Background: Functional electrical stimulation (FES) cycling has seen an upsurge in interest over the last decade. The present study describes the novel instrumented cycling ergometer platform designed to assess the efficiency of electrical stimulation strategies. The capabilities of the platform are showcased in an example determining the adequate stimulation patterns for reproducing a cycling movement of the paralyzed legs of a spinal cord injury (SCI) subject. Methods: Two procedures have been followed to determine the stimulation patterns: (1) using the EMG recordings of the able-bodied subject; (2) using the recordings of the forces produced by the SCI subject’s stimulated muscles. Results: the stimulation pattern derived from the SCI subject’s force output was found to produce 14% more power than the EMG-derived stimulation pattern. Conclusions: the cycling platform proved useful for determining and assessing stimulation patterns, and it can be used to further investigate advanced stimulation strategies. Lower-limb cycling devices are among the most globally available human-powered mechanical devices and are used for locomotive, sport or leisure activities. They come in numerous designs —the most important variations being the number of riders, their position on the device  and the number of wheels, depending on the specific functional needs ,2.As a result, cycling is one of the most widely used forms of exercise to increase cardiovascular health and build lower-limb muscle strength. For these reasons, this type of activity is ideal for individuals with lower-limb deficiencies, such as paralysis after a spinal cord injury (SCI), stroke, Parkinson disease or multiple sclerosis ,4. When Although invented in the 1980s  and LyonDespite the growing popularity of FES cycling, instrumented cycling devices for the assessment of FES-cycling strategies are not common. The existing devices are mainly designed around commercially available cycling ergometers or recumbent tricycles. Cadence-controlled cycling ergometers that provide motor and crank position data can be adapted for FES cycling, and the torque produced by the cyclist can be derived from the motor current . AnotherThe main limitation of the mentioned devices is versatility. The seating position is predefined and requires a transfer which is often difficult for individuals with certain disabilities. In addition, most of the mentioned devices do not record the torque produced by each leg separately. The torque recorded is one-dimensional, and it corresponds to the component which is perpendicular to the crank arm and contributes to the cycling motion. Thus, the only possible optimization method is to maximize that component. Recording three-dimensional torque allows for optimization techniques that would, in addition, try to minimize the power lost in forces exerted onto the pedals that do not contribute to the cycling motion.In order to optimize FES-cycling movements and protocols, we developed a novel instrumented cycling ergometer platform (ICEP) designed to evaluate the effectiveness of various FES-cycling strategies. The platform is adaptable to different reclined cycling positions and is outfitted with highly sensitive force sensors to directly measure the effects of different FES-cycling parameters. In addition, subjects can also be tested while seated in their wheelchair so a transfer is not required.The purpose of the present article is to describe and assess the ICEP. Furthermore, the capabilities of the ICEP are demonstrated through the example of determining and optimizing stimulation patterns. The platform described in this work can be easily reproduced and will hopefully motivate future in-depth specific studies to further progress the number of applications and designs of new FES-cycling devices.The platform consists of a modified bicycle frame fitted with pedal force/torque sensors, a crank encoder and a motor . The fraThe actuator system, consisting of a brushless motor  associated with a planetary 53:1 ratio gear-head , can produce a maximum torque of 228 Nm. It is connected to the crankset through a pulley and belt system . The motor rotational speed is controlled by a servo controller, and the power is supplied through a shunt regulator . It is set up to assist the cyclist with producing the cycling movement while maintaining a constant cycling cadence, which can be set from within a custom-made LabVIEW  graphical interface, with values ranging from 1 rpm to 100 rpm.Each pedal independently measures all three components of the force and torque applied to their surface, as well as the inclination angle of the pedal in reference to the crank arm . Force values up to 2.8 kN can be measured while the inclination angle is measured with a resolution of 0.072°. A magnetic ring encoder  placed around the spindle of the crankset acquires the crank angle with a resolution of 0.06°. Data are acquired at a 1 kHz sampling rate and displayed in real time, as well as recorded in a text file for later analysis.Leg orthoses  were modified to attach the legs to the force-measuring pedals. To ensure that there are zero degrees of movement between the leg orthosis and the pedal, custom connecting metal plates were manufactured  and attaA current-controlled electrical stimulator  is synchronized with the force measuring pedals through the custom-made LabVIEW graphical interface. This 8-channel stimulator produces asymmetrical biphasic pulses with exponential compensation . It can A data acquisition card  completes the platform and collects the data from the crank encoder, allowing for the synchronization of the stimulation with the pedaling cadence, as well as triggering the recording of the force measuring pedals, and setting up the motor cadence and stimulation parameters. Both the motor and the stimulator have an emergency stop button that disconnects them from the power supply.The force-measuring pedals are factory-calibrated by the manufacturer, while the crank angle and pedal inclination encoders are calibrated before starting each new trial. A crank angle of 0° is achieved when the left crank arm is in the forward position and parallel to the ground. Motor rotational speed control was verified for cycling cadences ranging from 10 rpm to 50 rpm in steps of 10 rpm.In FES cycling, a stimulation pattern is a set of crank angle intervals defined for when each muscle group should to be stimulated, in order to reproduce a functional cycling movement. Determining these suitable stimulation intervals can be a tedious process as it will vary according to the pilot’s physical condition, morphology, seating position and the number of muscle groups used; moreover, it has to be optimized in relation to the type of exercise  in order to achieve the best compromise between power and fatigue. As a result, determining and optimizing stimulation patterns served as an appropriate application for demonstrating the capabilities of the cycling platform.In the following parts, we will describe two different methods for determining FES-cycling stimulation patterns: from EMG measurements on an able-bodied subject and from direct measurements of the forces produced by each SCI subject’s muscle group during a crank revolution.A straightforward procedure for reproducing an FES-induced cycling movement is to measure the activation timings of an able-bodied subject’s muscle groups during cycling, through EMG recordings, then to apply these timings to the stimulation of the muscle groups of a paralyzed subject in order to try producing a similar motion ,24.One able-bodied adult male (26 years old) subject was chosen on the account of him having a similar height (185 cm) and leg dimensions  to the SCI subject participating in the second part of the study. Similar leg dimensions are important for achieving the same cycling position, with the same basin versus pedalboard geometrical configuration.EMG activities of five main muscle groups used in cycling  were acquired on the able-bodied subject, using a 6-channel EMG recorder . The electrodes were placed on shaved and cleaned skin, between 1.5 and 2 cm apart, parallel to the muscle fibers, in accordance with the surface electromyography