EnOcean, a commonly used control protocol in smart lighting systems, provides authentication, as well as message integrity verification services, and can resist replay attack and tamper attack. However, since the device identity information transmitted between sensors in smart lighting control systems is easily accessible by malicious attackers, attackers can analyze users’ habits based on the intercepted information. This paper analyzed the security of the EnOcean protocol using a formal analysis method based on the colored Petri net (CPN) theory and the Dolev–Yao attacker model and found that the protocol did not anonymize the device identity information and did not have a communication key update mechanism, so an attacker could easily initiate a key compromise impersonation attack (KCIA) after breaking the pre-shared communication key. To address the above security issues, this paper proposed an EnOcean-A protocol with higher security based on the EnOcean protocol. The EnOcean-A protocol introduced a trusted third-party server to send communication keys to communication devices because devices must obtain different communication keys from the trusted third-party server each time they communicated. Thus, this protocol could resist a KCIA and achieve forward security. Meanwhile, the device identity information was anonymized using a homomorphic hash function in the EnOcean-A protocol, and the dynamic update mechanism of the device identity information was added so that an attacker could not obtain the real identity information of the device. Finally, the formal analysis of the EnOcean-A protocol showed that the new protocol could resist a KCIA and ensure the anonymity and untraceability of the communication device, which had higher security compared with the EnOcean protocol. The smart lighting control system, a novel internet of things (IoT) product, has emerged quickly in the industrial and commercial markets due to the rapid development of wireless communication technology and sensor technology . Not onlThe application process for the smart lighting control system must gather data about users’ everyday lives, including their location and entry and leave times, in order to properly perform. Private information about users’ movements and positions is gathered by sensing devices to offer more intelligent service experiences ,4. HowevOne of the protocols used to ensure secure communication for IoT devices is Zigbee . Farha eEnOcean Alliance proposed the EnOcean wireless transmission system . In MarcIn this paper, we use CPN theory and the Dolev–Yao attacker model to formally analyze the EnOcean protocol. Through a security analysis, we find that the EnOcean protocol is able to provide authentication and message integrity verification services, but the EnOcean protocol does not anonymize the identity information of the communication devices, so attackers can analyze a user’s living habits based on the eavesdropped device identity information. The formal analysis reveals that the EnOcean protocol cannot resist a KCIA.To address the above security issues, this paper proposes the EnOcean-A protocol with higher security. The EnOcean-A protocol introduces a trusted third-party server to distribute communication keys to communication devices, and the devices can obtain new communication keys from the trusted third-party server before communication, which can resist KCIA and provide forward security. The EnOcean-A protocol uses a homomorphic hash function to anonymize the device identity information and adds a dynamic update mechanism for device identity information so that an attacker cannot obtain the real identity information of the device, thus providing unlinkability of the device identity information.Finally, the security of EnOcean-A protocol is analyzed by a formal analysis method, and it is found that the EnOcean-A protocol has higher security compared with the EnOcean protocol.Since smart lighting control systems are widely used in life, providing people with a more convenient and smarter life experience, most of the existing intelligent lighting control systems are able to provide message encryption, identity authentication, and message integrity verification services. However, because the device identity information transmitted between sensors in an intelligent lighting control system is easily accessible by malicious attackers, attackers can analyze a user’s living habits based on the intercepted information. Through the related literature, it can be found that most of the existing smart lighting control protocols cannot anonymize the device identity, so this paper proposes a protocol with higher security based on the EnOcean protocol. The main contributions of this paper are as follows:Several distinct anonymous approaches have been proposed for IoT devices. The traceability of device identities in smart home systems enables attackers to track device activity and infer users’ daily routines. Sadri et al.  proposedHofer-Schmitz  presenteThe literature mentioned above revealed that the majority of the current anonymous authentication mechanisms and schemes have the following issues: (a) The IoT terminal devices may not have enough computing power to support necessary activities if they rely on ECC public key encryption. (b) While ignoring the anonymous authentication between sensors, they focus primarily on the three-party authentication between the user, the sensor, and the gateway. (c) Since there is no method for dynamic identification information modification and only device information may be anonymized, sensor device untraceability is not achievable. Moreover, the existing security analysis of the EnOcean protocol did not suggest that there was no device anonymization operation in the EnOcean protocol. Under the condition that the sensor nodes are limited in power energy, communication capability, and computational and storage capacity of the chip, this paper introduces a trusted third-party server to send communication keys to the communication nodes and provides anonymization for devices using only homomorphic hash functions. The EnOcean protocol includes two phases: teach-in and authentication . For wirThe EnOcean protocol is shown below, and Step 1: Step 2: For the authentication phase, Step 3: After receiving the message, Step 4: Step 5: Homomorphic hash function refers to a hash algorithm with homomorphism ,37. If ZThen, the hash of the addition of two vectors It can be seen that the hash algorithm is homomorphic. Homomorphic hash functions also have a collision avoidance property. For a homomorphic hash function, for any two pieces of information The attacker does not exist in the probability polynomial algorithm, which can obtain CPN is a modeling language ,39 that The Dolev–Yao attacker model proposed by D. Dolev and A. Yao  formallyThe attacker has access to the open channel. The data transmitted between entities while the protocol is executing can be intercepted, altered, and replayed by the attacker;The attacker can encrypt, decrypt, split, and combine the original message through the known content to forge the message content;Using the identity of the sensor that was eavesdropped, the attacker can determine whether it was delivered by the same device;The attacker can break the long-used key and simulate the device to launch an attack using this key.The attacker has the following functions:The color set is established for the four messages exchanged between the receiver and the sender. First of all, communication information is composed of four pieces of meta-information: ID, RANDOM, KEY, and PAYLOAD. ID indicates the identity of the device chip, RANDOM indicates a random number, PAYLOAD indicates the payload sent by the sender, and KEY indicates the encryption key. The MSG1 type indicates that teach-in messages are sent from the sender to the receiver. The MSG2 type indicates that the sender sends an identity authentication request to the receiver. The MSG3 type indicates that the receiver sends a random number for authentication to the sender. The MSG4 type indicates that the sender sends the authentication calculation results to the receiver. The specific color set definitions are shown in In this study, a top-down formal analysis of the EnOcean protocol was modeled using CPN Tools. The protocol submodule was established after the protocol top-level model was defined. The transition was represented by a rectangle, the place was represented by an ellipse, and the substitution transition was represented by a double-line rectangular transition, indicating that the transition had more detailed submodels.The EnOcean protocol’s top model had 12 places and 7 substitution transitions. The substitution transition of Teach-in represented the unique procedure of the sender providing teach-in information to the receiver. The substitution transition of Learn represented how teach-in signals were received and analyzed by the receiver. The substitution transition of Connection represented the procedure through which the sender sent an authentication request and received a random number. The substitution transition of Connection represented the procedure where the receiver received the authentication request and delivered a random number to the sender. The substitution transition of Authentication represented the transmission of the CMAC value to the receiver after it was calculated by the sender. The substitution transition of Authentication’ represented the procedure through which the receiver compared the CMAC values supplied by the sender. A detailed explanation of the partial substitution transition follows. The sub-model that replaced the Teach-in transition is shown in State-space analysis methods were used to analyze the EnOcean protocol’s conformance. The numbers of nodes and arcs in a state-space were the same as the numbers of strongly connected nodes and strongly connected arcs, according to an analysis of the state-space results in The replay attack, tamper attack, and KCIA were introduced in the network transport layer of the EnOcean protocol model. The attacker could analyze whether the information was sent by the same device based on the intercepted device identity information, and when the attacker obtained the pre-shared key, he could decrypt the information transmitted between devices for a second time and tamper with the transmitted information. The places and transitions marked in blue in All state nodes in the attacker model of this protocol were reachable, as shown by the state space report on the attacker model in As indicated in The EnOcean protocol state-space analysis revealed that the protocol could successfully resist replay attacks and tamper attacks. The EnOcean protocol, however, was unable to resist the KCIA. An attacker could successfully gain the session key used by the device during communication if the attacker broke the pre-shared key. As a result, the attacker had access to all the private information shared via the communication devices. This protocol did not ensure the anonymity of the communication devices since the sender and receiver’s identification did not change during the two communication operations.In order to address that the communication device was not anonymized in the EnOcean protocol and was insecure against a KCIA, this paper proposed the EnOcean-A protocol. Under the premise of low performance of chip and memory, we introduced a trusted third-party server to send communication keys to communication devices, and communication devices must obtain communication keys from the trusted third-party server every time they communicated. Moreover, the homomorphic hash function was used to anonymize the device identity information, and the dynamic update mechanism of the device identity information was introduced. In the EnOcean-A protocol, when the communication device started the teach-in process, first the sender initiated a communication key application request to the trusted third-party server, and the trusted third-party server, after verifying the identities of the sender and the receiver, sent the anonymous identity information and communication key of the receiver to the sender, sent the anonymous identity information and communication key of the sender to the receiver, and the trusted third-party server updated the hash of the device information. When the sender and the receiver received the identity information and communication key from the trusted third-party server, they first updated the identity information hash of their own device, and then the communicating parties started the teach-in process and authentication process based on the original