 years, because after that, the fluctuation would be less than t = (xy)

(1) ±2 percent. Figure 3 shows the required number of sample size for Central Mesaria regions' rainfall data, based on the percentage variation of the standard deviations. As it can be noticed, the minimum number of data based on standard Is Calculated. Where x & y are the means of the deviation for Central Mesaria is chosen to be 34 years, considering the fluctuations less than ±5 percent. datas, sx & sy are the standard deviations of the datas and n & m are the number of data available for each data.

Consequently, the required minimum number of data is 34 years based on comparisons of means and standard deviations according to Table 1. 2 to 4 show the t-test result of various region of studies. As it can be seen in these tables, the calculated t is less than allowable t therefore the correlation exists between Central Mesaria and East Coast. But for the data below correlation doesn't exist between Central Mesaria and North Coast.

Knowing the wet and dry years is important. The wetness or dryness can be checked by several methods such as severity index, drought index. In this paper, an empirical method used which compare the mean RAINFALL DATA of any regions with each RAINFALL DATA of any years, and if it is larger than mean, it implies wetness of that year and if it less than mean it is named dry year. Below the results of study performed on rainfall data of Central Mesaria from year 1975 to 2013 is given. According to the result of this table, it can be understood the number of wet spells is 18 (means 47%), number of Dry spells is 21 (means 53%). Therefore, the Central Mesaria is in dry spell during the studied period. The Mean is 299.9 mm

Conclusions

Among the four probability distribution models, Normal, Log-Normal, Gumbel, and Gamma, the best representative for each meteorological region was determined through the best fitting curve approach. Except East Coast and West Mesaria which are Log-Normal, the other meteorological regions and TRNC obey the Normal distribution model. Rainfall of the 6 meteorological regions of North Cyprus and TRNC as a whole were analyzed and 10 years forecasting data were as well predicted. For this purpose, to determine the best time series model for each regions and for TRNC, the standardized MSE, MAPE, RMSE, and MAD were used. To be able to realize how the meteorological data is varying for a long run, wet and dry spells of yearly rainfall data as well studied. Interestingly all the data in all the meteorological regions suggests dry regions.

Figure 1 .

 1 Figure 1. Geographical regions map of Cyprus based on meteorological aspect (obtained from Meteorology Office, TRNC).

sFigure 2 .Figure 3 .

 23 Figure 2. Curve showing the required number of sample size for Central Mesaria regions' rainfall data, based on the percentage deviations of the mean values

Figure 4 .

 4 Figure 4. Normality test of Central Mesaria rainfall

Table 1 .

 1 Appropriateness of the data sample size of Central Mesaria for statistic and probabilistic studies Based on Mean (not more than 2% deviation)Based on Standard Deviation (not more than 5% deviation)

	28 < 39 OK

Table 2 .

 2 t-test between Central Mesaria and East Coast regions' and its result

Table 3 .

 3 t-test between Central Mesaria and North Sea regions'

	and its result
	n, m	39
	Central Mesaria Mean	299.9
	North Coast Mean	461.9
	Central Mesaria Sd	75.9
	North Coast Sd	100.62
	degree of freedom	37
	level of confidence	95%
	Allowable t	1.69
	t =-6.2458	Unacceptable

Table 4 .

 4 F-test between Central Mesaria and East Coast regions'

	and its result

Table 5 .