for the non-invasive assessment of muscles (SENIAM) project guidelines .The recordings were performed on the subject’s dominant leg, during constant-cadence motor-assisted cycling. The subject cycled seated in the Carbontrike, legs attached to the force-measuring pedals using leg orthoses, at a cadence of 50 rpm.The EMG recordings were processed and analyzed in Matlab . The raw signals were filtered with a  4th order band-pass Butterworth filter. The processed EMG signals were normalized for each revolution and subsequently averaged. The resulting signals were plotted against the crank angles on a 360° plot . They reAn obvious limitation of using an able-bodied cyclist’s EMG recordings to set up a paralyzed pilot’s FES-cycling pattern is that FES only allows for the stimulation of a limited number of muscles that are close to the skin’s surface, whereas volitional cycling also engages deep muscles, such as the iliopsoas muscle, that cannot be reached using non-invasive electrical stimulation. Therefore, the optimal activation timings of a limited number of surface muscles, in order to achieve an effective cycling movement, might substantially differ from the activation timings measured on an able-bodied subject, who would use those surface muscles in combination with additional muscles that remain out of the reach of FES.In order to take this limitation into account, a straightforward procedure is to record the tangential force . By comparing the forces produced during active (stimulation-induced) and passive (motor-assisted) cycling over a complete revolution, we can evaluate the individual contributions of each single muscle group. The difference between active and passive cycling over one revolution  will be called the muscle’s force profile (MFP)  and usedA positive value of the MFP indicates that the stimulated muscle contributes to cycling in that specific angular range; while a negative value of the force profile indicates an angular range where the stimulated muscle is hindering the cycling motion.To derive a stimulation pattern from the EMG recording from Based on In order to allow for a fair comparison of the measured power output with the EMG pattern, start and stop angles were chosen so as to have the same angular length as the EMG pattern (and therefore generate the same amount of muscle fatigue) and to maximize the area below the force profile. The resulting pattern will hereafter be referred to as the MFP pattern. Both EMG and MFP patterns are displayed in Regardless of the method chosen to determine the stimulation pattern, various delays must be considered. The delays are a product of the stimulator (1), the measuring equipment (2) and the muscles themselves (3). Estimating or measuring them will allow for compensating for them.S) is the internal stimulator delay and represents the time from the moment when the stimulator receives the command to generate a pulse, to the moment the generated pulse arrives to the electrode placed on the skin.The stimulator delay , is defined as the time it takes for the muscle to develop tension once the stimulation pulse reaches the motor nerve. Muscle delay is usually derived from literature, but it can also be measured.When recording passive and active profiles in order to measure the MFP, the muscle groups of interest are continuously stimulated. Thus, they are not affected by either of these delays. The delays should be compensated for only when the muscle stimulation follows a specific intermittent pattern.S is the stimulator delay [s], EMD is the muscle activation delay [s] and ω is the cycling cadence [rpm].To ensure that the muscles are activated at the correct position, the angular ranges of the stimulation patterns have to be shifted. To compensate for the stimulator delay, both start and stop angles must be shifted by the same amount. To compensate for the EMD, only the start angle has to be shifted. The required angular shifts depend on the cycling cadence and can be calculated using the following equations:Angular shifts, and therefore total delay, can also be directly measured by comparing the angle where the stimulation of the muscle begins and the angle where the muscle actually produces a noticeable change in force exerted on the pedals. In One adult male (46 years old) with a motor-complete SCI  Impairment Scale (AIS) B) participated in the present case study. The injury occurred 11 years prior to the study. The subject is 184 cm tall, with 50 cm calf and 50 cm thigh lengths. The subject is experienced with FES cycling as he competed in the 2016 and 2020 editions of Cybathlon’s FES-cycling races. He was asked to refrain from exercising at least for 24 h before the experiment as he was involved in the FES-cycling training program at the time of the study.The medical device used (Motimove 8) was operated strictly following its intended use. As such, the present study does not require the approval of an ethical committee according to French regulations. All procedures followed the usual practices and guidelines regarding rehabilitation of motor function in adult SCI patients, and the subjects gave their written informed consent for study participation.determining the force profiles for each muscle of interest;measuring the total delay;cycling using the EMG pattern;cycling with the MFP pattern.The experiment was conducted in one session. The session began with a two-minute passive cycling warm-up where the cycling cadence was gradually increased from 10 to 50 rpm. It was followed by four electro-stimulated phases respectively dedicated to:Each of these four phases began with 5 to 10 passive cycles, followed by 2 active cycles and ended with a 5 min period of rest.The subject was seated on the Carbontrike in a comfortable position with the legs secured to the ergometer. The trike was placed at the same distance from the pedals as for the EMG test with the able-bodied subject. Using one stimulation channel per leg, pulses were delivered through 9 × 5 cm electrodes  located over the motor points of the quadriceps muscle groups. As the subject has issues with stimulating hamstring muscles, this muscle group was not used. The stimulation frequency was set to 40 Hz, the pulse width to 350 µs and the pulse amplitude to 70 mA. Stimulation parameters were chosen based on the prior experience with FES cycling of the subject, who usually trains 2 to 3 times a week, one-hour sessions on either RT300  or Motomed .After the initial warm-up, the measuring began with obtaining the force profiles. As a compromise between the number of samples acquired and the muscle fatigue produced by the stimulation, the cadence was set to 30 rpm during the first phase. Throughout the other phases of the protocol, the cadence was set to 50 rpm. Following the rest period, the second phase of the protocol was carried out. During the break, recorded data were processed, and the MFP was analyzed using a custom-made Python script. The angular shift was measured to compensate for the delay, and the MFP pattern was set up. During the third and the fourth phases of the protocol, EMG and MFP patterns were respectively used.EMG) and with the MFP pattern (PMFP).The net-forces were calculated from the recorded cycling data. Angular velocity together with the net-forces were used to calculate the mean power produced during one cycle by muscles stimulated with the EMG pattern  was 14% greater than the mean power produced by the EMG pattern (PEMG = 8.8 W).The calculated net-forces produced by the quadricep muscles stimulated with the EMG pattern are shown in We built a wall-mounted instrumented cycling ergometer, designed to facilitate the assessment of advanced FES-cycling strategies. The motor cadence control accuracy was measured. As an example of the platform’s capabilities, we demonstrated how to determine delay-compensated FES-cycling patterns following two different methods and how to compare their efficiencies.In order to be able to make a fair comparison between EMG and MFP patterns, we determined the latter so as to generate the same amount of muscular fatigue as the first. This means that after determining the EMG pattern, the MFP pattern was determined by giving it the same