EnOcean protocol.The specific communication process of the EnOcean-A protocol is shown below. Teach-in phase:Step 1: When Step 2: After Step 3: After Step 4: After receiving the data sent from Step 5: After Step 6: After Step 7: After receiving the message, Step 8: Step 9: After receiving the message, Authentication phase:Step 10: Step 11: After Step 12: After the message is received by Step 13: After The EnOcean-A protocol was modeled using CPN Tools. The EnOcean-A protocol’s top model had 28 places and 8 substitution transitions. The substitution transition Authentication_Server stood in for the process by which the sender made a communication key request to the trusted third-party server and acquired the communication key and the receiver’s identification hash value. The substitution transition Authentication_A stood in for the process where the trusted third-party server transmitted a communication key and the hash value of the receiver’s identity to the sender. The substitution transition Authentication_B represented the module that the trusted third-party server transmitted to the receiver for both the communication key and the hash value of the sender’s identity. The substitution transition Authentication_Server′ represented the process through which the receiver acquired the communication key and the hash value of the sender’s identity. The substitution transition Send_Teach-in represented when the sender constructed the teach-in message. The substitution transition Receive_Teach-in represented that the receiver decrypted teach-in messages from the sender. The substitution transition Send_Message represented that the sender submitted the authentication request. The substitution transition Send_Message’ represented the process of verifying the sender for the receiver. The specific process of sending a communication key request from the sender to the server is shown below. The place SelectRandom sent a random number to the transition Compute_Hash1, and the transition Compute_Hash1 calculated the hash of this random number, sent the calculated hash to the transition SendToServer, and sent the random number to the transition Compute_Hash2. The hash′ was calculated using the random number and the identity ID, and the hash′ was sent to the transition SendToServer. Finally, the transition SendToServer sent the two hashes to the place Send_MSG1.The specific process of updating the identity ID at the sending end was as follows. When MSG1 was sent successfully, the transition Update_OldID obtained the new identity ID of the device and sent the new identity ID to the transition Update_NewID. The transition Update_NewID saved the received identity ID to the place OldID′ and used the received identity ID and a random number to calculate the new identity ID of the device, saving the new identity ID to the place NewIDa′.The specific process of receiving an identity request from the server at the sending end was as follows. Place Rec_MSG2 sent the message to the transition Split_MSG2. The transition Split_MSG2 decomposed the received message, sent str to the transition Compare_Str, and sent hash′, random′, and random to the transition Compute_ Str. The transition Compute_Hash1′ used the previously calculated hash′′ and the received hash′ to calculate the new hash and sent the hash to the transition Compute_Str. The transition Compute_Str used the random numbers random′ and random to decompose the hash into str, str′, and str′′ and saved str to the place str1′. str′′ was saved to place str2′, and str′′ was saved to place str3′. The transition Compare_Str compared str′′ with str. If different, the subsequent steps were stopped. If not, str′′ was sent to the transition Compute_XOR, which calculated the difference between id and XOR and sent it to the transition Send_MSG3.The process of saving the communication key from the server and the receiver’s identity hash on the sending side was as follows. Place Rec_MSG7 sent the received message to the transition XOR, which used str′ to compute the heterogeneous value of the received message and sent the computation structure to the place Store_Content1.The specific process of the authentication of the sender by the server was as follows. The place Rec_MSG1 sent the message to the transition Compare_Hash, which compared the hash in the message to prevent replay attacks. If a replay attack was detected, all the subsequent steps were terminated. Otherwise, the message was sent to the transition Split_MSG1. The transition Split_MSG1 split the message, sent the hash to the transition ComputeHash, and sent the hash′ to the transition CompareHash. The transition ComputeHash calculated the hash′ from the hash′. If hash_x was the same, the server authenticated the sender successfully, and the transition Update_ID′ and the transition Update_ID updated the hash value of the sender, saving the result to place DBHashID′.The process of sending an authentication request from the server to the sender was as follows. The transition Compute_Hash calculated the hash of a random number and sent the calculated hash to the transition Compute_Hash1. The transition Compute_Hash1 calculated the hash, hasholda, and hash′ and sent the hash to the transition Separate_Y. The transition Separate_Y divided the incoming hash into str, str′, and str′′ strings. Finally, the transition Send_MSG2 sent str, two random numbers, and hash′ to the place Send_MSG2.The exact process of sending an authentication request from the server to the receiver is shown below. Place Rec_MSG3 sent the message to the transition Split_MSG3. The transition Split_MSG3 split the received message and sent str to the transition Compare_str2. The transition Compare_str2 compared the received str with the str’ calculated by the server, and if it was the same, it meant the server successfully authenticated the receiver. The server sent the str to the XOR, which computed the message  and sent the result to the place store_ID.The server sent the communication key and the receiver’s identity hash to the receiver as shown below. Place SendIDb sent the received message to the transition Concatenate, which sent the receiver’s identity hash and communication key to the transition XOR’. The transition XOR’ performed an XOR operation between the received message and the string str and sent the result to the place Send_MSG7.The Dolev–Yao attacker model was introduced to attack the network level of the new scheme, including a tamper attack, replay attack, and KCIA. The purple part indicates the replay attack, the red part indicates the tamper attack, and the blue part indicates the KCIA. The details are shown in According to In the following, the proposed scheme was secure against various known attacks.Replay attack: The attacker eavesdropped the transmitted data and resent the eavesdropped data to the receiver in the next round of inter-node communication to achieve the purpose of cheating the receiver. In the EnOcean-A protocol, the sender and receiver sent hash values that generated random numbers when communicating with the server, so when the device received a message, it first determined whether the random number hash value in the message already existed; if it did, it directly discarded the message. The teach-in message sent by the sender also included a random number. When the receiver received the message, it checked whether the random number was already received. If it was found that the random number was already received, then the message was discarded directly.Impersonation attack: The attacker used the intercepted device identity information to initiate a session request to other devices. In the EnOcean protocol, the attacker could not obtain the device’s identity launch impersonation attack because the device information was anonymized before communication, and the device anonymization information was updated at each communication.Tamper attack: The attacker intercepted the message transmitted using plaintext and sent the tampered message to the receiving end. In the EnOcean-A protocol, the sender and receiver used partial hashes of identity for transmission when communicating with the server. Even if an attacker intercepted and tampered with the hash value of the message, when the two communicating parties received the message, they compared it with the hash value of their own saved identity and discarded the message if they found that the hash value was different. In the authentication phase, the sender used the session key to encrypt the calculated CMAC value, and the attacker could not tamper with the message without knowing the session key.Eavesdropping attack: The attacker used a passive attack to eavesdrop on the data transmitted in the network and analyzed the data to launch an attack on the node. In the EnOcean-A protocol, since the sender and receiver sent partial hash values of the devices when communicating with the server, even if the attacker eavesdropped on the transmitted messages, they could not construct a complete hash of the device identity.KCIA: In the EnOcean-A protocol, the communication key was sent from the trusted third-party server to both communicating parties, and both communicating parties obtained the communication key from the trusted third-party server before each communication. Even if an attacker broke the communication key used during a certain communication, he could not use this communication key to decrypt the contents of messages transmitted before or after. The freshness of the communication key was also guaranteed. This scheme could provide backward and forward security.Anonymity: In the EnOcean-A protocol, the sender must obtain the hash of the receiver’s identity from the trusted third-party before communicating with the receiver, and when the sender communicated with the receiver, the sender also used the hash of the identity for message delivery. Therefore, the communication process could ensure the anonymity of device information.Unlinkability: In the EnOcean-A protocol, the sender used an updated hash each time it communicated with the trusted third-party, and the trusted third-party server also updated the hash of the receiver. Therefore, the attacker could not deduce the specific communication device from all the hash values eavesdropped after obtaining the communication information.Due to the limited memory and performance of EnOcean device chips, the new protocol introduced a trusted third-party server to address the EnOcean protocol’s security issues. To guarantee that the protocol was resistant to a KCIA, the trusted third-party server produced and delivered the communication key to the communication parties. The EnOcean-A protocol used a homomorphic hash function that could be run securely on lightweight devices such as EnOcean. In addition, the EnOcean-A protocol could ensure that communication devices remained untraceable and anonymous. This paper addressed the security problem that sensitive data transmitted by devices in intelligent lighting control systems can be easily obtained by malicious attackers and used to analyze the personal privacy of users based on intercepted messages. It took the EnOcean protocol as the research object. The formal analysis of the EnOcean protocol using CPN theory and the Dolev–Yao attacker model revealed that the EnOcean protocol was insecure against a KCIA, and the identity information of communication devices was not anonymized, so an attacker could analyze a user’s life status based on the eavesdropped device identity information. To address the above issues and due to the limited computing power and storage control of EnOcean devices, a EnOcean-A protocol was proposed. The improved protocol introduced a trusted third-party server to send communication keys, as well as each time the communication device needed to obtain a new communication key from the trusted third-party server, which was designed to resist a KCIA and provide forward security. The device identity information was dynamically updated so that the attacker could not analyze the user’s usage from the eavesdropped device identity information, ensuring the unlinkability of the device identity information. A formal analysis of the EnOcean-A protocol revealed that the improved protocol could effectively resist the security problems existing in the EnOcean protocol and provide stronger security. In this paper, we only focused on improving the security of the protocol and did not sufficiently consider the real-time aspect of the protocol communication. In future work, we plan to consider the protocol to improve the security and reduce the time cost to achieve real-time requirements as much as possible.


