The present study investigated the visual perimetry and color vision of two Amazonian populations differently exposed to mercury. Ten riverines environmentally exposed to mercury by fish eating and 34 gold-miners occupationally exposed to mercury vapor. The visual perimetry was estimated using the Förster perimeter and the color vision was evaluated using a computerized version of Farnsworth–Munsell test. Riverine and gold-miners’ hair mercury concentrations were quantified. Mercury hair concentration of the riverines was significantly higher than that from gold-miners. Riverines had lower perimetric area than the gold-miners. The errors in the hue ordering test of both Amazonian populations were larger than the controls (non-exposed subjects), but there was no difference between themselves. Riverines had significant multiple association between the visual function and hair mercury concentration, while the gold-miners has no significant association with the exposure. We concluded that the different ways of mercury exposure led to similar visual outcomes, with greater impairment in riverines (organic mercury exposed subjects). Since the end of the 1980s, there has been a growing concern with the environmental contamination of the Amazon region by mercury. The “gold rush” in the Amazon region brought about the unselective use of mercury in the process of mineral extraction, resulting in a large deposition of mercury in the Amazon rivers . This haHuman exposure in the Amazon may occur in miners, directly by inhalation of metallic mercury vapor in the process of gold extraction through occupational exposure, or in riverines, indirectly by consumption of fish containing methylmercury accumulated in the food chain . After tOur knowledge about the visual consequences associated with mercury vapor exposure came from investigations with workers of factories that manipulated mercury in some stage of the productive process , 2008. FAs the mercury biochemical pathways in the human body are different for mercury vapor and methylmercury from food, the comparison of visual functions between two populations with similar genetic background, but different exposure type could help to understand the visual function changes associated with mercury exposure. In the present study we compared the visual field perimetry and the hue ordering of Amazonian populations that had mercury exposure to methylmercury through fish consumption or to mercury vapor through occupational exposure.This is a cross-sectional descriptive and analytical observational study. All subjects gave written and informed consent to participate in this study. All procedures were evaluated and approved by the Ethics Committee in Research in Humans of the Tropical Medicine Center of the Federal University of Pará (Protocol #021/2009-CEP-NMT/UFPA).The sample is comprised of 44 total subjects, forming two groups according to the type of mercury exposure: 10 riverines  environmentally exposed to mercury by fish eating who lived in the Tapajós River basin, Pará, Brazil; and 34 gold-miners  occupationally exposed to mercury vapor from Serra Pelada mining, Pará, Brazil. The riverside communities from the Tapajós River basin are located near Itaituba a medium sized port city in the West of Pará State, Brazil. These villages are located around regions historically known as mineral extraction regions that used mercury in the artisanal process of gold extraction, an important source of environmental contamination. Moreover, there is important deforestation around the city of Itaituba that should be considered as source of mercury in the region. No participant from Tapajós river communities inhaled mercury vapor, and mercury exposure was mainly dependent on fish consumption. Serra Pelada village is located near the small city called Curionópolis, in the Southeast of the state of Pará, Brazil. It is a region that constituted one of most important sites of gold extraction mining in the 1980’s and was still active at the moment of the study. The workers involved in this activity were strongly exposed to mercury vapor originated from amalgamation of gold in the metal extraction process.These communities shared the same culture, language, and socio-environmental conditions and they are in the same state of Brazil. They also had little education, poor sanitation, and low-paying jobs. All the participants from both communities reported a non-systematic smoking habit or even alcoholic beverage drinking habit.On our arrival to each village, the invitation procedure to join this study was similar: a meeting was called by the local community health nursing aides to explain the study purposes to the villagers and to invite them to participate. The study took place at the Community Public Health Post and a questionnaire including socio-demographic information, smoking and drinking habits, fish weekly intake, and medical and work history was given by interview; the entire procedure took approximately 1 h. We tested a different number of participants for each visual test, depending on their availability.Hair samples were analyzed using cold vapor atomic absorption spectrometry  according to a previously published protocol . AnalytiHuman hair material (IAEA-086) was the reference to validate the mercury concentration.All the subjects had visual acuity of 20/40 or better in both eyes. We chose the eye with better visual acuity to be tested.All tests were carried out monocularly. The visual perimetry was estimated using the Förster perimeter. Foster perimeter is a broad semicircular arc that can be rotated manually on its axis. There is a fixation point at the arc center and a white dot at the arc that can be moved along the arc. The patient was instructed to fixate on the center of the equipment. The experimenter moved the white dot from the border of the arc toward to the center. The patient was instructed to inform the moment that the white dot is detect. The test is performed in different rotating angles of the arc, and the experimenter recorded the angle at the arc which was detected the white dot. At the end of the experiment, we quantified the perimetric area.2) of different hues and same saturation. Four sets of caps were shown separately in the same order of the conventional test. Initially, the correct sequence of the caps was presented to the participant, followed by its disarrangement. The participants were instructed to reorder as close as possible in the original hue sequence. We measured the arrangement errors for each cap position and the total error score (TES) such as done in i and in the neighbor positions i+1 and i-1. For each cap, the correct ordering resulted in a PES value of 2.The hue ordering test was a home-made computerized version of the Farnsworth–Munsell 100 hue test . It consTotal error score was considered as the sum of all 85 PES minus 170. The perfect performance resulted in a TES of 0. The hue ordering results were transformed to square root values.n = 41 male volunteers). All the controls had no history of systemic or neurological diseases that influenced the visual function and had normal or corrected to 20/20 visual acuity. We considered the perimetric area of 57.07 cm2 as reference value for normative results of the visual perimetry as informed by the device manufacturer .The hue ordering score of the exposed groups were compared to the database of an age-matched control group that lived in an urban region without relevant contact to Hg contamination sources  = 5.159, p = 0.0006].The t(31.57) = 3.613, p = 0.001].F = 5.764, p = 0.02], but there was no difference between the results obtained from the two mercury-exposed groups and between riverines and controls. Although, we have observed no difference between controls and riverines, the riverines had error closer to the gold-miners performance than to the controls.The results of the multiple linear correlation among visual outcomes, age and hair mercury concentration are shown in the p = 0.004), that was described by a negative correlation with linear coefficient of 0.97. For the gold-miners, no significant correlation was observed for their visual evaluation .We correlated the visual outcomes from each group. We found a significant linear correlation between the visual evaluation results obtained from the riverine population  the riverines had higher exposure to the mercury than gold-miners; (ii) riverines had worse performance for the visual perimetry than the gold-miners, but gold-miners had smaller performance in the color vision test than riverines; (iii) riverines’ visual outcomes were highly correlated, the poor color vision, the smaller perimetric area, but the same was not found for the gold-miners what can be indicative of lower influence of the mercury exposure on the visual system in this participants.The comparison between the mercury exposure suffering by riverines and gold-miners should be made carefully, because both groups have distinct types of mercury exposure and the metabolism of the metal in their bodies is completely different. We observed that the riverines had higher hair mercury exposure than the gold-miners. Our results showed that the riverines had higher fish weekly intake than the gold-miners. The fish intake is positively associated to the hair mercury concentration .The visual function has been used as biomarker of the mercury exposure. No specific mechanism of visual loss has been fully described, but probably involves alterations since from the optical apparatus of the eye up to visual cortex. Mercury has a cataractogenic potential because it can induce aggregation of human lens proteins , electroOther investigations evaluated the visual field of subjects exposed to mercury vapor . ExposedPreviously, other investigations have shown color vision loss in fish consuming riverine populations  in the AWe cannot assert that all the visual disturbances that we found are caused by mercury, but as both communities have similar socioeconomical profile , age, environmental condition (sunlight exposure and climate), we consider that the difference of mercury exposure is associated to the visual differences between the communities. The inhalation of the mercury vapor is the primary route of entry into the body for inorganic mercury. Its absorption is fast by diffusion in the lungs and the half-life estimated in the body is about 60 days. Its excretion is mainly by the feces and urine elimination . In the We concluded that the Amazonian population exposed to different mercury forms showed similar visual deficits, with greater impairment in riverine communities. Our findings indicated that these different populations need specific health and education programs to become conscious of the dangers of exposure to mercury. People could very well be aware of the dangers of mercury, but avoiding it could be a greater challenge as fish is a dietary mainstay for the riverine population and gold extraction is one of the few economical activities in the Serra Pelada region. Larger scale interventions should aim at reducing mercury at the source, and the delivery of health services should also be improved.All procedures were evaluated and approved by the Ethics Committee in Research in Humans of the Tropical Medicine Center of the Federal University of Pará (Protocol #021/2009-CEP-NMT/UFPA).All authors contributed to the conception of the work, drafting and revising the manuscript, approved the final version, and agree to be accountable for all aspects of the work. LS, MP, and DV designed the experiments. MC, EL, and AR carried out the psychophysical experiments. GS and EL analyzed the data. EL, GS, and DV wrote the components of the manuscript.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.


