Trust and trustworthiness are essential to an efficient economy and play crucial roles in social life. Previous evidence from behavioral experiments has revealed that the trustworthiness of individuals is closely related with their altruistic preference. It has been demonstrated that the ventromedial prefrontal cortex (vmPFC) is associated with decisions involving trustworthiness. Moreover, vmPFC lesion patients showed less trustworthiness and altruism than control subjects, indicating the indispensable role of this specific brain area in human social interactions. However, the causal relationship between this neural area and trustworthiness, as well as altruism, has not been fully revealed. The potential neural basis behind the behavior of trustees’ repayment has also seldom been discussed. In the present study, we aimed to provide evidence of a direct link between the neural and behavioral results through the application of transcranial direct current stimulation (tDCS) over the vmPFC of our participants. We found that activating the vmPFC could promote both the trustworthiness and altruism of our participants. We also show that enhancing the excitability of the vmPFC using tDCS increased the trustworthiness of the participants, and this promoting effect might be attributable to the enhancement of individuals’ altruistic preference. In addition, we revealed that the enhancing effect in trustworthiness and altruism might be specific to the activation of the vmPFC by applying tDCS over another brain region within the prefrontal cortex as a control site. Crucially, our findings provide direct evidence supporting the critical role of the vmPFC in cooperative behaviors in economic interactions, especially the trustees’ repayment in the trust game and the dictators’ altruistic transfer in the dictator game. It is wHomo economicus hypothesis  studies revealed that neural activity in the medial prefrontal cortex (mPFC) predicted greater empathy and altruistic motivation . ClinicaIn accordance with behavioral studies, numerous neuro-science studies have investigated the neural basis of trust behaviors , while tIn contrast, brain stimulation techniques such as transcranial direct current stimulation (tDCS) that interfere with brain activity non-invasively could establish causal connections between the brain and decisions without many of the confounds inherent to natural lesion studies. In the current study, we applied tDCS in which the target electrode was placed over the vmPFC and the reference electrode was placed over visual cortex, which is trust irrelevant according to Sixty right-handed healthy subjects  with no history of neurological or psychiatric problems participated in the study for payment. All of the participants were naïve to tDCS, the trust game and the dictator game, had normal or corrected-to-normal vision, and gave their written informed consent, which was approved by the Zhejiang University ethics committee. The whole experiment lasted approximately 60 min, and each participant received a payment of around 46 RMB Yuan (approximately 7.012 US dollars) on average after finishing their tasks. No participants reported any adverse side effects concerning pain on the scalp or headaches after the experiment.2). The current was constant and was delivered by a battery-driven stimulator . It was adjusted to induce cortical excitability of the target area without any physiological damage to the participants. Various configurations of the current had various effects on cortical excitability. Generally speaking, anodal stimulation enhances cortical excitability, whereas cathodal stimulation suppresses it , cathodal tDCS over vmPFC  or sham stimulation . For anodal stimulation, the anodal electrode was placed over vmPFC, at the Fpz position according to the international EEG 10/20 system, whereas the cathodal electrode was placed over Oz . For sham stimulation, the procedures were the same, but the stimulation was turned off after 30 s without the participants’ knowledge. The participants may have felt the initial itching, but there was actually no current for the rest of the stimulation. This method of sham stimulation has been shown to be reliable . Because social interaction experiments such as the trust game, dictator game, public good game, and ultimatum game require the simultaneous interaction of a number of subjects, eliminating their suspicion of whether they are playing with real person which may alter their behaviors , they completed two economic decision tasks programmed by z-Tree . To elimehaviors , we manaThe trust game followed the classical design originally performed by In our Trust Game task, after our participants passed two profit-calculating questions  ensuring that they fully understood the trust game, each participant had to decide how much of the original endowment (ten tokens) to transfer to another participant player B (trustee) when he or she was playing the role of player A (trustor). Consequently, each participant was asked to estimate the amount sent back by her partner in each possible condition. We used the strategy method that has been proved reliable , and eacWe applied the dictator game originally designed by Firstly, after our participants passed one profit-calculating question  ensuring that they fully understood the game, each participant was asked how much to transfer to player B (receiver) when playing the role of player A (dictator). Consequently, when playing the receiver, each participant was asked to estimate the amount transferred by her partner in the role of dictator. Correct estimation  was again rewarded one extra token. Our participants were also informed about how their decisions would determine their final payments: the game was played only once with each participant randomly paired with another participant, and in the final stage of the experiment, the role that he or she played in this game would be randomly assigned by the computer. In this case, our participants would never know who their partner was in each task. Each participant played four trials in total . Since there were 10 participants in one experimental session, five pairs of partnership were performed for each session. The decisions made by the computer for the trust game and the dictator game were independent which means that the partnerships and the roles played in the former game did not influence those in the latter game.When all of the participants finished the two tasks, they were asked to complete a questionnaire before receiving their payments. Then, our participants were shown which roles they played in each game and received their payments according to their own choices and the choices of their partners. The exchange rate for game tokens and RMB Yuan was 1:1, and each participant received an extra 20 RMB Yuan for participation.Behavioral data were statistically evaluated using SPSS software . The significance level was set at 0.05 for all analyses. In the trust game, the amount transferred (trust investment) in the role of trustor indicates our participants’ trust, while the rate of amount sent back in the role of trustee indicates their trustworthiness. Notably, given a certain level of trust investment, the absolute repayment amount of the trustee does not represent a trustee’s trustworthiness level. It is reasonable to normalize the amount transferred back to the tripled investment amount. We defined the repayment rates of the transfer back to the tripled investment as Ratio that is a valid measurement of our participants’ trustworthiness. The trust investment of each participant is defined as SelfTrust (measuring trust). In the dictator game, the amount transferred in the role of dictator is defined as DGgive .t(18) = -0.594, p = 0.560, independent sample test] or in the altruistic preference . Although the sequences in our experiment were counterbalanced across tDCS stimulations, the trustworthiness and the altruism were also analyzed by means of analyses of variance (ANOVAs) with tDCS stimulation type and sequence as between-subjects factors. We observed neither a main effect of sequence  nor interaction effects of stimulation type and sequence .First, we tested whether there is any sequence effect. No significant difference between the two different sequences in our sham group was observed either in the trustworthiness [p = 0.033, Pearson correlation), and such a positive correlation was also found in the anodal group  as well as the cathodal group . The result revealed that the more altruistic participants tend to be more trustworthy in a trust game and such an observation was robust through all the three tDCS groups. It indicated that tDCS stimulation may have little influence over the correlation between trustworthiness and altruism. There is a steeper increasing trend of trustworthiness with the increase of altruistic preference in the line of best fit for anodal group comparing to those for cathodal and sham groups . The quadratic curve of best fits may indicate that the relationship between trustworthiness and altruism seems tighter among participants with higher altruistic preference in anodal group than those in cathodal and sham groups.Secondly, results similar to previous studies were observed. The average Ratio in the trust game of each participant was significantly related with the DGgive in the dictator game in our sham group participants . Post hoc analyses (Bonferroni) showed that there were no significant differences either between the anodal group (mean = 6.30) and the sham group  or between the cathodal group (mean = 4.75) and the sham group .Investment of the trustor (SelfTrust) in the trust game from the anodal and cathodal tDCS over vmPFC groups and the sham group were analyzed via analyses of variance (ANOVAs) with tDCS stimulation type  as a between-subjects factor. No significant effect of stimulation type was observed . There was an increasing trend of repayment level with the increase of the investment level . There was also a significant main effect of tDCS stimulation . The comparison of the mean Ratios of three tDCS groups is shown in Table 1. Post hoc analyses (Bonferroni) showed that the Ratios in the anodal group (mean = 0.536) were significantly higher than those obtained in the sham group  or those obtained in the cathodal group . No significant difference between the cathodal group and the sham group was observed (p = 1.000).Ratios of the trustees in the trust game from the anodal and cathodal tDCS over vmPFC groups and the sham group were analyzed via repeated measures analyses of variance (ANOVAs) with investment level (possible investment level of partner) as a within-subjects factor and tDCS stimulation type  as a between-subjects factor. A significant influence of investment level was observed . Post hoc analyses (Bonferroni) showed that the altruistic preference in the anodal group (mean = 3.75) was significantly higher than that obtained in the sham