 5 Numerical representation of wet and dry spells of West Mesaria region based on the mean of the data

	Hydrologic Year	Rainfall (mm)	Wet\ Dry	0: Dry 1: Wet	Hydrologic Year	Rainfall (mm)	Wet\ Dry	0: Dry 1: Wet
	1975-1976	351.8	wet	1	1993-1994	279.8	Dry	0
	1976-1977	270.3	Dry	0	1994-1995	286.5	Dry	0
	1977-1978	288.4	Dry	0	1995-1996	209.6	Dry	0
	1978-1979	350.9	wet	1	1996-1997	281.5	Dry	0
	1975-1976	351.8	wet	1	1997-1998	252.2	Dry	0
	1976-1977	270.3	Dry	0	1998-1999	283.9	Dry	0
	1977-1978	288.4	Dry	0	1999-2000	214.9	Dry	0
	1978-1979	350.9	wet	1	2000-2001	385	wet	1
	1979-1980	343.3	wet	1	2001-2002	427.7	wet	1
	1980-1981	314.1	wet	1	2002-2003	510.3	wet	1
	1981-1982	224.3	Dry	0	2003-2004	361.7	wet	1
	1982-1983	235.6	Dry	0	2004-2005	331.3	wet	1
	1983-1984	275.2	Dry	0	2005-2006	265.2	Dry	0
	1984-1985	295.3	Dry	0	2006-2007	329	wet	1
	1985-1986	309.1	wet	1	2007-2008	107.5	Dry	0
	1986-1987	345.4	wet	1	2008-2009	257	Dry	0
	1987-1988	369.7	wet	1	2009-2010	433.8	wet	1
	1988-1989	284.5	Dry	0	2010-2011	288.9	Dry	0
	1989-1990	233.9	Dry	0	2011-2012	314.6	wet	1
	1990-1991	138.1	Dry	0	2012-2013	360.5	wet	1
	1991-1992	342.6	wet	1	2013-2014	224.3	Dry	0
	1992-1993	319.9	wet	1


Benoît Piranda

Guillaume J Laurent

Julien Bourgeois

Cédric Clévy

Sebastian Möbes

Nadine Le Fort-Piat

A New Concept of Planar Self-Reconfigurable Modular Robot for Conveying Microparts

Keywords: Electro-permanent magnets, reconfiguration, self-reconfigurable robot, part feeder

Modularity and self-healing are two interesting properties that could help to design more flexible conveyors of micro-objects. In the Smart Blocks project, we propose to design a 2D modular and self-reconfigurable robot composed of centimeter-scale sliding blocks that embed their own actuators and control electronics. This article presents a proof-of-concept of the linkage and of the traveling system as well as an algorithm able to reconfigure a set of blocks from a spatial configuration to another one. Prototype blocks have been realized using electro-permanent magnets which show a good motion speed while saving power consumption during the linkage. Our reconfiguration algorithm is implemented in a simulator software showing in real-time the reconfiguration of the robot.

Introduction

Conveyors are usually designed as monolithic entities solving one problem at a time. If monolithic design fits the need of fixed types of environments and/or objects, it lacks flexibility to environment changes and failures that occur at small scales [START_REF]Microrobotics for Micromanipulation[END_REF]. Furthermore, to convey micro-objects, a MEMSbased monolithic conveyor is limited by the size of a wafer and it will use more surface than a modular one. To solve these problems, our idea is to build a modular conveyor composed of hundreds of similar blocks that can detect micro-objects with sensors, move them with MEMS actuators and communicate with each other to form a flexible conveying path. A further idea is that the blocks will be able to move by themselves through the use of side actuators to enable self-reconfigurability. A self-reconfigurable conveyor will be able to automatically replace blocks that have failed with working ones (self-healing). Furthermore, some environments like medicinal production have very detailed guidelines [START_REF]The rules governing medicinal products in the European Union, Eudralex[END_REF] to maximize the quality of the products and to lower the possibility of product contamination. Human intervention for conveyor reconfiguration will contaminate the conveyor. There are, therefore, direct benefits to have a self-reconfigurable conveyor. Building this conveyor is the objective of a bigger project called Smart Blocks 1 .