This paper presents a sensor-orientated approach to on-orbit position uncertainty generation and quantification for both ground-based and space-based surveillance applications. A mathematical framework based on the least squares formulation is developed to exploit real-time navigation measurements and tracking observables to provide a sound methodology that supports separation assurance and collision avoidance among Resident Space Objects (RSO). In line with the envisioned Space Situational Awareness (SSA) evolutions, the method aims to represent the navigation and tracking errors in the form of an uncertainty volume that accurately depicts the size, shape, and orientation. Simulation case studies are then conducted to verify under which sensors performance the method meets Gaussian assumptions, with a greater view to the implications that uncertainty has on the cyber-physical architecture evolutions and Cognitive Human-Machine Systems required for Space Situational Awareness and the development of a comprehensive Space Traffic Management framework. The ever-increasing number of Resident Space Objects (RSO) is strongly highlighting the need for an evolution from traditional Space Situational Awareness (SSA) capabilities towards Space Domain Awareness (SDA) ,2. AnaloAlthough ground-based systems will continue to be a vital aspect in filling the SST role, the feasibility of Space-Based Space Surveillance (SBSS) is being explored to monitor the Low Earth Orbit (LEO)  and Geos“The process of determining the various sources of errors and uncertainties, properly characterizing these errors and uncertainties, and the roll up of these in the prediction of the quantities of interest” .The.ThetrustFirstly, radar tracking (TRK) and navigation (NAV) error models are developed, including common transformations required to represent the uncertainty in a convenient frame. Attention is then turned to methods to assess the “realism” of the uncertainty under Gaussian assumptions using two common approaches - the Average Mahalanobis Distance (AMD) statistic metric and Cramer–von Mises (CVM). A Monte-Carlo framework is then presented to obtain the required Empirical Distribution of both tracking and navigation uncertainty.σ: Target radar cross-section (RCS) [R: Range from radar to target [m]F: Noise figure of the receiver subsystemL: Radar system losses T0: Standard Temperature [290 K]k: Boltzmann’s constant [1.38064852 × The SNR  of the radar is a key measure of its performance, which is defined as the ratio of signal power to noise power at the output of the radar receiver.Target state vector information is measured relative to the radar site in a spherical coordinate system in range, elevation and azimuth (ctively) a The meaRadar angular measurements are commonly made using monopulse receive antennas that provide a difference pattern characterized by a deep null on boresight. The difference pattern formed by these beams may be used to measure target angular position with a single signal transmission. The measurement accuracy in each angular coordinate is characterized by the RMS of the SNR dependent random angular measurement error, angular bias, and random measurement error. As with the range error, we assume angular bias and random measurement error to be 0 under the Zero-mean conditionAs with the range errors, the SNR dependent error dominates the radar angle error:The RSW satellite coordinate system is chosen to express position uncertainty of RSO. At the time of observation, we assume that the nominal spacecraft position (SP) is centered at the origin of the RSW axis The Radial (R) axis always points from the earth centre along the radius vector towards the satellite. The S-Axis is pointed tangentially to the track’s direction, where, in the case of elliptical orbits, it is only parallel to the velocity vector at apogee and perigee. The W (cross-track) axis is normal to the orbital plane and completes the right-hand triad b. The coThe transfer matrix(s) between the RSW and ECI coordinate systems is then following: Positional errors from the on-board navigation system are then expressed as deviations, Navigation uncertainty is assumed to be Gaussian, and can then be expressed in terms of covariance, where the assumption of zero main is made:Similarly, tracking measurement errors are expressed as measurement deviations in the spherical dimension,  the RSO .(15)δXTThe tracking error of the radar is then expressed in terms of covariance:To combine NAV & TRK uncertainty from the spacecraft and tracked RSO both covariance matrices must belong to the same coordinate frame. In this case, a transformation from the spherical to the Cartesian system must be performed. Position and velocity measurements (and uncertainty) should be expressed in a reference frame that is most convenient to the user, where in this case a Cartesian Earth-Centered Inertial (ECI) frame is chosen. As such, the navigation covariance matrix must be transformed to the Cartesian Earth-Centred inertial (ECI) frame. As this is a linear process (cartesian to cartesian), a simple coordinate transformation can be applied to the covariance matrix. Following the derivation of the RSW to ECI transformation matrix previously described we can write:In contrast, the tracking covariance matrix is expressed in a spherical coordinate system within the radar frame. This requires both a transformation from spherical to Cartesian system and then a translation to the ECI frame. As the transformation between these systems is nonlinear, a basic coordinate transformation is not sufficient, and mathematical tools such the Jacobian of the spherical to Cartesian transformation matrix must be calculated to linearize the process. The spherical to Cartesian Jacobian (D) is expressed as the following, where c, s and represent the cosine and sine of the radar angular measurements.The transformation from spherical tracking error matrix in Radar coordinate system to the Cartesian ECI is then given by the following:Within the SSA/Astrodynamics community, the assessment of covariance realism  has been predominately focused upon identifying the point at which Gaussian assumptions in the propagation of orbital uncertainty breakdown. As discussed, this paper interested at applying this approach to the sensor level and in turn validating when gaussian assumptions of navigation and tracking error break down. In doing so, 2 commonly used statistical metrics and goodness of fit tests have been adopted. The Mahalanobis distance  providesn, where n is the dimension of the state vector i-th Monte Carlo trial. Let k be the total number of independent trials.The expected value of n degree of freedom system being analyzed. Where the results are from a Monte Carlo simulation of the measurement error model with N samples. Specializing to A stronger test for uncertainty realism is to consider the statistical distribution determined from the measurement model in the form of a physics-based Monte-Carlo simulation. As such, the second covariance realism metric test used is the Cramer–von Mises goodness of fit test statistic ,10. ThisSorting the Mahalanobis squared distance of the samples, Given a significance level As described the Squared Mahalanobis Distance Metric and the Cramer–von Mises distribution matching test require the generation of an Empirical Distribution. In doing so, a measurement model using the calculated uncertainty of the radar and tracking error models is constructed, generating N observation samples about the nominal measurement. Under the assumption that each measurement variable is independent (non-correlated):The navigation Error contribution, (considered only for SBSS platform), is given by:The tracking contribution is given by:The total uncertainty about the object when tracked from the space-based platform is then described by:Under the assumption the position of observation is well known and therefore the error is negligible, the total uncertainty from the ground station is:The aim of the first case studies is to apply the above framework for the typical scenario of RSO tracking from a radar ground station for the practical purpose of identification and assessment of a potential collision with an operational spacecraft . TypicalThe coordinate system is constructed using the site position vector, The transfer matrix between the RSW and ECI coordinate systems is then following:Within the SEZ coordinate frame the tracked RSO range, azimuth and elevation QTOFollowing from reference REF Based on proposed MMW SBR systems and documented GPS system performance, we outline here a mathematical framework to combine tracking and navigation uncertainty with the aim providing a rigorous methodology to describe and analyse the position uncertainty of a tracked RSO from a SBSS Radar platform. As with the ground-based scenario, we focus on the case of representing uncertainty expressed in a common satellite coordinate system to a convenient Earth-Centred Inertial (ECI) reference frame. In this case, the RSW coordinate system is used for both navigation and tracking observations, where the MMW radar (TRK) and GNSS (NAV) system is assumed to be centered about the origin. The reference geometry and the key symbols for this scenario are introduced in w is the misclosure vector. To quantify the total error about the RSO position, we reformulate the framework described in is the covariance matrix of observations.Equation (43) is then:The assumption is made that all navigation and tracking observations errors are independent, so covariance terms between the 2 observation sets in the matrix The aim of both scenarios was to demonstrate an effective framework for measurement uncertainty analysis while gaining a deeper understanding on the limits of a normally distributed representation of the uncertainty of the measurement models. In the first scenario, radar design parameters were selected based on ground-based radar tracking stations in the SSA SST network where in the second case radar parameters were selected from proposed spaceborne MMW Radar designs for larger orbiting platforms such as the ISS. As described in Define a range to target and debris size, calculate the performance of the radar system and fuse the tracking + navigation errors using the approach outline in Section 2.1Generate N Monte Carlo points based on the measurement model performance as described in Calculate the corresponding average Mahalanobis distance metric (AMD) and Cramer–von Mises (CVM) goodness of fit statistic.Repeat steps 1–3 for every range to target for each RSO size.Plot the averaged uncertainty metric (AMD) and the Cramer–von Mises test statistic versus range to target for each tracked RSO sizeDetermine the range to target when the averaged uncertainty metric and the Cramer–von Mises test statistic first pierce a pre-defined confidence interval – and decTo test the covariance realism of the total position uncertainty the RSO the average Mahalanobis distance metric and Cramer–von Mises test statistic outlined in Due to the significant impact on the calculated SNR of the radar system, assessing the covariance realism in relation to the specific range to target and debris size provide a practical relationship to defining an acceptable magnitude of measurement errors. Mathematically, the confidence interval represents the point at which the