group  and that obtained in the cathodal group . No significant difference between the cathodal group and the sham group was observed (p = 1.000) .The amounts transferred (DGgive) in the dictator game by the participants from the anodal and cathodal tDCS over vmPFC groups and the sham group were analyzed via analyses of variance (ANOVAs) with tDCS stimulation type  as a between-subjects factor. There was a significant main effect of tDCS stimulation (Table 1).Previous studies have revealed that trustworthiness is statistically correlated with the participant’s altruistic preference . A similNeuroimaging studies have demonstrated that the vmPFC has special importance in human social cognition and behavior . Given tfMRI studies have shown that neural activity in the mPFC predicted greater empathy and altruistic motivation . MoreoveBecause convergent evidence has demonstrated that individuals with greater altruism and empathy are more trustworthy than those who have less empathy toward their partners, along with our observations that the anodal tDCS stimulation significantly increases altruistic preference as well as enhancing trustworthiness in tDCS experiments, we conclude that the vmPFC is closely associated with trustworthiness and altruism and that altering the activity of a brain region shared by those traits, such as the vmPFC, could significantly improve the cooperative behavior of trustees by enhancing their altruistic preferences.Moreover, there is no significant effect of trust between different tDCS stimulations, which is consistent with another tDCS study . We inteAlthough To further elucidate this issue, a control experiment was performed (Experiment 2) to rule out the influence of visual cortex. In Experiment 2, we tested two more groups with the target electrode placed over another position within the prefrontal cortex (right dlPFC) and the reference electrode placed over visual cortex. Then, the observations including trustworthiness and altruism from anodal and cathodal tDCS over dlPFC groups were compared with those from the sham group. If no significant differences were observed between the participants’ trustworthiness and altruism from the anodal and cathodal dlPFC groups and those from the sham group, we could conclude that the promotion of cooperative behaviors revealed by comparing the observations from participants receiving anodal tDCS over vmPFC with those from participants receiving sham stimulation could only be due to the anodal stimulation effect of the specific target (vmPFC) rather than to a cathodal stimulation effect of the visual cortex.A new sample of 40 right-handed healthy subjects  with no history of neurological or psychiatric problems participated in the study for payment. As in Experiment 1, all participants were naïve to tDCS, the trust game and the dictator game, had normal or corrected-to-normal vision, and gave their written informed consent. Participants also received a written explanation of the tDCS and of any possible adverse effects, but no information about the type of stimulation or the experimental hypotheses. The protocol was approved by the Zhejiang University ethics committee.n = 20, 11 females) or cathodal tDCS over right dlPFC . For anodal stimulation, the anodal electrode was placed over right dlPFC, at the F4 position according to the international EEG 10/20 system, whereas the cathodal electrode was placed over Oz. For cathodal stimulation, the electrodes were reversed .The apparatus, tasks and procedure were exactly the same as that in the Experiment 1 with the following exception. Because the Experiment 2 served as a control to verify that the tDCS stimulation effects observed in Experiment 1 are specific to vmPFC, we tested two more groups with the target electrode placed over another position within the prefrontal cortex: the right dlPFC. The participants were randomly assigned to receive anodal tDCS over right dlPFC . Given that Experiment 2 placed the tDCS stimulation over another position within the prefrontal cortex as a control site to verify that the enhancing tDCS effects in Experiment 1 was due to the stimulation over vmPFC, rather than the stimulation over visual cortex, observations measuring trustworthiness and altruism from the anodal dlPFC and cathodal dlPFC groups were compared with those from the sham group. As in Experiment 1, Ratios of the trustees in the trust game from the anodal and cathodal tDCS over dlPFC groups and the sham group were analyzed via repeated measures analyses of variance (ANOVAs) with investment level as a within-subjects factor and tDCS stimulation type as a between-subjects factor. Only a significant influence of investment level was observed , while no significant effect of stimulation type was observed . Post hoc analyses (Bonferroni) showed that there were no significant differences either between the anodal dlPFC group (mean = 0.411) and the sham group  or between the cathodal dlPFC group (mean = 0.394) and the sham group . We also compared Ratios of the trustees in the trust game from the anodal and cathodal tDCS over vmPFC groups and the anodal and cathodal tDCS over dlPFC groups via repeated measures analyses of variance (ANOVAs) with investment level as a within-subjects factor and tDCS stimulation type and stimulation site (vmPFC vs. dlPFC) as between-subjects factors. Similar results were observed and there were also a significant main effect of stimulation site  and significant interaction effects of stimulation site by stimulation type .F = 0.211, p = 0.810). Post hoc analyses (Bonferroni) showed that there were no significant differences either between the dlPFC anodal group (mean = 2.40) and the sham group  or between the cathodal dlPFC group  and the sham group. We also compared the amounts transferred (DGgive) in the dictator game from the anodal and cathodal tDCS over vmPFC groups and the anodal and cathodal tDCS over dlPFC groups via repeated measures analyses of variance (ANOVAs) with tDCS stimulation type and stimulation site (vmPFC vs. dlPFC) as between-subjects factors. There were also a significant main effect of stimulation site  and significant interaction effects of stimulation site by stimulation type .Moreover, as in Experiment 1, the amounts transferred (DGgive) in the dictator game by the participants from the anodal and cathodal tDCS over dlPFC groups and the sham group were analyzed via analyses of variance (ANOVAs) with tDCS stimulation type as a between-subjects factor. No significant main effect of tDCS stimulation was observed (The results of this experiment ruled out the possibility that the more cooperative behaviors observed in anodal vmPFC group of Experiment 1 were due to the stimulation effect over visual cortex rather than activating the excitability of vmPFC. Because previous studies have demonstrated that the right dlPFC is closely associated with repayment of trustees and because modulating the activity of that specific brain area alters the trustworthiness of participants in both tDCS and TMS studies , it is rAlthough the repayment ratios in the trust game and the transferred amount in the dictator game by individuals receiving anodal tDCS over the dlPFC were slightly higher than those receiving cathodal tDCS over the dlPFC and those receiving sham stimulation, no significant differences in trustworthiness and altruism between participants in the anodal dlPFC group and those in the sham group were observed. We interpret the inconsistency between our observations and previous studies as a result of measuring trustworthiness with different task procedures. Previous studies have also revealed that reducing the activity of the right dlPFC would decrease the rejection rates of unfair offers in the ultimatum game , 2008, aIn addition, since the mechanism of tDCS is that anodal stimulation enhances cortical excitability, whereas cathodal stimulation suppresses it, typical anodal-excitation and cathodal-inhibition effects should be observed. However, in both Experiments 1 and 2 of our current study, relatively few significant cathodal-inhibition results have been revealed in comparison to anodal-excitation effects. Such an asymmetric stimulation effect also exists widely in previous tDCS studies, especially among cognitive or perceptual tasks. This issue has been discussed in depth by In this study, we extended studies regarding the function of the vmPFC in altruism and trustworthiness behaviors, revealing that activating this neural region can promote the cooperative behaviors in both the dictator game and the trust game. Moreover, our finding demonstrates that anodal tDCS over the vmPFC could particularly alter the trustworthiness of trustees and their altruistic preference, but no significant influence over interpersonal trust was observed. Our observations indicate that other-regarding preferences such as altruism are closely correlated with trustworthiness and that modulating the activity of vmPFC could enhance trustworthiness of trustees through increasing their altruistic preference. In previous studies, the activity of vmPFC has been revealed associated with social preference , valuatiOne limitation of the current study is that although our findings for the vmPFC were consistent with previous observations, the potential neural mechanism of the specific brain area influencing trustworthiness through altering our participants’ altruistic preference remains to be revealed and discussed. Future brain imaging studies may focus on the dynamic activation of the vmPFC while the participants play the trust game or the dictator game. Another deficiency of our study is that the reason why stimulating vmPFC alters trustworthiness and altruism without producing a similar effect on our participants’ interpersonal trust levels has not been fully demonstrated. Further neural imaging studies specifically focusing on the trust of individuals might answer this question.In sum, our findings provide important information about the impact of tDCS on healthy participants, especially with respect to the trustworthiness of trustees and their altruism. Activating the vmPFC by tDCS can enhance the trustworthiness in the trust game, specifically through increasing the altruism of our participants, who transferred more in the dictator game. Moreover, the vmPFC is specific for the trustworthiness of trustees and the altruistic preference of the dictator, while no tDCS stimulation effect was observed in the trust of trustors.HZ, DH, SC, SW, WG, JL, HY, and YC designed experiment; HZ, DH, SC, SW, WG, JL, HY, and YC performed experiment; HZ and SC analyzed data; HZ drew figures; HZ, DH, SC, JL, and YC wrote the manuscript; HZ, DH, SC, SW, WG, JL, HY, and YC revised the manuscript; and HZ, DH, SC, SW, WG, JL, HY, and YC finally approved the version to be published.