Several projects have influenced our work, but the first thing to mention is the Smart Surface project2 which is our direct predecessor. Different hardware and software systems have been developed to produce an air cushion in order to move small, flat objects. One of these, a tilted-air-jet surface, reached a size of 9mm×9mm [START_REF] Zeggari | Design and fabrication of a new two-dimensional pneumatic micro-conveyor[END_REF] and gave therefore the target system dimensions for the Smart Blocks project. Ciliary motion systems [START_REF] Malapert | Power-regulated thermal actuator based on uv-patterned polyimides for a ciliary motion system[END_REF] are also good candidates since they required only low voltages and match the target dimensions. Additionally, there were algorithms developed in order to control multiple sensor-actuator units with their own processor in a decentralized way [START_REF] Boutoustous | Distributed control architecture for smart surfaces[END_REF] and more general work conducted [START_REF] Bourgeois | Distributed intelligent mems: Progresses and perspectives[END_REF]. Other interesting ideas come from the modular robot field. The projects like M-TRAN [START_REF] Kurokawa | Distributed self-reconfiguration of M-TRAN III modular robotic system[END_REF], Superbot [START_REF] Salemi | Superbot: A deployable, multifunctional, and modular self-reconfigurable robotic system[END_REF], Roombots [START_REF] Spröwitz | Roombots: Reconfigurable robots for adaptive furniture[END_REF] and Molecube [START_REF] Zykov | Evolved and designed self-reproducing modular robotics[END_REF] have already shown motions of autonomous parts and self-assembly albeit in bigger dimensions. The miniaturization of their mechanical connection systems is complex and does not seem to be the right solution for a smaller system. Another connection system has been realized by Neubert et al. [11] using a Fields Metal solder, melting at 60 • C. This principle uses electrical heating of the contact area where the solder is deposited, to melt it and to let it solidify again. The connection is very strong and can also be used for power or data connections. The problem is that there is no attraction force to move the modules. In terms of connection and attraction, the most inspiring work comes from the Pebbles project [START_REF] Gilpin | Robot pebbles: One centimeter modules for programmable matter through self-disassembly[END_REF] using small cubes (12mm×12mm), capable of forming two dimensional shapes using electro-permanent (EP) magnets. The advantage of EP magnets is that they are able to keep their polarity after a short energizing phase. However, Pebble's cubes cannot move, they are just able to disassemble.

In the Smart Surface project, we conveyed small objects using arrayed-MEMS actuators. Our new modular conveyor will use these actuators so that each block will embed arrayed-MEMS actuators on its upper face. Miniaturization of the block is one of the key aspects of the project. The final block edge length is foreseen to be of 10 mm, including everything from supplying the MEMS array and connecting the blocks but also to move them. Figure 1 shows a representation of the final conveyor.

The focus of this article is twofold. First, we propose to use EP magnets to design a linear motor able to move 1cm 3 blocks. Using this motor, one block can slide on another one and can be stopped in every state keeping a strong connection without any power consumption. This means that after the system has formed its optimal configuration it can perform its conveying function using no other resources for the linkage. Second, using this special kind of actuation, we have also proposed a distributed reconfiguration algorithm which is able to form any 2D shape required for the conveyor. This algorithm is implemented in our simulation software VisibleSim simulating exchanges of messages and showing in real-time the reconfiguration of the robot.

Sliding blocks

This part presents the design of a new kind of self-reconfigurable modular robot based on sliding blocks. We propose to use EP magnets inside a linear motor able to move blocks directly on one another.

Electro-permanent (EP) magnets

The basic part of the motor unit is the EP magnet. It consists of a coil with a specific permanent magnet core, like AlNiCo. This material is an alloy made from aluminum, nickel and cobalt which has a remanence similar to neodymium magnets (around 1.2T), but a relatively weak coercive field strength around 50 to 100kA m -1 (in contrast to neodymium magnets which have a coercive field over 1000kA m -1 ). The result is a strong magnetic force (depending on the remanence), but also the ability of a very easy magnetization and demagnetization (depending on the coercive field strength). Wrapping a coil around the AlNiCo core, a magnetic field can be generated to switch the magnet polarity in a very short time. The result is a bistable system, able to have an attraction or a repulsion mode like a switchable permanent magnet.