original curvilinear distribution described by the radars spherical uncertainty can no longer be truthfully represented as rectilinear covariance within the cartesian ECI system. To illustrate this point further; As previously highlighted, the importance of quantifying uncertainty at the sensor level is to meet the required assumptions of covariance realism for SSA activities such as orbit determination and uncertainty propagation for RSO collision probability analysis and subsequent avoidance activities. In effect, covariance realism at the sensor level provides means of covariance “fidelity” to these processes. Previously published studies on covariance realism for orbital propagation demonstrate that the initial AMD and CVM metric should tend unity and (1/12k) respectively to demonstrate that a large enough Monte Carlo sample size of the initial covariance matrix (of RSO position uncertainty) has been taken. Nonetheless, the sensor level analysis performed in this paper show that the initial covariance matrix used for these analyses may, in fact, vary in its actual realism/gaussianity if its intrinsic observation uncertainties have been mapped from its original coordinate system. For example, if an observation is taken under a certain tracking performance , the subsequent covariance goodness of fit determined by the CVM test will lay somewhere along plot as shown in Turning attention now specifically to the second case of an SBSS platform. Using the Gauss–Helmert errors in variables framework a measurement model was produced that combines both navigation and tracking errors to generate a position uncertainty of the tracked RSO. We are interested in identifying the influence of the navigation error on the total position uncertainty and any effect on the covariance realism tests described previously. In doing so, plotting the range to target against the ratio between NAV + TRK . Additionally, by addressing under what specific sensor performance RSO uncertainty (gaussian) assumptions maintain realism, Model-Based Uncertainty is also explicitly quantified providing both a top down and bottom up methodology to sensor performance requirements. Nonetheless, future Trusted Autonomous Systems (TAS): will be required to address not only the aleatoric elements discussed but also epistemic uncertainty. Importantly, within the context of future STM/SSA and the CHMI2 concept, uncertainty quantification translates into the confidence-building measures required to inform a trusted closed loop decision-making process between the space analyst and the machine (system autonomy).The aleatoric benefits of the presented framework and covariance realism studies are quite clear – by accurately modelling all prominent sources of error that contribute to RSO uncertainty a realistic uncertainty regarding the position of an RSO is determined Ground and space-based surveillance platforms will form a necessary aspect in the categorisation and maintenance of resident space object databases, required for timely and effective SSA operation within a future Space Traffic Management (STM) system. Nonetheless, for this to be a viable and useful asset, it is necessary that a sensor focused approach is taken when determining position uncertainty of Resident Space Objects (RSO). Through a representative case study of a Ground-Based and Spaceborne MMW radar, this paper aimed to demonstrate an error model that captures both the navigation and tracking errors in determining RSO position uncertainty. Practically, the results show that sensor performance must be determined under different tracking conditions to uphold uncertainty realism assumptions and support key SSA decision-making processes. Nonetheless, an effective STM system will require a deeper understanding of the orbital environment, where forms of traditional uncertainty in space object position and trajectory must extend to space object operational intent, modes, and other important decision-making criteria. In effect, this requires that decision making tools must evolve from addressing not only parameter (inputs) and model-based uncertainty (models that process inputs) but also the epistemic uncertainty within the on-orbit environment Future research will focus on addressing the human centric cyber-physical system challenges associated with a future STM system, while exploring promising Low SWAP-C space surveillance sensors and cooperative net-centric data-sharing systems for SSA.


In addition to retaining high levels of customer satisfaction, sustainability of businesses is also heavily reliant on the efficiency of their internal and external processes. Continuous performance evaluations using key performance metrics to leverage operations are essential in maintaining a sustainable business while achieving growth objectives for revenue and profitability. Traditionally, companies have considered various financial criteria, quality characteristics, and targeted levels of service as their primary factors for performance evaluation. However, increasing environmental and social awareness and accompanying governmental legislations are now requiring companies to integrate these two aspects into their performance evaluations. With this motivation, this study proposes a Balanced Scorecard (BSC)-based approach combining Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Network Process (ANP) methodologies for performance evaluation. The grey system theory has been utilized in order to capture the vagueness and the uncertainty in decision making. To demonstrate the functionality of the approach, a case study is conducted on a U.S.-based food franchise. The results of the algorithm and a discussion elaborating on the findings are provided. The food industry has always been one of the essential contributors to the United States economy. The USDA (U.S. Department of Agriculture) Economic Research Services stated that in 2016, with a 12.6% share, the food and related industries ranked third after housing 33%) and transportation (15.8%) in a typical American household's expenditures  methodologies where only independent and hierarchical criteria are considered and do not include the interdependencies and interactions among the decision criteria. With this motivation, this study presents a Balanced Scorecard-based holistic performance evaluation framework that integrates environmental and social sustainability criteria into performance evaluation. Proposed approach measures the influences of each criterion on others leading to more reliable and accurate assessments. This novel approach extracts the weights of main and sub-criteria without requiring additional pairwise comparisons. Uncertainty and vagueness are also additional factors that are considered in the model.The paper has the following structure. The literature review, providing information regarding the related work, is provided in section Literature Review. In this section, the focus is on the performance evaluation practices in food industry, the Balanced Score Card (BSC), Decision-Making Trial and Evaluation Laboratory (DEMATEL), and Analytic Network Process (ANP) methodologies, and Grey Systems Theory, respectively. Section Problem Description provides the problem description. A detailed explanation of the proposed methodology is presented in section Materials and Method. The practical application of the methodology is delineated in section A Food Industry Case Study with the help of a food industry case study. Conclusions and the implications of the work for future research are given in section Conclusions and Discussion.A sustainable business contributes to sustainability by delivering economic, social, and environmental benefits simultaneously . To ensuThe balanced scorecard is a widely used strategic planning tool for performance measurement where financial and non-financial measures are integrated with corporate visions. In the literature, a variety of studies apply BSC to various fields including finance, human resources, supply chain management, sales, and marketing, and so on in order to pursue an effective and efficient visionary improvement of an organization. Even though the BSC model is proposed by Kaplan and Norton in 1992  is more Several studies on BSC also involve sustainability approach in order to implement the performance evaluation center around multi-criteria decision-making approaches. Kongar  proposedDecision-Making Trial and Evaluation Laboratory , 23 and Uncertainty and incomplete information are two issues commonly encountered in multi-criteria decision making environment. Decision makers tend to use linguistic preference relations to express their preferences where there is lack of information . However, these linguistic preferences usually contain uncertainty and vagueness in the decision making process. Grey system theory  can be uA review of the existing literature reveals that no earlier study combining Grey System Theory, BSC, and DANP methodologies has been proposed to integrate environmental and social sustainability criteria into performance evaluation in the food industry. To the best of our knowledge, this study is the only research determines the weights of influenced criteria in franchised food retail stores via utilizing the methods mentioned above.Increasing awareness of environmental and social sustainability has resulted in many companies making significant investments to integrate these measures into their performance evaluations. Determining the performance criteria and the criteria weights based on the particular industry in focus have been the subject of several studies in the literature. Compared to conventional manufacturing industries, establishing appropriate measures for service industries is a more challenging task. Particularly, as mentioned in section Introduction, fast food restaurant businesses are striving hard to implement various sustainable practices in that are suitable for the specific operations. Therefore, there is a need for an approach capable of considering the specific needs of businesses when defining the sustainability measures for that particular business.Traditional AHP is highly capable of obtaining criteria weights via pairwise comparison in a hierarchical structure. However, the contemporary research in multi-criteria decision-making suggests that the evaluation criteria are influenced by one another and hence need to be represented as a network instead of hierarchically. With this motivation, this study propose a Balanced Scorecard-based DANP approach to determine the weights of the criteria. A case study in the food industry is also presented to illustrate the applicability of the proposed model.Kaplan and Norton  stated twhite system if the system information is fully known; and a black system if the information is not known at all. A system with partially known information is called a grey system. A grey number is a number with uncertain and/or incomplete information and can be mathematically expressed as X contains two real numbers X (the lower limit of ⊗X) and X) is defined as below:X is a black number with no meaningful information,If X is a white number with complete information,Else if X is a grey number with insufficient and/or uncertain information.Otherwise Grey system theory was first introduced by Deng et al.  to deal Let there be two sets of grey numbers denoted by In