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin–myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.The online version of this article (doi:10.1007/s00285-016-1008-2) contains supplementary material, which is available to authorized users. In a variety of physiological processes such as wound healing, immune response, or embryonic development, crawling cells play a vital role  end and a slow-growing minus (pointed) end  results in the formation of completely detached lamellipodial fragments, lacking a cell body, microtubules and most other cell organelles. Remarkably, these fragments can either remain stationary while adopting a circular shape, or can move on their own, adapting their appearance to the same crescent-moon shape as the keratocyte itself .The connections exert twisting forces on the connected actin filaments towards the equilibrium angle The connections can be stretched against an elastic restoring force.The key to the bistability results presented in the next sections is the assumption that the myosin activity (specified below) depends on the angle between crossing actin filaments. This is supported by data reported in Reymann , the s-value of the binding site will change due to the aforementioned treadmilling effect (caused by actin polymerization) and the myosin motor activity. Therefore at time t the myosin filament binds to the actin filament att of the binding site on the a of an active myosin connection between the filaments with label t. Following classical modeling for age-structured populations we assume Now let The main Eq.  of the FStep 2: Scaling The key scaling assumption of the original FBLM is that the average lifetime of a cross-link or adhesion is small compared to the average time a monomer spends inside a filament, a ratio denoted by mentclass2pt{minimt and the indices This raises the question of what to assume about the average lifetime of a myosin filament. In Svitkina et al.  it was oThe scaled energy contributions take the formStep 3: Variation and macroscopic limit The next step in the derivation is to calculate the variations a. They take the formStep 4: Euler–Lagrange Equations The final step in the derivation is to formulate the corresponding Euler-Lange equations. Together with the original terms given in ::\documenWith the planar lamellipodium ansatz, the Eqs.  and 11)11) becomy-direction orthogonal to the leading edge, i.e.The membrane stretched around the lamellipodium exerts a force on the polymerizing barbed ends. On the other hand, we assume that the filaments at the rear of the lamellipodium are connected to stress fibres pulling them backwards, another consequence of actin–myosin interaction. Both the membrane force and the stress fibre force will be described as acting in the negative  the Eq.  for the Bistability can now be obtained with appropriate assumptions on the parameters. The right hand side of  can be wIfUnder the assumptions of Lemma tial Eq.  with thetial Eq.  possesseAgain the proof is straightforward. For the stable steady states, the lamellipodium has the constant protrusion speedsFinally, the steady states also produce lateral flow with constant speedsAs a caricature of a cell fragment, we consider two back-to-back planar lamellipodia see Fig. e. For nomentclasspt{minimae system  with unkply that  is used y and Adding the Eq.  for y anLet the assumptions of Lemma e system –20) has has\docuA and From  we obtaiation of –20) can can25\doFor the steady states the protrusion speed of the fragment is constant and given byy states , 22), t, t26\docy states . The asyy states  and 24)26\documeFinally, we also mention the case of a constant stress fibre force and a size dependent membrane force:The simplifications of the two preceding sections lead to several (testable) statements. This section can be seen as a discussion of the results so far.Protrusion speed versus adhesion strength For the coupled lamellipodium of Sect. ution of  into theution of  (resp. (ution of ) shows tsions of  and 20)ProtrusioIt is not clear if the FBLM in its present form is able to describe the second regime, which might be caused by long-lived focal adhesions, contradicting the assumption of rapid adhesion turnover. It should also be noted that it has been hypothesized of  for \doc. In Yam  the numbProtrusion speed versus myosin strength In the presented model two parameters characterize myosin strength, the elasticity coefficients of myosin filament stretching t et al.  where myIn this section we demonstrate that with the additional term describing myosin within the lamellipodium, the model is able to produce cells/cell fragments that, depending on the initial conditions, will either remain stationary or start moving. In contrast to the simulations presented in Manhart et al. , b, hereParameter values Parameter values are chosen as in Manhart et al. , and the cell starts moving. What is apparent in these simulations is that myosin tends to locate at the back of the lamellipodium (away from the membrane). This is also in good agreement with experimental findings. It is remarkable that both for the analytical setting as well as in the numerical simulations, movement is an self-organized behavior, once an initial asymmetry has been established. It is known that keratocytes exhibit little if any chemotaxis, i.e. directed movement to outward cues.An important issue remains to be addressed: The analytical model, dealing only with pieces of lamellipodium at the front and at the rear of the cell, avoids the transition zone separating the two parts of the lamellipodium with an intact network on the one hand and, on the other hand, compression to a rear bundle. It can be expected that due to lateral flow, actin filaments are drawn into the bundle in these transition regions. However, we expect that this happens with the pointed ends first entering the bundle, as opposed to the simulations presented here. A model supporting the necessary change of orientation in the transition zone is not available so far, and its derivation is the subject of ongoing work.Supplementary material 1 (avi 2632 KB)Below is the link to the electronic supplementary material.


With the rapid development of smartphones and wireless networks, indoor location-based services have become more and more prevalent. Due to the sophisticated propagation of radio signals, the Received Signal Strength Indicator (RSSI) shows a significant variation during pedestrian walking, which introduces critical errors in deterministic indoor positioning. To solve this problem, we present a novel method to improve the indoor pedestrian positioning accuracy by embedding a fuzzy pattern recognition algorithm into a Hidden Markov Model. The fuzzy pattern recognition algorithm follows the rule that the RSSI fading has a positive correlation to the distance between the measuring point and the AP location even during a dynamic positioning measurement. Through this algorithm, we use the RSSI variation trend to replace the specific RSSI value to achieve a fuzzy positioning. The transition probability of the Hidden Markov Model is trained by the fuzzy pattern recognition algorithm with pedestrian trajectories. Using the Viterbi algorithm with the trained model, we can obtain a set of hidden location states. In our experiments, we demonstrate that, compared with the deterministic pattern matching algorithm, our method can greatly improve the positioning accuracy and shows robust environmental adaptability. Nowadays, with the rapid development of smartphones and wireless networks, people can conveniently access location-based services (LBSs) with mobile applications. Location information has become the cornerstone of several new technologies and applications including big data, cloud computing, Internet of things, and online-to-offline. The accurate positioning of the users is the key to providing LBS guaranteed by quality of experience (QoE).The localization technology is mainly divided into outdoors and indoors. The outdoors localization technology is relatively mature, and mainly includes the Global Positioning System (GPS) and cellular positioning systems . HoweverThe WLAN fingerprint system is an economical and practical positioning system. Bahl et al. ,4 have iAlthough there are some classical WLAN fingerprint systems, the research objective is always focused on a static target. There are few papers discussing pedestrian positioning, which is more relevant in a real environment. Due to distance variation and human body interference, the RSSI of moving targets will fluctuate over a large range, especially at a relatively slow speed . MoreoveIn order to offer users LBS services with better positioning accuracy in a real environment, in this paper, a pedestrian positioning method using a Hidden Markov Model (HMM)  with a FThis paper is organized as follows: In recent years, research on indoor fingerprint positioning has been conducted actively. We will discuss some representative works here, especially the ones that employ HMM in their systems. To reduce the calibration work, Wallbaum et al. ,8 employSeitz et al.  improve Liu et al.  presenteA novel solution named HIPE (Hybrid Indoor Positioning Engine)  has applColeri et al.  employedIn previous studies, there is a simple scheme of pattern recognition in indoor positioning. It is assumed that each position is associated with a unique set of RSSI values, so the distance between a user’s measured location and the reference location can be calculated by Equation (1):Although this deterministic pattern matching algorithm with better positioning accuracy can be easily implemented in a WLAN fingerprint system, it is based on an accurate radio map and high precision sampling of RSSI, the latter being almost impossible while people are walking due to the vulnerabilities of the RSSI. Compared with the static positioning measurements, we can see that the RSSI values show significant variations while people are walking due to the sophisticated propagation of the radio signal. The RSSI deviations caused by the different measurement conditions (static or dynamic) will introduce critical positioning errors. Meanwhile, we find that most of the dynamic positioning measurements also follow the propagation and attenuation law, whereby the RSSI fades with the increasing distance between the measuring point and the AP. From this rule, the RSSI variation trend can be used to indicate the relative direction and distance from the initial location to the positioning point. For example, if the RSSI is stronger than at the initial location, it means the positioning point is closer to the AP than the initial location. If there are enough RPs in the area, it can be easily compared to determine the relative locomotion of the pedestrian.