angular range while maximizing the total amount of force produced. However, since the angular stimulation range of the EMG pattern was very wide , there was little room for variation, and as a consequence, the variation of the power produced when shifting the pattern was limited. Despite being ceiled, the increase in power was still substantial, which is consistent with the results of the previous study . AlthougRegardless of the EMG pattern, in order to determine how to optimize the MFP pattern, we need to understand for what type of exercise this pattern is intended. It can be optimized for maximum power production, in which case it would also induce an early onset and rise of fatigue. In that case, the start angle would be set at the first zero transition before the maximum, and the stop angle at the first zero transition after the maximum, which we would call the “full-range” MFP pattern.However, if the pilot needs to exercise for a substantially longer period of time, a compromise is needed between force and fatigue. In that case, using the full-range MFP pattern is most likely sub-optimal. A threshold would need to be defined as a percentage of the maximum force to be exceeded in order to trigger the stimulation. Optimizing the value of that threshold and quantifying the efficiency of the resulting patterns is typically the type of investigation that this platform facilitates.When measuring the angular shift with the fresh SCI subject, we found a 16° value which, at the cadence of 50 rpm, represents a total delay of 53.3 ms. Considering that the stimulator delay is constant (3.2 ms), we can deduce that the EMD equals 50.1 ms, which is in concordance with . HoweverOne limitation of the present study is that only the quadricep muscles were used for the SCI subject. The latter is a trained FES cyclist that has been using only quadricep muscles and has never trained his gluteal or hamstring muscles. As a consequence, we were not able to get repeatable measurements from these muscles, probably because they were too weak, and possibly spastic. They would need to be progressively trained with TENS prior to FES.The process of determining the stimulation patterns for additional muscle groups remains identical. However, combining the effects of multiple muscle groups might also introduce uncontrolled muscle synergies , which sFES strategies that are currently being investigated using the platform include variable-frequency trains and spatially distributed sequential stimulation (SDSS). In order to extend its capabilities, the platform is being continuously improved. For instance, although it was originally designed for FES cycling, the addition of a new motor position control system will allow for its use in isometric studies. A more powerful motor unit could also permit volitional cycling with able-bodied subjects producing higher torques.An instrumented cycling ergometer platform for the assessment of advanced FES-cycling strategies was designed and presented in this work. The capabilities of the platform were demonstrated by determining stimulation patterns for the stimulation of paralyzed quadricep muscles. The description of the platform provided in the present article will hopefully enable other research groups to replicate and improve upon this work and, thus, further contribute to the advancement of the assessment of novel stimulation strategies.


This work explores the utilization of plasmonic resonance (PR) in silver nanowires to enhance the performance of organic solar cells. We investigate the simultaneous effect of localized surface plasmon resonance (LSPR), surface plasmon polariton (SPP), and waveguide plasmonic mode on silver nanowires, which have not been thoroughly explored before. By employing finite-difference time-domain (FDTD) simulations, we analyze the plasmonic resonance behavior of a ZnO/Silver nanowires/ZnO (ZAZ) electrode structure. Our investigations demonstrate the dominance of LSPR, leading to intense electric fields inside the nanowire and their propagation into the surrounding medium. Additionally, we observe the synergistic effects of SPP and waveguide plasmonic mode, contributing to enhanced light absorption within the active layer of the organic solar cell. This leads to an improvement in photovoltaic performance, as demonstrated by our previous work, showing an approximate 20% increase in photocurrent and overall power conversion efficiency of the organic solar cell. The incorporation of metallic nanostructures exhibiting these multiple plasmonic modes opens up new opportunities for improving light absorption and overall device efficiency. Our study highlights the potential of these combined plasmonic effects for the design and optimization of organic solar cells. The interaction of light with certain nanoscale conductive materials can induce a well-known phenomenon in the literature, referred to as plasmonic resonance (PR). At a specific wavelength for each material with enough available electrons, an electric field is created due to the oscillation of conduction electrons around the atoms of the material. These electron oscillations are called surface plasmons, and the nanomaterials that support surface plasmons are referred to as plasmonic materials ,2,3. Thi−4 cm2·V−1·s−1) and the short diffusion length in most organic semiconductor materials [In organic photovoltaic (OPV) devices, the relatively low mobility of charge carriers Qz,λ=Q represents the absorption as a function of the position (z) within the device stack, wavelength (λ), α(λ) denotes the absorption coefficient, in and n0 are the refractive indexes of the i layer and the surrounding medium, and E(z) and E0 represent the electric fields at position z and the incident electric field, respectively.Here, This equation establishes a direct relationship between the absorption of the active layer and the electric field resulting from the surface plasmon resonance. However, it should be noted that the propagation of this electric field is limited in terms of distance, as further discussed in this investigation. By enhancing absorption, the generation of electrons can be improved, consequently enhancing the external quantum efficiency. Alternatively, achieving similar absorption with a thinner active layer can mitigate the challenges associated with charge diffusion length commonly observed in organic solar cells. Furthermore, this effect can be exploited in organic solar cells with a thick active layer for better efficiency .Far-field scattering results in the optical path of incident light being lengthened, which can enhance photon absorption. The size of the metal nanoparticles that best matches the far-field scattering effect is generally greater than 30 nm .For plasmonic nanostructures embedded in layers at the interface of transparent electrodes  in conventional-type solar cells or ETL (electron transport layer) in inverted-type cells), forward scattering is required. The geometry and interface of plasmonic nanostructures can be optimized to minimize surface reflection. In addition, the optical paths of incident sunlight in the absorbing medium and their interaction time are thus increased, resulting in improved absorption efficiency of the active layer .The direction of scattering can be adjusted by controlling the size and geometry of the plasmonic nanostructures. Starting with nanoparticles around 50 nm in diameter, photons are scattered forwards and backwards in comparable quantities . As partNanoparticles (NPs) whose size is below the above-mentioned intermediate range exhibit low scattering, which induces insufficient optical absorption in the active layer linked to this component. In addition, the conductivity of the device is negatively affected as more charge-trapping sites are formed at the interfaces of the NPs due to their large surface-to-volume ratio. For plasmonic nanostructures integrated outside the active layer, these losses cancel out the possible advantages of small NPs , which can accentuate the coupling of the plasmonic field close to the active layer .There are four modes of plasmonic resonance , which cLocalized Surface Plasmon Resonance (LSPR)When a surface plasmon is confined to a NP of a