Linear motor design

A linear motor is an electric motor that has its stator and rotor "unrolled" so that instead of producing a torque (rotation) it produces a linear force along its length. We propose to use this principle to move a "rotor" block along "stator" blocks. The rotor part is composed of two cylindrical 1mmby-1mm neodymium magnets. The stator part consists of three EP magnets per blocks which have a size of around 2mm in diameter and 3mm in length.

To be able to move the magnets in a chosen direction, the distance between the two neodymium magnets has to be 50% bigger than the distance between two EP magnets on the other side. As each block must be able to move along one another, we put on every block two active sides, each one containing three EP magnets and two passive sides, each one containing two permanent magnets. A working configuration needs to have two equal sides next to each other, as seen in Figure 2.

The block housing, seen in Figure 2a, has been made by rapid prototyping with a fused deposition modeling machine. To build the EP magnets, the AlNiCo core which has a diameter of 1mm and a length of 3mm, has been placed in a vice and wrapped with 60 turns of 0.1mm enameled copper wire in three layers. To avoid uncoiling, the whole part is covered by a thin layer of cyanoacrylate-based glue. The final assembly has been done by placing and gluing all magnets in the lower part of the block, before gluing the upper part on it. The separate parts and the final assembly can be seen in Figure 3.

Electronics design

To supply the EP magnets with current in both directions a H bridge per coil is required. To reduce the number of components, we used three halfbridges linked to a shared one. As it can be seen in Figure 4, every coil has its own half-bridge, allowing the choice of the direction of the electric current through its EP magnets. Additionally there is a fourth half-bridge, able to decide which chosen current direction should be powered. Every half-bridge consists of two MOSFETs, a P-channel for the upper side and a N-channel for the lower side. Because the resistance of the coil is very low, a 15V difference causes more than 15A current in the wires. On the one hand, it would be a thermal problem for the 0.1mm wire to be powered for more than a few micro-seconds, on the other hand, most power supply are not fast nor powerful enough to guarantee this current. Therefore, a capacitor is used to store and to deliver the required energy.

The power supply of the blocks is external. Some specific electric pushpins will be designed on lateral sides to enable the transmitting of the power between blocks. However a capacitor is required in each blocks to store enough power for a current pulse.

Motor control

With regard to a standard linear motor, we are using only two states for the EP magnets. Actually, most electric motors are using a sinusoidal control to reach a smooth motion. To move the "rotor" block from one "stator" to another, six states are required. The state transition and its effect on the movement can be seen in Figure 5.

If the polarization of the motor unit should show, for instance, a SSN3 state, the first two half-bridge bipolar transistors will get a 5V signal, opening the upper side transistor. The third one will stay with no signal and an opened low side transistor. Because the fourth half-bridge has got no signal and connects therefore all EP magnets to the ground, the current will flow from the two first upper sides over the corresponding magnets mainly to the fourth low side and to the ground. Hence, the first two magnets have been powered but not the last one. For this, the fourth half-bridge needs to be switched, whereby only the third EP magnet will be powered. The result is that if the switching of all magnets is necessary, two shots4 has to been done successively.

The capacitor needs some time to recharge after a shot. This time depends on the voltage supply, on the resistor in front of the capacitor and on the duration of the last shot. The capacitor voltage will therefore be read over a one to ten voltage divider with an analog-digital-converter (ADC) channel, so that the next shot can be started as soon as the sufficient voltage is reached. To generate the switching sequence presented in Figure 6, we used a Microchip dsPIC30F4011. Four output pins are used to give the signal to the half-bridges and one ADC input measures the capacitor voltage. In the final solution, we will need 8 I/O pins for running two motor units. A suitable and smaller IC from Microchip would be the 28 pin PIC16F723A in QFN design with a size of 4mm × 4mm.

Experimental results

Motion and speed

We carried out some experiments to validate this concept of sliding blocks. The motion is stable and reproducible but a bit jerky due to on-off state transitions. Figure 7 show a complete sequence which can be further appreciated in the video clip accompanying this paper 5 .

