Amaël Arguel
email: amael.arguel@mq.edu.au

Oscar Perez-Concha

; Simon

Y W Li

Annie Y S Lau

THEORETICAL APPROACHES OF ONLINE SOCIAL NETWORK INTERVENTIONS AND IMPLICATIONS FOR BEHAVIORAL CHANGE: A SYSTEMATIC REVIEW Running Title: ONLINE SOCIAL NETWORK AND BEHAVIORAL CHANGE

Keywords: Online social network, health intervention, social media, behavioral change, health psychology, Social Cognitive Theory

The aim of this review was to identify general theoretical frameworks used in online social network interventions for behavioral change. To address this research question, a PRISMA-compliant systematic review was conducted. A systematic review (PROSPERO registration number CRD42014007555) was carried out using three electronic databases (PsycINFO, Pubmed, and Embase). Four reviewers screened 1,788 abstracts; 15 studies were selected according to the eligibility criteria. Randomized controlled trials (RCTs) and controlled studies were assessed using Cochrane Collaboration's "Risk of Bias" tool, and narrative synthesis. Five eligible articles used the Social Cognitive Theory (SCT) as a framework to develop interventions targeting behavioral change. Other theoretical frameworks were related to the dynamics of social networks, intention models, and community engagement theories. Only one of the studies selected in the review mentioned a well-known theory from the field of health psychology. Conclusions were that guidelines are lacking in the design of online social network interventions for behavioral change. Existing theories and models from health psychology that are traditionally used for in-situ behavioral change should be considered when designing online social network interventions in a healthcare setting.

INTRODUCTION

Online social networks seem to be an effective mean to influence health-related behaviors for consumers and patients [START_REF] Maher | Are health behavior change interventions that use online social networks effective? A systematic review[END_REF][START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Ramadas | Web-based interventions for the management of type 2 diabetes mellitus: a systematic review of recent evidence[END_REF]. Some diseases such as obesity, depression, or diabetes proved to be sensitive to social media and social network interventions [START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Ramadas | Web-based interventions for the management of type 2 diabetes mellitus: a systematic review of recent evidence[END_REF][START_REF] Lau | Social and self-reflective use of a Web-based personally controlled health management system[END_REF][START_REF] Hwang | Social support in an Internet weight loss community[END_REF]. With the spread of consumer digital devices, online social media are expected to play an increasing role in the prevention and management of diseases [START_REF] Coiera | Social networks, social media, and social diseases[END_REF]. Although there is increasing empirical evidence on how social networks influence our health behaviors [START_REF] Maher | Are health behavior change interventions that use online social networks effective? A systematic review[END_REF], there is still a lack of clarity on the inner mechanisms of how this is done [START_REF] Cohen | Psychosocial Models of the Role of Social Support in the Etiology of Physical Disease[END_REF]. Social and health psychology provide several theoretical frameworks that explain behavioral changes induced by social influence [START_REF] Baum | Handbook of health psychology[END_REF][START_REF] French | Health psychology[END_REF]. Numerous studies have also pointed out the importance of incorporating theory in the design of an intervention to effectively induce behavior change [START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Noar | A health educator's guide to theories of health behavior[END_REF]). Yet, are theories being used at all when designing social network interventions?

What is the state of the art of theoretical approaches in the healthcare domain? The aim of this review is to identify theoretical components that have been used in online social network interventions to influence behavioral change. The review also aims to identify possible theoretical frameworks that could be used for designing online interventions addressing quantifiable behavioral changes, and which would present a certain degree of consensus for studies from different fields.

MATERIAL AND METHODS

A PRISMA-compliant systematic review was conducted [START_REF] Liberati | The PRISMA Statement for Reporting Systematic Reviews and Meta-Analyses of Studies That Evaluate Health Care Interventions: Explanation and Elaboration[END_REF], with a focus on experimental studies.

The review targeted online or computer-based studies in which theory-based interventions using social media were designed to produce certain behavioral changes.

Registration

The protocol of this systematic review was registered and is openly available in PROSPERO (international prospective register of systematic reviews) database (registration number CRD42014007555) [START_REF]PROSPERO -International prospective register of systematic reviews[END_REF].

Eligibility criteria and search strategy

The literature search was systematically performed on 3 electronic databases on July 27 th 2016: PsycINFO (via OvidSP), PubMed, and Embase (via OvidSP). The complete search strategy is available in Appendix 1. The selection of search terms was analogous to some previous systematic reviews on similar topic [START_REF] Maher | Are health behavior change interventions that use online social networks effective? A systematic review[END_REF][START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Cugelman | Online interventions for social marketing health behavior change campaigns: a meta-analysis of psychological architectures and adherence factors[END_REF]. Several pilot searches were conducted to adjust the terms and the filters, and the electronic databases chosen for the search. This iterative protocol led to the following search terms: social network, social media, social web, social influence, study, intervention, randomized controlled trial, trial, experiment, experimental, behavior, behavioral change, decision, online, internet, Facebook, Twitter, and web. Terminology of search terms was controlled using MeSH keywords when available and different spellings were used to address studies written in American English or British English. We set up the following filters in the electronic databases: [START_REF] Maher | Are health behavior change interventions that use online social networks effective? A systematic review[END_REF] articles in English, (2) published within the last 12 years (2003 to 2015), and (3) where the abstracts are available. The search was limited to articles describing experiments on adult participants.

For gray literature, an additional search was undertaken in consumer search engines (Google, Yahoo, and Bing); however no other references were retrieved.

Insert Table 1 here

A comprehensive list of inclusion and exclusion criteria is presented in Table 1 as well as a description of the population, intervention, comparator, outcomes, and study design (PICOS) (see Table 2).

Insert Table 2 here

The search strategy targeted articles covering four overlapping dimensions: 1) Social media in the intervention (e.g. social network, forum, discussion group, etc.), 2) Online interventions (e.g. computer-mediated interactions), 3) Primary outcome comprises a behavioral change (e.g. adoption of a new behavior or intention to adopt), and 4) Experimental methodology (e.g. involving at least one comparison group).

A study was eligible for inclusion if all the four criteria were satisfied.