size smaller than the wavelength of the incident light, the free electrons of the NP participate in the collective oscillation, which is called localized surface plasmon resonance LSPR, a. The LSNPs smaller than 30 nm act as sub-wavelength antennas during LSPR excitation. In such cases, the absorption enhancement comes mainly from the LSPR effect, rather than the scattering effect . The neaPlasmonic cavity modeWhen specific metal–dielectric configurations are built, the spectral wavelength ranges for absorption enhancement can be extended further due to plasmonic coupling modes. For example, a metal–dielectric–metal (MDM) structure is obtained when the active layer is sandwiched between the metal electrode and the metal NP layer. By appropriately selecting NP geometries, surface plasmon stationary waves can be generated due to constructive interference in the finite cavity, reducing light leakage from surface plasmon generation in the lateral gaps between NPs. Thus, the plasmon cavity mode is excited in the MDM and a strong electromagnetic field is confined to the light-absorbing layer. Interestingly, the field enhancement from the plasmon cavity mode b is indeSurface plasmon polariton (SPP)Unlike LSPR, surface plasmon polariton  often oThe photonic waveguide modeIn addition to the SPP mode, a further mode type can be excited at planar metal–dielectric interfaces during incident radiation, which also contributes to absorption enhancement. It is called the “waveguide mode” because of its similarity to the propagation model in dielectric waveguides. Along its lateral propagation, part of the waveguide mode can be absorbed by organic semiconductors, in which excitons are generated ,36.Excitation of the waveguide mode is independent of the polarization of the incident irradiation. This means that waveguide modes can be generated irrespective of whether the polarization direction of the excitation is parallel or orthogonal to the directions of the metal nanostructures .Given the architecture of the device and the structure of the metal nanostructures to be used, some modes will be much more favorable than others. In our case, we are using metal nanowires that have a cylindrical shape with a diameter of 35 nm and a length of 25 µm based on our previous investigation showing an experimental increase in the efficiency of an organic solar cell despite its thick active layer . Later iIn this work, we will first explore the concept of plasmonic resonance, followed by the study of plasmonic resonance in silver nanowires using finite-difference time-domain (FDTD) simulation software, in which a ZnO/AgNWs/ZnO (ZAZ) electrode model will be constructed with the different materials used. We will observe the spatial distribution of the electric field as a function of wavelength and the type of plasmonic resonance.2). The optical indexes used to model ZnO and silver nanowires (AgNWs) were taken from references [2 is characterized by an almost constant real optical index equal to 1.46 and 0 imaginary part in the visible spectrum [The ZAZ electrode was modeled according to the structure described in ferences ,39, respspectrum . All of z-axis, periodic along the x-axis, and Bloch along the y-axis. The spatial mesh size is 0.25 nm, minimum, and the time mesh size is 3.36 × 10−18 s. The surrounding medium is air, and the illumination source consists of two polychromatic plane waves polarized at 90° to each other, with the aim being to obtain unpolarized illumination. Various monitors were introduced into the simulation to observe the transmission and spatial distribution of the electric field around the AgNWs.All of our simulations are performed in three dimensions. The simulation area is delimited by PML (perfect matched layer) boundary conditions along the In this section, we investigate plasmon resonance around a single silver nanowire in order to observe the behavior of the electric field as a function of the wavelength. The diameter of the silver nanowire is 35 nm, which corresponds approximately to the diameter of the AgNWs used experimentally . The lowRegarding the small absorption peak observed near 575 nm, it is important to note that this peak is a result of a numerical artifact related to the fit of the refractive index of the silver used in the electrode. It does not significantly affect the overall performance or application of the electrode. The main absorption peak of ZAZ, which is located at approximately 350 nm, is the primary focus for extending the absorption spectrum and enhancing the performance of organic solar cells, as mentioned in our previous work .The LSPR is the privileged plasmonic resonance mode in this configuration. A multi-wavelengths investigation  represenAt 347 nm, corresponding to the AgNW absorption peak, a significant portion of the electric field remains confined within the AgNW, with a high concentration at the AgNW/ZnO interface, as mentioned in the paragraph above. Absorption inside the nanowires is limited after 387 nm, which makes it possible for most of the light to be absorbed. Radiation is almost uniform around the AgNW, with a low intensity but higher than those observed before the absorption wavelength. There is a strong localization of the field, which means a high proportion of plasmonic resonance.2·m−2). The electric field distribution changes shape as a function of wavelength. This is due to the interaction of light with silver being strongly related to wavelength. For wavelengths between 347 and 387 nm, the field distribution is almost uniform around the AgNWs. However, for wavelengths above 387 nm, we note an increasingly localized distribution towards the lower section of the AgNW. High-intensity hotspots at the AgNW/ZnO interface reflect very intense local confinement of the electric field at certain wavelengths.Beyond 347 nm, we see a significant increase in the electric field up to 608 nm from the majority of lobes due to scattering. At 416 nm, we find the maximum electric field intensity  are also present for several AgNWs through the undulation of the electric field along the wires. For example, in In The electric field transmission mode difference between horizontally and vertically placed AgNWs on the longitudinal cross-section arises from the interplay of two key factors: the polarization of the incident light wave and the interference of electric fields originating from different AgNWs. The orientation of the AgNW relative to the polarization direction of the incident light wave and the constructive or destructive interference between electric fields at the intersections of multiple AgNWs contributes to the observed variations in the electric field distribution.The simultaneous existence of these different modes of plasmon propagation is very interesting for organic solar cells, as it would allow us to increase their absorption without increasing the thickness of the active layer.In this work, we discussed the concept of plasmon resonance. There are four main modes: LSPR, SPP, waveguide, and photonic cavity. These modes can be classified as propagative and non-propagative. SPP and waveguide are classified as propagative modes, while LSPR and photonic cavity are classified as non-propagative modes. Considering the ZAZ electrode configuration, the photonic cavity mode cannot be excited due to the geometry of the AgNWs used.To observe the electric field distribution resulting from plasmon resonance, we used the FDTD method. This enabled us to visualize the spatial distribution of the electric field across and along the cross-section of a AgNW. Excitation of the LSPR mode is evident, with significant confinement of the electric field around the cross-section of the AgNW and mainly located outside the ZnO layer. The latter functions as the role of a spacer. The distribution of the electric field along the AgNWs revealed the presence of different waves at certain wavelengths. We hypothesized that a superposition of the SPP and waveguide modes is the cause of the electric field fluctuations observed at certain wavelengths.All of these mechanisms related to plasmon resonance are of major benefit for integration into organic solar cells to enhance their photovoltaic performance.