An important means for preventing and managing cardiovascular disease is the non-invasive estimation of blood pressure. There is particular interest in developing approaches that provide accurate cuffless and continuous estimation of this important vital sign. This paper proposes a method that uses dynamic changes of the pulse waveform over short time intervals and calibrates the system based on a mathematical model that relates reflective PTT (R-PTT) to blood pressure. An advantage of the method is that it only requires collecting the photoplethysmogram (PPG) using one optical sensor, in addition to initial non-invasive measurements of blood pressure that are used for calibration. This method was applied to data from 30 patients, resulting in a mean error (ME) of 0.59 mmHg, a standard deviation of error (SDE) of 7.07 mmHg, and a mean absolute error (MAE) of 4.92 mmHg for diastolic blood pressure (DBP) and an ME of 2.52 mmHg, an SDE of 12.15 mmHg, and an MAE of 8.89 mmHg for systolic blood pressure (SBP). These results demonstrate the possibility of using the PPG signal for the cuffless continuous estimation of blood pressure based on the analysis of calibrated changes in cardiovascular dynamics, possibly in conjunction with other methods that are currently being researched. Cardiovascular disease (CVD) is one of the major contributors to human mortality worldwide . A primaPeople who are diagnosed with hypertension take medication in an effort to keep their BP under control. Any undiagnosed or untreated hypertension in early stages can potentially result in myocardial infarction, ischemic and hemorrhagic stroke, heart failure, chronic kidney disease, cognitive decline, and early death . Blood pThe most common physiological signals used in cuffless BP measurements are the electrocardiogram (ECG) and the photoplethysmogram (PPG). The ECG reflects the electrical excitation of the heart, while the PPG indicates blood volume changes in peripheral circulation . These tPTT is defined as the time that the pressure wave takes to travel between two arterial sites , and it PAT is defined as the time interval between electrical activation of the heart and the arrival of the blood to the periphery from the aorta , and it PWV is the speed of the pulse wave moving along the arterial vessels, and it is inversely related to PTT and PAT but is directly related to BP . PWV is In addition to methods based on PAT, PTT, and PWV, there has been some work on BP estimation based on pulse wave analysis. In these methods, features are extracted from the pulse waveform, typically obtained with a single PPG sensor, which are then used in various machine learning estimation models. Most such features are generated from pulse morphology within individual beats . In partSome of the methods for the cuffless estimation of BP rely on mathematical models, which are usually established through the use of a transfer function , WindkesIn previous work, we used a calibration-free method to estimate blood pressure using information from dynamic changes of the pulse waveform over brief time intervals . In thisIn this study, the bio-signal data from the University of Queensland Vital Signs Dataset  is used.In our work, we used only the PPG and noninvasive arterial BP signals from the dataset. Reference  does notTo detect peaks and troughs of the PPG signals, we used a modified version of Pan and Tompkins’ QRS detection algorithm . In thisAfter filtering, the signal goes through a moving average filter of length 38. A threshold is then set for the output of the moving average filter to determine the peaks of the signal based on the local maxima within a preset time interval. These maxima mark the locations of the arterial pulse waveform peaks or the PPG peaks. The troughs of the arterial pulse waveform or the PPG are detected by inverting the original signal and finding the peaks for the inverted waveform. We extracted features linked to cardiovascular dynamics from inter-beat intervals (IBIs) of the PPG signals through time domain, frequency domain, and nonlinear analysis. The analysis was performed on the last ten minutes of each of the thirty signals. For collecting IBI features, we used the open-source heart rate variability analysis software (HRVAS) . The timFor the IBI time domain analysis, both statistical and geometric measurements are considered. Statistical measurements are calculated directly from the IBI series and include: the mean IBI, the standard deviation for the IBI series (SDANN), the pulse rate variability triangular index (PRVti), the triangular interpolation of IBI (TINN), the root mean square of successive differences of the IBI series, the number of successive differences that are greater than a user-defined threshold (NNx) in milliseconds , and the percentage of NNx over the duration of the signal.To compute SDANN, first, the IBI series is divided into an equal number of segments with no overlaps; then, the mean IBI for each segment is calculated, and the standard deviation of all the means is determined. The following equation represents the above steps for calculating SDANN .(1)SDANIn this equation, Geometrical measurements are calculated based on the IBI histogram . The meaTo obtain triangular interpolation of the IBI histogram, a triangular function q(t) is established in a way that the vertices of the triangle are Y, M, and N, where M and N are selected such that q(t) = 0 for The triangular interpolation of the IBI histogram (TINN) is then calculated as:The IBI frequency domain analysis is performed by using the Lomb–Scargle periodogram (LSP) . In the In this method, the power spectral density of an IBI signal is calculated and divided into three sections labeled as very low frequency , low frequency , and high frequency . The resistance to errors from data removal and resampling makes LSP a preferred method for power spectrum calculation for IBI signals .A Poincaré plot, sample entropy, and detrended fluctuation analysis are used to analyze the nonlinear behavior of IBI signals. The Poincaré plot or return map is used to quantify self-similarity by mapping two consecutive IBIs in relation to each other . An elliSample entropy is a measure used to quantify signal complexity . It is rDetrended fluctuation analysis (DFA)  is anothThe above-mentioned process is repeated over different ranges of window sizes; then, the linear relationship between To create a mathematical model for the estimation of blood pressure, we used the Bramwell–Hill and Moens–Korteweg equations. The blood pressure can be calculated based on the theory of pulse wave velocity using the following equation:e change . Since, periment .In this study, we used a particular type of PTT called reflective PTT (R-PTT), whose main advantage is that it can be determined from the PPG signal obtained with a single optical sensor placed on the skin at a peripheral site, such as at the wrist. R-PTT is the duration that the pulse wave takes to travel from the radial artery to the end of the limb and reflect back to the radial artery again , and it PWV can also be measured using the Moens–Korteweg equation :(14)PWV=ained by , the elaained by :(15)Ein=d out by  for the d out by ,39,40. MBy substituting (13) into (16), the DBP value can be calculated using:The peak of the reflected wave can be located using the second derivative of the PPG signal (diastolic peak) . The sepAn open-source software, PulseAnalyse , was useWe then considered the last ten minutes of the dataset for each of the 30 patients to estimate the blood pressure using the developed mathematical model. Using this segment of the signals for estimation gave us the most separation from the calibration interval and thus provided a more realistic performance result of the model for real applications. For the estimation segment (last ten minutes of the waveform), we substituted the earlier calculated and calibrated parameters  from the Deep Learning Toolbox version 13.0 in Matlab R2019b was used for regression. An ANN with a two-layer feed-forward network structure, a sigmoid layer followed by a linear output layer, was used. We tested different numbers of neurons to find the best structure for the network and chose a hidden layer with ten neurons based on the performance. To train the network, we used a Bayesian Regularization backpropagation algorithm and fixed the structure of the network prior to applying it to the test data. A separate network was trained for each of the two feature sets for SBP and DBP.The estimation performance was evaluated based on the mean error (ME), the mean absolute error (MAE), and the standard deviation of error (SDE) obtained with the test data. The ME and MAE are calculated using the following equations:The SDE was calculated based on the following equation:Sensitivity analysis (SA) predicts the level of sensitivity of a model output to changes in parameter values . Models In this work, we used an open-source toolbox in Matlab called Sensitivity Analysis For Everyone (SAFE)  to analyFor a generic model, s of X~i .It is to be noted that, although training the model can be somewhat time-consuming, testing is not, especially because, in a real-world application, testing would be done on a single set of measurements and not 30, as was done here .Information from cardiovascular dynamics was used to estimate blood pressure. This is a calibration-free method that we developed in our previous work . The bloCalibrated mathematical model to estimate blood pressure, as was described in the methodology section. The blood pressure estimation based on this method is presented in Information from cardiovascular dynamics, in addition to the calibrated mathematical model, is used for blood pressure estimation. The estimation results using this method are shown in In this work, we proposed a model-based approach to calibrate estimates of blood pressure using PPG signals. In this process, we estimated both systolic and diastolic blood pressure with the 30 patients using the following three methods:We also performed sensitivity analysis for the proposed mathematical model to determine the stability of the model and evaluate the relative importance of each of the calibration parameters in the system. This analysis provided a ranking for the model parameters based on their influence on the system. The results of this research indicate that the proposed approach based on IBI dynamics over short intervals in conjunction with a mathematical calibration model using only a single photoplethysmogram signal could be used for cuffless blood pressure estimation. This approach may be used on its own or as a complement to other cuffless BP estimation methods. The advantage of this method is that, since the IBI dynamics of PPG signals rely only on the timing