order to deal with the problems in a grey environment, an effective whitenization (grey aggregation) method is required. Opricovic et al.  developep (decision maker), that will evaluate the influence of criterion i on criterion j. Then the followingLet Step 1: NormalizationwhereStep 2: Determination of a total normalized crisp valueStep 3: Calculate crisp valuesGenerate the direct relation matrixThe DANP is a novel approach that combines the original DEMATEL and ANP methods to utilize total relation matrix for the criteria and the clusters, viz., the BSC dimensions in this study, and to build a network relation map (NRM) of the decision model. Based on the network relation map, the influential relationships are then obtained . The basA is an n × n matrix where aij indicates the degree that the criterion i affects the criterion j and A = [aij]nxn.The initial step in this process is to obtain the decision maker assessments regarding the direct influence among the criteria. These assessments are represented as grey numbers and can be represented by one of the following five levels; “no influence,” “low influence,” “medium influence,” “high influence,” and “very high influence,” Here, the initial direct-relation matrix Normalize the direct relation matrixX = [xij]nxn can be obtained throughThe normalized direct-relation matrix s value representing the maximum values of the sums of all the rows and the sums of all the columns is calculated via Equation (13).Here, the normalized initial direct-relation matrix is obtained via Equation (12), and the Obtain the total relation matrixT = [tij]nxn can be obtained by utilizing Equation (14) where I is the identity matrix:The total relation matrix T to build the NRM.Furthermore, the method utilizes the sums of each row and column of the matrix ith row of matrix T and shows the sum of direct and indirect effects of criterion i on the other criteria. Similarly, Equation (16) represents the sum of the jth column of matrix T and shows the sum of direct and indirect effects that criterion j has received from the other criteria. Furthermore, (d+r) indicates the importance of the criterion. Here, if (d–r) results in positive value it is implied that the criterion has an effect on others. Similarly, when (d–r) obtains a negative value then the criterion is affected by the others.Here, Equation (15) represents the row sum of the Formation of an unweighted super-matrixm criteria, while the second one, n dimensions, i.e., clusters, as shown in Equations (17) and (18).The weighted super-matrix is obtained by dividing each element in a column by the number of clusters with each cluster having equal weights. However, the equal weight assumption for each cluster is not always feasible due to the different degrees of influence among the criteria . In ordeNormalize the total relation and total influence matricesThe normalized total relation matrix of criteria where Similar to Build a weighted super-matrixwhere the sum of each cluster is defined as UC is the matrix transposed from the normalized total relation matrix for the criteria The unweighted super-matrix W is obtained by incorporating the unweighted super-matrix UC and the normalized total influential matrix for clusters The weighted super-matrix Limit the weighted super-matrix to obtain criteria weightsW is raised to a sufficiently large power z until it converges and becomes a long-term stable super-matrix:In order to obtain the final influential criteria weights, the weighted super-matrix The case study is conducted in a U.S. based fast food restaurant company that owns several franchise retail stores inthe northeast region. The company management is in the process of introducing sustainability into their performance evaluation system and is investigating how these perspectives interact with each other. With this motivation, this study applies the proposed methodology using the data collected from the subject matter experts in the company.Based on the balanced scorecard approach, the literature review, expert opinions, and interviews with the upper level management of the company, the performance evaluation criteria are determined. The criteria and their respective definitions are provided in Table As mentioned in the proposed methodology section, Balanced Scorecard-Based Grey-DANP approach is applied to determine the global weights of the dimensions in BSC and the criteria. The decision makers used linguistic terms to assess the influences between the criteria. The assessment scale used in Grey-DANP is provided in Table The direct relation matrix is formed according to franchisee and supervisors point of view and demonstrated in Table The whitened assessments in the direct relation matrix are obtained via utilizing modified-CFCS method from Equations (7–11). Following this, the total relation matrix is obtained by utilizing Equations 12–14). The results are provided in the Appendix . The resThus, the influence diagram, a.k.a. the network relation map (NRM) from the DEMATEL method can be obtained as illustrated in Figure UC can be derived by transposing the normalized matrix as shown in Equation (22). The weights of the BSC dimensions (clusters) can be derived from the improved DANP method without employing further surveys as shown in Equation (21) instead of using additional pairwise comparisons amongst dimensions (W can be obtained through Equation (23). The final influential weights of each criterion can then be obtained by limiting the power of the weighted super-matrix until it converges into a steady state as shown in Equation (24). Resulting matrices are provided in Appendix According to the results of the total relation matrix provided in Table A2, the influential weight of each criterion is obtained via the ANP algorithm. The normalized super-matrix mensions . TherefoIntegrating environmental and social sustainability into business processes is becoming crucial to remain competitive in the current business environment. However, contemporary literature focusing on food service industry performance measurement is solely based on economic indicators and falls short in integrating these considerations into the evaluation process. Aiming at filling this gap, this study proposed an integrated approach combining social, environmental, and economic aspects together in the performance evaluation system of a fast food restaurant company. A Balanced Scorecard based Grey-DANP approach is applied to reveal the influences among the evaluation criteria and rank them with respect to their importance weights. A fast food restaurant company is selected as a case study to demonstrate the applicability of the approach.Besides being the earliest study in combining Balanced Scorecard and Grey-DANP approaches in integrating sustainability aspects into performance evaluation framework, this research identifies the environmental and social performance measures a food store could utilize. Previously published studies consider the sustainability measures independent from one another and hence, mostly avoid the inter-influences which are not compatible with real world applications. Moreover, this study highlights that avoiding these criteria interactions may result in misleading criteria weights. The proposed approach revealed that although financial measures had higher importance values, environmental, and social measures also had significant influence. For instance, as it can be observed from Table GD and EK devised the project, the main conceptual ideas and proof outline. GD worked out almost all of the technical details, and performed the numerical calculations for the case study. MT provided the data and information regarding the case study. EK and KR verified the analytical methods. All authors provided critical feedback and helped shape the research and analysis. All authors discussed the results and contributed to the final manuscript.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.


Several studies report that dolphins, either captive or wild, can expel air from their blowhole to form ring bubbles. By means of an experimental setup consisting of an orifice coupled to a computer-controlled solenoid valve to simulate the dolphin’s blowhole and a vessel as the lungs, we examined the formation mechanism of a ring bubble under varying experimental conditions. With a better record than the most talented dolphin, we show that two aspects were demonstrated as essential to the successful generation of a ring bubble in water: the valve’s opening duration, and the pressure inside the vessel. The present findings suggest that during ring bubble production, dolphins are likely to anticipate their action by both adjusting a suitable air pressure inside their lungs and controlling their muscular flap for an adequate opening timing of their blowhole. This could provide some evidence in favour of suggested cetaceans’ self-control capacities. Delphinapterus leucas) mimicked human sounds by changing the nasal traction pressure and making suitable muscular adjustment of the vibrating phonic lips while over-inflating their vestibular sacs.Air-breathing cetaceans always generate bubbles when expelling air in both solitary and social contexts. In particular, dolphins can release air from the blowhole, and the evacuated air rises to the free surface in a ring-shaped bubble ,2,3,4. TPreviously, ring bubbles were observed by Walters and Davidson  in the c−3 m3 pressurized vessel was used to simulate the dolphin’s lungs. A pressure transducer  with an accuracy of 50 Pa indicated the air pressure inside the vessel. To mimic the blowhole, air bubble generation was done through a submerged cylinder made of a polyvinyl chloride (PVC) pipe with an inner diameter of 2 mm, a wall thickness of 2 mm, and a length of 50 mm, at the bottom section. The orifice had a flat exit. A computer-controlled micro-solenoid valve of high precision , mounted between the vessel and the orifice to mimic the dolphin’s muscular action, permitted bubbles to be injected with a desired opening duration [The respiratory system of a dolphin is mainly composed of the blowhole and lungs. Unlike other mammals who breathe through their nostrils and mouth, dolphins breathe through the blowhole that is centred at the top of their head. The dolphin must contract the muscular flap to open the blowhole that is naturally closed. In our mimicking experiments a, ring bduration . DiffereA high-speed video camera Phantom v711 ranging from 20 to 10,000 frames/s  was used to visualize the formation of a ring bubble at the orifice. Flow velocity fields around a ring bubble in liquid were quantified using particle image velocimetry . Laser illumination sheets were generated by means of two pulsed neodymium-doped yttrium aluminium garnet (Nd:YAG) lasers  arranged side-by-side and crossing the vertical axis of the ring bubble. Unlike the high-speed camera, the PIV device had a limited measure rate of 25 frames per second. Fluorescent Rhodamine B beads of 5 µm (Dantec Dynamics) were added to the liquid as seeding particles. An orange filter placed in front of the camera avoided the reflection of the lasers on the bubbles and allowed only the passage of fluorescent light of the particles. The camera, placed orthogonal to the laser sheet, took two successive images, each at the intensity peak of the laser impulse intensity. These images