The objective of this study is to investigate the behavior of the Bayesian exponentially weighted moving average (EWMA) control chart in the presence of measurement error (ME). It explores the impact of different ranked set sampling designs and loss functions on the performance of the control chart when ME is present. The analysis incorporates a covariate model, multiple measurement methods, and a conjugate prior to account for ME. The performance evaluation of the proposed Bayesian EWMA control chart with ME includes metrics such as average run length and standard deviation of run lengths. The findings, obtained through Monte Carlo simulation and real data application, indicated that ME significantly affects the performance of the Bayesian EWMA control chart when RSS schemes are employed. Particularly noteworthy is the superior performance of the median RSS scheme compared to the other two schemes in the presence of ME. The CCs discussed in this context have a recognized capability to identify notable changes in the production process. The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) CCs, initially introduced by Page2 and Roberts3, are widely acknowledged as examples of memory-type CCs. This is because they make use of both current and historical sample data in their calculations. The CUSUM and EWMA CCs exhibit greater sensitivity in identifying small and moderate shifts in process parameters when compared to the classical Shewhart CC. These memory-type CCs, specifically EWMA and CUSUM, hold significant value in chemical and industrial production processes. Al-Omari and Bouza4 presents a literature review on RSS, a sampling method proposed as an efficient alternative to SRS for estimating population mean. The review covers different modifications of RSS and its wide range of applications. Ali et al.5 proposes a new non-parametric CC for monitoring manufacturing processes using sign statistics and RSS. Through simulation and comparison with existing CCs, it demonstrates robustness and improved detection of process shifts, validated by a practical application in substrate manufacturing. Abbas et al.6 suggested nonparametric CC for monitoring manufacturing processes, using the Wilcoxon signed rank test and RSS. The CC outperforms existing methods in detecting shifts in process location. Ali et al.7 studied nonparametric CC utilizing sign statistic and RSS for monitoring non-normal manufacturing processes. It effectively detects small and persistent shifts in process location, outperforming other alternatives, and is demonstrated using real-world data on piston ring diameter. This is primarily due to their enhanced ability to identify and promptly respond to minor to moderate disturbances, which often carry significant consequences. However, measurements of the variables required for construction of the CCs affect the efficiency of these charts during the process control, if not correctly measured.Quality product is the ultimate satisfaction of the customer, which leads to an increase in the profitability of the producer. ISO-9000 certification not only leads the producers to produce high quality goods but also compels them to enhance the product quality to remain in the main steam of their business. Therefore, quality control techniques are the basic requirement to maintain quality standards during production and to save the raw material losses due to defective production. The statistical process control (SPC) provides techniques to perceive variations in the production processes prior to produce defective goods. Control charts (CCs) are valuable tools in SPC that enable quality engineers to efficiently monitor and enhance product quality. Shewhart8 investigates the impact of ME, specifically gauge imprecision, on the effectiveness of Shewhart-type X embodies the true value of the study variable, Y represents the observed value during the measurement process. Stemann and Weihs9 conducted a comprehensive study exploring the use of the EWMA 10 performed an analysis on the effectiveness of the 11 investigated the influence of ME on multivariate CCs. Maravelakis et al.12 suggested the application of the EWMA CC in the presence of ME, incorporating a model with linear covariates. Additionally, they investigated the implications of multiple measurements and a linearly increasing variance. Afterwards many authors studied the impact of ME on the efficiency of the CCs during industrial production e.g., Huwang and Hung13, Wu14, Hu et al.16, Sabahno and Amiri 17, Riaz et al.18, Javaid et al.19, Noor-ul-Amin et al.21 etc. Imran et al.22 examined the influence of ME on multivariate CUSUM CCs for compositional data (CoDa). ME had a significant impact on the CCs, particularly due to the error variance–covariance matrix. Subgroup size and the powering operator enhanced the CCs by reducing ARL. Conversely, an increase in the number of variables had an adverse effect, leading to higher ARL values. Real-world examples illustrated the practical application of these CCs in uncoated aspirin tablet manufacturing and muesli production machine monitoring. The researchers employed various techniques, including the covariate method, multiple measurements of the same sampled variable of interest, and the linearly increasing variance method. These techniques were used to compare the performance of CCs in the presence and absence of ME. The study’s conclusion emphasized that ME has a significant influence on the effectiveness of the CCs.The performance of the CCs is affected when measurement error (ME) creeps in during measurements of collected data regarding study variable(s) from sample chosen for construction of the CCs. Sometimes, the variation arises due to ME because of the deviation from actual measurement of the study variable which causes quality disturbances and undesired results. Consequently, the detection power of the CCs to find out-of-control signals is affected due to inaccurate measurements of the variables under study. To tackle the challenge of ME, researchers have introduced various methods for CCs. Mittag and StemannP) distribution to seamlessly integrate sample information with prior knowledge. Menzefricke23 introduced a CC for the location parameter of a process by employing Bayesian theory. Within the Bayesian framework, the utilization of a LF serves the purpose of mitigating risks linked with the estimator, ultimately aiming to achieve the optimal Bayes estimator. In a study by Wu and Tian24, the CUSUM CC was recommended for monitoring both the process mean and variance, considering the weighted LF of the production process. Menzefricke25 conducted a study on variance CCs using the distribution applying Bayesian methodology. Additionally, Serel26 recommended a Bayesian-EWMA CC for both the process mean and variance, employing different LF techniques. Noor et al.27 investigates the application of Bayesian theory in control charting, incorporating symmetric and asymmetric LFs with informative and non-informative priors to create a hybrid EWMA (HEWMA) CC. The effectiveness of the offered chart is assessed using ARL and SERL measures, with simulations and a real data example provided. A novel adaptive EWMA (AEWMA) CC that integrates the Shewhart chart and EWMA chart to detect both large and small/moderate shifts in process mean suggested by Noor-ul-Amin and Noor28. The AEWMA chart is implemented using Bayesian theory, considering various LFs, informative priors, and performance measures like ARL and SDRL. A comparative study compares the suggested AEWMA chart with existing Bayesian EWMA charts, supported by a real-data example and a Monte Carlo simulation study for assessment. Noor et al.29 introduced a EWMA CC based on the Bayesian approach that incorporated diverse LFs, demonstrating the efficacy of their proposed approach.CCs typically rely on the classical approach, which considers only sample information and disregards prior knowledge. In contrast, the Bayesian analysis utilizes the posterior  of a uniform distribution is typically expressed as When there is insufficient information about a parameter in the prior distribution, it is known as a non-informative prior. In such cases, the prior has minimal impact