The search produced a total of 1,788 responses which were exported into EndNote X4 (15). The duplicates were then removed from the resultant list and subsequently, titles, authors, year of publication, and abstract of articles were extracted and exported. Articles were randomly distributed into two subsets in order to be screened by two independent teams. Each team consisted of two of the co-authors (AA and OP were assigned to Team 1; AL and SYWL to Team 2) who independently screened article abstracts. Each article was coded as either accepted or rejected or 'uncertain'.

Cohen's Kappa inter-coder agreement coefficients for team 1 and team 2 were κ = .40 and κ = .47 respectively, which are considered to be of fair and moderate agreement strengths [START_REF] Altman | Practical statistics for medical research[END_REF].

Within each team, all articles accepted by both investigators were selected for further investigation.

In case of disagreement, a third party moderator decided about the paper's inclusion or exclusion.

Disagreements were defined as articles accepted by one investigator and rejected (or labeled as 'uncertain') by the other; or articles labeled as 'uncertain' by both investigators. AL and AA were moderators for disagreement cases that had arisen from team 1 (a total of 39 disagreements) and team 2 (34 disagreements) respectively. After moderation, 35 articles in total were identified for fulltext assessment. The same eligibility criteria used for abstract screening was used to screen the 35 articles; 20 were rejected and 15 were selected for full analysis in this review (see Figure 1). The features of the selected articles are summarized in Appendix 2.

Insert Figure 1 here

RESULTS

Description of included articles

In total, 15 experimental studies were identified. The domains covered by these studies were diverse and were not limited to health-related interventions. Within the studies which were health-related, the topics varied from physical activity and healthy lifestyle [START_REF] Centola | The spread of behavior in an online social network experiment[END_REF][START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF], to hip fracture prevention [START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF], uptake of vaccination [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF], coronary heart disease prevention [START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF], sexual transmissible infection prevention [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF], and smoking cessation [START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF]. Within the studies which were not health-related interventions, four papers dealt with online shopping or brand community [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF][START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF] and one paper addressed the topic of activism engagement [START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF]. The countries of origin of participants were United States of America for 9 studies (17-22, 27, 28, 31), with the remaining in Hong Kong [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF], Brazil [START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF], Germany [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF], United Kingdom [START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF], Taiwan [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF], and New Zealand [START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF].

The methodologies used in these studies involved random allocation to either an intervention or a control group, with an exception of one study [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF], which used a quasi-experimental design with a control website as a comparison group. All the other studies involved randomized controlled trials (17-22, 24, 26) and controlled laboratory experiments [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF][START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF][START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF][START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF].

In all these studies, the outcomes were associated with behavioral changes, either as an adoption of a new behavior (e.g. physical activity, smoking cessation, registration on a website, etc.) [START_REF] Centola | The spread of behavior in an online social network experiment[END_REF][START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF][START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF][START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF][START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF] or the intention of new behaviors (e.g. intention to get vaccinated, purchase intention, intention of engaging in a community, or of joining an activist group) [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF][START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF][START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF][START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF].

The participants were either university students [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF][START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF][START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF], or they were recruited according to their specific medical condition, or their assumed risk to develop a specific condition. These conditions included: sedentary lifestyle [START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF], risks of coronary heart disease [START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF], HIV and STI [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF], smoking [START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF], and relapsing-remitting multiple sclerosis [START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF]. The rest of the studies involved healthy participants, who were mainly recruited online [START_REF] Centola | The spread of behavior in an online social network experiment[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF][START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF][START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF].

Risk of bias evaluation

We used the 'Cochrane Collaboration' risk of bias tool to assess the quality of randomized controlled trials [START_REF] Higgins | Cochrane handbook for systematic reviews of interventions[END_REF]. The results of that evaluation are available in Table 3.

Insert Table 3 here

Overall, risks of bias were considered relatively high due to the lack of reported information in the methodology. In the majority of cases, the provided information did not allow the assessment for the presence or absence of a defined risk of bias since these cases did not report the concealment of allocation of experimental and control groups. In general, studies from fields other than medicine and health management received more 'high risk of bias' notations. However, since the risk of bias tool has been primarily designed for RCTs and medical and pharmacological studies, this tool may not be well suited for studies from other domains, such as marketing. The lack of consistency in reporting risks of bias in study designs among non-medical disciplines suggests the need for setting standards in bias reporting in these disciplines.

Theoretical frameworks

Various theoretical frameworks were used in the 15 studies reported: Social Cognitive Theory (SCT) was cited as a basis for social network interventions in five articles [START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF][START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF]; electronic Word of Mouth (eWOM) effects in two articles [START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF]. Other theoretical models that were reported in at least one article were: (a) Technology acceptance model (TAM) [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF], (b) the Theory of Planned Behavior (TPB) [START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF], (c) "strength of weak ties" theory ( 17), (d) perceived risk influence [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF], (e) learning from peer-facilitated interactions [START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF], (f) Internet popular opinion leader (i-POL) model ( 25), (g) a model of the degrees of personalness of networks [START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF], and (h) a model of online brand community [START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF].

Social Cognitive Theory

SCT was the most commonly used theoretical model reported in these studies [START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF][START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF].

The SCT model is based on social learning theory that describes human behavior with three major factors: personal factors (e.g. knowledge, expectations, affects), behavioral factors (e.g. skills, selfefficacy), and environmental factors (e.g. reinforcements, social norms, influence). SCT is well adapted to interventions that target health-related behavioral changes, notably because it states that social learning from observation and imitation of others can influence decision-making [START_REF] Bandura | Health promotion from the perspective of social cognitive theory[END_REF][START_REF] Bandura | Self-efficacy in health functioning[END_REF].

Certain components of SCT attempted to engage participants in online social network interventions.

For example, the self-efficacy principle in the SCT theory was cited in all five studies [START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF][START_REF] Whittaker | A theory-based video messaging mobile phone intervention for smoking cessation: randomized controlled trial[END_REF], and measured with scales in four of them [START_REF] Carr | Randomized controlled trial testing an internet physical activity intervention for sedentary adults[END_REF][START_REF] Motl | Internet intervention for increasing physical activity in persons with multiple sclerosis[END_REF][START_REF] Joseph | Print versus a culturally-relevant Facebook and text message delivered intervention to promote physical activity in African American women: a randomized pilot trial[END_REF][START_REF] Nahm | Effects of a social cognitive theory-based hip fracture prevention web site for older adults[END_REF]. Other SCT constructs were also addressed in these interventions. For example, a common strategy was the use of role models allowing for social influence and/or observational learning. This is achieved via the use of video-clips, discussion forums, and Questions & Answers with experts in all of the four studies. Other interventional features focused on promoting self-belief in achieving goals, such as via educational material in the written form.