were divided into several thousand small interrogation areas of 32 × 32 pixels in size. A cross-correlation was then carried out on the two corresponding interrogation areas. This correlation then computed both the liquid flow field and the rise velocity of the ring bubble.The typical, complete sequence of the generation of a stable ring bubble in water—from the formation of a ring bubble near the injection orifice to its progressive rise towards the free surface—is shown in The generation mechanism of a ring bubble is clearly shown by the high-speed camera recordings with a front view a, duringMcCowan et al.  proposedThe experimental data and the quantitative observation of four juvenile dolphins  are collThese data show that by means of a well-controlled mimicking setup, we can certainly surpass the most talented dolphin in the performance of ring bubble production with the highest successful rate of 52%. However, the production of ring bubbles is not always successful, mainly due to the dissymmetric flow turbulence and high instability at the bubble interface, as shown in Unlike a gas–gas system such as smoke rings, which are usually formed when a puff of smoke is suddenly injected into clear air, the turbulence induced by the air in the ring bubble formation in water as gas-liquid system should be more intensive to overcome the water drag that is much higher than that opposed by the still air surrounding the outer parts of the puff for smoke rings. Due to the significant difference of both density and viscosity between air and water, an excessive turbulence during the initial stage of ring bubble generation (as shown in As shown in During the rise of a stable ring bubble, the plane of the ring is usually perpendicular to the direction of the rising. When the ring bubble moves progressively upwards, the rise velocity diminishes with the increase of the ring diameter and the shrinkage of the cross-section of the air core. The perfect symmetric flow field a around Our study provides some insight into the level of control that dolphins may exercise on themselves as well as on their surrounding water medium. Clearly, the complex mechanisms behind some of the apparently trivial behaviors of cetaceans could be understood better still by mimicking them under well-controlled operating conditions. Although our experimental device needs consideration of alternatives and improvements, the optimal conditions for ring bubble generation (as shown in 2 capture.In addition to the biomimetic aspect as mentioned above, the successful production of ring bubbles in water or other liquids could bring new challenges for modeling the rising morphological evolution of classical bubble shapes ,16. The


We propose a peak seeking algorithm to extract the damage characteristic-variation of central wavelength to monitor the crack damage status in aluminum alloy plates using surface bonded fiber Bragg grating (FBG) sensors. The FBG sensors are sensitive to the uniform and non-uniform strain distribution along their longitudinal direction, and the effect appears in the power spectrum of the reflected light from the gauge section. In this paper, we propose a fast-self-adaptive multi-peak seeking algorithm to detect the central wavelength shifting of the FBG reflection spectrum with the crack propagation. The proposed peak searching algorithm results point to a significant improvement compared to other conventional methods. Then the central wavelength shifting is applied to explain the crack propagation behavior of the aluminum plates under quasi-static tensile test conditions. The different damages feature changing intervals which are associated with the crack position and the FBGs location, demonstrating that central wavelength shifting performs as an indicator to detect structural crack damage. Structure health monitoring (SHM) is a critical process for enhancing structural integrity or validity. Sensing technologies using various sensors for intelligent structure have also been investigated . FBG senThe proposed approach has two key advantages over previous studies. First, the proposed self-adaptive multi-peak algorithm can effectively extract the damage features of central wavelength shifts and the experimental results show that the performance of the proposed algorithm is superior to that of other traditional peak seeking algorithms in pm accuracy and self-adaption. Second, the different characteristic variation intervals can be associated with different crack propagation states by a detailed analysis. Additionally, the damage feature proposed in this paper represents the average strain loaded in the gratings and has a connection with the crack length.The traditional peak seeking algorithms such as the maximum and extremum algorithm , first-oThe proposed algorithm can be adapted to extract the damage characteristic, the central wavelength shift which is used to detect the hole-crack damage under fatigue loading. The holes drilled in plates for assembly or functional requirements will cause regional stress concentrations and lead to further varying degrees of structural damage under external loading . For theThe paper is organized as follows: in External loads can lead to uniform or non-uniform strain field distributions along the sensor grating. Takeda  found thIn this paper, a fast-central wavelength seeking algorithm is proposed. First, the improved wavelet thresholding combined with variational mode decomposition method is applied to denoise the FBG signals. Then, the peak range detection method is proposed to confirm the number and scope of target peaks in a multi-peak spectrum. When the crack propagation is near the FBG sensors, the non-homogeneous strain field results in spectrum broadening and a shift in the spectrum peak. Considering the subordinate peaks and the low powered clutter, it is necessary to quantity the range of the primary peak at the 3 dB bandwidth region. Finally, the central wavelength is obtained by the centroid algorithm and the shifting is defined based on a comparison between the healthy and damage spectra. The kernel of the algorithm presented in this paper is the peak-recognition which is developed by fully considering the shape characteristics of spectra, demonstrated to be effective as a deformation spectrum. The flowchart of the central wavelength shifting detection algorithm is shown in The FBG sensing system is subject to interferences from external noise caused by electrical devices and the loading environment that affects the peak shape. The peak features such as spectral broadening, asymmetry, top fluctuation and side lobes then limit the peak detection precision. It is suggested that smooth de-noising should effectively eliminate top fluctuation. Therefore, FBG signal de-noising before peak detection is necessary. A variational mode decomposition combined with the wavelet threshold denoising method is proposed in this paper to deal with the FBG signals. In 2014, Konstantin  first inBased on the previous research , the proK is set as 6 and the best balance parameter N is decomposed into the given number K band-limited intrinsic mode functions (BLIMFs) Step 1: The best decomposition number Step 2: A translate wavelet is executed using thresholding for each BLIMF. Based on literature research, the high-order BLIMFs parts which are significantly corrupted by noise can be locally excluded. Then, the DWT system 5 is adopted as the wavelet basic, and the decomposition level is set as 6 . AccordiHere, the Here, and 2.01 .Step 3: After the processes of de-noise on each scale separately, then, we reconstruct the de-noising signal by summing all the threshold denoising BLIMFs. Processed by the improved wavelet method proposed in this paper, the noise contained in spectral signal is effectively removed, laying the foundation for the multi-peak detection operation. The multi-peak central wavelength detection algorithm is used to handle the issue of precise multi-peak detection, particularly with regards to the deformation reflection spectrum. The improved algorithm is divided into two-sub-tasks: multi-peak splitting and central wavelength detection. The first section is a spectral splitter that splits the reflection spectrum and seeking the multi-peak pre-positions. The second section is a Bragg wavelength detector that extracts the central wavelength from each split spectrum. Those two sections contain six steps as the algorithm flow in In this section, the de-noised spectral signal are processed with the Hilbert transform to achieve the peak number and pre-position detection of the multi-peak spectral signal. According to the previous research , the peaThe Hilbert transform in the time domain is a convolution integral between the real continuous spectrum signal According to one of the Hilbert transform relations, the phase spectrum is only different between The reflection spectra of four FBGs in plate 1 are shown in Compared with the traditional constant thresholding peak detection method, the proposed automatic peak detection algorithm can overcome the limitation that the lower value peaks are not detected and false spurious peaks resulting from the existence of sidelobes or peak distortion shown in a are detN is the size of the spectrum points vector, Based on the pre-position of the peak and the peak region segmentation, a 3 dB window function is added to suppress the side lobes in the pre-processing. Then, the centroid algorithm is used to detect the precise central wavelength in multi-peak in . CompareThe experimental platform with surface bonded FBG sensors on an aluminium alloy plate is set up to monitor the hole-edge crack states by analysing the damage characteristics which are extracted from healthy and deformation reflectivity spectra. The crack defects will reduce the light intensity and disturb light transmission. Then, the central wavelength shift Five parallel experiments with the same design and operation were carried through to reduce the uncertainty shown in c. The coThe FBG sensor network design is critical for damage detection. Considering the effect of the crack damage on the axial strain profile, the FBG sensors are placed at the end of the crack tip in this paper. Based on the previous finite element analysis under different crack lengths  showing The experimental platform for fatigue hole-edge crack damage detection contains three major parts: an optical sensing and data acquisition system, a fatigue crack measurement system, and a fatigue load-cycling system, which are shown in FBG sensors (FSSR5025) from the Changcheng Institute of Metrology and Measurement  were used to acquire the strain information in the regions vulnerable to fatigue crack damage. The optical demodulator system  was used to record the reflection intensity spectrum at various crack lengths from 1–30 mm; the measurement accuracy is 1 pm resolution and the stability is less than 1 pm. A spectrometer of 1 pm resolution is used to obtain the real FBG reflection spectrum. The real cracks were monitored by a traveling optical microscope with a charge coupled device (CCD) camera during the fatigue cycling load testing by a hydraulic MTS fatigue machine at constant temperature. The theoretical peak value is equal to the standard spectrometer results. A constant amplitude tensile loading was applied to the bottom of the specimens with the