variation between the peaks or troughs of the signals, it is likely less sensitive to changes in sensor placement or to different skin colors. This may make blood pressure estimation using this method more favorable compared to methods, including those based on deep learning, that rely on within-beat PPG pulse morphology.In this work, we looked into both a calibrated model as well as a calibration-free model for the cuffless estimation of BP. We collected 16 features from PPG IBI variability which were examined in our previous work . We usedWe also used a mathematical model for calibration based on the reflective PTT and initial non-invasive blood pressure measurements. Sensitivity analysis and parameter ranking showed that one of the parameters was dominant in terms of the sensitivity of the model to it. Considering this model, we selected three features to be used with the ANN for both SBP and DBP estimation using the wrapper subset evaluation with the forward greedy stepwise search method. It is seen that adding the mathematical calibration model led to a substantial reduction in most of the error measures, particularly the critical measures of SDE and MAE. These measures were reduced by 45% and 42% for SBP and 36% and by 35% for DBP, respectively.The lower errors found for DBP vs. SBP may be partly explained by the strong relation that has been found between HRV indices and both SBP and DBP in females, while for males, there was no relation between these indices and SBP . For theReference blood pressure values were taken invasively, whereas, in our study, these values are collected through noninvasive methods.In , becauseThe input in those studies was based on segmented windows of the collected data with overlaps. This could cause the network to be exposed to the test data during training and result in a higher reported accuracy.In our previous work, we estimated blood pressure based on features from cardiovascular dynamics without calibration . In the Regardless of these limitations, we showed that changes in IBI dynamics extracted from the photoplethysmogram (PPG) can be used to estimate BP. The estimation accuracy was further improved with the use of a mathematical calibration model. Even greater improvement might be achieved by combining the method proposed in this study with other approaches for cuffless BP estimation.The concept of blood pressure estimation based solely on cardiovascular dynamics is different from current prevalent approaches that use pulse transit time or pulse morphology within individual beats. It is understood that the cardiovascular dynamics carry useful information that can help to recognize conditions such as hypertension . This waIn this paper, we compared the estimated values for both SBP and DBP using a calibration-free model and the proposed calibrated model. The overall estimation results were in line with the expectation that the cardiovascular dynamics contain valuable information for the estimation of blood pressure. In addition, the result also showed that the calibration stage improved the accuracy in both SBP and DBP estimation. However, to further improve cuffless BP accuracy measurement, in future work, this approach may be combined with widely used methods based on the pulse morphology within beats or the pulse transit time.


Graph thresholding is a frequently used practice of eliminating the weak connections in brain functional connectivity graphs. The main aim of the procedure is to delete the spurious connections in the data. However, the choice of the threshold is arbitrary, and the effect of the threshold choice is not fully understood. Here we present the description of the changes in the global measures of a functional connectivity graph depending on the different proportional thresholds based on the 146 resting-state EEG recordings. The dynamics is presented in five different synchronization measures  in sensors and source spaces. The analysis shows significant changes in the graph’s global connectivity measures as a function of the chosen threshold which may influence the outcome of the study. The choice of the threshold could lead to different study conclusions; thus it is necessary to improve the reasoning behind the choice of the different analytic options and consider the adoption of different analytic approaches. We also proposed some ways of improving the procedure of thresholding in functional connectivity research. One way to understand this network comes from mathematical graph theory which can describe complex structures and dynamics within networks2. The network approach is based on a pairwise matrix of connections between nodes and was used in various studies, to examine the relations between brain characteristics of brain networks with different psychological phenomena, such as cognitive processes, personality, or psychopathology8 based on functional magnetic resonance imaging (fMRI) or diffusion tensor imaging (DTI), electroencephalography (EEG), magnetoencephalography (MEG) and functional near-infrared spectroscopy (fNIRS)10 data.Brain connectomics is a rapidly developing field of research that investigates the interactions between relatively homogeneous brain cell circuits (or brain areas). In response to the external environment, the various areas across the cortex begin to interact, forming a macroscale whole-brain network11 for a review) creates a full adjacency matrix that makes no sense anatomically or mathematically. The next step is usually the creation of the sparse matrix by choosing some threshold value as a cut-off point below which the values are removed12. However, while thresholding is a good way to reduce the possibility of too much influence of spurious or weak connections, it leads to confounds related to the arbitrary choice of the calculation routines.Network neuroscience is a new and developing area, and one of its challenges is considerable variability in the connectivity calculation routines, which is not always detailed and explicitly motivated in studies. Estimation of the functional connections graph via various indexes . In a recent DTI study (Diffusion Tensor Tomography16) the thresholding procedure has been shown to lead to differences in connectivity metrics if more than 70% of the connections between the nodes were removed. Also, it has been shown that calculating the connectivity metrics without thresholding is feasible and, thus, there is now no practical utility in this step of the analysis for DTI data.There is no consensus in the scientific society as to how to choose the specified thresholds. There are two main ways to estimate the threshold value—an absolute and proportional thresholding. An absolute threshold is a specific value of a connection strength, and a proportional threshold is a percentage, below which the connection is considered spurious and deleted from the graph. An important issue is the selection of the specific value  and, accordingly, the number of edges in the resulting network. The thresholding procedure has been criticized in numerous studies, both from theoretical and practical positions18). In the brain imaging data, the spanning-tree approach could be very useful, but a direct comparison of the results obtained with thresholding approaches and various data-driven approaches is needed.While the thresholding procedure is widely used, there is also another, data-driven way to prepare brain data for network analysis, which is based on an algorithmic reduction of the number of nodes. The most popular algorithms are based on the spanning tree procedure , which constructs a unique and acyclic sub-network with a fixed number of connections  report, for M/EEG studies “there is no clear consensus on the statistical thresholds for the confirmation of a significant effect at the scalp or source-level”21. As far as we know the effect of the thresholding for the calculation of the EEG-derived connectivity graph metrics has never been directly assessed.Initially, connectivity studies were mostly based on various types of MRI  data. However, a considerable part of brain activity cannot be captured by MRI due to its poor temporal resolution. The M/EEG allows the analysis of quick or high-frequency oscillations22 and presents an extended analysis.The article is based on a study first reported in the Journal of Physics: Conference SeriesThe connectivity graphs could be influenced by the individual differences in connectivity strength. Figure 14, however, structural properties of the graph should remain the same. For the thresholds that lead to low graph densities the problem of a disconnected graph might appear which will lead to the inability to estimate the path length and clustering coefficient of the overall network.The shape of the distribution of the mean and standard deviation in the sample point out the variability of absolute values and fluctuations in the shape of the individual connectivity strength distributions. The differences in the absolute connectivity strength could impact the graph measures  between nodes persisting across all thresholds with weak connections vanishing. However, the probability of some connections seems to be lowered with the thresholding procedure. For example, relatively strong connections between frontal and parietal/occipital areas estimated with coherence and PPC at the 0.7 threshold are absent at the 0.9 threshold. On the imcoh-derived networks, the probability of connection between electrodes FT9 and P7 weakened at the 0.9 threshold while connections of electrode TP9 are significantly higher at the 0.9 threshold. This inconsistency of scaled probabilities remains in the network analysis of source data e.g. connection between left-hemisphere parahippocampal and right-hemisphere lateral orbitofrontal areas in incoh-derived network is stronger on the 0.5 threshold than on both 0.3 and 0.7 thresholds. This variability of relative probabilities across different thresholds might be a result of various factors. First, it might indicate the inconsistency of the network estimation via proportional thresholding. Second, variability might be a direct consequence of individual differences in brain functional connectivity networks. Third, the variability might be rooted in the very process of EEG functional connectivity estimation, as there seems to be a clear difference between different functional connectivity measures considering the values and topology of networks, but the head-to-head comparison is beyond the scope of this paper.17 to represent the data-driven techniques as it is believed that this method creates denser and potentially more meaningful networks. The direct comparison of the networks requires the same density in both networks. The mean density of the OMST-derived graph is 0.45 ± 0.01, which is