The speed of displacement has been evaluated through one hundred sequences and measuring the time. The mean speed was about 0.61s for 1cm (or 10 blocks distance in 6.1s) that is to say 16.4mm/s.

Force in mN

Voltage in V Figure 8: The magnetic force between the three EP magnets of the active motor unit side and the two neodymium magnets of the passive motor unit side using a specific magnetizing voltage and two shots.

Holding force vs. Voltage

We tested the holding force between two motor units. After a proper demagnetizing, changing the polarity of all magnets while decreasing slowly the switching voltage, we measured the force for different magnetizing voltages using each time two shots. We therefore put a motor unit below a second one that is attached to a bracket. The motor units are placed as if they were within aligned blocks. Then, we used measured balance weights, hanging them carefully on a special built anchor to the lower motor unit, until the connection broke. We made this several times to guarantee repeatable measurements of the tensile force.

The result can be seen in Figure 8. Below a voltage of 6V, the magnetic field is too weak to start a proper magnetization of the AlNiCo core. From 6V up to 16V, the holding force increases with the voltage. This is the linear magnetization region of the AlNiCo. Over 16V, the magnetization is saturated and the holding force reaches 45mN. This graph shows that voltages over 16V do increase the strength a lot. On the other hand, the higher the voltage is, the longer the charge of the capacitor will be. Charging to 18V instead of 15V takes 66% longer but increases the attraction force just by 10%. Thus, using voltages around 15V-16V is the best compromise.

Force in mN

Pulse duration in µs Figure 9: The magnetic force between the three EP magnets of the active motor unit side and the two neodymium magnets of the passive motor unit side using 15V and two shots with a specific shot time.

Holding force vs. pulse duration

The next test was to check how a shorter or longer shot influences the force. The magnets were therefore demagnetized as before and, then, magnetized with a shorter or a longer 15V shot from a 470µF capacitor. The result can be seen in Figure 9, showing the force function of the shot time.

We found out that it is useless to increase the shot time over 25µs, because while the coil is powered, the voltage of the capacitor is shrinking, causing a gradually lower current in the coil. So, after 25µs the current seems to be too low to polarize the magnet any further.

We also tested if multiple shots could increase the holding force. We found no hint of stronger force after ten or even hundred shots, because just a stronger magnetic field changes the remanence, the duration is irrelevant after a certain time (25µs).

Energy consumption

During a shot, the voltage drops around 2V. Knowing the capacitance, we can deduce that the magnets consumed an energy around 13mJ. That means that the 10mm move of a cube will consume around 78mJ.

Blocks reconfiguration algorithm

The travelling system presented above allows considering the development of blocks composed of a processing unit, sensors and actuators. Each block is a small conveying area but, when linked with other blocks, it creates a conveying path for moving objects over larger distance. Side actuators allow a block to slide on another one and to form different conveying surfaces with different geometries. Furthermore, it reduces cost and avoids human interventions to replace a defective block. The second part of this paper presents a distributed algorithm which reconfigures a set of blocks, placing them in a new geometrical configuration.

Our algorithm allows reconfiguring a set of connected blocks considering that each block runs the same code and may exchange messages with 4 neighbors. This algorithm consists in a finite state machine, driven by the exchanges of messages in this network of connected blocks. This algorithm is implemented in our simulator software, named VisibleSim, that shows in real-time the exchanges of messages and the displacements of blocks (see Figure 10).

Operating principle of the blocks

The algorithm is based on exchanges of messages between neighboring blocks where each message may contain transmitted data. In order to write this algorithm for block reconfiguration, blocks are considered as entities with their own memory, able to execute a set of instructions. Each block is connected with 1 to 4 neighbors and communicates using asynchronous message exchange. The algorithm presented requires only data stored within each block, which can run independently in autonomous units of computation. One of the blocks is chosen to propagate the actions of the reconfiguration algorithm to the other blocks. We call this block Master Block, it is connected to an external module that manages the reconfiguration. The desired configuration is stored in a 4-way connected map, where the number of cells to fill corresponds exactly to the number of blocks that receive the map. Figure 11.a shows an example of a map where the cells to fill are colored in gray.