(1)Given an initial RP (2)Measure RSSI vectors there are:t = ;st – 1=(rss1(t–1),rss1(t–1),…rss1(t–1))sfor{if (j = 1oelse if (j = −1oElsej = 0o}(3)Compare each AP’s RSSI of (4)For estimating the position of the pedestrian, we need to separately compare the RSSI variation trend by performing a bitwise logical XOR operation between there are:if  is a well-known statistical model which has been successfully applied to acoustic treatment, biological information and natural language processing. Until now, it is still widely used in speech recognition . DiffereEmploying HMM can effectively improve pedestrian positioning accuracy in a WLAN fingerprint system. The HMM can be mathematically defined as a triple λ = ion area , N is thGiven a set of RSSI variation trends, sequence . The obsTo find the most likely sequence of the location, i.e., marking the path of the actual location transition in Through the procedures, we can learn that the transition probability has an important role in the Viterbi algorithm. Not only is the computation complexity of the Viterbi relative to the transition probability, but also the positioning accuracy is dependent on the transition probability. So far, the problem has been centered on how to calculate the transition probability.Transition probability is the most critical parameter in the pedestrian positioning model. The positioning accuracy of the Viterbi algorithm depends on the precision of the transition probability. To obtain the transition probability which can reflect the pedestrian walking pattern, we utilize the FPR algorithm to estimate the transition probability using a rebuilt radio map and planned path.The pre-existing radio map stored the RSSI and the corresponding position coordinates. To reduce the RSSI deviation caused by different measurement conditions, we use the fuzzy pattern recognition algorithm to rebuild the pre-existing radio map. A comparison of the two kinds of radio maps is shown in The left part of In indoor areas, people will follow certain rules in moving, such as a limited walking speed, that there is no way through the walls, and that they walk in a straight line in a corridor. Using these rules, we can reasonably plan the user’s path, and use these trajectories as the HMM training samples so as to effectively improve the positioning accuracy. For training the HMM with the FPR algorithm, a set of consecutive RSSIs are recorded by volunteer sampling along the planned path. The planned path should contain all the RPs , so it wAs mentioned before, the pedestrian locomotion is limited to a certain walking speed (2 m/s in this study) in an indoor environment. (1)Compare the (2)The (3)According to the comparison results between there are:(4)If there are multiple training trajectories from other directions, we use the above steps to estimate the transition probability from other directions, and the final results are the arithmetic means of the transition probability from different directions. In this way, we use the FPR algorithm to estimate the transition probability, which provides strong support for the pedestrian positioning with the Viterbi algorithm.The main goal of the FPR algorithm is to consider the adjacent RPs as the possible pedestrian locations in the next state, as shown in To validate our algorithm and method, we perform some experiments in two real indoor environments. The first scenario is an office area located on the fourth floor of the YiFu building, and the second scenario is an open area located in the library.To meet the needs of our experiment, the RSSI collection was performed using a Samsung S5 smartphone, in which the API supports scanning the RSSI with an interval of one second. If not otherwise specified, all measurements are collected with this smartphone. During the offline phase, we have taken a series of measures to improve the RSSI measurement accuracy. To mitigate the impact of the distribution difference of RSSI in different directions, we collected the measurements in four directions. Then, we collected 40 measurements at each reference point to decrease the random noise effects (thus 10 samples for each direction). Finally, we conducted the collection at midnight to avoid the interference caused by walking people. In the experiments, we mainly use the cumulative distribution function of error (CDF) and root mean square error (RSME) to calculate the positioning error.This office area includes a horizontally H-shaped corridor and some rooms, as shown in After the radio map of this office area has been built, we can perform the experiments. The measurements are collected by a user walking alone the planned paths at about 1.5 m/s. The planned paths are shown in ion (PL) ,20 algorFrom To fairly compare the positioning error, To test the adaptability of the FPR algorithm to different devices, we used a XIAOMI HM2 and an iPhone 4S  to repeat the experiments. There was little change in the positioning error, which means the FPR algorithm has good adaptability to different smartphones, as can be seen in From the above experimental results, we can see that the FPR algorithm can offer better positioning accuracy over a certain range of speeds and has good adaptability to different devices, but it also has two drawbacks: one is that its positioning accuracy is limited by the RP interval, the other is the accumulating positioning error when direction-hopping is happening.In the HMM method testing, the red line and the yellow line are treated as the model training trajectories, and the walking path is the green line as shown in The estimation of the user position along the green path is shown in It can be seen in After testing the method in the office area, we chose a relatively open indoor area to further evaluate our method. The open area is on the first floor of our university library , which has dimensions of As in The positions in the open area estimated by different methods are shown in It is more obvious in In In this paper. A method for precise pedestrian positioning in an indoor environment using a trained HMM with a fuzzy pattern recognition algorithm was proposed. The presented fuzzy pattern recognition algorithm can offer better positioning accuracy during pedestrian walking because this algorithm utilizes the RSSI variation trend of the different locations to replace the specific RSSI values, which display significant deviations during dynamic measurement. To improve the positioning accuracy and mitigate the effect of direction-hopping, we introduce the trained HMM with the FPR algorithm in the WLAN fingerprint system. We use a rebuilt radio map and training trajectories to train the HMM with the FPR algorithm; thus, the most likely position of the pedestrian can be estimated by employing the Viterbi algorithm in the HMM. In our experiments, we demonstrate that the fuzzy pattern recognition algorithm has acceptable positioning accuracy and good environmental adaptability, and the accuracy is better after we embedded the fuzzy pattern recognition algorithm into the trained HMM. Future studies will focus on optimizing features of the proposed method, such as the AP selection, planned path selection and multi-sensor fusion.


The Mahalanobis Taguchi System (MTS) is considered one of the most promising binary classification algorithms to handle imbalance data. Unfortunately, MTS lacks a method for determining an efficient threshold for the binary classification. In this paper, a nonlinear optimization model is formulated based on minimizing the distance between MTS Receiver Operating Characteristics (ROC) curve and the theoretical optimal point named Modified Mahalanobis Taguchi System (MMTS). To validate the MMTS classification efficacy, it has been benchmarked with Support Vector Machines (SVMs), Naive Bayes (NB), Probabilistic Mahalanobis Taguchi Systems (PTM), Synthetic Minority Oversampling Technique (SMOTE), Adaptive Conformal Transformation (ACT), Kernel Boundary Alignment (KBA), Hidden Naive Bayes (HNB), and other improved Naive Bayes algorithms. MMTS outperforms the benchmarked algorithms especially when the imbalance ratio is greater than 400. A real life case study on manufacturing sector is used to demonstrate the applicability of the proposed model and to compare its performance with Mahalanobis Genetic Algorithm (MGA).  Classification is one of the supervised learning approaches in which a new observation needs to be assigned to one of the predetermined classes or categories. If the number of the predetermined classes is more than two, it is a multiclass classification problem; otherwise, the problem is known as the binary classification problem. At present, these problems have found applications in different domains such as product quality  and speeThe classification accuracy depends on both the classifier and the data types. The classifier types can be categorized according to supervised versus unsupervised learning, linear versus nonlinear hyperplane, and feature selection versus feature extraction based approach . On the The assumption of an equal number of observations in each class is elementary in using the common classification methods such as decision tree analysis, Support Vector Machines, discriminant analysis, and neural networks . ImbalanTo handle the classification of imbalanced data problem, the research community uses data and algorithmic or both approaches. For the data approach, the main idea is to balance the class density randomly or informatively  either eliminating (downsampling) the majority class observations or replicating (oversampling) the minority class observations or doing both. While at the algorithmic approach, the main idea is to adapt the classier algorithms towards the small class, a combination of the data and algorithmic levels approaches is also used and known as cost-sensitive learning solutions.The problems reported  using daWhile the problem reported  using thFinally, the problem in using the cost-sensitive learning approach is the assumption of previous knowledge for many errors types and imposing a higher cost to the minority class to improve the prediction accuracy. Knowing the cost matrices in most cases is practically difficult.While data and algorithmic approaches constitute the majority efforts in the area of imbalanced data, several other approaches have also been conducted, which will be reviewed in Literature Review.To overcome the pitfalls of data and algorithmic approaches to solve the problem of imbalanced data classification, the classification algorithm needs to be capable of dealing with imbalance data directly without resampling and should have a systematic foundation for determining the cost matrices or the threshold. One of the promising classifiers is the Mahalanobis Taguchi System (MTS), which has shown good classification results for imbalance data without resampling, it does not require any distribution assumption for the input variables, and it can be used to measure the degree of abnormality , but unfortunately it lacks a systematic foundation for threshold determination .The Receiver Operating Characteristics (ROC) based approach has been reported in the research domain  for SuppThe aim of this work is to enhance the Mahalanobis Taguchi System (MTS) classifier performance by providing a