equivalent to the 0.55 quantile threshold. The following comparison is performed between OMST-derived and 0.55 quantile graphs. The results are presented in Table To avoid the arbitrarily chosen thresholds data-driven approaches have been developed. We chose the orthogonal MST methodThe results of comparison between OMST and thresholded graphs show substantial differences between the two. The direction of the changes is ambiguous and unstable across different synchronization measures both in sensor and source spaces, e.g. OMST CPL is lower in PPC—sensor networks and higher in the ciPLV-sensor networks. This might indicate the influence of the individual synchronization strength distribution on the estimation of orthogonal MSTs. In the Figs. In the source space, there is a difference between the edge probability in the OMST-graphs and thresholded graphs. This might reflect individual differences in the graphs. The probability of the edge existence in the OMST-graphs is lower than in the traditional approach and the probability of edge existence is uniformly distributed across all edges in the network. The thresholded networks exhibit areas with higher probability, thus reflecting the existence of more frequent edges in the individual networks across the sample. The structure of OMST-derived probability of edge existence graph might indicate that the OMST algorithm is more prone to individual differences in brain functional connectivity networks.The main aim of the functional connectivity studies is to estimate the specificity of brain networks in different conditions, such as gender, different levels of intelligence, or specific task. However, the chosen thresholds could affect the characteristics of the groups, leading to the absence or the presence of the effect of interest depending on the thresholding value. The subjective choice of thresholds results in differences in the absolute values of graph metrics at different levels, values, but these differences will not necessarily be reflected in the experimental results. Here we use the gender differences to model the effect of the thresholding procedure on the outcome of group comparison. The results are shown in Figs. As the idea of the thresholding procedure implies the removal of weak or spurious connections in the data, retaining only strong and important ones, one might expect that ‘cleaning’ of the network due to removal on “noisy” connections should give (1) continuous segments of significant differences, (2) significant differences should appear on higher thresholds. Our analysis suggests that our expectations were not fully met, and the results of the group comparisons might differ depending on the threshold level. For example, for the participation coefficient gender differences are non-significant for the majority of the thresholds, but not all of them. It is important to note that those thresholds are scattered across the threshold levels. For other metrics, there are monotonic changes in the magnitude of the group differences with the “significant” intervals. These intervals, however, can start far below the most widely used thresholds, located around the 0.8 threshold. In contrast, at high levels of the thresholds, there is variability in the effect size, which indicates considerable instability in the estimation of group differences. There are also intervals of the significant differences on the lower thresholds (around 0.25 threshold), indicating the possible group differences specifically for the weak connections. Fourth, in our data a peculiar case occurs, the SWI for the PPC in sensor space has two significant intervals with the opposite Cohen’s d values. At low thresholds, the males have higher values of SWI than females, while at high thresholds the effect was the opposite. In this case, the choice of threshold determines not only the conclusion about the presence or absence of an effect but also its direction. Overall, the choice of threshold might significantly alter the experimental conclusions as even two adjacent thresholds might give different results.Global graph metrics vary as a function of density level.Density-related graph measures  dynamic have a substantial linear component.Proportional thresholding led to substantial distortions in the graph structure across thresholds, demonstrated by the structure of correlations between different thresholds and the structure of edge probability graphs.Participation coefficient is the metric most affected by the thresholding procedure.Data-driven algorithms may give significantly different results from the traditional thresholding procedure of corresponding density.The chosen threshold may influence the outcome of the analysis .The present article aimed to analyze the effect of the thresholding procedure on graph construction from EEG resting state data. According to our results, the thresholding procedure leads to substantial variability in the data. Overall, we have found that:13 with fMRI and Civier and et al.16 with DTI, showing that in EEG studies the thresholding should be used with considerable caution. Our study shows that the networks on the different thresholds are obscured by the global measures, as similar values of global measures could be estimated from the variety of structurally different networks. Most importantly, the network structure estimated for the different thresholds may lead to different conclusions of a study. The basic idea of the thresholding procedure (clearing the weak edges out) implies that detecting a stable experimental effect is only possible in the absence of spurious connections (at high thresholds). Our results indicate that the presence of an effect can also be detected at significantly lower threshold levels and its direction can even be the opposite if the weak connections are preserved. This requires a more thoughtful and informed approach to the thresholding procedure.These discrepancies between the network structure and graph-based metrics on different thresholds are extremely important in light of the widely discussed reproducibility crisis in modern science making it hard to estimate the comparability of the results performed with different analysis pipelines. Overall, according to our results, the way the researcher solves the thresholding issue heavily affects the outcome of the connectivity analysis. Our results add to the previous results by Garrison and et al.17. The MST is supposed to reduce the influence of the spurious connections within the brain by considering strong connections within the brain that don't form cycles or loops thus achieving higher specificity of network topological properties. However, several studies have shown that weak connections can play a significant role when investigating the links between network properties and individual differences in behaviour. The importance of weak connections for network stability has been established for various complex systems, from protein-to-protein interaction23 to mobile communication networks24, biological functions25, or social networks26. According to the recent anatomical studies with tracing the connections within the cortical, the brain indeed has a lot of weak connections that have a substantial impact on maintaining the intermodular connections between functional brain modules. Weak connections may also play a significant role in the individual differences in intelligence28 and its abnormality may be related to the symptomatology of schizophrenic patients29.One of the main challenges in the functional connectivity thresholding problem stems from the fact that there is by now no “ground truth” method on how to define the best threshold value. The data-driven approach based on the MST algorithms has been proposed as a solution to the problem of choosing the arbitrary threshold for network constructionTo date, the informed guide on the thresholding procedure seems to be non-existent and many researchers are left to themselves in the procedure that seems crucial for the outcome of the studies. It is still important to provide a basis under the used threshold level and the procedure itself.30, or permutation testing31 and others that should be tested. Component extraction methods aim at the extraction of a single connected component of the network, e.g. extraction of a Minimum Spanning Tree  or a giant connected component . Integration approaches require the estimation of measures across various thresholds and the following integration to yield the Area under the curve (AUC) as an integrated measure29. Windowed thresholding30 suggests the separation of an initial network into independent networks by extraction and analysis of networks belonging to discrete windows of edge weights. Permutation testing31 is based on the assumption that any significant effect should be visible over the continuous range of thresholds. In this approach the significant effects are clustered on the threshold axis, AUC is calculated over the range of thresholds that define clusters and the AUC value is compared to the null model. Recently, an approach to choose the thresholding value according to the entropy of the functional networks32, as well as some other “optimizational’ measures33, were suggested, however, its validity and reliability are yet to be established. Integration and permutation methods could be useful when graph measures and experimental effects change monotonously with the change in the thresholding value. However according to our results this is not always the case. Windowed approaches might struggle with overall integration of the structures of different windowed networks into a one model.Our study was mostly limited to density thresholding, but there are other methods of network extraction, such as component extraction methods, integration measures, windowed thresholding34, which is important for brain functional connectivity analysis, where networks are mainly undirected by construction. As shown in our study, global network measures, such as average pathlength or clustering coefficient, may be not representative of the topology of the network. As functional connectivity analysis aims to describe connections within the brain, more detailed description and analysis of network topology might be a better option for this purpose than global connectivity measures.Overall, we believe that there are several ways to improve the analysis of brain functional networks and achieve more robust results. First, the way to overcome the existing thresholding-related problems with network analysis may be to widen the description of the networks with local  measures and to describe the network topology more thoroughly with different methods, such as graphlets. Graphlet can be defined as an induced subgraph isomorphism class in a graph. Graphlets