Steps of the algorithm

The algorithm for blocks reconfiguration is divided into four major stages. A preliminary step, executed only once, transmits the target configuration map to each block. After this preliminary step, three successive steps will be repeated:

1. Computing the distance between blocks and empty areas, 2. defining the direction of movement, 3. moving the blocks.

Each iteration is intended to make the current configuration getting closer to the target configuration.

Sending the map

The first step is to send the map to all the blocks (broadcast) and to receive an acknowledgment (convergecast). The Master Block sends the map to its neighbors. Then, when a block receives a map for the first time, it sends it to its other neighbors and waits for an answer from each of them. This stage is ending when the Master Block has received an answer from each of its neighbors, certifying that each block of the set has received the map. The position of each block is relative to the Master Block. During the broadcast, each map message contains coordinates of the sender so that when a block receives a message, it deduces its position from the sender position. In order to save memory, it is possible that the entire map will not be transmitted to every block. A solution is to decompose the map into several parts and distribute these sub-maps over the sets of blocks. In the current state of our algorithm, we are transmitting the entire map to each block, this optimization will be the subject of future enhancements. The algorithm detailed below allows to start the computation on all blocks by broadcasting (without cycles) the start order. At the end of the computation, the initial block receives an acknowledgment stating that the algorithm has been performed on all blocks. The Figure 12 details this algorithm. We recall that the same program is executed on every block. The program behaves like a finite state machine where the evolutions of states are triggered by receiving messages.

During the first step, the 'Master Block ' receives the first message from an external module. For each type of information conveyed to the blocks, we define a dedicated message. For example, the message called MAP MESSAGE is used to send data about the final map. It contains the following parameters:

A pointer to the transmitter block (which is necessarily a neighbor of the receiver), the size of the map (width and height of this area), the bit array indicating whether each cell must be filled or not, the transmission time is added to the message in order to simulate the transfer delay.

When a block receives a message type MAP MESSAGE, two actions are possible:

1. If there is already a map stored in the block, then it returns a message to the sender (ACK MAP MESSAGE ); 2. Else, it copies the map into its memory and broadcasts a new message MAP MESSAGE containing the map data to its neighbors (except to the one who sent him theMAP MESSAGE ). Then, it stores the sender id of the message (in a local variable named sender ) and the number of neighbors to whom he sent this message (in the local variable named waitedAnswers).

When a block receives a message ACK MAP MESSAGE, it decrements the variable waitedAnswers. Then, if waitedAnswers is null, which indicates that all its neighbors have already answered, the block sends an acknowledgment to the 'sender ' with ACK MAP MESSAGE.

Figure 11.b shows the result of the map transmission to a set of blocks. Blocks that are already well placed are colored in dark gray and in light gray otherwise.

Calculating distance between blocks and empty areas

This phase consists in searching for each block, the shortest distance to a free position in the final configuration map, as shown in Figure 11.c. In this example, the value placed over each block (in a myDistance variable) is the distance from the block to the closest empty spot. This algorithm is based on two steps, each of them needing to broadcast information to the set of blocks. The first step initializes all distances stored in the blocks to the infinity value. Then, during the second step, each block that has an empty place executes the following. Using the map, it checks if this spot should be empty at the end of the reconfiguration. In this case, it deduces that its distance value is equal to 1 (myDistance = 1) and broadcasts this information to its neighbors. Every block must have a distance corresponding to the minimum distance from their neighbors plus 1. Then, to determine the distance value for each block when a neighbor updates its distance, it will propagate this information to its neighbors using a message containing its own distance. When a block receives a message from a neighbor, it compares its own distance value (myDistance) to the received one (receivedDistance), and, updates myDistance if myDistance > receivedDistance.