Theories based on the structure of networks

The rest of the articles did not involve SCT, but instead they used various models or some components borrowed from other theoretical models. The common approach of most studies was to consider the structure and characteristics of the adopted online social networks and test for their effects on the new behaviors. The different theoretical components used are as follow:

• Electronic Word of Mouth (eWOM):

Two studies (28, 29) used eWOM, which could be considered as an approach more than a proper theory; it explores social influence of consumers regarding commercial products [START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF][START_REF] Sandes | Electronic word-of-mouth impacts on consumer behavior: Exploratory and experimental studies[END_REF]. These studies considered network structure (i.e. density, tie strength, position in the network), and the influence of positive and negative comments in order to explain the effect of eWOW on online purchase intentions. The valence (i.e. positive or negative) of opinion concerning a product was interpreted in regard to the Prospect Theory, which was developed to describe decision processes in the domain of behavioral economics [START_REF] Tversky | The framing of decisions and the psychology of choice[END_REF].

• Network structure (clustered-lattice vs. random network structure):

A study by Centola (17) tested the effect of network structure (i.e. clustered-lattice vs. random network structure) on the spread of health behaviors. Clustered-lattice networks are defined as networks in which ties link each node with others in their neighborhood but without links to distant nodes. In random networks, links between nodes are evenly distributed among nodes, whatever their location in the network. In his study, Centola showed that behavior adoption spread faster and farther in clustered-lattice networks than in random networks.

• Internet Popular Opinion Leader (I-POL) model:

One study [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF] investigated the effect of Internet popular opinion leaders with i-POL model, which is an adaptation of the popular opinion leader (POL) model [START_REF] Ko | Effects of Internet popular opinion leaders (iPOL) among Internet-using men who have sex with men[END_REF][START_REF] Kelly | Sexually-Transmitted Disease Prevention Approaches That Work -Interventions to Reduce Risk Behavior among Individuals, Groups, and Communities[END_REF]. The POL model was itself based on the diffusion of innovation theory, which considers social network structure and its influence on behavioral changes [START_REF] Rogers | Diffusion of innovations[END_REF].

• The degrees of personalness of social networks: Nekmat et al. [START_REF] Nekmat | Source effects in the micro-mobilization of collective action via social media[END_REF] explored the effects of online social networks in engaging participants in activist collective actions. In a controlled laboratory-based experiment the so-called personalness of fictional social networks were tested. Depending of the condition, participants were told that the source of a message was from a close network (e.g. "someone to whom you are very close"), from more distant network (e.g. "someone who is a friend of someone you know") or from an organizational source such as a student association. The study provided evidence that the degree of personalness can influence the participation of novice individuals in some collective actions.

Other theoretical basis

The remaining studies [START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF][START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF][START_REF] Lindsay | The health impact of an online heart disease support group: A comparison of moderated versus unmoderated support[END_REF][START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF] used different theoretical approaches to test and explain behavioral changes in social network interventions.

• Cavallo et al. [START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF] used the Theory of Planned Behavior (TPB) in order to design an online intervention aiming at increasing physical activity. The intervention specifically addressed some TPB variables related to physical activity, such as perceived behavioral control, intention, and attitude. Although traditional TPB variables were able to explain only small to medium impacts on the outcomes, the authors developed an extended version of the TPB that could explain 27% of the variance observed in physical activity and 59% for intention.

• A study on online heart disease support groups (24) used a theory of "weak ties" networks [START_REF] Granovetter | The strength of weak ties[END_REF] to test effects of peer-to-peer interactions and types of moderation in virtual discussion rooms in a randomized controlled trial.

• Another study described an intervention designed to increase vaccination rate [START_REF] Betsch | Effect of narrative reports about vaccine adverse events and biasawareness disclaimers on vaccine decisions: A simulation of an online patient social network[END_REF]. Using a simulated online patient social network similar to the website patientslikeme.com, the authors manipulated the perception of a risk of adverse events related to vaccination.

Across different conditions, information from the website was manipulated, mainly the frequency of vaccine adverse events, the type of information (narrative vs. summary statistics), and the presence or not of a bias awareness disclaimer. That theoretical approach was similar to some early cognitive theories in health psychology such as Health Belief Model (HBM), which states that the perception of a threat, and the belief one can have about measures to reduce that threat, can together have an influence on the likelihood of engaging in some behavioral changes [START_REF] Janz | The Health Belief Model: a decade later[END_REF].

• In the field of online shopping, a study cited the technology acceptance model (TAM) as a theoretical basis for designing an ad hoc research model [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF], which explains consumer's purchase decisions on an experimental website used in a controlled laboratory study. The website pretended to sell cinema tickets and included an online discussion forum. The theoretical model used in this study integrated the components from an early version of TAM (perceived usefulness and perceived ease of use), and an additional component corresponding to positive informational social influence [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Davis | Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology[END_REF].

• Another ad hoc model was presented in the field of online consumer engagement: the "online brand community engagement behavior" model [START_REF] Lee | The impact of online brand community type on consumer's community engagement behaviors: Consumer-created vs. marketer-created online brand community in online social-networking web sites[END_REF]. The model was based on both attribution theory and social identity theory [START_REF] Kelley | Processes of Causal Attribution[END_REF][START_REF] Tajfel | Social Identity and Intergroup Behaviour[END_REF]. Attribution theory was used in this case to describe when online brand community could be perceived as result of extrinsic motives (e.g. profit of a company) or intrinsic motives (e.g. altruism of consumers) [START_REF] Mizerski | The attribution process in consumer decision making[END_REF]. Social identity theory was defined as an individual self-concept linked to knowledge of a membership of a social group that involves an emotional significance [START_REF] Dholakia | A social influence model of consumer participation in network-and small-group-based virtual communities[END_REF]. The online brand community engagement behavior model suggested that the types of online brand community (i.e. marketer-created vs. consumer-created) had an influence on the quality of community engagement behaviors.