on the The P distribution, characterized by parameter Y, the PP distribution is derived by treating the P distribution as a prior distribution. This method enables us to integrate the information gleaned from the observed data and revise our predictions for the new data point. By employing the P distribution as a prior, we take into account the uncertainty associated with parameter estimation, resulting in a distribution that captures our refined understanding. Essentially, the PP distribution combines the existing data with the P distribution to furnish an informed prediction for the new data point Y. which is mathematized asWhen we encounter a new data point In the Bayesian theory framework, LFs play a crucial part in curtailing the risk connected with the Bayes estimator. This study aims to explore the utilization of two specific types of LFs, namely symmetric and asymmetric, to address the research objectives at hand.30 conducted a study on SELF as a symmetric LF, in which the study variable X and Gauss31, which efficiently estimates the population parameter while mitigating the risks linked with the Bayes estimator. Mathematically, the LLF can be described as follows:The LLF is an asymmetric LF proposed by Varian32 initially introduced the concept of the RSS, which holds particular significance in cases where accurately measuring the study variable poses challenges. The estimator based on the RSS scheme is recognized for its superior efficiency when compared to simple random sampling (SRS). RSS combines the benefits of SRS using the additional sources of information, including auxiliary information, personal judgment, or expert knowledge. The comprehensive methodology for sample selection using the RSS scheme is elaborated upon within this context.MclntyreStep 1 To implement the RSS scheme, the initial step involves identifying the m sets of equal size, and all the units within the m sets are arranged in ascending order.Step 2 Once the units have been ranked, the selection process commences by choosing the first unit from the first set, the second unit from the second set, and so on, until the last unit is selected from the last set. This cycle of selecting units completes one iteration of the RSS with a size of m.r times to achieve the anticipated sample size of n = mr. This repetition ensures that the sample size reaches the intended value.If required, the above steps can be repetitive The mathematical description of the mean estimator based on the RSS scheme is as follows:33 proposed the MRSS scheme as an altered rendition of RSS, with the objective of improving the estimation of the population mean. The succeeding two steps offers a comprehensive impression of the sample selection methodology utilized in MRSS:MuttalkStep 1 Following a similar approach to RSS, the MRSS scheme involves identifying m2 units from the population under study. These units are subsequently allocated into m sets, each comprising m units of equal size. The units within each set are organized in ascending order.Step 2 After the ranking process is complete, if the sample size (represented as m) is an odd number, select the unit located at the m. To acquire an MRSS sample with a size of n = mr, the aforementioned steps can be repeated r times.Applying MRSS, the mean estimator with single cycle, for an odd sample is expressed as follows:In the MRSS design, if the sample size is even, the population mean estimator for single cycle can be expressed as:34. This modification is particularly beneficial when gathering a collection of units becomes more challenging than selecting extreme units alone. The authors provided a comprehensive explanation of the entire process involved in selecting an ERSS sample.A modified version of Ranked Set Sampling (RSS), known as the Extreme RSS (ERSS) design, was introduced by Samawi et al. Step 1 By randomly selecting m2 elements from the target population and distributing them into m sets, each of the same size, we ensure that the elements within each set are representative of the variable under consideration.Step 2 In the ERSS process, after ranking the units, the selection of extreme units depends on the sample size. If the sample size is even, the smallest unit from the first However, when the sample size is odd, the ERSS scheme involves selecting the smallest unit from the first n = mr observations. When dealing with a uniform sample size in a single cycle, the mathematical representation for calculating the mean estimator of ERSS can be expressed as follows:If deemed necessary, the above-mentioned two steps can be iterated r times to acquire an ERSS sample consisting of For odd sample size, the estimator of ERSS in case of with one cycle is defined asMeasurement error refers to the variation between the observed value and the true value of a specific measurement. It is characterized by a constant magnitude that remains consistent across different observations. In this study, the covariate model has been employed to address ME. Additionally, to minimize the impact of ME, the multiple measurements technique has been utilized. This technique involves taking multiple measurements for each observation, allowing for a more precise estimation of the true underlying value.35. The model is defined as follows:The inspiration of ME on the Shewhart CC is examined by employing the model proposed by BennettX follows a normal distribution with a mean of 10 conducted further investigation on the covariate model, which is defined as follows:The covariate model assumes that the variable under study Y. Y is assumed to follow a normal distribution with a mean of Aθ + B and a variance of i.e.Y can be defined as follows:Assuming the known parameters involved in the model and the independence of X and Let 10 proposed a method, also adopted by Maravelakis et al.12 and Abbasi36 that is useful in minimaxing ME by taking multiple measurements instead of a single measurement per sampling unit. If the number of repeated measurements increases indefinitely, the variability of ME component tends to decrease towards zero. However, it should be noted that by increasing the number of measurements, the additional cost and time will be added at each additional measurement and these two factors cannot be ignored by the quality expert. Maravelakis et al.12 investigated how multiple measurements impact the effectiveness of the EWMA CC. They derived the plotting statistic specifically for the EWMA CC with multiple measurements as follows:Linna and Woodallt, the control limits for the EWMA CC with multiple measurements can be described as follows:k is the number of measurements taken for the same sampling unit.Assuming In this section, we explore the utilization of various LFs within RSS schemes for the Bayesian-EWMA CC. The resulting P distribution, obtained through the implementation of a conjugate prior , is presented as follows:The suggested statistic for the EWMA CC based on Bayesian analysis under different RSS strategies is written as:The Bayes estimator utilizing Bayesian-EWMA CC, considering various RSS schemes under the SELF for P distribution, is as follows:P distribution, are given by:The asymptotic control limits for the EWMA CC, taking into account various RSS strategies under the assumption of SELF for the P distribution, is as follows:P distribution with the multiple measurement’s method, are mathematized as follows:The estimator for the EWMA CC using Bayesian methodology, considering distinct RSS strategies under the SELF for The Appendix Tables A = 0 and B = 1. Additionally, the table presents results for different values of Tables λ = 0.25. For example, at Another aspect of these tables can also be elaborated that ARL values of the Bayesian MRSS technique are smaller than the RSS and ERSS techniques for all the tables for any shift which indicates that the MRSS technique is efficient as compared with other two techniques of ranked set sampling and it performs better under the ME problem. It is also clearly seen from above mentioned values of Table When we compare the Tables mentclass2pt{minimThe EWMA CCs are efficient in detection of moderate to minor process shifts as shown from ARL and SDRL values in all the six tables for