Wait for messages

MAP_MESSAGE ACK_MAP_MESSAGE

4.2.3. Defining the direction of movement B max is the farthest block to an empty spot. It is identified easily as its distance is greater than all its neighbors distance. Then, B max has to find a path to a block, neighbor of an empty spot. This path is calculated by following the decreasing distance values as shown in Figure 11.d. The neighbor of B max that admits the smallest distance is chosen. If distances have equal values, the order West, North, East, and South (WNES is here a convention) is followed. The relative position of this neighbor defines the movement direction for the block and it is stored in the direction variable.

The two previous steps can be repeated as it exists a path linking a free position and a not well-placed block. In order to avoid deadlocks, we set the distance stored in these moving blocks to the infinity value (they are marked with ∞ in Figure 13). Thus, each block can only participate to one reconfiguration at a time but many movements of blocks are possible simultaneously.

The motion of the blocks

The last step of the algorithm consists in starting the physical displacement of the blocks and waiting for them to reach their destination before beginning the next sequence. The whole movement is composed of an ordered list of one-block movements. When two neighbors have different movement directions, a priority has to be given to avoid collisions. The first block in the list must wait for the second one to end its movement.

The real-time simulator

We developed a software call VisibleSim [START_REF] Dhoutaut | Efficient simulation of distributed sensing and control environment[END_REF] to visualize in real-time the states of the blocks during the reconfiguration algorithm. This software, developed in C++, allows observation of the asynchronous execution of the code on the different blocks.The small program associated with each block, called BlockCode, is written in C++ too. VisibleSim helps debug the program by changing the color of the blocks during the program or by writing debugging text, to name a few. The simulator calculates the simultaneous evolution of the blocks state taking into account the message transmission delay. Thus, the emission of a message and its reception cannot be achieved simultaneously. After each movement, the positions of the blocks are displayed in real-time. Some screen captures are presented in Figure 14 and examples of reconfiguration can be visualized in a short video attached to this paper, or downloaded at this address : http://smartblocks.univ-fcomte.fr/anim_blocks.mp4.

Experiments on reconfiguration time

The total reconfiguration time mainly depends on the difference between the initial configuration of the blocks compared to the final map. Even more than the average distance traveled by each block, the complexity of the 4-connected path separating blocks is an important parameter of the reconfiguration complexity. We performed two types of reconfigurations, a first one defining a map with a fairly simple pattern representing a large conveyor tree (composed of 546 blocks), and a more complex one formed by the text: 'Mechatronics' (875 blocks) as shown in Figure 14.

For each of these situations, several initial configurations were tested:

Horizontal lines: Blocks organized as horizontal lines beginning on the bottom left end side and ending on the right end side.

Two horizontal lines: Same as horizontal line except that lines are placed on the top and on the bottom.

Diagonal lines: Diagonal lines starting on the upper left corner and ending on the lower right.

Sinusoidal: a sinusoidal curve.

Two vertical lines: Same as horizontal lines, except that the lines are verticals.

For each configuration, the numbers of steps to reach the goal is shown in Table 1. This value represents only the number of repetitions of the algorithm required for reconfiguration without taking into account the duration of displacement of the blocks.

One can notice that the speed of convergence of the algorithm varies significantly depending on the initial configuration. The algorithm seems to be more effective with the horizontal lines for the second case because it places blocks in a configuration close to their final distribution.

Conclusion

In this paper, we proposed a proof-of-concept of a self-reconfigurable robot based on sliding blocks. At the hardware level, several blocks have been realized integrating electro-permanent magnets in order to save energy between moves. The experiments show that a block is able to move along one another at an average speed of 16.4 mm/s and produces a holding force of 45mN. The blocks are powered externally but the housing of all the electronic parts in a 10mm cube is possible. A future improvement could be to use the EP magnets to sense the "rotor" block position using the different inductance of the different positions.

If the speed and energy consumption of the system are adequate to built large robots with hundreds of blocks, the holding force should still be improved. The gliding side of blocks should also be carefully design to minimize the friction forces and to avoid that a block braces against other ones.