scientific, rigorous, and systematic method using the ROC curve for determining the threshold that discriminates between the classes.The organization of the paper is as follows: In this section, an overview of the imbalance classification approaches, the Mahalanobis Taguchi System concept, its different areas of applications, weakness points, and its variants is presented.Solutions to deal with the imbalanced learning problem can be summarized into the following approaches : samplinRandom undersampling∖oversampling of the negative∖positive observationsTargeted undersampling∖oversampling of the negative∖positive observationsMixing approach from the above two itemsData level approach  is mainlDetermining the best class distribution or imbalance ratio for given observations: in Weiss and Provost , the relUndersampling the negative data can lead to loose important information, whereas oversampling the positive one may cause noise interference .The uncertain criterion for selecting samples for within-class concept: that is, the class itself consists of several subclasses .The problems reported in data approaches are as follows:Algorithmic level approach solutions are based upon creating a biased algorithm towards positive class. The algorithmic level approach has been used in many popular classifiers such as decision trees, Support Vector Machines (SVMs), association rule mining, back-propagation (BP) neural network, one-sample learning, active learning methods, and the Mahalanobis Taguchi System (MTS).The adaptation of decision tree classifier to suit the imbalance data can be accomplished by adjusting the probabilistic estimate of the tree leaf or developing new trimming approaches .Support Vector Machines (SVMs) showed good classification results for slightly imbalanced data , while fTherefore, in this paper, SVM was selected as one of the benchmarked algorithms to compare with ours; the results showed that SVM classification performance largely degrades with a high imbalance ratio, which supports the previous findings of the researchers (more details will be presented in Results).Association rule mining is a recent classification approach combining association mining and classification into one approach –22. To hOn the other hand, one-class learning , 25 usedActive learning approach is used to handle the problems related to the unlabeled training data. Research on active learning for imbalance data reported by Ertekin et al.  is basedThe problem with the algorithmic approach is that it needs an extensive knowledge of specific classifier , also understanding the application domain is critical .Cost-sensitive methods use both data and algorithmic approaches, where the objective is to optimize  the total misclassification cost while giving a positive class a higher misclassification cost , 32.Cpos,neg be the cost of wrongly classifying positive instant as a negative one, while Cneg,pos is the cost of the contrary case. In imbalance data classification, usually, the revealing of the positive instant is more important than the negative one; hence, the cost of positive instance misclassification outweighs the cost of negatives ones , with correct classification cost equal to zero .Cost-sensitive methods used different costs or penalties for different misclassification types. For example, let Modifying the weights of the data space: in this approach, modification to the training data density is performed using the misclassification cost criteria, in a way that the density is adjusted towards the costly class.Making the classifier objective cost-sensitive: instead of minimizing the misclassification error, the objective is tuned to reduce the misclassification cost .Using risk minimization approach: in a binary c4.5  classifier, the assignment of a class type to a leaf end is based on the high-frequency class that reaches the end, while for the cost-sensitive classifier, the assignment of the class label is based on minimizing the classification cost .The problem of using the cost-sensitive approach is that it is based on previous knowledge of the cost matrix for the misclassification kinds, while in most cases it is unavailable.Different types of cost-sensitive approaches have been reported in the literature:MTS is a multivariate supervised learning approach, which aims to classify new observation into one of the two classes . MTS was used previously in predicting weld quality , exploriThe step of determining the optimal threshold is a critical one for effective MTS classier. To determine the appropriate threshold, loss function approach was proposed by ; howeverThe other research area in the MTS is related to the modification of the Taguchi method not in the threshold determination. Due to the lack of a statistical foundation  for the Finally, the aim of this research is to enhance the Mahalanobis Taguchi System (MTS) classifier performance through providing a scientific, rigorous, and systematic method of determining the binary classification threshold that discriminates between the two classes, which can be applied to the MTS and its variants .The proposed model, A  represents the optimum theoretical solution (best performance) for any classifier. The closer the classifier performance to this point is, the better it is. The curve drawn in the figure represents the MTS classifier performance for different threshold values. Changing the threshold will change the point location on the curve . Therefore, the problem of finding the optimum threshold can be reformulated into the problem of finding the closest point that lies on the curve to point A .The proposed model is based on using the Receiver Operating Characteristics (ROC) curve  for the MMTS can be summarized in the following steps.Assume there are two classes: negative (the one with majority observations) and positive (the one with the minority observations). A set of data is sampled from both classes. Using the negative observations only, reference Mahalanobis Distances are calculated using  with allIf the stopping criteria  are not met yet, an optimization model  is invoked to obtain a better threshold value that minimizes the desired fitness function. Accordingly, new features will be selected using the orthogonal array approach, and true positive rate, false positive rate, and the fitness function will be also updated.If the stopping criteria are met, then the training stage is done, and the model is ready for testing observations.In this stage, the optimum threshold and the associated features are determined from the previous stage and the Mahalanobis Distance for the new observation is calculated based on those parameters. If the Mahalanobis Distance for this observation is less than the optimum threshold, then it will be classified as negative; otherwise, it will be classified as positive.Now, after providing an overview of how MMTS algorithm works, detailed calculation of the Mahalanobis Distance, the true positive and the negative rates, and the fitness function will be presented in the followings subsection.Np and the number of negative observations is Nn, and both positive and negative observations consist of k variables (or features).In order to demonstrate the MTS threshold determination mathematically, let us assume that negative data  and the positive data  are available, where the number of positive observations is Nn, the Mahalanobis Distance (MD) for the ith observation can be calculated byi = 1 ⋯ Nn,  j = 1 ⋯ k, k is total number of features (or variables), Zij is the normalized vector obtained by normalizing the values of yij: that is, Sj are the average and the sample standard deviation of variable j, respectively, ZijT is the transpose of observation i and variable j for Zij, and R−1 is the inverse of the correlation matrix of the negative variables.Given a sample of size R−1, Sj, the inverse of the correlation matrix, the mean, and the sample standard deviation of the feature j, for the negative data, respectively, the MD of the positive observations can be calculated.Using , R−1, y¯x that will be used to discriminate the negative observations from the positive ones based on the MD magnitude, which means that the new observation i can be classified into either a positive or negative observation according to the following criteria: if MDi < x, the observation is negative; otherwise, it is positive.The next step is to determine the threshold The contribution of this paper mainly is in the area of establishing a reliable and systematic threshold for classification. A rough method for determining the threshold is to plot the positive and negative MD observations versus their orders and decide upon the threshold manually. This method is not accurate, especially when dealing with the overlapping values of the MDs.The essential classifier performance can be explained by examining the confusion matrix x).TNx).FNx).FPx).TPNow, the true positive rate and the false negative rate at the threshold x can be defined asFrom the confusion matrix, ratex)( and FPratex)( (ratex)( (The ROC plot is an Prate(x)  is plott(rate(x)  is plottratex)( uses the right column in the confusion matrix and FPratex) versus disadvantages  of the classifier relating to data density.Since TPB, C, and D represents the different threshold for MTS classifier). The closest point lies on the curve  to point A  which is considered the optimum threshold among the other candidates. Mathematically, this can be converted into the following optimization model.x that discriminates between the negative and the positive observations, depending on minimizing the Cartesian distance between the MMTS ROC classifier curve and the theoretical optimum point ( = 0).dAx is Euclidean distance between point A and any point x that lies on the ROC curve such as B, C, or D. FPrateA)( = 0). The first two constraints ))A” pointtraints ( and 9)))A” pointSince more features mean a higher cost of monitoring and require more processing time, it is important to exclude the unnecessary features from having an efficient classifier. MTS approach uses orthogonal array (OA) experiments to screen the important features. Each factor in the orthogonal array design can be calculated independently of all other factors since the design is balanced   “the larger the better” criterion, which can be calculated for different treatment i usingi is an index that represents run or row in the orthogonal design and its domain varied from 1 to 2k, where k is the total number of features. Based on the above equation, the feature mean gain can be calculated byj is an index that represents the feature, j ∈ [1 ⋯ k], and k is the total number of features. The feature j will be included if it has a positive gain; otherwise, it should be excluded.The metric of the Taguchi orthogonal array is the signal-to-noise ratio, where In this section, the description of the dataset used in this study, brief of the used benchmarked classifiers, an overview of the