have been suggested for the analysis of the topological structure of the undirected networks35. This is evidence toward the tremendous amount of interindividual variability of network characteristics. More cautious and thorough consideration of individual differences in brain functional networks seems necessary for the better understanding of network properties, underlying psychological functions. be a unique fingerprints of individual brain activity.In addition to this, some studies have shown that it is easier to estimate an individual functional connectivity fingerprint than task-related functional connectivity among the group36. However, while the structure–function relationships are an essential part of complex natural systems, it seems that the link between structural connections and functional connectivity can be fundamentally imperfect. Even though the architecture of the structural connectivity networks shapes the boundaries of the functional network, the actual neural dynamics may not be perfectly aligned to it37.Third, a possible way to deal with the thresholding problem is linked to the constraining functional connectivity matrices by anatomical structure of connections within the brain. Recently, a two-step pipeline was developed to constrain functional activation with clusters of structural connectivity38 framework. This framework allows comparison of empirical networks with random or pseudo-random networks with estimating the chance of getting empirical results randomly. Null model network acts pretty much as a null hypothesis for an empirical network to test against. Despite having some methodological considerations38, null models framework provides a powerful tool in statistical inference. However, we believe that this framework could be improved further. Typical null model networks are created by reshuffling an empirical network or by creation of an artificial network, constrained by properties of the empirical network, such as edge weight distribution or node degree distribution. But imperfections in the very process of functional connectivity estimation could lead to biased networks. We think that spatio-temporal reshuffling of initial biosignals might be a better option for the purpose of creating null models.Fourth, the thresholding problem can be addressed with the null modelsFifth, one might expect more important connections in the network to be more stable over time. Introducing a time dimension and assessing dynamic connectivity during the experiment and choosing only the most stable edges might be valid for the purpose of extracting the most valuable connections in networks.Last, we think that the introduced concept of edge probability graphs might be useful in estimation of the most important edges in the networks. The edge probability graph removes the effect of variable absolute connectivity strength in the sample, retaining the position of the node strength among the other edges in the individual network. That could ease the non-stationarity of brain functional networks, caused by individual differences and imperfections in the process of connectivity estimation. Assessing the most probable edges instead of the strongest connections or averaging across multiple adjacency matrices might be a better tool in description and analysis of diverse individual networks, network stability in time or trial-by-trial stability and variability. However, this approach should be developed further in more detail.39. To directly estimate the role of such variability in the EEG research the open EEG Many Pipelines has been launched (https://www.eegmanypipelines.org/).The variability in the ways of graph-metrics estimation related to thresholding procedure is just a part of a bigger problem of the variability in the analysis pipelines in neuroimaging data. Recently, the results from 70 research teams focused on analyzing the same datasets showed that the analytic choices, made by researchers, lead to the substantial affect variability in the research conclusions40). Another way to overcome the huge variability in the data analysis are pre-registration practices41. The idea of pre-registration is to have a record  of the detailed analysis plan prior to the data collection. Current experience shows that pre-registration leads to higher level of the replicability of the research42. Finally, analysis of complex datasets can be performed according to the multiverse approach43. According to the multiverse approach the overall conclusion regarding the effects of interest can rely only on comparing various analysis procedures44. To additionally increase the integrity and the reproducibility of these analyses the analysts can also be “blinded” regarding the initial hypothesis of the research. Recently, the guideline for multi-analyst research emerged45 wrapping up the techniques of strengthening the robustness of scientific results. As the different analysis pipelines used by research groups could possibly lead to different conclusions, authors encourage independent researchers to perform an analysis on the same data, inferring the robust result where results from the different researchers converge.What could be done to choose among the vast amount of possible analytic choices? One solution may lie in data sharing, that opens the possibility to test whether different analysis will lead to the comparable results  with no report of head traumas or psychiatric or neurological disorders took part in our study. Written informed consent was obtained from the participants or their legal guardians for their participation in the study. No monetary reward was given to the participants. The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the ethical committee of the Psychological Institute of Russian Academy of Education.Brain Products ActiChamp was used for the 64-channel EEG recording with a 500 Hz sampling rate. Cz electrode was used as a reference. EEG preprocessing included four steps: (1) Downsampling to 256 Hz, (2) Re-reference to a common reference, (3) Filtering from 1 to 30 Hz and (4) artefact removal. An artifact removal consisted of manual removal of artifacts, removal of ocular artifacts via an infomax Independent Component Analysis and topographic interpolation of the noisy channels.The experimental procedure consists of five alternating 2-min intervals with closed and open eyes. Total 10 min per participant were recorded with 3 closed-eyes intervals. Only closed-eyes condition was used in the study.46. The source reconstruction was performed based on a three-layer BEM model with 1026 sources per hemisphere. The three layers represent the inner skull, outer skull and outer skin and the conductivity of the layers was standard for the MNE package . To construct the BEM model, the standard FreeSurfer model head, Colin27, was used. The individual source reconstruction was performed with the individual inverse operator using the dSPM method. Cortical parcellation was achieved via the MNE function mne.extract_label_time_course with the "pca_flip" method with the Desikan-Killiany Atlas47.Source reconstruction was performed using the pipeline mentioned in the documentation to the MNE package48), Imaginary part of Coherency (imcoh49), coherence, corrected imaginary phase locking value (ciPLV50) and the Pairwise Phase Consistency (PPC51). Each of these measures has their own assumptions and are easily available via common EEG-analysis packages (e.g. MNE for Python). Synchronization was estimated in alpha band 8–13 Hz frequency range for sensor and source space with each synchronization measure for eyes-closed condition.Five measures were used to estimate synchronization: weighted phase lag index  to 0.99 (1% of the strongest connections included) with 0.01 step. Edges with weight below the threshold were eliminated. On each step, disconnected nodes were removed and are reported as isolated nodes. In case the graph divides into separate subgraphs only the biggest component remains. The graph structure on each threshold was constructed based on the probability of edge existence in the whole sample. The probability of edge existence for each edge was defined as the ratio of adjacency matrices with non-zero edge weight to the total number of adjacency matrices. The probability graphs were constructed for each threshold. The probabilities of edge existence for each measure were scaled across all thresholds to [0:1] range for better visibility of edges with high probability.The NetworkX package17. The orthogonal MST method implies the consequent extraction of MSTs from the full graph. The MST on each step is removed from the original graph , but it is transferred to a new, thresholded network. The algorithm ends when an equilibrium between global efficiency and edge removal cost is reached. We compare the data-driven graphs with the same density traditionally thresholded graph.Another way to construct the graph is based on the minimum spanning tree (MST) algorithms. The minimum spanning tree is a set of edges that connects all nodes with minimum possible edge weight. We use the orthogonal MST algorithm developed by DimitriadisFor each graph, we calculated four measures to describe the network structure: Characteristic Path Length, Clustering Coefficient, participation coefficient and SWI.The Characteristic path length is defined as the median of the distribution number of edges between two nodes in the shortest distance between them.The clustering coefficient is a measure of the tendency of nodes to form interconnected groups. For each node clustering coefficient is a proportion of the existing number of connections in a neighbourhood to a total number of possible connections.Participation coefficient is a measure of node edge distribution across networks calculated for each node. Nodes with uniform link distribution with other nodes will have participation coefficient 1, if a node has edges among one specific community, the participation coefficient will be 0. The mean participation centrality across all nodes is presented.53) is a measure of a small-worldness of the graph via the comparison of the characteristic path length and clustering coefficient of a given graph with the measures in the set of random graphs.SWI , statistical analysis was performed in R in stats (https://www.r-project.org/) and exactRankTests (https://CRAN.R-project.org/package=exactRankTests) packages.Linear regression analysis was performed to estimate the graph measure dynamic. A permutation t-test was used to estimate the differences between traditional and data-driven approaches and group differences. Spearman correlation coefficient was used for estimation of the similarity between different thresholds. The connectivity matrices were created via the MNE packageSupplementary Information.