DISCUSSION

The first finding of this review suggests that the most common theory in health-related studies designed for online social network interventions was SCT. Originally, SCT was not specifically constructed for designing online social network interventions, but some authors have adapted that theory to online interventions. Other studies reported in the review cited various models and theories as rationales for their experiments. Two of them mentioned the eWOM, and others cited: the theory of the "strength of weak ties", an adapted version of the TAM, the perceived risk influence, and an ad-hoc model of online brand community engagement.

The second finding suggests that none of the studies selected in this review has mentioned any wellknown theories or models from the field of health psychology, with the exception of (20). This finding is somewhat surprising given some of the identified studies were about health interventions in particular. Examples of well-known health psychological theories include the HBM, which is widely used in health education programs when engagement of new behaviors is sought. Similarly, the TPB and the Transtheoretical Model of Behavioral Change were surprisingly virtually absent from the studies in our review but one [START_REF] Cavallo | The role of companionship, esteem, and informational support in explaining physical activity among young women in an online social network intervention[END_REF], despite being widely used in other health-related interventions [START_REF] Prochaska | Stages of change[END_REF][START_REF] Ajzen | The Theory of Planned Behavior[END_REF]. Numerous reviews have emphasized the importance of incorporating a theoretical approach when designing interventions for behavioral change, especially for health [START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Ramadas | Web-based interventions for the management of type 2 diabetes mellitus: a systematic review of recent evidence[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Cugelman | Online interventions for social marketing health behavior change campaigns: a meta-analysis of psychological architectures and adherence factors[END_REF][START_REF] Painter | The use of theory in health behavior research from 2000 to 2005: a systematic review[END_REF].

Our hypothesis is that there might be two reasons behind the absence of use of health psychology theories in the articles of our review. Firstly, health psychology theories are not technology-oriented, and might appear inadequate for online interventions at the first instance to researchers unfamiliar with them [START_REF] Riley | Health behavior models in the age of mobile interventions: are our theories up to the task? Translational behavioral medicine[END_REF]. Health psychology theories can typically be categorized into two groups: (1) the continuum models, which consider linear predictions of likelihood behaviors (e.g. SCT), and (2) the stage models, which examine the chance of progression of individuals in several discrete stages (e.g. Transtheoretical Model) [START_REF] Noar | A health educator's guide to theories of health behavior[END_REF][START_REF] Lippke | Theory-based health behavior change: Developing, testing, and applying theories for evidence-based interventions[END_REF]. When selecting a theoretical framework, it is possible that researchers prefer to use a continuum approach rather than stage models, which are more complex as they require the implementation of staging algorithms [START_REF] Noar | A health educator's guide to theories of health behavior[END_REF][START_REF] Lippke | Theory-based health behavior change: Developing, testing, and applying theories for evidence-based interventions[END_REF]. That could partially explain why SCT was found to be the most used theory for health-related interventions in our review. Secondly, each discipline or field seems to have its own "favorite" theories. For example, health-related interventions mostly use a limited set of theories from health psychology (50), while eWOM is widely used for marketing research [START_REF] Cheung | The impact of electronic word-of-mouth communication: A literature analysis and integrative model[END_REF] and TAM for information system research [START_REF] Schepers | A meta-analysis of the technology acceptance model: Investigating subjective norm and moderation effects[END_REF]. Hence, each discipline would tend to adopt the theory based on its common disciplinary practice rather than the appropriateness of the theory.

All selected studies were experimental and involved comparison groups to test the effect of social media, such as online discussion forums, presence of opinion leaders, type of feedback from other users, and different characteristics of the networks (structure, density, size, type of moderation). The domains covered in the studies were diverse and did not focus only in the field of healthcare. In addition, there was a large variation in the duration of the interventions, ranging from 10 minutes to 9 months. Four studies in the review were targeting online shopping or online consumer communities. We chose not to restrict the review to medical publications because we believed that the cognitive mechanisms underlying behavioral change from online social network interventions would be independent of the nature of the domain (i.e. health-related or not). However, we observed that the most eligible studies from different fields of research did not share a similar theoretical background according to the field of the research (e.g. health interventions vs. product selling). All in all, it seemed that there was not a consensus in the approaches used to explain online social network effects on behavioral changes. Instead, the studies seemed to reuse traditional approaches in their own field and try to adapt them to online social media.

The review illustrated the diversity of theoretical approaches that were used in social network intervention studies. There is currently a lack of consensus on what theories should be used in social network interventions. Although the choice of an appropriate theory can be dependent on many factors [START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF] and we have also suggested a number of possible reasons to explain this, researchers can refer to previous research that was conducted to guide choice of theory for online interventions in general [START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Noar | A health educator's guide to theories of health behavior[END_REF]. These resources provide guidance on ways to choose an appropriate theory depending on parameters such as: the consideration of a continuum/stage model [START_REF] Lippke | Theory-based health behavior change: Developing, testing, and applying theories for evidence-based interventions[END_REF], the type of component thought to be important to the behavior sought [START_REF] Noar | A health educator's guide to theories of health behavior[END_REF], whether the behavioral change is expected to be maintained at short-term or long-term [START_REF] Rodney | Applying Psychological Theories to Promote Long-Term Maintenance of Health Behaviors[END_REF], the mode of delivery, the technological platform, the demographics, and the associated behavior techniques involved [START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Noar | A health educator's guide to theories of health behavior[END_REF]. We believe that these parameters would provide a good starting point to base the choice of theory for investigation and overcome problems of unfamiliarity of theories from other disciplines or adopting theories based on common disciplinary practice.

Strengths and limitations

The main strength of this review is the inclusion of experimental studies coming from any field of application, each of them with different scientific methodologies. This wide-inclusion decision ensures that we have covered all relevant articles on the subject of online social network interventions. However, the strategy also brings a mixed collection of different scientific standards making analysis more difficult.

Although there were only 15 studies, the review proceeded according to the PRISMA-compliant protocol with no changes introduced during the process. Our search methodology is based on peerreviewed systematic reviews in the area (for example, the choice of search terms, data base selection, and article selection criteria). In fact, the number of included articles is in line with a few of recent systematic reviews on social network interventions [START_REF] Maher | Are health behavior change interventions that use online social networks effective? A systematic review[END_REF][START_REF] Laranjo | The influence of social networking sites on health behavior change: a systematic review and meta-analysis[END_REF][START_REF] Webb | Using the internet to promote health behavior change: a systematic review and meta-analysis of the impact of theoretical basis, use of behavior change techniques, and mode of delivery on efficacy[END_REF][START_REF] Akesson | Health care consumers' experiences of information communication technology--a summary of literature[END_REF]. The criteria of using theory and a quantifiable behavioral measure may have limited the number of eligible articles.