top boundary fixed, the maximum amplitude was 75 MPa, the stress ratio was 0.1 and the load frequency was 5 Hz. In addition, the fatigue testing experiments were paused under the maximum strain for data acquisition, and the processing was repeated twice to eliminate any operational error during each of the pauses and account for system hysteresis. Fiber Bragg gratings are some of the most used devices to measure strain and deformations in many smart structures. In these applications, the FBG measures the total deformation including strain due to forces applied to the structures as well as thermal expansion . The relIn practice, The Bragg wavelength of an FBG sensor depends mainly on strain, but it shifts slightly with any temperature change. With a change of 1 °C, the measurement strain typically has an error of 11 με . On the με , differeμε , and fibμε ,50. In this paper, the damage monitoring experiment aims to detect the strain effect caused by crack propagation with FBG sensors. Therefore, the thermal-strain cross effect may be limited in the experiment design part and the measurement signal needs to be processed to eliminate the temperature influence.In order to control temperature effects, the damage monitoring experiment was carried out under the constant temperature with a central air-conditioning control system set at 27.6 °C, and data acquisition time within seconds, therefore the slight temperature fluctuations during the process are assumed negligible. Additionally, the reference signals of each FBG which was bonded on the specimen were acquired before the fatigue experiment under no crack environment with the loading fixed at 75 MPa, and the temperature set at 27.6 °C. Then, the crack propagation after fatigue cycles and the damage signals of each FBGs were detected at different crack lengths under fatigue testing paused at 75 MPa with same temperature and bending state of the reference signal. Besides, the central wavelength shift of each FBG is defined as the difference between the damage signals and the reference signals. Then the central wavelength shift at every crack of the FBGs are subject to the strain change without thermal expansion and bending effect.Furthermore, the Bragg wavelength relative shift is proportional to the axial strain, or in other words, FBG converts strain into wavelength shifts, which is an absolute parameter, immune to optical power drifts along the measurement chain. In addition, strain is exerted on the attached optical sensor, which in turn modifies the sensor spectral response. However, on account of the hysteresis error of the optical measuring system of this sensor due to the hysteresis and non-linear phenomena taking place in such substrate materials do not obey Hooke’s law perfectly . In deta1 and ε2 .Even the hysteresis is a limiting factor concerning the global performance of the device, the accurate and reliable modelling of its effects allows the sensor to achieve sufficient accuracy. To this end, plastic materials are accurately modelled in order to compensate for hysteresis. However, recently, hysteresis modelling has seen great progress ,55, resuIn this paper, the hysteresis effect limiting method is applied in the developed damage measurement experiments and yielded to a more linear response of the sensor for a reliable reconstruction of the strain field. Firstly, the data acquisition under the maximum strain stabilization paused with the loading fixed as 75 MPa was proposed and the processing was repeated twice to eliminate the operational errors during each of the pauses. This process limited the system hysteresis under the loading and unloading cycles to be minimum. In addition, the relation between the component strain and the strain on a surface-attached optical fiber is governed by the effectiveness of shear transfer through the adhesive and the polymeric coating on the optical fiber . When coThe damage monitoring experimental procedure was carried out as described in To validate the feasibility and dependability of the multi-peak central wavelength detection algorithm, the traditional algorithms such as direct-peak located algorithm, centroid algorithm, polynomial fitting algorithm and Gaussian fitting algorithm are applied for comparison. The traditional algorithms have high requirements for the spectral type and the environmental noise. In order to evaluate the algorithm effectively, the detected error and the standard deviation are proposed as the assessment indicators. The detected error is the discrepancy between the measured peak value and the theoretical peak value equaling to the standard spectrometer results. The detected error  occurs bConsidering the stability of the optical demodulator system (SM125) is 1 pm., the accuracy of the signals acquired by the system would be influenced, then the highest precision of the peak seeking algorithm would also be limited to pm level. Moreover, in order to evaluate the peek seeking algorithms’ performance, the data processed by the different algorithms were the same. Therefore, the uncertainty fluctuation of the data has the same variation effect on each of these algorithms. In summary, the absolute error and relative error can be presented as the assessment indicators. It is observed that the proposed peak seeking algorithm have the best performance in algorithm precision with the minimum absolute error within the range of , while the maximum algorithm had a maximum error in the range of , as shown in Additionally, considering the accuracy of the measurement equipment, the relative error results shows that the proposed algorithm has the minimum value while the maximum algorithm has the maximum relative error in . TherefoN is the number of the spectrum collection times, When algorithm robust is considered, the detection wavelength standard deviation It is observed that the proposed algorithm has the smallest The analysis of the experiment results shows that the proposed algorithm guarantees the best combination of versatility, precision and accuracy. Consequently, the algorithm in this paper could satisfy the requirements of detecting the promising central wavelength. The central wavelength shifting of the FBG reflection spectrum is chosen as the damage feature due to its sensitivity characteristic to the strain distribution caused by crack propagation. The wavelength shift, What is more, according to the previous research , no cracshown in . The relshown in .When the crack propagation to the FBGs, the materials around the crack tip under high stresses field, and the effect of the stress on z direction shrinkage is constrained by the surrounding materials. Then the strain filed at the crack tip According to the finite element analysis of fatigue crack propagation near the FBG sensor by ANSYS software, the fiber grating senses the nonhomogeneous strain shown in , the refOn constant temperature condition, when the nonhomogeneous strain distribution along the grating, the central wavelength changes no more than a linear function with the strain. In a non-uniform strain field, where the strain components are functions of the axial position While the spectrum response of a Bragg grating is quite simple to interpret when the strain is homogeneous, its response in the presence of strain gradients becomes more complicated to characterize. Indeed, the reflection spectrum becomes broadened with multiple peaks and is said to be chirped.The crack length versus the FBG reflection spectrum is presented in It is possible to observe some differences in the evolution of the wavelength shift because the position of the sensor and the crack related to the applied moments is different. The FBGs are placed perpendicular to the crack propagation direction with a distance of 1 mm, and their reflection spectrum gradually recovers its original shape, then the spectrum returns to the Gaussian shape and the central wavelength tendency shift to the short-wavelength direction (in The FBGs are bonded at the place where the crack crosses, and it is obvious that the reflection spectra continue to deform when the crack passed through fiber grating owing to the damaged gauges (in It is observed that the central wavelength shifting of the FBG sensors located symmetrically along both sides of the hole show similar turning points and increasing tendency with the crack in . In the In the end, for the FBGs bonded up and down perpendicular to the crack direction, the change of central wavelength becomes steady and a back return trend is seen when the crack passes away from the sensor, as the field around the grating returns to an approximately uniform strain condition, shown in region C in The processing period is divided into three stages: gradual increase, quick increase and steady increase. Since the turning points are different in the three periods of each curve on account of the sensor placed at different positions, the analysis of central wavelength slopes and turning points in the three stages caused by the changing average strain and strong stress concentration during the crack extension could help us to judge whether the crack is approaching the FBG sensors’ position. However, when the sensors are in the symmetrical position on both sides of the hole, the two curves are also imperfectly superposed due to the signal uncertainty. The reasons for the differences are many, such as the discrepancy of elastic properties, the crack orientation, as well as the geometry features, and an analysis of these factors will be studied in the future. In this way, the central wavelength can be used to monitor whether the crack is propagating towards the FBG sensors. Accordingly, the central wavelength can be regarded as a damage parameter to monitor the fatigue crack propagation lengths when the FBGs are located at the near-end stress field.In this work, a self-adaptive multi-peak detection algorithm is developed to extract the damage characteristic variation of the central wavelength to detect the crack damage status in aluminum alloy plates using FBG sensors. The peak searching results reflect that the proposed algorithm presents a significant improvement in accuracy and robustness compared to other conventional methods. Additionally, the ability of fiber Bragg gratings bonded on aluminum materials to detect and track cracks by connecting the response of a sensor to a specific fracture/damage phenomenon was demonstrated. The central wavelength shifts detected from the FBG reflectivity spectrum are sensitive to the uniform and non-uniform strain distribution along their longitudinal direction, and can be used as a tool to monitor and evaluate different damage status during a crack growth event in quasi-static tensile tests for aluminum plates. The curve of the characteristic parameter variation during a crack growth event is divided into three regions: gradual increase, quick increase, and steady increase, corresponding to the initial stages of crack propagation at a far distance from the FBGs, the crack proportion near and through the FBGs stage, and the cracks far away from the FBGs stage, caused by the tensile and compressive stress in the crack tip plasticity area. This technique was successfully validated under experimental cycle loading conditions, and very promising results demonstrate the possibility of crack quantitative detection based on FBG sensors.