metrics used for imbalanced data classifiers, and the results of classifiers performance for different datasets will be presented.The binary or multiclass imbalance ratio threshold, which is the ratio between negative to positive observations border that separates balance from imbalance dataset, is still an open area for the research community. In this paper, we investigated a wide range of IR, from 1.25 up to 2088, considering a dataset to be imbalanced if IR is equal or higher than 1.25. f-ratio) is also considered as a major factor in classifier performance degradation. A low value of f-ratio means that observations are mixed together and overlapped regions are large, and therefore it is difficult to discriminate between these observations. Estimates of the different metrics were obtained by means of 10 repetitions; the data has been randomly partitioned by 35% as the training set and the remainder of the testing set for each repetition. MMTS and the benchmarked algorithms have been evaluated for each of the ten repetitions simultaneously.It should be noted in this study that the imbalance ratio effect on the classification results should be explored. Accordingly, the datasets were selected related to this criterion . Unfortunately, imbalance ratio is not the only reason that causes degradation in classifier performance. The maximum Fishers Discriminant Ratio  is a variable vector of size n and C is the class.Bayes theorem is the center of Naive Bayesian classifier (NB) in which class conditional independence is assumed. This assumption means that the influence of features on a given class is independent of each other. Mathematically,Even with such unrealistic assumption, Naive Bayes still found noticeable success stories comparable with other types of sophisticated classifiers, for example, NB used in text classification , medicalMMTS: the MMTS does not need any tuning parameters, which is one of the important benefits of using MMTS over the traditional MTS.PTM: for the PTM algorithm, a small parameter is set to 0.05, based on the recommendation from .SVM: for the SVM algorithm, to map observations from the data space to the kernel space, the linear function was used.NB: for the NB algorithm, kernel distribution was selected to fit the conditional features distributions.The parameters values setting for the examined classifiers were selected from the suggestions of the corresponding authors as follows:It is worth mentioning that no tuning parameters for any of the examined classifiers were performed; consequently, baseline line comparisons among the classifiers with the default setting were established, which leads to the most robust classifier selection .Finally, MATLAB R2013a was used for the data analysis on HP machine with a processor Intel (R) Core (TM) i7 CPU 2.2 GHz and 4.00 GB RAM. For the genetic algorithm, the following parameters were used in the implementation: population size, 20 chromosomes, with the number of features corresponding to the bit number, 0.8, a crossover fraction, 0.01, a mutation rate, 100, and the limit for the number of generations, and for the stopping criteria, value of the fitness function cumulative change was less than 10–6 over 50 iterations.Gmeans 15)) reveGmeans [Fmeasure [In order to overcome the above problem, several metrics such as Gmeans  19), th, thGmeanGmeans , and FmeGmeans and Fmeasure, where the last one uses weighted importance of the recall and precision , which results in better assessment than accuracy metric, but still biased to one class [Gmeans will be used as a main metric for the analysis criterion.The most common used metrics for the evaluation of the imbalance data classification performance are ne class . TherefoIn this section, performance presentation for the classification results of MMTS with the other four investigated classification algorithms: Support Vector Machines (SVMs), Probabilistic Mahalanobis Taguchi System (PTM), Naive Bayes (NB), and Mahalanobis Taguchi System (MTS) . In order to investigate the robustness performance of the studied classifiers related to the class imbalance criterion, fourteen different UCI  datasetsGmeans values of the investigated data for the five classifiers. In order to discriminate between the classifiers performances among each other, nonparametric pairwise comparison Wilcoxon test was performed to test the null hypothesis that the two classifiers have equal medians versus the alternating hypothesis that the first classifier's median is larger than the second one; the results of these comparison are summarized in the ranking score of each classifier for each dataset. Based on this table, one can observe the following:The MMTS classifier has a higher classification performance than MTS across the whole fourteen investigated datasets.The MMTS has a superior classification performance comparable with the other benchmarked classifiers when the imbalance ratio (IR) is high .The MMTS and SVM have equal classification performance when the imbalance ratio (IR) is medium .The SVM has a superior classification performance comparable with the other benchmarked classifiers when the imbalance ratio (IR) is low .The MMTS has the most robust classification performance over the investigated IR range .The NB has the least classification performance comparable with the other benchmarked classifiers over the investigated IR range.f-ratio is dominated by the imbalance ratio (IR) effect .The effect of the Many published works , 53, 54 Therefore, in order to assess the MMTS classification performance against imbalance data classifiers, UCI datasets and their classification performance results using SVMs, SMOTE, ACT, and KBA from  were useGmeans performance metrics in the form of the 95% confidence intervals are reported in Gmeans of the MMTS classifier are higher than those for the benchmarked classifiers at relatively high imbalance ratio , while for the yeast dataset, MMTS Gmeans were less than KBA and ACT but better than SVM and SMOTE. Finally, MMTS was the least performance among the classifiers for the car dataset.Using the performance classification results obtained from  and the Gmeans MMTS classification results for the examined datasets have the highest values comparable with the others.Using the same dataset in , modifieThe case presented will be in the manufacturing sector in the area of resistance spot welding. Due to its cost and simplicity, resistance spot welding is the dominant joining process in the autoindustry. The reasons behind chosen spot welding joining process over other joining processes can be summarized as follows: being inexpensive and having fast process, its applicability to join different types of materials  with varying thickness, and its relative robustness to the different noise factors existing in the plant such as fit-up variations. Despite the above-mentioned advantages, weld quality cannot be estimated with high certainty due to factors such as tip wear, sheet metal debris, variation in the power supply; therefore, it is common practice in the autoindustry to add extra welds to increase their confidence in the structural integrity of the welded assembly .Recently worldwide competition pushes automotive OEMs to improve their productivity, reduce nonvalue added activity, and reduce cost. Therefore, autoindustry is extremely concerned with the elimination of these redundant welds. To achieve this objective of using the optimum number of required welds that sustain the required strength of the structure, weld quality must be achieved.To achieve an acceptable weld quality, nondestructive weld assessment should be performed. This assessment can be translated into the problem of classifying the dynamic resistance profile  for those welds into normal or abnormal welds.The welding data, summarized in The first step after obtaining the dataset was to split them into training and testing groups. In this case, the training data was 1,153 observations , in which two observations were expulsion welds , and the others were normal welds .Gmeans, and Fmeasure. In addition, the suggested threshold is reported for the MMTS and PMTS algorithms. As mentioned before, Gmeans will be used as the main metric, but the results for other metrics will be reported here for future researchers to use.Running the MMTS and the other benchmarked algorithms, in addition to the Mahalanobis Genetic Algorithm (MGA)  over theGmeans), p value obtained from performing this test on the welding data is 0.000, which reveals that there is at least one classifier performance that is significantly different from the others. In order to rank the classifiers, the pairwise Mann–Whitney test is used.In order to determine if there is a significant difference among the classifiers performances  values for the examined classifiers .rate = 100% and FPrate = 0%) is used to determine this threshold.The Mahalanobis Taguchi System (MTS) is one of the most promising binary classification approaches to handling the imbalance data problem. Unfortunately, the MTS suffers from the lack of a systematic rigorous method for determining the threshold to discriminate between the two classes. In this paper, a nonlinear optimization model with the objective of minimizing the Euclidean distance between MTS classifier ROC curve and the theoretical optimal point  is dominated by the imbalance ratio (IR) effect . MMTS showed a very robust classification performance across the range of the imbalance ratio; it also showed better classification performance results comparable with KBA, ACT , HNB, NBtree, and other modified Naive Bayes classifiers when imbalance ratio is relatively high.In order to assess the suggested algorithm, the MMTS has been benchmarked with several popular algorithms: Mahalanobis Taguchi System (MTS), Support Vector Machines (SVMs), Naive Bayes (NB), Probabilistic Mahalanobis Taguchi System (PTM), Synthetic Minority Oversampling Technique (SMOTE) with SVM, Adaptive Conformal Transformation (ACT), Kernel Boundary Alignment (KBA), Hidden Naive Bayes (HNB), and other improved Naive Bayes algorithms over benchmarked datasets with a wide range of imbalance ratio . The results showed that the MMTS has a superior performance for high imbalance ratio , while for the medium imbalance ratio , the MMTS has an equal classification performance with the SVMs. For the low imbalance ratio (IR ≤ 189), the SVM was the best among the classifiers. It has been noticed that the effect of the maximum Fishers Discriminant Ratio (In order to demonstrate the MMTS applicability, a case study in the welding area was used. The results showed that the MMTS classifier performance outperformed the benched marked classifiers performances and MGA. The case results emphasize that the MMTS is one of the most suitable classifier algorithms when there is a high imbalance ratio.For future research work, the problems of multiclass imbalanced data and the mixed data need to be tackled thoroughly.