However, these criteria are essential as they provide answers to how we can design interventional studies that involve social networks and produce quantifiable changes. In addition, the small number of eligible studies is an indication of the scarcity of publications in this area. The field of using social networks to change behaviors is relatively new. Despite its rapid growth, the number of theory-based studies is still limited in social network interventions, highlighting the need for further research in this area. The first step in the article selection process was focused on titles and abstracts as suggested by PRISMA guidelines [START_REF] Liberati | The PRISMA Statement for Reporting Systematic Reviews and Meta-Analyses of Studies That Evaluate Health Care Interventions: Explanation and Elaboration[END_REF]; there might be a slight probability that some articles were erroneously rejected from the review. In addition, the review targeted only articles in English. This limitation might have resulted in the exclusion of some relevant articles written in other languages than English.

Several studies in the review (18-21, 24, 25, 27, 28, 31) did not provide enough information in their material and methods sections. Modest scores in the risk of bias assessment illustrated that lack of information. This was particularly obvious for studies from the field of marketing [START_REF] Lee | Consumer's decision to shop online: The moderating role of positive informational social influence[END_REF][START_REF] Sohn | Disentangling the effects of social network density on electronic word-of-mouth (eWOM) intention[END_REF], which did not seem to follow scientific protocols as rigorous as for studies from the field of health.

Finally, this review follows a rigorous methodology: the review was conducted to be strictly compliant with a protocol designed and openly available prior to the search of selected articles.

During the selection process, two assessors reviewed independently each abstract and a third party mediated in case of disagreement.

CONCLUSION

The main lesson learnt from our review was that we observed a lack of consensus when applying theoretical frameworks in the design of online social network interventions to induce behavioral change. In order to ensure the effectiveness of interventions and to be able to reuse this knowledge in the long run, a theoretical approach is necessary. Through this review, we suggest that existing theories and models from health psychology that are traditionally used for in-situ behavioral change should be considered when designing online social network interventions for healthcare. However, research on behavioral change produced by online social network is still in its infancy, like were health psychology theories twenty years ago [START_REF] Lippke | Theory-based health behavior change: Developing, testing, and applying theories for evidence-based interventions[END_REF]. Theses theories were derived from other psychological disciplines and now, they constitute an independent branch of knowledge. Similarly, it is plausible that in the future, online social interventions will be based on new theories, integrating theories from health psychology and theories from other domains.

  POL: Popular Opinion Leader SCT: Social Cognitive Theory TAM: Technology Acceptance Model TPB: Theory of Planned Behavior

Funding

Financial support for this study was provided by the National Health and Medical Research Council (NHMRC) Centre of Research Excellence in E-Health (1032664). The funding agreement ensured the authors' independence in designing the study, interpreting the data, writing, and publishing the report. The following authors are employed by the sponsor: AA, AYSL.

Author Disclosure Statement

No competing financial interests exist.


Simon Enjalbert
email: simon.enjalbert@uphf.fr

Yassine Boukal
email: y.boukal@gmail.com

On the Eco-driving Trajectory for Tramway System

Keywords: Optimal control problem, Minimization of energy consumption, Non-linear algorithm, Tramway system, Human Machine Systems

In this work, the problem of reduction of energy consumption based on calculated speed, called eco-driving trajectory for tramway system is investigated, where some constraints on the states, control input and travel time are considered. Thanks to the operating speed range of the tramway, the non-linear model of the system can be approximated by linear one and is given in a state space distance based formulation. The problem studied in this work is to determine the speed profile that minimizes the cost function defined as the energy consumption. Firstly, the constrained optimization problem is formulated as Kuhn-Tucker conditions, which is the general form of the Pontryagin maximum principle, that yield to a local minimum. Then, the control strategy that ensure the efficient consumption for the tramway system is deduced based on the optimal control approach. This leads to the well known driving trajectory for the railway system, which is divided into four phases: acceleration, speed holding, coasting, and braking. On the other hand, the energy consumption analysis allows us to write the cost function as a sum of the kinetic energy to move the train and the resistance forces, by taking into account the gradient and limitations. Based on this analysis,the necessary condition for a is obtained. That ensure method is used to find energy-efficient driving trains. In this paper, we show how to calculate the critical switching points for an optimal strategy non-linear programming algorithm is used to solve the optimal control problem.

INTRODUCTION

In the last years, the attention of many researchers has been attracted by the significant increase of railway traffic volumes and their emissions of the pollutant particles. This is one of the reasons for what the issue of speed profiling becomes a new problem with specific characteristics, which must be resolved. Generally, the goal is to optimize the energy consumption or/and running times by involving one or several objectives. For this reason, the question of speed profiling becomes a specific issue, which must be handled in the development phase of ecoaware transportation systems (see [START_REF] Howlett | Energyefficient train control[END_REF]; [START_REF] Coleman | Using simulation to assess the benefits of energy-efficient driving strategies[END_REF]; [START_REF] Albrecht | Energy-efficient recovery of delays in a rail network[END_REF]; [START_REF] Feng | Optimization of target speeds of highspeed railway trains for traction energy saving and transport efficiency improvement[END_REF]; [START_REF] Gupta | A two-step linear programming model for energy-efficient timetables in metro railway networks[END_REF] and the references therein). This paper focuses on the continuity of study initiated by [START_REF] Cacciabue | Unified driver model simulation and its application to the automotive, rail and maritime domains[END_REF]; [START_REF] Enjalbert | Validation of a unified model of driver behaviour for train domain[END_REF]; La [START_REF] Delfa | Eco-driving command for tram-driver system[END_REF] on the Eco-driving command for tram-driver system where the authors objective was to define a trajectory profile to reduce energy consumption and its impact on the driver vigilance with compliance to the network procedures. This work has led to patent driving assistance device for a railway vehicle by [START_REF] Miglianico | Driving assistance device for a railway vehicle, comprising progressive means for indicating instructions[END_REF]. Then it has been complemented to avoid the impact of the driver bad maneuver or behavior in following the tramway system eco-driving reference which affect the system dynamic by [START_REF] Boukal | Observer-based tracking design using H∞ criteria: Application to ecodriving in a tramway system[END_REF]. In this work, authors will define switching points between the four driving phases: acceleration, speed holding, coasting, and braking. A strategy based on a non-linear programming algorithm is used to solve the optimal control problem. The obtained ecodriving trajectory could be implemented in future humanmachine interfaces in tramway cabins. : curvature radius (m) g : gravitational constant (9.81m.s -2 )