proposed charts.That ME has negative effect on the efficiency of the recommended CCs which is also discussed above.The MRSS performs better than other two i.e., RSS and ERSS even during the problem of ME for detection of process shifts earlier. The same is clear from all the ARL values shown in the tables constructed for proposed CCs.The multiple measurements reduce the error effect as is clear from ARL values of Tables Based on the analysis of P and PP distributions in the Bayesian framework, it can be observed that the offered Bayesian EWMA CC in the existence ME, implemented under the MRSS scheme, demonstrates reduced sensitivity to ME compared to other RSS designs. These observations are derived from the utilization of informative priors and the consideration of both LFs.On the basis of above discussion, we can devise main findings here.37 in the context of the hard-bake process in semiconductor production. The dataset consists of 45 samples, where each sample consists of 5 wafers, resulting in a total of 225 data points. The measurements of the flow width are recorded in microns, with a fixed time interval of one hour between each sample. The first 30 samples, comprising 150 observations, are classified as the under-control process (referred to as the phase-I dataset). Conversely, the remaining 15 samples, totaling 75 observations, are considered the out-of-control process (referred to as the phase-II dataset).In this article, we showcase the application of the proposed Bayesian-EWMA CC with ME using data obtained from Montgomery To implement the proposed Bayesian-EWMA CC under covariate model utilizing RSS strategies with SELF, we consider various values of the error ratio mentclass2pt{minimFigures This article examines the impact of ME on the EWMA CC utilizing Bayesian methodologies when utilizing distinct RSS designs applying LFs, specifically SELF and LLF. The effectiveness of the suggested CC with ME is assessed through the evaluation of the ARL and SDRL. The ARL values provide insights into the simulation results of Bayesian-EWMA CCs using RSS schemes for both the covariate method and multiple measurements. Our findings indicate that the proposed Bayesian-EWMA CC, implemented with the MRSS scheme, demonstrates improved efficiency compared to other RSS schemes in the presence of ME. Based on these results, we recommend employing the Bayesian-EWMA-MRSS CC for effective monitoring of process mean shifts in the presence of ME.When faced with a large sample size, computing the Bayesian EWMA CC with ME under RSS strategies can be complex. The Bayesian updating process entails calculating the distribution for both the process mean and variance at each sample point, which can be time-consuming and demanding in terms of resources. Additionally, the Bayesian approach necessitates the careful specification of prior distributions for the process mean and variance. If these priors are not chosen with care, they can negatively impact the performance of the CC. Furthermore, selecting appropriate prior distributions often involves subjectivity and relies on expert knowledge, introducing the potential for bias in the analysis.The Bayesian EWMA CC with ME and RSS designs has the potential for broader application beyond its original context. It can serve as a foundation for developing other CCs that incorporate memory. Additionally, this approach shows promise in accommodating distributions beyond the normal distribution. For instance, it can be adapted to handle data that follows a Binomial or Poisson distribution. In such cases, adjustments to the likelihood function used in Bayesian updating may be necessary. Expanding the proposed approach to encompass a variety of CCs and non-normal distributions presents an opportunity to enhance the efficiency and effectiveness of quality control processes in various industries, including finance, healthcare, and production.Supplementary Information.


Drawing the clothing plan is an essential part of the clothing industry. However, the irregular shape of clothing, strong deformability and sensitivity to light make the fast and accurate realization of clothing image retrieval a very challenging problem. The successful application of the Transformer in image recognition shows the application potential of the Transformer in the image field. This article proposes an efficient and improved clothing plan based on ResNet-50. Firstly, in the feature extraction section, the ResNet-50 network structure embedded in the Transformer module is used to improve the network’s receptive field range and feature extraction ability. Secondly, dense jump connections are added to the ResNet-50 upsampling process, making full use of feature extraction information at each stage, further improving the quality of the generated image. The network consists of three steps: the sketch stage, which aims to predict the color distribution of clothing and obtain watercolor images without gradients and shadows. The second is the thinning stage, which refines the watercolor image into a clothing image with light and shadow effect; The third is the optimization stage, which combines the outputs of the first two stages to optimize the generation quality further. The experimental results show that the improved network’s IS and first input delay (FID) scores are 4.592 and 1.506, respectively. High-quality clothing images can be generated only by inputting line drawings and a few color points. Compared with the existing methods, the image generated by this network has excellent advantages in realism and accuracy. This method can combine various feature information of images, improve retrieval accuracy, has strong robustness and practicability, and can provide a reference for the daily work of fashion designers. Drawing a clothing plan is an essential part of the clothing industry. Clothing renderings focus on the specific form and design details to accurately grasp the designer’s design intention in garment production . The firetc.  has been widely used in image processing, which will cascade representation and classification learning. It can adaptively mine useful feature information from images through a backpropagation algorithm . There aAt present, CNN-based methods have achieved excellent performance in clothing. However, these methods can not extract fine-grained features in clothing images. Also, it is challenging to learn global semantic information and semantic information with relatively far pixels, which leads to poor feature extraction effect of clothing images by the network. Recently, inspired by the great success of Transformers in natural language processing, researchers plan to introduce Transformer into the field of image processing . For exa(1) Effectively integrate ResNet-50 and Transformer, obtain local information of clothing images through ResNet-50, and Transformer obtains global information, further improving the network’s ability to extract different features of clothing images.(2) Introducing dense skip connections in ResNet-50 further improves the ability of the network to utilize feature information at various levels, completing more accurate clothing image generation tasks.To achieve more accurate and efficient feature extraction of clothing images and help clothing designers draw more stylish clothing plans, this article proposes a clothing image generation network based on Transformer and CNN, which can automatically generate realistic clothing renderings only by specifying a few color points on clothing line drawings. The specific innovations are as follows:This article proposes a clothing image generation network based on ResNet-50 and Transformer. Users only need to input a clothing line drawing and specify a few color points on the line drawing to generate realistic clothing images according to their design intentions.(1) Sketch stage: the input data in this stage are line drawings and color points, and the target is watercolor clothing images. Watercolor image is characterized by color block distribution, without gradient and light and shadow effects. After training, the sketch model can generate watercolor clothing images to obtain approximate color distribution information.