Big sensor data provide significant potential for chemical fault diagnosis, which involves the baseline values of security, stability and reliability in chemical processes. A deep neural network (DNN) with novel active learning for inducing chemical fault diagnosis is presented in this study. It is a method using large amount of chemical sensor data, which is a combination of deep learning and active learning criterion to target the difficulty of consecutive fault diagnosis. DNN with deep architectures, instead of shallow ones, could be developed through deep learning to learn a suitable feature representation from raw sensor data in an unsupervised manner using stacked denoising auto-encoder (SDAE) and work through a layer-by-layer successive learning process. The features are added to the top Softmax regression layer to construct the discriminative fault characteristics for diagnosis in a supervised manner. Considering the expensive and time consuming labeling of sensor data in chemical applications, in contrast to the available methods, we employ a novel active learning criterion for the particularity of chemical processes, which is a combination of Best vs. Second Best criterion (BvSB) and a Lowest False Positive criterion (LFP), for further fine-tuning of diagnosis model in an active manner rather than passive manner. That is, we allow models to rank the most informative sensor data to be labeled for updating the DNN parameters during the interaction phase. The effectiveness of the proposed method is validated in two well-known industrial datasets. Results indicate that the proposed method can obtain superior diagnosis accuracy and provide significant performance improvement in accuracy and false positive rate with less labeled chemical sensor data by further active learning compared with existing methods. Chemical industries have always been concerned about methods for reducing the risk of accidents because they may commonly occur in extreme environments, such as extraordinarily high temperature or pressure, which may result in public damage and large economic losses . AccordiThree types of methods are currently used in fault diagnosis from data processing perspective, namely model-based, signal-based and knowledge-based methods . Model-b(a)The poor ability of learning complex nonlinear relationships because of such a shallow architecture ;(b)The features are only extracted based on signal-based techniques, and the model performance strongly depend on expert and a priori knowledge, which have significant limitations in terms of applicability.As a principal part of artificial intelligence techniques, machine learning techniques, which are the main part of knowledge-based methods, have shown significant potential in fault diagnosis. This method is also called intelligent fault diagnosis method, where artificial intelligence techniques are combined . This meDeep learning is a type of semi-supervised learning that holds significant strengths in overcoming the aforementioned weaknesses in current knowledge-based methods through multiple non-linear transformations and approximate non-linear functions for various diagnosis issues. Deep learning demonstrates significant ability in data expression compared to shallow learning and is able to learn the feature of input patterns adaptively for intelligent fault diagnosis rather than just depending on manual extraction. Hinton et al.  proposedThe objective of active learning is to learn a function that improves the model while requiring as little sensor data labeling as possible. Active learning has been investigated for many real world problems, such as image classification ,28, biomThis study presents a novel DNN with active learning using large amount of chemical sensor data for chemical fault diagnosis. It is a combination of deep learning and a novel active learning criterion that targets the difficulty of consecutive fault diagnosis in chemical systems. The initial DNN model employs a deep architecture with stacked denoising auto-encoder (SDAE) and works through a hierarchical successive learning process where deep learning technique is applied for the feature representation of diagnosis sensor data. The features learned are added to the top Softmax regression layer to construct the discriminative fault characteristics for diagnosis in a supervised manner. For further fine-tuning of the DNN, in contrast to the available methods, we select the most useful samples by the combination of the proposed criterion Best vs. Second Best (BvSB) and Lowest False Positive (LFP), which improve DNN actively for labeling through a novel active learning criterion to target the chemical sensor data, which has better improvement in accuracy and false positive rate than existing methods. (1)Deep learning is able to learn the feature of diagnosis sensor data adaptively for intelligent fault diagnosis rather than merely relying on manual extraction.(2)The method performed excellently in obtaining the potential information and fault characteristics of raw sensor data by multiple non-linear transformations and approximate non-linear functions and presented higher diagnosis accuracy than methods based on shallow architecture. Therefore, the proposed method is a preferred approach for diagnosis in complex chemical systems.(3)The combination of deep learning and active learning is proposed in the chemical fault diagnosis, which improves the existing diagnosis methods significantly. Compared with available active learning methods, a novel active learning criterion combined with BvSB and LFP is presented, which is an active labeling method for the cost-effective selection of chemical sensor data to be labeled and achieves the selection of the most valuable samples for inducing the DNN in chemical fault diagnosis, thus improving the model performance maximally.Compared with the existing related methods, the contributions of the proposed method are summarized as follows:The remainder of this paper is organized as follows: The applicability analysis and preparations related to the proposed method are formally introduced in We first present the merit and applicability of deep learning with chemical sensor data for fault diagnosis in complex chemical processes in this section. Subsequently, we present several details about the model preparation by presenting an overview of the sparse auto-encoder and the method of data preprocess involved in the construction of DNN. The aim of machine learning is to learn knowledge from data for application through specific algorithms. Mining the discriminative feature concealed in the data is a prerequisite, that is, an abstract concept that is provided for classification or recognition. Feature selection is a major part of machine learning that requires a considerable investment of resources in particular areas, including fault diagnosis . Deep leThe majority of traditional models, such as SVM, MLP, and radial basis function (RBF), are considered as shallow architectures that have less than three layers of computation units . Recent Most of the collecting chemical sensor data are unlabeled data that are ignored in traditional supervised models like ANN and SVM. Furthermore, the number of quality sensor data is much less than that of the processing data because of the disparity in sampling rate . TherefoAuto-encoder is a symmetrical neural network that learns the feature of an input in an unsupervised manner. The auto-encoder is composed of the input layer, hidden layer and output layer . The basn is the number of samples for each diagnosis input. In the phase of encoder network, the encoder transforms the input vector From the measured chemical sensor data for diagnosis, the unlabeled sensor dataset can be represented as z:In the phase of decoder network, a reconstruction function denoted by x and reconstruction z. For dataset In the model learning perspective, the weights of encoder and decoder are learned simultaneously during the reconstruction of the original sensor data as long as possible, that is, attempting to incur the minimization of the loss function that denotes the discrepancy between the input signal KL divergence), which denotes the relative entropy between The sparse penalty term is added to the auto-encoder to obtain the complex nonlinear relationship between features, such that the learned features are of the sparse constraint that captures the most significant factor of the input patterns . We will and ρ^j . KL(.) iW and bias b can be solved by minimizing the loss function with sparsity constraint. The optimization process can be realized using the back-propagation (BP) algorithm [The optimal parameters of the sparse auto-encoder lgorithm . For an Data preprocessing is the foundation for the preeminent performance of models, especially the feature normalization that standardizes the range of values stored in different features . In the Z-score normalization is a data preprocessing approach based on the mean and standard deviation of raw data. It has become a traditional approach in the field of fault diagnosis and health monitoring, which take advantage of not knowing the maximum and minimum of attributes beforehand and the significant effect of reducing the effect of noise . The detm is the number of samples and n is the number of attributes. Z-score method normalizes For the sensor dataset denoted by matrix We propose a chemical fault diagnosis method with active DNN in this section. DNN is utilized in this method to excavate potential information on chemical sensor data and is combined with a novel active learning criterion to obtain fault diagnosis in an effective manner. The general framework of the proposed method is indicated in The auto-encoder without any constraint is prone to copy the input to the output directly. The model exhibits poor performance with greater reconstruction error, especially when the difference between the training and test data is predominant. Denoising auto-encoder attempts to make the learned feature representation robust rather than simply repeating input by adding partial corruption to the input pattern, which can be employed to train the stacked auto-encoder to initialize the deep architecture . SDAE acFirst, random noise is added into the original input via a random map: The activation function can be represented as:The reconstruction of the input pattern is represented in same manner as the spare auto-encoder:n represent the number of layer about the constructed SDAE.The reconstruction error is computed from the difference between The SDAE process is shown in T is the objective element:After the completion of the unsupervised pre-training phase through the greedy layer-by-layer approach, fine-tuning is utilized in the next step of the DNN training by adding a Softmax classifier on top of the network as shown in found in .The supervised learning stage attempts to utilize a small amount of labeled sensor data to reduce the training error further and improve the classification performance of DNN. The main problem of DNN training about poor local optima, which can cause catastrophic failure, is successfully addressed by the combination of the greedy layer-by-layer pre-training and supervised fine-tuning . This seThe acquisition of labeled sensor data in the application of chemical fault diagnosis is expensive and time consuming because of the high complexity of industrial systems and the variety of fault types, which require a lot of resources and manpower, such as seeking for an expert mark ,32. In cU and initial labeled sensor dataset L. Active learning allows us to