MATHEMATICAL MODEL

The dynamic of the tramway is modelled to control the tramway position and velocity at any time during the defined path between two stations. This modelling requires the knowledge of some basic parameters like the traction and brake intensities, adhesion coefficient, track profile, in addition to the weather conditions such as wind speed if available. Usually, the brake and traction curves are given by the constructor. By applying the fundamental Newton's law on the tramway, we obtain its dynamic equation states the relation between the exerted forces on the system, its mass m and the acceleration

v = p m v = F T (v) -F R (v)
(1) where F T (v) is the traction effort that the tramway produces in the running phase, and F R (v) represents the resistance which is the sum of the line F Rl (v) , curve F Rc (v) and vehicle F Rm (v) resistances. These later are given as

F Rl = mg sin(β) (2a)
F Rc = mg k e r c (2b)
F Rm (v) = a 0 + b 0 v + c 0 v 2 (2c) F Rm (v) = a 1 + b 1 v (2d)
From the equations (2), we can see that the line resistance F Rl (v) depends on the train mass and the slope angle β, and the gravity constant g. Furthermore, the curve resistance F Rc (v) concerns the passage of a tram in some inclined portions of path, and depends on the track gauge coefficient k e and the curvature radius r c . In addition, due to the low value of c 0 and the velocity range [v min ; v max ] relatively low also, the vehicle resistance F Rm (v) against tram move can be approximated in the following by a 1 + b 1 v by using the least squares method.

Time domain

The equations of motion for a point mass train are

dx dt = v(t) (3a) dv dt = 1 m u(t) - b 1 m v(t) - a 1 m + g sin(β) + g k e r c (3b)
Now, the tramway dynamics can be represented in a state space model as ẋr (t) = Ax r (t) + B u u r (t) + d r (4a) y r (t) = C y x r (t) (4b) where

x r (t) = p(t) v(t) , A = 0 1 0 -b1 m , B u = 0 1 m C y = [1 0] , d r = 0 -a1 m + g sin(β) + g ke rc

Space domain

From the fact that the track gradient, speed limitations depends on position, it is often convenient to rewrite the equations of motion in the form

dt dx = 1 v(t) (5a) v(t) dv dx = 1 m u(t) - b 1 m v(t) - a 1 m + g sin(β) + g k e r c (
5b) where the equations (5) are formulated with x as the independent variable. The elapsed time t = t(x) ∈ [0, T ] is the new state space model variable, where T is the total time allowed to travel between two stations. Now the state space variables, which are the speed time t and the speed v, are derived with respect to x.

PROBLEM FORMULATION

The power generated by the train is obtained by multiplying the tramway speed by the force delivered by its electric motor. Then, the consumed energy is deduced by integrating the obtained power. We assume, in the energy balance of the tramway, that the energy consumed is equal to the energy delivered by the engine, i.e. the tramway does not recover energy during the braking phase. Based on the energy conservation law, the cost function is deduced from the computation of the total energy consumption, i.e. the energy consumption is considered as the objective function of the considered non-linear programming problem. It will be convenient to cast our optimization problem into the following particular form. This is no a restriction since any optimization problem can be cast into this form

minimize u∈U T 0 (uv) dt (6a) subject to v = 1 m u - 1 m (a 1 + b 1 v + g k e r c + g sin(β(x))) (6b) x(0) = 0 (6c) x(T ) = L (6d) v(0) = 0 (6e) v(T ) = 0 (6f)
The control input u(t) is composed of two forces and is given as

u(t) = u f f (v) -u b b(v) (7)
where Now, by applying the Pontryagin maximum principle to solve the problem as specified in ( 6) with its constraints. This leads to find an optimal strategy for optimal control problem. Since the associated Hamiltonian to the problem defined as in ( 6) is given by

£ u f is the relative traction force, where u f ∈ [0, 1]; £ f (v)
H(x, v, λ 1 , λ 2 , u) = uv + λ 1 v + λ 2 [ 1 m u(t) - b 1 m v(t) -( a 1 m + g sin(β) + g k e r c )] (8)
the adjoin equations are defined as

dλ 1 dt = - ∂H ∂x = -λ 2 g d sin(β) dx (9a) dλ 2 dt = - ∂H ∂v = -u -λ 1 -λ 2 - b 1 m (9b)
Furthermore, we know that the Hamiltonian is constant along the trajectory produced by the optimal control. Despite the fact that the controller of the speed holding is a singular one, it is still the key to the optimal control strategy. From the Hamiltonian (8), it is easy to see that

∂H ∂u = v + λ 2 1 m (10)
In fact, the optimal control strategy of the problem ( 6) have one of the following five possible optimal driving modes [START_REF] Liu | Energy-efficient operation of rail vehicles[END_REF])

• Full power (FP). u f = 1, u b = 0, exists when λ 2 > mv. • Partial power (PP). u f may vary, u b = 0, exists when λ 2 = mv > 0. • Inertia motion or coasting (C). u f = 0, u b = 0, exists when 0 < λ 2 < mv. • Partial braking (PB). u f = 0, u b may vary, exists when λ 2 = 0. • Full braking (FB). u f = 0, u b = 1 , exists when λ 2 < 0. Remark 1. The PB driving mode is used by the driver in case of unpredictable noise models an unusual situation. This case is not discussed in this work.

According to the obtained solution of the optimization problem, the driving strategy is energy-efficient if it respects the five possible optimal driving modes given previously. Instead of solving the optimization problem given below to ensure the minimal energy consumption, the problem can be reformulated as find the switching points that guarantee the same result, i.e. to be energy-efficient. In this new formulation, the objective function is evaluated and minimized with respect to the new decision variables and constraints, where the considered decision variables are the switching speeds and the duration of each phase. In fact, solving the the optimization problem given as a non-linear programming model leads to obtaining a speed trajectory with less energy consumption. Due to a small number of decision variables in comparison with other approaches, this new formulation of the optimization problem is easy to solve. As a result, the speed reference trajectory is obtained from the decision variables, within a few seconds, making the method fairly suitable for realtime implementation, as detailed in what follows. Assumption 1. We assume that the mass m is constant during the trip between two stations.