This state of difficulty may be observed either in planning the strategy to deal with the situation, evaluating consequent target trajectories for the actuators, the catabolic mediators and the activators, or regulation of the biological systems through these trajectories. Catabolic mediator excesses are proposed as scaling the level of difficulty in maintaining allostasis. The excess proportion of cortisol load (EPCL) is consequently proposed to scale the stress level. A first proof-of-concept of this indicator is realized using the Physiostress dataset, by asserting that it is, as predicted from its theoretical basis, more in phase with the stress level expected from the nature of the task and participant-reported stress compared to common indicators based on the cortisol response magnitude itself.Our paper aims to redefine the concept of stress in the context of maintaining allostasis; the term has been reserved for situations that concomitantly involve established physiological and psychological stress components. In particular, we analyze how novelty, unpredictability, threat to the ego, and low sense of control challenge allostasis. The concept of stress is then related to  Hellhammer et al.  provide excess of catabolic mediators, with respect to the actual energetic needs for the task, is generally not addressed. Yet, this notion was introduced by Romero et al. . This framework is based on the allostasis theory proposed by Sterling and Eyer , in whicAnalyzing the physiological effects of N.U.T.S in the context of maintaining allostasis, and proposing a definition of stress that is closely related to these effects.Proposing a consequent, practical solution to measure acute stress.Physiostress.Our framework is presented in section Framework of Allostasis Control. Section Traditional Indicator: Cortisol Response Magnitude describes previous indicators of acute stress based on cortisol concentration, followed by our proposed indicator. In section Example of Application Using the Physiostress Data Corpus, a first proof-of-concept of this indicator is realized using the open-access data corpus allostasis, Sterling and Eyer . In order to be effective, this high-level strategy must by supported by coherent control of the muscles and organs by the nervous system. A strategy can thus be implemented through interconnected conscious, subconscious, and autonomic nervous functions (A unctions .activation is related to the application of a specific strategy. It involves coordinating a group of setpoint trajectories. We distinguish trajectories that relate to: the desired movements of the actuators (muscles); the targeted deployment of catabolic mediators; and the targeted organs' activation. Hence, our framework is based on the hypothesis that the neural system jointly supervises the activities of the actuators, endocrine system, and adrenal system. Thus, the hypothesis is supported by the synchronicity, namely the consistency, and capacity of activity improvement through the realization of common physical activities. This framework is a logical model of brain functions, implemented through complex neural networks, that is responsible for allostasis control.The process of In response to a contextual situation, each trajectory of anticipated setpoints feeds a regulation system that aims to maximize the correspondence of the actual body parameters with the setpoint trajectories. Each trajectory is updated every moment according to the current interpretation of the contextual situation and the current states of the internal parameters. The useful anticipation time (thus the trajectory length) varies with the strategy and regulated parameters. For example, it could be ~1 hour for the actuators (in order to plan macro actions) and catabolic mediators (due to the slow regulation loop) while only seconds for the activation.inactive, while unbound glucocorticoids (hydrocortisone or cortisol) are considered active since they activate cellular processes. The circulating half-life of cortisol varies between 70 and 120 min , secreted by the sympathetic nervous system via the adrenal medulla . They inand Eyer .The nervous system develops, through experiences, complex strategies to deal with each type of situation, varying with the hereditary background of the subject, their biological sensitivity to context , and thesuccessful a strategy that enables the subject to feel satisfied with his or her performance, and as unsuccessful a strategy that leaves the subject feeling unsatisfied. The satisfaction feeling could incorporate complex psychological components up to primitive ones related to survival. The success/failure of the strategies, combined with the amount of stressor exposure and the related experienced emotional load, are important factors for explaining the impact of stressful ordeals on health  and “the range of the mediator needed to respond to unpredictable or threatening environmental changes.” We suggest that the large anticipation time observed in catabolic mediator secretion is consistent with the slowness of its regulation loop. Namely, slowly increasing the mediators' concentration is a good strategy to ensure a sufficient concentration level at the time of the activity while facilitating regulation. This type of anticipative closed-loop system is mathematically modeled by Lenbury and Pornsawad , and cortisol.Anticipation in catabolic mediators is observed in the typical stress response studied from early experiences , where cornsawad  through Anticipation of activation is also observed with a typical increase in heart rate and breath rhythm that precedes a stressful task. The fact that the sympathetic nervous system finely adapts catecholamine secretion to each activity requirement (except in stress scenarios) suggests the presence of a finely supervised control.a priori for each parameter value and applied during the task regardless of the actual value of the system parameters. These systems are impracticable even in very specific and controlled environments, because the error of the target state, even if small, accumulates rapidly during the task in a butterfly effect. One solution to make the systems functional is to add a sensor to the system that measures the actual state of the parameter  and to develop closed-loop control to remove the error between the actual state and the reference. The success of body regulation systems to converge through well-adapted states suggests the presence of a closed-loop control, which has been especially studied for regulation of actuators and catabolic mediators.Very preliminary attempts to control a system parameter  could be based on open-loop systems, where a specific command is calculated The actuator control system is entirely ensured via nerves from command to feedback [see ], a desiRegulation of activators involves two problems: (1) adapting the concentration of catecholamines for activating the organs in a manner to sustain the catabolic activities required for the task, and (2) finely control secretion of catecholamines in levels which are consequent to (1). These two problems responsible for the catecholamine concentration must have distinctive interconnected control loops.To the best of our knowledge, literature does not identify any hormone sensed by the brain clearly involved in a closed-loop regulation of the organs through catecholamine concentrations. Variations in organ activities are detected by nerves, but the role of these inputs in regulation of organs, which may be part of complex neurological pathways, has still to be investigated. A closed-loop regulation system for this system is not biologically assessed. Besides, the hypothesis of an open-loop system does not explain by which mechanisms the sympathetic nervous system may finely adapt, even in anticipation, the organs activities (through secretion of catecholamines) to each activity requirement.presynaptic autoreceptors of sympathetic neurons may contribute to a closed-loop regulation of the neurotransmitter release.Starke et al.  propose The rapidity of the organ responses to catecholamines allows a fine synchronization of their activation to the needs of the actuators. The short half-life of catecholamines (under 2 min) limits their impact on the arousal load in comparison to catabolic mediators such as cortisol.Regulation of the catabolic mediators is performed via the Hypothalamic-Pituitary-Adrenal (HPA) axis in a much slower regulation loop than for control of actuators and activators, due to the blood transmission, cascade of intermediate reactions in the loop, and hormone half-lives. Secreted by the paraventricular nuclei of the hypothalamus, the neurotransmitter corticotropin releasing hormone (CRH) activates adrenocorticotropin secretion by the pituitary gland, which in turn activates glucocorticoid secretion (cortisol and cortisone) by the adrenal cortex . The gluSecurity and conservation of resources are important trade-off criteria –39 in thhomeostatic overload by 40) due to control loop delay. Curves B and C increase, compared to curve A, the arousal load with useless mediators. In curve D, the mediators required to realize the strategy are not reached, a phenomenon that would impair the completion of the strategy and/or reduce the hormonal level below its baseline and compromise vital functions (termed homeostatic failure by 40). A hormonal secretion well-adapted to a strategy is sufficiently high to enable the body to efficiently perform the task and acceptably low to be mostly consumed after the task, thus without significant excess.Minimizing the catabolic mediators, and thus reducing the arousal load, is performed when evaluating target trajectories with regards to regulation capability. As addressed in the introduction, the contemporary concept of stress tends to be restricted to situations that impact the body's health, as observed with the interpretation of every-day situations as novel, unpredictable, threatening to the ego, and that decrease the sense of control. These situations could, in fact, be viewed as related to one or many issues in the body's response in (i) strategy planning, (ii) targeting setpoint trajectories, and/or (iii) regulation.Novelty causes problems in strategy planning (i) and targeting setpoint trajectories (ii). A novel situation involves researching, developing, and testing novel strategies of uncertain energy consumption levels. Consequently, the anticipated setpoints may not accurately fit the effective resources required for task realization. In practice, we would rather talk of degree of novelty. For maximizing security, the brain would evaluate the required catabolic mediators based on the most demanding experiences similar to the current situation. This task requires the brain to evaluate a set of degrees of proximity between the current situation and previous ones. An original situation is subject to being fairly equidistant to many heterogeneous experiences, which must increase the probability of a high reference level. An original situation requires more anticipation time to assimilate the information, plan proper strategies, and activate the body.freeze reaction, as commonly observed with an animal that crosses a street when a car is approaching. This freeze response could result from a freezing strategy , (ii), and (iii). It could provoke a kind of panic scenario in which the strategy selection, targeted catabolic resources, and effective activation must be processed quickly, at the risk of hormonal overproduction, as presented in scenario C of strategy  as well If the brain strives to maximize security and self-being while avoiding long-term resource waste, protecting self-esteem is of main importance. Basically, a low self-esteem, in addition to a lack of self-love, involves a disagreement with our behavioral modes, thus the need to change them and a requirement for novel strategies to cope with our environment. This lack of confidence in our normal strategy planning mechanisms imperatively compromises our sense of control, discussed in the next point. A threat to the ego emphasizes the global consequences of a failure to control the threat and thus justifies spending more resources on beating it, with more demanding strategies, and/or a larger reserve of catabolic mediators allowing an efficient reaction to unpredictable events.a priori undefined or subject to change in progress, the required catabolic mediator levels are accordingly difficult to optimize and subject to being either preventively high or unstable over time.Lack of control means that the brain knows no efficient strategy to effectively control the situation. The brain is therefore in a search mode where it continuously develops and tests new strategies. Since the strategies are a state of difficulty in maintaining allostasis, which typically results in a prolonged state of tension from the consequent excess of catabolic mediators.In light of the consequences of the N.U.T.S situation, we can consider stress as With this view, the form of stress may be differentiated into interrelated categories, namely strategic (trouble in performing strategy planning), activation , or regulation . Strategic stress thus involves issues in evaluating a proper strategic response