rank the final sensor dataset The labeled sensor dataset to be diagnosed is denoted by The posterior probabilities of associating a sample to a given class Best vs. Second Best criterion (BvSB): the samples that having the lowest difference between the two highest posterior probabilities.Lowest False Positive criterion (LFP): under the condition of the exception class by model outputs, the samples that have the lowest difference in posterior probabilities between this exception class and the corresponding normal class.k samples were selected for final fine-tuning by the integration of the two criteria that can be described as:For the BvSB criterion, the difference between the two highest posterior probabilities is indicative of the manner in which a sample is shown and the uncertainty of classifier. The classifier confidence is low when the two highest values are close. In the second criterion, the selected samples are most probably prone to false positives, which result in fault missing. It is worth noting that the running with failure for a long time results in potent damage in industrial systems . Thus, tAlgorithm 1: AL-DNNInput:Labeled sensor dataset: Unlabeled sensor dataset: Parameters of DNN: the number of hidden layer n; learning rate Iterations: ITERkNumber of chosen samples at the each iteration: Output:The result of fault diagnosisMain step:Data preprocessing: data normalization by (Equation (6))U to train a SDAE layer-by-layer, compute the weights of SDAE by minimizing the cost Function (Equation (10)): Pre-training (unsupervised): Use all samples in Use Obtain the overall parameters of trained DNN: U using the constructed DNN: Classify all unlabeled samples in Initialization: Active learning stage:U: postCompute the posterior probabilities of all unlabeled samples in post by (Equation (15)): Select the samples having the lowest difference between the two highest values in Select the samples that will most probably show the false positive using (Equation (16)): U by the combination of two criteria: Obtain k chosen samples Ask an expert to label the sensor dataset Update the unlabeled sensor dataset: Augment the active training set: Update the weights of DNN by fine-tuning using For iteration = 1: ITEREndThis section presents the development of the chemical fault diagnosis based on the proposed method in two diagnosis cases. The University of California Irvine(UCI) dataset is employed to evaluate the capability and superiority of the proposed framework compared with other framework in the viewpoint of general situation and we further validate the method in Tennessee Eastman (TE) dataset that for a chemical process. Its performance is compared with other related methods. The experimental data used here are from the UCI machine learning repository, and are provided by a real sensor signal. We employed the proposed method to validate the superiority of active DNN framework in model performance. In the dataset, features are extracted from electric current drive signals by empirical mode decomposition (EMD). The drive has intact and defective components. This results in 11 different classes with different conditions. Each condition measured several times using 12 different operating conditions, that is, by different speeds, load moments and load forces. The current signals are measured with a current probe and an oscilloscope on two phases. Six classes of the current conditions are used in this study to test the performance of the proposed method. Type A corresponds to the normal condition whereas B-F corresponds to the different fault types caused by defective components. A total of 5319 samples for each health condition were used. Twenty thousand samples were selected as unlabeled data and used in pre-training, whereas 500 samples were selected as initial labeled data for fine-tuning. The other samples were selected as test data. TEP is a benchmark simulation model that tests the fault diagnosis approaches of process control in real chemical processes . TEP hasThe experimental dataset is generated by the TEP simulation model, and 21 types of faults can be simulated. The simulation times of the training and the test sets are 24 h and 48 h, and the faults appear after 1 h and 8 h, respectively. In this study, six classes of known faults and an unknown fault (IDV17 of the dataset) are used for the experiment, labeled 1–7, respectively. Thus, the dataset includes 8820 samples; 100 samples were selected as the initial labeled data for fine-tuning and 2000 samples for testing. The other samples were selected as unlabeled data for pre-training. The specific description of fault in the experiment is indicated in In this study, DNN has four layers that are designed using cross validation. The unit number of the input layer is determined by the dimension of the diagnosis input, whereas the unit number of the output layer is determined by the number of fault states. For the two experimental datasets, the numbers of units in the hidden layer are set to {200,100} and {100,50}, respectively. The activation function of the DNN is sigmoid. Sparsity penalty was adopted in the DNN for the two datasets and is an effective method to prevent over fitting as well as improve the generalization ability of the DNN. The details of the DNN parameters for the two datasets are shown in Shallow architecture accounted for most parts in the current fault diagnosis for chemical industry. Two widely used algorithms in fault diagnosis that have shallow architectures, namely, neural network with single hidden layer (SNN) and support vector machine (SVM) are employed with same active learning criterion for comparison to verify the superiority of proposed approach. We try to validate the merit about the deep architecture and the employment of deep learning in DNN, so we take the above shallow architecture to the same dataset. Meanwhile, the back propagation neural network (BPNN) that shares the same architecture and trained by the same parameters with DNN is included in the comparison to further demonstrate the performance of deep learning in the construction of DNN, since BPNN lacks feature learning in the pre-training stage relative to the proposed method. We call the above methods active learning for single neural network (AL-SNN), active learning for support vector machine (AL-SVM), and active learning for back propagation neural network (AL-BPNN), respectively. It is worth mentioning that the performance in the tenth trial using BPNN-based method was good while performing unsatisfactorily in presenting large result fluctuations in different trails. In trials, BPNN-based method failed catastrophically as it is a deep architecture for random initial parameters. Taking the seventh and ninth trials as examples, the errors of these trials in the different number of epochs are indicated in We include the results obtained by random selection and entropy selection criteria in DNN for comparison, which are referred to as DNN-random and DNN-entropy, respectively, to highlight the benefit of using the proposed active learning criterion. The number of samples for fine-tuning is 500 initially. We update the weights of DNN by fine-tuning 50 new samples obtained by different selection criteria. We repeat the above experiments on the TE dataset to further assess the generalizability and applicability of proposed method. It is worth mentioning that the methods for comparison are identical to those in the above experiment. The detailed classification result using different diagnosis approaches with 100 labeled data is demonstrated in The main contribution of this study is the construction of DNN with active learning to realize a reliable and effective fault diagnosis with chemical sensor data. The proposed method is a novel idea that utilizes deep learning with big chemical sensor data for both fault feature extraction and intelligent fault diagnosis in chemical processes. An active learning criterion achieves the selection of the most valuable sensor data for inducing the DNN model which is a novel active learning method compared with available active learning criterion for the cost-effective selection of collecting sensor data to be labeled, and improves the model performance maximally. We validate the method on two well-known industrial datasets. The results obtained show that the proposed method provides significant improvements in diagnosis accuracy and false positive compared with the existing methods. The proposed method is compared with state-of-the-art methods in two perspectives, namely, in that of the model and criterion of sample selection. For the diagnosis models, we have taken two widely used algorithms which have shallow architectures for comparison, namely, a general ANN-based and SVM-based methods, and the two method that have shallow architecture have been employed in TE dataset that can be found in ,11,41. MThe number of hidden layer in DNN has a significant effect on performance, owing to the feature learning in hidden layer works is the basis of DNN . We repeThe criteria of active learning are manifold and have their own advantages in different scenarios, which require the further summarization for different occasions. Furthermore, the construction of DNN is largely dependent on the regulation of parameters, which relies on experience. The architecture selection of DNN is still an open problem that will be investigated further in the future work.(1)It is able to adaptively mine the feature from the measured sensor signals or data by multiple non-linear transformations and approximate non-linear functions that provide more potential information for various diagnosis issues;(2)It is an efficient approach for the use of unlabeled sensor data that improves the nature of the diagnosis model in an unsupervised learning;(3)It relies on a novel active learning criterion compared with available methods to select the most valuable sensor data and improve the DNN significantly, which requires less labeled sensor data during the iterative labeling process.This study presented a DNN with active learning for chemical fault diagnosis using chemical sensor data. Deep learning technique is employed as a novel method provided for feature representation of original sensor data. The DNN model employs a deep structure with multiple SDAE and works through a hierarchical successive learning process to construct the diagnosis models. A novel active learning criterion for the particularity of chemical process, that is, a combination of BvSB and LFP, is applied in combination with DNN for further fine-tuning that improves the performance of the model in an active manner, which achieves the selection of the most valuable sensor data for inducing the DNN model during the interaction phase. This approach shows several desirable proprieties:Compared with the state-of-the art methods on two well-known datasets, the proposed method is able to achieve fault diagnosis with high performance and utilize labeled sensor data effectively. Moreover, this method performs excellently, and is especially superior in diagnosis accuracies and improvement of false positive with less labeled sensor data. Accordingly, the proposed method exhibits significant applicability and potential for fault diagnosis in complex chemical systems that involve multidimensional heterogeneous sensory signal and highly nonlinear relationships between the original senor data and diagnosis results through an effective manner of data utilization. In future research, we also intend to investigate the combination of DNN and parameter optimization technique further.