A block is moving by sliding on other blocks, which create an original way of moving. At the software level, we therefore need a special reconfiguration algorithm which would take into account this way of moving. We proposed a distributed algorithm which reconfigures a set of blocks according to a target map. All the blocks use the same program and are able to organize themselves by exchanging asynchronous messages. This reconfiguration algorithm has shown to be effective, i.e. reconfiguration of a set of blocks is working, but the number of simultaneous blocks moving can still be increased. Furthermore, the entire map is sent to each block, which is not necessary. An future work would be to reduce the target map to local positions.

In the future, this work will be used as a basis to realize the Smart Blocks project. We have therefore given suggestions, hints and solutions to problems that will be faced in later work, when the actuators will be integrated to form a modular and reconfigurable conveyor.

Figure 1 :

 1 Figure 1: Example of using reconfigurable blocks for conveying objects.

Figure 2 :

 2 Figure 2: View of the linear motor units within a block with the EP and the neodymium magnets. The block is a 10mm cube and consists of an upper and a lower part.

  (a) Three EP magnets (with AlNiCo core) in front of two neodymium magnets (b) Rapid prototyping parts of the cube, one block is assembled with three EP magnets (active side, stator) and another one with two permanent magnets (passive side, rotor).

Figure 3 :

 3 Figure 3: Separate parts and an assembled block

Figure 4 :

 4 Figure 4: Schematics of the motor unit electronics

Figure 5 :

 5 Figure 5: The motor state diagram shows the 6 different states of the EP magnets and the changed position in respect to the passive sides of two blocks. The magnetic poles are marked with S and N for South and North.As every block has two permanent magnets on each of its passive sides, six states move the "rotor" block from one "stator" to another (10mm).

Figure 6 :

 6 Figure 6: The timing diagram shows the signals, coming from the IC, I/O PIN are labeled from 0 to 3. Additionally, the voltage of the capacitor and the displacement of the block is shown.

Figure 7 :

 7 Figure 7: Snapshots of the motion (six-states sequence).

Figure 10 :

 10 Figure 10: Captured image from the simulator software showing blocks with conveying actuators on the top. The floor is covered by tracks that guide the blocks during their displacement.

Figure 11 :

 11 Figure 11: Some steps of the reconfiguration algorithm: a) The goal map. b) The initial configuration of the blocks. c) The distance from each block to the closest empty space. d) The path from one block to a free cell.

Figure 12 :

 12 Figure 12: Algorithm of diffusion of the map over the set of blocks.

Figure 13 :

 13 Figure 13: Algorithm for determining the direction of simultaneous displacements of many blocks.

Figure 14 :

 14 Figure 14: Some screen captured from the simulator interface during the calculation of the reconfiguration. On the left, the last step of reconfiguration of the 'conveyor' shape. On the right, four reconfiguration steps from the horizontal line (on the top) to the text 'Mechatronics' (on the bottom). Red blocks are already well placed, yellow blocks have just reached their final position, and grey blocks are not well placed.

Table 1 :

 1 Number of steps to reach the goal from different initial shapes.

	Shape Goal Conveyor Mechatronics
	Horizontal line	121	22
	2 horizontal lines	136	119
	Diagonal line	108	42
	Sinusoidal line	71	30
	2 boxes	132	130

http://smartblocks.univ-fcomte.fr

http://www.smartsurface.cnrs.fr

S stands for south and N for north, meaning the state of the magnetic pole that points outside. It is noticeable at the block sides.

The short signal from the controller, causing an opening of certain upper side transistors and therefore the switching of one or more magnet polarities will be called "shot".

also available at this address: http://smartblocks.univ-fcomte.fr/actuation_ EP_magnets.avi

Acknowledgment

This work has been funded by the Labex ACTION program (contract ANR-11-LABX-01-01) and ANR/RGC (contracts ANR-12-IS02-0004-01 and 3-ZG1F) and ANR (contract ANR-2011-BS03-005)