to a situation, i.e., due to novelty or unsuccessful experiences. Activation stress involves trouble in evaluating proper setpoint trajectories for strategy achievement. Regulation stress involves issues in controlling the system structures according to the setpoint trajectories. The intensity of each form of stress has complex, situation-specific relationships with one other. For example, in the case of a fast and complex incoming threat, a high strategic stress level is expected, without there necessarily being significant activation and regulation stress if the importance of the threat is low-ranked (thus not justifying a significant body activation). In the case of a predictable sport  performed by a novice, a high level of activation stress is expected without important strategic stress. The strategy of running, with its sub-strategies that decompose body movements, are indeed usually implicit. A task that must be performed sooner than expected can generate high activation and regulation stress levels with possible low strategic stress. Biological impairments in the HPA axis could firstly generate regulation stress. Over repeated experiences, it should follow activation stress (since anticipation is based on the regulation capability). Biological impairments could also generate strategic stress as improper levels of arousal affect the effectiveness (and even the success) of strategies.Strategic stress involves mainly conscious mechanisms (with some subconscious mechanisms), since strategies are linked with concrete action plans to deal with the situation. Hence, we can expect it to be more related to the stress felt by the subject rather than other subconscious forms of stress, although they could also be involved in the feeling of being able to handle the threat. However, only activation and regulation stresses are responsible for the cortisol response magnitude, as well as the cortisol excess considered in the evaluation of stress indexes based on salivary cortisol. The possible discrepancy between the intensity of strategic stress vs. activation and regulation stresses could thus contribute to explain the typical low correlation between the stress felt and the ground truth of physiological data. For the rest of the paper, we will use the term stress alone as inclusive of all forms without differentiating them.maximum cortisol increase (MCI) or the global cortisol increase using the area under the curve (AUC) of the cortisol response.The cortisol response magnitude is currently a gold standard indicator for stress assessment. This indicator assumes that the cortisol increase during an experience is directly related to the stress level. It can be computed using different methods, e.g., based on the MCI is typically evaluated with the increase of cortisol following the task, i.e., the difference between the maximum cortisol value after the beginning of the task up to the end of the recovery period and its minimum value before the task beginning. This increase can be normalized based on the minimum (or average) cortisol values during the period of rest (anticipative and recovery periods):where “pre” refers to the period before the stressful experience and “post” the period after.C) from the area under the curve with respect to increase (AUCI). The authors assert that the second quantity, theoretically more related to acute stress, is sensitive to the error on the cortisol sample that precedes the stress test .AUC can be evaluated by integrating the cortisol response parts. By linking the cortisol point with straight lines, we obtain the integral by summing a set of trapezoidal areas, as detailed by Pruessner et al. . These aThe assumption that the cortisol response magnitude indicates the intensity of acute stress could be unrealistic for the following reasons:Problems of underestimation. In the first rest period, it is assumed that the participant is not stressed. This assumption could be unrealistic if the first period of rest follows a stressful task or if the participant anticipates the stressful task of the following period. A consequent high cortisol level during the period of rest causes an underestimation of the cortisol response.Problems of overestimation. The maximum cortisol increase does not account for the catabolic needs of the upcoming task. In our stress definition, the stress concept is linked only with the excess of catabolic mediators and not with the part effectively consumed to perform the task, which may result from an efficient allostasis control. The consumed part of catabolic mediators overstates the intensity of acute stress.In section Stress and Control Issues, we discussed that issues in processing the body's response, especially observed in N.U.T.S situations, typically provoke catabolic mediator overproduction. Catabolic hormone excesses, compared to the quantity required to perform the task, then appear as a relevant stress indicator.cortisol load. The area b, delimited by the baseline and the curve of cortisol concentration, represents the cortisol load consumed for the activity plus an excess secretion. Due to the elimination time of cortisol (see section Framework of Allostasis Control), this excess must still be observed in the recovery period. Moreover, due to the slowness of disengagement with the task combined with the slowness of the hormonal regulation (as discussed in section Regulation), a potential prolonged over-secretion may continue during the recovery period. Consequently, the recovery period will allow estimation of the total excess secretion related to the experience, related to area a. Area c is not considered in the excess part, since it may be related to a preparation for activities expected after the recovery period. In order to evaluate area c, we spin clockwise a straight line around the last cortisol point (see s7) until it reaches either the baseline at the beginning of the recovery period (see p0) or a previous cortisol point during the recovery period (see s4–s6). Area c is delimited in each point with the higher limit between this straight line (which crosses p0-s7 in A and s5-s7 in B) and the cortisol baseline.excess proportion of cortisol load (EPCL), which is the proportion between the excess cortisol load (area a) and the cortisol load related to the activity (area a and area b):The proposed stress indicator is the state of difficulty in maintaining allostasis (namely the stress definition of section Stress and Control Issues), in opposition to traditional indicators based on the cortisol response magnitude which implicitly relate a catabolism increase to stress. Hence, it would bring a measure more in phase with the established psychological and physiological stress components. In Equation (2), the excess part is scaled with the needs of the individual for the specific task, represented in area (b), which enables the use of EPCL to compare the stress response of individuals who have different catabolic needs for achieving the task.This indicator level denotes how much, on a 0–1 scale, the cortisol load generated for the task exceeds its needs. EPCL then scales the Our data corpus presented in Boucher et al.  is consiDuring both days:The participants' salivary cortisol was sampled throughout the experiment approximately every 15 min and again during transitions between the tasks.The participants indicated their level of perceived stress  every 2 min during the rest and the recovery periods and at the beginning, middle, and end of each task. The stress of the participants was thus considered for both days.The TSST is a recognized test for inducing moderate acute stress in a majority of participants . The expThe participant has a rest period of 15 min;The participant is advised to prepare, for 10 min, a 5-min oral presentation to convince, in a second room, three evaluators (two in our version) that he, or she is the best candidate for a monitor job at a summer camp with children.The participant goes into the second room and performs his or her presentation for 5 min. The evaluators attempt to display a neutral attitude without emotional expression. After the presentation, the evaluators ask the participant to perform an arithmetical task as fast as they can.The participant returns to the first room for a 45-min rest period.On the second day, the stress task is replaced by a short conversation with the instructor, who does their best to keep the conversation pleasant and relaxed for the participant. The task preparation in the first room is replaced with an additional 10 min of rest. After the social task, the instructor guides the participant through a 10-min series of 30-s exercises (standstill running and squats) split by 10 s of rest in order to provoke a physiological activation.G, and AUCI, in comparison with our proposed measure (EPCL), and the average stress felt by each participant in both situations.Based on salivary cortisol levels in the Physiostress corpus, we illustrate the problems of underestimation and overestimation presented in section Traditional Indicator: Cortisol Response Magnitude. These problems could explain many unrealistic stress evaluations based on the response magnitude, namely numerous low cortisol magnitude responses observed in our corpus for day 1, and many high cortisol magnitude responses for day 2 because of the physical activity. Indeed, I and AUCG on day 1, respectively. AUCI was even negative for 10 experiences on day 1. Besides, all participants except one reported higher average stress felt during the task on day 1, as expected by the nature of the tasks (Panel A). Therefore, we could consider either that many participants overestimated their stress for day 1, or that the cortisol response magnitude is not a realistic indicator of the stress felt by those participants, plausibly because of the problems of underestimation and overestimation presented in section Traditional Indicator: Cortisol Response Magnitude.Eight out of 25 participants (27%) had a lower maximum cortisol increase on day 1 of the TSST (stress task) than on day 2 with the social talk and sporting activity (Panel D). In panels (B) and (C), 8 and 15 participants had lower AUCPanel (E) of G, and −0.32 for AUCI), which appears coherent with the low correlation expected between the intensity of the strategic stress and the intensity of the activation and regulation stresses (related to the EPCL).In panel (A), the average stress felt dropped 36.8% from day 1–2, while the average EPCL decreased by 30.8%. Indeed, the experience of the social conversation and physical activity of day 2 did not generate important strategic stress, data that would explain why participants reported lower stress levels for this day. The correlation coefficient between the stress felt and the EPCL was 0.305 . These correlations mean that the relative stress from day 1–2, and from one participant to another, varied in a specific manner, often contradictive, for each index.Each stress index produced values that were slightly correlated with those of other indexes . For example, further works could investigate the neurological properties of strategic stress and their involvement in the development of neurological disorders.In this paper, we propose a framework for depicting the main components of allostasis control, which is deployed on three levels for strategy planning, evaluation of target trajectories, and regulation. In order to map physiological and psychological stress components into a same biological phenomenon, we define Activation and regulation stress commonly cause an oversecretion of catabolic mediators, including cortisol. Consequently, the EPCL is proposed as an indicator of stress. Experiments in section Example of Application Using the Physiostress Data Corpus demonstrate the potential of this stress indicator, which offers, with our data corpus, stress levels that are more consistent with the psychological components of stress, and less sensitive to physical activity. These results also present drastic variations of stress assessment of a participant from an indicator to another, which suggests that the choice of the stress indicator may impact the conclusion of a study. The EPCL applicability to long-term and chronic stress should be investigated in further works.In our view, the quality of each stress indicator must be addressed based on their theoretical fundamentals. The stress indicators, with the stress concept itself, have in all likelihood evolved together so as to become more and more informative on the health state of the subject and their predisposition to develop health problems. We believe that the proposed theoretical framework provides a step in this direction by clarifying the nature of stress in the problem of maintaining allostasis.The datasets generated for this study are available on request to the corresponding author.The protocol for generating the Physiostress data corpus was approved by the ethical committee of the CIUSSS of the East-Island of Montreal (project 2015–218).PB developed the theory and the proposed the method with the support of PP, who contributed to important aspects during the process to ensure the quality of the content and the form of the article.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.