MAIN RESULTS

The main idea is to develop and solve an optimal control strategy to minimize the energy consumption of the tramway by focusing on the optimization of profile of the tramway speed referred as "Eco-Driving", where the different road conditions, including the effects of road gradients and their variations, is also taken into consideration in the optimization problem.

One phase optimal control model

The proposed optimal problem is obtained by considering the tramway kinetic energy on different speed profile section, i.e. the work needed to accelerate the tramway from rest to its stated velocity, and to maintain certain desired speeds. Now, we consider the possible driving modes from the optimal speed trajectory in figure 1 where each point P i is characterized by a spatial localization x i , a speed v i , and the passage time t i . In addition, for each mode i or section, the transit time ∆T is given as ∆T i = t i+1 -t i , and the travelled distance ∆X is obtain also as ∆X i = x i+1 -x i . • Full power (FP) P 1 → P 2 :

E F Pi = 1 2 v 2 1 = 0 (11a)
E F P f = 1 2 v 2 2 + g∆h F P (11b) E F P = (E F P f -E F Pi ) + E R F P (11c) v 1 = 0 (11d) ∆T F P = v2 v1 dx 1 m u -1 m (a 1 + b 1 v + g ke rc + g sin(β(x))) (11e)
∆X F P = v2 v1 v.dx v m u -1 m (a 1 + b 1 v + g ke rc + g sin(β(x))) (11f)
• Partial power (PP)P 2 → P 3 :

E P Pi = 1 2 v 2 2 (12a )
E P P f = 1 2 v 2 3 + g∆h P P (12b)
E P P = (E P P f -E P Pi ) + E R P P (12c) ∆X P P = ∆T P P .v 2 (12d) v 2 = v 3 (12e)
• Inertia motion or coasting (C) P 3 → P 4 :

E Ci = 1 2 v 2 3 (13a) E C f = 1 2 v 2 4 + g∆h C (13b) E C = (E C f -E Ci ) + E R C (13c) ∆T C = v4 v3 1 -1 m (a 0 + b 0 v + g ke rc + g sin(β(x))) dv (13d) ∆X C = v4 v3 v -1 m (a 0 + b 0 v + g ke rc + g sin(β(x))) dv (13e)
• Full braking (FB) P 4 → P 5 :

E F Bi = 1 2 v 2 4 (14a) E F B f = 1 2 v 2 5 + g∆h C (14b) E F B = (E F B f -E F Bi ) + E R F B (14c) ∆T F B = v 4 b (14d) ∆X F B = v 2 4 b (14e)
The following parameters v 2 , v 4 and ∆T P P are considered as the decision variables in the optimization problem to be solved, where the cost function is equal the total energy consumption defined by adding the energy consummated during the first (Full power) and second (Partial power) modes: E = E F P + E P P (15) Assumption 2. We assume that no energy is consumed nor recovered during braking, i.e E F B = 0.

Notice that, the total travelled distance is equal to the distance between two stations, and is equal also the sum of the distances of the phases. Similarly, the total running time is linked to the travel time of each phase, and is equal to the required one.

4 i=1 ∆T i = T (16a) 4 i=1 ∆X i = L (16b)
In the following theorem, we provide new formulation for the tramway speed profile optimization as a non-linear programming problem ensuring the minimization of the energy consumption, i.e. the energy-efficiency. Theorem 1. The higher energy efficiency of a tramway is ensured if the optimization problem given below minimize u∈U E = E F P + E P P (17a)

E = 1 2 v 2 2 + g∆h F P + g∆h P P g∆h + E R F P + E R P P E R (17b) subject to 4 i=1 ∆T i = T (17c) 4 i=1 ∆X i = L (17d) ∆X i > 0, i = 1, . . . , 4. (17e) ∆T i > 0, i = 1, . . . , 4. (17f) v i > 0, i = 2, 4.
(17g) has a solution, where the decision variables of this nonlinear programming model are v 2 , v 4 and ∆T 2 . Then, the total energy consumption per mass unit is minimized by following the speed trajectory defined by v 2 , v 4 and ∆T 2 .

The presented optimal control problem is less complex, this comes form the fact no partial differential equations are involved to solve it. The switching points, indicating that a train must reach the position P i at the specified time t and speed v, can be deduced from the solution of the optimal control problem. Consequently, which allow us to identify the complete optimal control sequence. These switching points and the optimal controls represent the complete solution for the optimal control problem.

Multiple-phase optimal control model

It is not possible to solve the optimal control problem to achieve energy efficiency from the cost function, dynamic constraints, path constraints and boundary constraints form the optimal control problem given by ( 18) in subsection 4.1, since the path constraints (the speed limits) and the dynamic constraints (gradients) change along the tramway trajectory. So, the considered optimal control problem can be represented as multiple-section optimal control problems. To achieve that, the trajectory is divided into sections, where any section has its own cost function, dynamic model, path constraints, and boundary conditions. Firstly, let T i = 4 j=1 ∆T ij denotes the travel time of each section k. In fact, the total run time between a station i and the next one i + 1 is denoted by T , where T is equal the sum of the travel time T i of all sections, i.e. T = n i=1 4 j=1 ∆T ij . In addition, the total run time is equal to the sum of a fixed value T i f and a value T iv that must be minimized, i.e. T i = T i f + T iv . The variable T iv will be used to relax the optimization problem. On the other hand, the terms S i = 4 j=1 ∆S ij denotes the travel distance of each section k. In fact, the total distance between a station i and the next one i + 1 is denoted by S, where S is equal the sum of the travel distances S i of all sections, i.e. S = n i=1 4 j=1 ∆S ij . In this case, the optimal solution is obtained by assembling the all phases of trajectory sections. The advantages presented by this approach are the speed limits and gradient are constant in each section. In addition, the speed v 5 of a section i is equal to v 1 of the section i + 1, this boundary conditions link the sections together. The total energy consumption is given by summing the cost functions of all phases. Finally, the optimal trajectory is obtained by solving the minimization problem defined by new total cost function subject to new constraints depending on limits and gradients of each section. Theorem 2. The higher energy efficiency of a tramway is ensured if the optimization problem given below

minimize u∈U E = n i=1 E i (18a)
E i = 1 2 v 2 i2 + g∆h iF P + g∆h iP P g∆hi + E R iF P + E R iP P E iR (18b) subject to n i=1 4 j=1 ∆T ij = T (18c) n i=1 4 j=1 ∆X ij = L (18d) ∆X ij > 0, i = 1, . . . , n; j = 1, . . . , 4 (18e) ∆T ij > 0, i = 1, . . . , n; j = 1, . . . , 4 (18f) v ij > 0, i = 1, . . . , n; j = 2, 4 (18g)
has a solution, where the decision variables of this nonlinear programming model are v i 2, v i 4 and ∆T i 2. Then, the total energy consumption per mass unit is minimized by following the speed trajectory defined by v i 2, v i 4 and ∆T i 2.