The roll-to-roll manufacturing system is extensively used for mass producing products made of plastic, paper, and fabric in several traditional industries. When flexible substrates, also known as webs, are heated and transported inside the dryer, an inconsistent temperature distribution occurs on the material in the machine direction (MD) and cross-machine direction (CMD). If rollers are not aligned in parallel on the same plane in the roll-to-roll web handling process, or if roller misalignment exists, strain deviation occurs in the web, resulting in lateral displacement and web wrinkles. Therefore, this study examined a wrinkle, which is a thermal deformation that occurs when an inconsistent web temperature distribution is formed on the material inside a dryer. The changes in the elastic modulus and thermal expansion of the web were also examined. Experiments were conducted using a PET film, and its elastic modulus and thermal expansion were examined. The results showed that the presence of a web wrinkle defect can cause a thickness deviation in the functional layer manufactured on the web. Moreover, an appropriate operating speed should be set to reduce the CMD temperature deviation, thereby reducing instances of wrinkle defects. The roll-to-roll manufacturing system is a continuous manufacturing process, in which high-speed manufacturing enables mass production ,2,3. TraThe web is heated inside a dryer to evaporate the solvent applied on the web during the process of manufacturing the functional layer. Various types of heat sources are applied, such as infrared lamps and hot air . Due to Furthermore, we examined the possibility of other causes of wrinkles that may occur on a web inside a dryer and conducted research accordingly. In general, temperature deviation occurs in the machine direction (MD) and in the cross-machine direction (CMD) of the web in the dryer when manufacturing the coated or printed layers through the roll-to-roll manufacturing process. This temperature deviation induces an elastic modulus and coefficient of thermal expansion, which are mechanical properties of the web that ultimately cause strain deviation. Large strain deviation in the web causes deformation in the ZD, which may generate visually observable wrinkles. When wrinkles are generated in the web, these wrinkles cause a thickness deviation in the machine direction (MD) and CMD during the coating or printing processes of the manufactured functional layer, which ultimately leads to degradation in the final products ,39.Shin et al. developed a mathematical model that explains the web tension behavior in the open loop section based on the law of conservation of mass, which states that the mass of a material transported within a controlled volume is constant . As showThe polymer-based webs mostly used in roll-to-roll manufacturing are generally very thin (approximately 0.1 mm or less) and long . TherefoAn experiment was conducted to examine the actual behavior of a material under high-temperature conditions, as shown in Equation (4). In the roll-to-roll manufacturing system, which is installed at Konkuk University, Seoul, Republic of Korea, shown in This study conducted an experiment using a PET film  commonly used in roll-to-roll manufacturing. PET film is transparent, has great tensile strength, and has a high-temperature resistance, and it is therefore widely used. The properties of the PET film used in the experiment are presented in In general, the elastic modulus and coefficient of thermal expansion of a PET film vary depending on the temperature. The maximum operating speed was set to ensure that there was time to sufficiently heat the material, considering the total length of the dryer and drying conditions. The minimum operating speed was selected as the minimum value within a range where the tension could be properly controlled while considering the specifications of the roll-to-roll manufacturing system used in the experiment. The maximum operating tension was set based on the recommendation that the operating tension of PET film should be set to a 6.67% yield strength or below . The dryWe deduced a web strain profile by using the estimated web temperature distribution results as the boundary conditions of a structural analysis model. To accurately predict the elastic and thermal strains, the elastic modulus in The temperature distribution inside the dryer and the PET material temperature distribution were predicted based on the CFD analysis. The web temperature distribution was measured to verify the predicted material temperature distribution based on the CFD analysis. Under the operating speeds shown in A structural analysis was performed by setting the predicted web temperature profile to the boundary conditions and applying tension through the velocity difference of the driven rolls on both sides of the web. The results of predicting the maximum strain deviation from the operating speed and operating tension are shown in This study performed a computer simulation and experiment for web wrinkle defects that may occur in the roll-to-roll manufacturing process. Due to the nature of the roll-to-roll manufacturing system, an inconsistent temperature distribution occurs on the material in the MD and CMD when the web is simultaneously heated and transported inside the dryer. In general, the flow pattern inside the dryer changes according to the operating speed, and the heating time of the web inside the dryer also varies; thus, the material temperature distribution is substantially affected by the operating speed. Because the elastic modulus and thermal conductivity of the web vary depending on the temperature, strain deviation occurs at different parts of the tensioned web. Therefore, strain deviation increases when the operating tension increases under an uneven temperature distribution, which was confirmed to cause ZD deformation. When the web temperature was measured using thermocouples, a maximum CMD temperature deviation of 3.8 °C was generated on the PET film inside the dryer system, and the web wrinkle defect was visually observed when a strain deviation of at least 0.0000769 mm/mm occurred. The presence of a web wrinkle defect can cause a thickness deviation in the functional layer manufactured on the web, thus causing difficulty in assembling the final products or reducing the performance uniformity.The results suggest that an appropriate operating speed should be set to reduce the CMD temperature deviation and hence reduce the instances of wrinkle defects. The speed range must be set so that the minimum speed range ensures the drying time of the printing or coating layers and so that the maximum operating speed guarantees a sufficient productivity of the roll-to-roll manufacturing system. The CMD temperature deviation should be considered to optimize the operating speed. In addition, the results also imply that the maximum tension range must be set by considering the changes in the mechanical properties caused by the web temperature profile inside the dryer, and the appropriate operating tension must be selected by predicting the maximum possible strain deviation.


To investigate the effects of viscoelasticity on the stick-slip behaviour, a new model reproducing the partial slip of viscoelastic materials under fully coupled conditions is developed in this paper. The ratio of retardation time to relaxation time is employed to characterize the rheological property of a viscoelastic material. It is found that materials with higher ratios exhibit more fluid-like behaviours while those with lower ratios perform more like solid. As long as the contact input (load or displacement) is constant, the stick ratio (ratio of stick area to contacting area) is found to be insensitive to the viscoelasticity of materials. However, the separation pattern of the stick and slip regions varies with time when different contact phenomena (creep or stress relaxation) are encountered in the lateral and normal directions. The transition process from partial slip to gross sliding of viscoelastic materials, unlike the elastic response, tends to be abrupt when fully coupled conditions between shear tractions and pressure are introduced. When identical contact parameters are specified for different viscoelastic materials, the more fluid-like material always experiences a quicker transition from partial slip to gross sliding. Owing to the dimensional stability and capacity to sustain loads over long periods of time, viscoelastic materials have been extensively applied in many engineering fields, for example, as rubbers in automotive parts  and polyGreat efforts have been made over the past few decades to provide solutions to various viscoelastic contact problems. Based on the assumption that the contact area increases monotonically without surface adhesion, a solution to the spherical indentation problem of linear viscoelastic materials was developed by Lee and Radok . An esseApart from indentation problems, the sliding or rolling contact of viscoelastic materials has been one of the most investigated topics in the last few decades. Based on the correspondence principle, the rolling contact of a rigid cylinder on a viscoelastic half-space was analyzed by Hunter . The solCompared to the above-mentioned models of the frictionless sliding or rolling contacts of viscoelastic surfaces, less attention has been paid to the partial slip aspect of tangential contact problems. Under such a contact condition a global relative sliding does not occur. Instead, the contacting area is separated into stick zones, in which no relative motion happens, and slip zones, in which local relative movement exists. This type of contact phenomenon is commonly encountered in practice when two contacting surfaces are subjected to a tangential load that is not enough to induce gross sliding. An early viscoelastic partial slip solution was obtained by Goryacheva , where aThe assumptions and approximations implemented in these tentative viscoelastic partial slip solutions become inapplicable when it comes to the contact of two dissimilar materials due to the significant interactions between normal pressures and shear tractions. Considering that a metal–polymer contact is one of the most common interfacial material combinations used in engineering practice, such as in medical devices , the couBy applying the elastic–viscoelastic correspondence principle, the novel conjugate gradient method (CGM)-based algorithm for the coupled normal and tangential contacts of dissimilar elastic materials, developed by the authors of the current manuscript , was extTo explain how the viscoelastic model is developed, some of the basic principles about viscoelasticity are reviewed here for clarity. Viscoelastic materials exhibiting a linear relationship between stress and strain at any time point are known as linear viscoelastic materials. The viscoelastic surfaces being addressed in this work are assumed to behave linearly and the simulation of the nonlinear viscoelastic contact problems is beyond the scope of the current paper. Considering that viscoelastic materials are usually soft, they can hardly deform plastically. Therefore, plastic contact is not considered in the modelling work. In addition, the temperature during contact is assumed to be constant.t)) and relaxation modulus function (Ψ(t)). As their names suggest, the creep compliance function reveals the creep phenomenon and mathematically it describes the viscoelastic strain response to a unit change in stress. On the other hand, the relaxation modulus function characterizes the stress relaxation of viscoelastic materials and mathematically it represents the viscoelastic stress response to a unit change in strain. The Boltzmann hereditary integral is applied to characterize such a contact behaviour, where the response to sequential excitations