CASE STUDY

In this part, numerical simulations are presented to illustrate the effectiveness of the proposed methodology. Firstly, different study cases are considered, where the speed limitations are arranged in different order, sometimes increasing, decreasing, or a varied order between increasing and decreasing. The traffic on these lines is provided by Alstom Citadis type 302 trams. The mechanical characteristics of the considered model and line geometry have been parametrized and introduced in the simulated model. A comparison between energy consumption of fast, average and slow times is made. In fact, the fast travel time is obtained by rounding the 105% of the minimal time in multiples of 5s. Also, by rounding the fast time by 110% in multiples of 5s, we get average travel time. Finally, the slow travel time is obtained by adding the difference between the average and the fast time to the average time, i.e. T f -T s = 2 × (T a -T f ) where T f is the fast time, T a is the average time and T s is the slow time. In this scenario, the consumption energy used during a trip with an increasing speed limits is studied. From the solution of the optimization problem, the switching points and the duration of partial power phase are deduced for different trip time constraints. In fact, the speed trajectories can be drawn by using these informations. As a result, the speed trajectory of the minimal trip time is plotted in the figure 2 for a travel distance S i = 550m. In addition, the speed trajectories of the fast and slow trip times are plotted also in figures 3, and 4 respectively.

From figures 3-4, we can remark that, by lengthening the trip time, the reached maximum speed is less than the imposed speed limitation. In addition, the coasting phase becomes more solicited. This leads to minimize the energy used to make the make the trip.

Decreasing limits

In this scenario, the consumption energy used during a trip with a decreasing speed limits is studied. From the solution of the optimization problem, the switching points and the duration of partial power phase are deduced for different trip time constraints. In fact, the speed trajectories can be drawn by using these informations. As a result, the speed trajectory of the minimal trip time is plotted in the figure 5 for a travel distance S i = 550m.

Varied order

In this scenario, the consumption energy used during a trip with a varied order of speed limits is studied. From the solution of the optimization problem, the switching points and the duration of partial power phase are deduced for different trip time constraints. In fact, the speed From Table 1 where energy results and associated savings for all cases studied are merged, it is clear that lengthening the trip time saves up to 50 percent of the energy consumed during the fast time. Consequently, this fact confirms that lengthening the imposed trip time saves the consumed energy.

CONCLUSION

In this paper, the control strategy to reduce energy consumption for the Tramway system is deduced based on the optimal control approach. The calculation of the critical switching points between acceleration, speed holding, coasting, and braking phases is realized thanks to the presented non-linear programming algorithm. The perspective of this work is to simulate the proposed methodology on The PSCHITT platform (Hybrid and Inter-modal Collaborative Simulation Platform in Land Transport). The PSCHITT platform is a versatile simulator that can be fitted with different cabins (Reduced Mobility Person, Rail, ...) according to the scientific objectives and experimental needs, for example PSCHITT-Rail 1 . Cases based on the commercial tramway of Valenciennes city in France which is composed of two lines, with about 33.8km of tracks and 48 stations will be studied. The evaluation of the impact on traffic for several tramways operating on the same time in a city network and the concept of mobility resilience based on previous work on the domain of transportation (see [START_REF] Enjalbert | Assessment of transportation system resilience[END_REF]; [START_REF] Enjalbert | A hybrid reinforced learning system to estimate resilience indicators[END_REF]) should be enhanced.

1 https://www.uphf.fr/LAMIH/en/PSCHITT-Rail

a 0 ,

 0 b 0 , c 0 : coefficients of the mass, mechanical, : air resistances a 1 , b 1 : linearised coefficients of the mass, : mechanical & air resistances m : train mass (Kg) β : slope angle ( • ) r c

  is the specific maximum traction force; £ u b is the relative braking force, where u b ∈ [0, 1]; £ b(v) is the specific maximum braking force.

Fig. 1 .

 1 Fig. 1. The four phases of tramway driving: acceleration, speed holding, coasting, and braking

Fig. 2 .

 2 Fig. 2. The speed trajectory of the minimal trip time and his characteristics T i = 64.4, E = 1.0257e 7

Fig. 3 .Fig. 4 .

 34 Fig. 3. The speed trajectory of the fast trip time and his characteristics T i = 70, E = 4.7801e 6

Fig. 5 .

 5 Fig. 5. The speed trajectory of the minimal trip time and his characteristics T i = 55.2, E = 1.0348e 7

Fig. 6 .

 6 Fig. 6. The speed trajectory of the minimal trip time and his characteristics T i = 57.74, E = 1.0024e 7

Table 1 .

 1 The energy consumption for fast, average and slow times trajectories can be drawn by using these informations. As a result, the speed trajectory of the minimal trip time is plotted in the figure6for a travel distance S i = 550m.

	Type	Fast	Average	Slow
	Increasing	E f = 4.78e 6	Ea = 3.15e 6	Es = 2.26e 6
			-34.05%	-52.77%
	Decreasing	E f = 4.80e 6	Ea = 3.15e 6	Es = 2.43e 6
			-34.3%	-49.29%
	Varied	E f = 4.07e 6	Ea = 3.16e 6	Es = 2.74e 6
			-22.35%	-32.69%

ACKNOWLEDGEMENTS

The present research work has been supported by: The European Community, The Ministry of Higher Education and Research, And The Hauts-de-France Region. The authors gratefully acknowledge the support of these institutions.

This work has been funded by the Project: ELSAT 2020 by CISIT / GS2RI: Greener & Safer Rail Road Interaction.