can be the summation of the responses that would have been generated by each excitation applied alone. Within the framework of linear viscoelasticity, the responses of stress/strain to successive strain /stress stimuli are cumulative. The constitutive law of linear viscoelastic materials can be explained by two Heaviside step response functions to excitations known as the creep compliance function σ(t)=When the input quantity is the stress instead of the strain, the following relationship is obtained via an analogous derivation:Unlike the case of an ideal elastic contact problem where the compliance and elastic modulus are mutually reciprocal, the relationship between the creep compliance and the relaxation modulus of viscoelastic materials is expressed as follows :(5)∫0tΦΦ¯(s)i-th spring.Such time-dependent behaviours of linear viscoelastic materials can be expressed in terms of rheological models established with linear springs (perfectly elastic body) and dashpots . When a spring and a dashpot are arranged in a series as presented in With the generalized Weichert model, the relaxation modulus function of any linear viscoelastic material can be expressed mathematically by fitting the experimental data collected from the conducted relaxation test to the following equation (Prony series ) and adjIt is noted that the spectrum of relaxation times of linear viscoelastic materials can be characterized by introducing as many exponential terms as needed to attain the expected accuracy of the curve fitting. Once the relaxation modulus function is available, the corresponding creep compliance function can be easily determined as well utilizing their mathematical relationship in the Laplace domain (Equation (6)). If the material is characterized by one relaxation time as in this case, such a three-element model is known as the Zener model or standard linear solid model. replace the constant elastic contact compliance subdivide the pressure history in the simulation time superpose the contributions of pressures in all subdivided time intervals by making use of the hereditary integral  and (4)) add the third argument to the problem parameters and subsequently bring about complications when addressing the viscoelastic contact problems, the field equations still possess certain mathematical features. It makes the viscoelastic solution  readily accessible instead of deriving it from scratch. A common practice is to adapt the existing well-developed elastic solutions to make them applicable to linear viscoelastic materials following the elastic–viscoelastic correspondence principle. Steps to take for the transition from elastic solutions to the viscoelastic counterparts when dealing with a typical half-space contact problem , the noThrough the manipulation of elastic solutions, all the continuous equations accounting for the effects of loading history on the surface displacements during the viscoelastic contact period can be obtained.A proper discretization is a prerequisite for the development of a valid viscoelastic contact model. Apart from the spatial discretization where the area of interest between two contacting bodies is meshed into equally spaced rectangular elements with a size of i, j) of the spatial mesh under the effect of a uniform pressure of l, m) in the n-th time step after the reference time, with As a result of the spatial and temporal discretizations, the continuous form of Equation (10) is modified into the following piecewise definition:x, y, and z directions, nodal displacements of a linear viscoelastic surface induced by an arbitrary history of nodal tractions can then be expressed as follows:After determining the closed-form discretized solutions of all influence coefficient matrices relating the surface displacements and contact tractions in the ependent  but is aLoad balance:With the equations and assumptions described above, a sequence of discretized contact problems with complementary conditions can be constructed to search for the solution that accurately reproduces the history of the viscoelastic contact process. The boundary conditions in discretized viscoelastic contact problems are in an analogous form to the elastic ones summarized by Johnson , except The sum of the traction distribution at the contact interface should be strictly equal to the input load in the corresponding direction at any specific time point during the discretized simulation period:2.The deformation of viscoelastic surfaces must meet the following geometrical conditions at any specific time:h, and In the normal direction, the following condition of surface separation should be met:x and y directions at a specific time point, whereas x and y directions, respectively, as shown in In the two tangential directions, the following displacement equation should be met:3.Complementary conditions should be satisfied at any specific time over the contacting surfaces:In the normal direction, the product of the pressure and surface gap must always be zero over the whole computational domain Equation (17) implies that the investigated surfaces are impenetrable and the surface adhesion is not considered in the given contact analysis.In the lateral directions, the shear traction magnitude must be lower than the local friction and no slip should exist in the time-dependent stick zone according to Coulomb’s friction law. As to the slip region, the norm of the shear tractions must be equal to the local friction. In addition, the direction of the shear stress should be opposite to that of the slip distance. Such contact conditions are expressed as follows:In order to search the time-dependent contact tractions and surface deflections meeting the conditions described above, CGM is adopted considering its guaranteed convergence for quadratic optimization problems with inequality constraints. For each time step, the corresponding surface gap When the loads or displacements are just applied at the first time point, there are no effects on the loading history. Hence, the viscoelastic contact problem being addressed temporarily becomes a time-independent coupled elastic one, for which the constant material property is the instantaneous modulus eference , after wAccording to Equation (19), the extra deformation for After adjusting the geometrical conditions of deformation (Equations (15) and (16)) by converting the surface deformation The viscoelastic stick–slip contact problem is thus transformed into a sequence of instantaneous elastic counterparts, for which an algorithm similar to that given in the work of Wang et al.  is emploDue to the limited literature concerning the coupled partial slip of viscoelastic materials, the validation work for the developed model is separated into two separate sections, in which reference solutions are given. First, the coupled stick–slip aspect of the model has been validated by simulating the partial slip contact between a rigid sphere and an elastic half-space, of which a detailed description is given in the work of Wang et al. . Second,To simulate the normal contact problem of a rigid sphere indenting an incompressible viscoelastic half-space, the time-dependent behaviour of the viscoelastic material is simplified and described by a Maxwell model in which the creep compliance and relaxation modulus are characterized as follows:The geometry and material properties of the contacting surfaces are given in A step load of 100 N is applied instantaneously at the beginning of the simulation window a3 and simulation results (solid lines) can be found in To account for an arbitrary history of loading conditions, the contact of a rigid sphere ):A time-independent Poisson’s ratio .’s work . The areThe pressure distributions at different time points are presented in ’s model , as showAnother validation in terms of the evolution of the rigid body indentation with the varying indentation load is given in The validated model is employed to simulate how the separation of stick and slip regions within the contacting area evolves in a viscoelastic frictional contact problem. Based on a material parameter that characterizes the rheological property of materials, a new unified explanation of the viscoelastic contact behaviour under different conditions is provided here. These simulation results are somehow counterintuitive from the perspective of the traditional theory of elastic solid contact.Before the stick–slip simulation study, we want to raise an argument regarding an intrinsic behaviour affecting the normal pressure distribution in viscoelastic contacts.In a few studies concerning viscoelastic contact analysis ,39, the i et al. . The soli et al. , the norConsidering the limitation of Maxwell models to quantify the viscoelastic response of materials, several simulation attempts using Zener models were conducted. The relaxation modulus and creep compliance of a Zener model are usually defined in the following general form in several numerical studies ,21,22,23earchers ,21,22,23To investigate the physical meaning of the ratio  and stress relaxation (DC) encountered in the To study the effects of the material properties Now, to vary the contact input in the normal direction, the Zener model  in the normal and tangential directions are constant. However, the separation pattern of the stick and slip regions depends on the contact phenomena experienced by the viscoelastic surface in the normal and tangential directions. When different contact phenomena are encountered (different types of contact inputs are specified) in the normal and tangential directions, the separation pattern of the stick and slip regions varies with time. Otherwise, it tends to be time-independent. To investigate the transition from partial slip to gross sliding for different viscoelastic materials, a dynamic loading profile is specified in the lateral direction. The simulation starts with the semi-coupled condition, where only the coupling between the pressure and shear traction in the To switch to the fully coupled condition, under the same increasing rate of displacement, the tested more fluid-like material  remains constant.However, the separation patterns of the stick and slip regions within the contacting area can be different even though the contact inputs are constant. This is determined by the contact phenomena encountered by the viscoelastic surface. When the same contact phenomenon (creep or stress relaxation) is experienced in both the normal and tangential directions, the evolution of the stick region follows a certain pattern. Otherwise, the way the stick and slip regions are separated would vary with time.Unlike that in an elastic solution, the transition from partial slip to gross sliding of viscoelastic materials tends to be abrupt under fully coupled conditions. Under the same contact inputs, a quicker transition can be achieved for a more fluid-like material. Compared to the case where a stress relaxation phenomenon is encountered in the normal direction, it requires a longer time for the viscoelastic surface to be in the gross sliding state when a creep phenomenon is encountered. Our findings suggest for the first time that a fully coupled contact condition leads to significantly different results than a semi-coupled one and that future analysis of the stick–slip or sliding of viscoelastic materials needs to be developed with consideration of fully coupled normal and tangential loads.The three main contact phenomena of viscoelastic materials including creep, stress relaxation, and hysteresis are reproduced using the newly developed viscoelastic contact model. The ratio of retardation time to relaxation time Although valid partial slip solutions can be achieved from the developed viscoelastic half-space model, films with finite thickness rather than a half-space, are the most common applications of viscoelastic materials, as stated by Zhang et al. . A frict