(2) Refinement stage: The input data in this stage are watercolor images, line drawings and color points, and the generation target is clothing images. After obtaining the approximate color distribution, the refined model can further optimize the generation effect and generate realistic clothing images after this training stage. The input data of line drawings and color points help refine the model and correct the unreasonable generation results in the sketch stage.(3) Optimization stage: Both sketch and refinement models are trained simultaneously in this stage. The watercolor image generated by the sketch model, line drawings, and color points are taken as the thinning model’s input, and the thinning model and the training loss term of the thinning model are taken as a part of the loss term of the sketch model. This stage aims to fine-tune the parameters of the converged sketch model and refined model so that the input and output data of the two models can be more coordinated and the generation quality can be further optimized.Two deep learning network models based on ResNet-50-Transformer hybrid architecture are used: the sketch and refinement models. The training process is divided into three stages: sketch, refinement, and optimization, as shown in After the model is trained, it is only necessary to input the line draft and color points into the sketch model and then input the output of the sketch model, line draft, and color points into the refined model to generate the clothing effect map.The sketch and refinement models have different input dimensions, but the other structures are identical. They comprise a ResNet-50, a Transformer, and a Cascaded Upsampler (CUP).Firstly, the local features of the input image are extracted by down-sampling using ResNet-50, which is divided into three down-sampling stages. See In The input feature map is analyzed Trainable linear mapping is used to map vectorized image blocks. The transformer coding structure consists of This article introduces CUP into the decoding part, composed of multiple up-sampling and multi-layer jump connections to decode the hidden features to get the final generated image . After tThe skip connection in the CUP is used to fuse the multi-scale features of the encoder with the upsampling features. However, in the first stage, the down-sampling only extracts the shallow features of the image, and it will lose a lot of information if it is directly fused with the last feature of the up-sampling. Hence, this article adds a dense jump connection to connect every scale in the horizontal direction. After the two feature maps are spliced by the bilinear interpolation upsampling method, the number of channels is halved by 1 × 1 convolution. The specific operation is shown in The discriminator is essential for the clothing image generation network. The discriminator used in this article consists of a simple multi-layer convolution and a fully connected layer at the tail. It is a discriminator network based on reference . All itsThe total loss items used in the training process are:(1) Reconstruction loss (2) Feature loss  methods . A pre-t(3) GAN losses In this article, 5,000 clothing renderings were collected from the official website of fast fashion consumer brands such as Uniqlo and Muji, and the OpenCV image processing library standardized the images. See (1) Authenticity evaluation: The experiment adopts human perceptual research, (HPR). Given ten groups of images generated by each method, 20 volunteers must choose the most accurate method from each group based on their first impressions. If a volunteer selects each method, one point will be scored, and the final score will be averaged.(2) Accuracy evaluation: Inception score (IS) and Frechet Inception Distance score (FID) , which aThree quantitative evaluation indexes are used to quantitatively evaluate the authenticity and accuracy of clothing images generated by PSPNet , VGG Ta, ResNet The specific formula of FID is as follows.This research also compares the ablation experiment with the pure ResNet-50 network. To observe and analyze the information processing process of each module, the network in this article is split and reorganized. The data from relevant comparative experiments are shown in Compared with the ResNet-50 network, our model combines CUP and Transformer. The accuracy of the proposed model is much better. During the experiment, although Transformer and CUP modules compressed the feature map, the accuracy of the image generation IS decreased by 8.138%, and the FID increased by 9.437%. Still, the video memory occupation of 71.696% and the training time of 69.683% are reduced. This shows that Transformer and CUP modules can effectively reduce the calculation, play a role in optimizing the model or improve the quality of image generation.To further verify the effectiveness of the network, the ablation experiments of different numbers of Transformer layers are continued, and the effects of three other numbers of Transformer layers are carried out, which are two, eight and 12 layers, respectively. The experimental results show that with the increase of Transformer layers, the IS score of the network increases and the FID score decreases, which further verifies the effectiveness of the Transformer structure.In practical application, due to the limitation of shooting conditions, there are disturbances such as rotation, low resolution, and illumination in the imaged clothing image. Therefore, the robustness of the clothing plane image generation network is one of the requirements for practical application. The robustness of the proposed network and the traditional ResNet-50 are tested. Ten images were randomly selected from the data set for rotation transformation, scaling transformation, and brightness transformation, respectively, and the random range of each transformation parameter was increased in turn. The 10 images were tested five times, and the generation accuracy was taken as the average of five tests. The results of the robustness test are shown in From Suppose a fashion designer can get one or more corresponding real images of clothing by drawing a rough sketch of apparel. In that case, it will significantly increase the inspiration of fashion designers and greatly reduce their workload. This article uses the advantages of CNN and Transformer to generate clothing images. The model is a generic network that integrates the ideas of Transformer, ResNet, and CUP. Like other network structures, the network consists of the encoder, decoder, and hop connection. The encoder is built based on ResNet-50 and Transformer. After a multi-layer CNN feature extraction structure, the input clothing image is divided into non-overlapping image blocks. The image blocks are combined into image block sequences and input to the encoder based on Transformer to learn global features. Then enter the decoding layer based on CNN to up-sample the extracted multi-level features, fuse the multi-scale features in the down-sampling process through jump connection, and restore the feature map to approximate the resolution size of the input image to complete the clothing image generation at the pixel level. Through a series of experiments, it can be seen that the work done in this article has a certain degree of innovation. The combination of ResNet-50 with jump connections and Transformer can extract more clothing features, and can generate different clothing real images through simple clothing sketches, which helps improve the design efficiency and design philosophy of clothing designers.This research proposes a new clothing image generation network, which combines the advantages of CNN and Transformer to obtain information from different dimensions and realizes the task of generating realistic clothing renderings through three stages: sketching, refining, and optimization, which can provide more design inspiration for clothing designers and complete diversified clothing plan drawing. In the experimental comparison, this method surpasses similar methods in different evaluation indexes and can generate a more realistic and clear clothing plan. Future work will consider further improving the performance and speed of the network, for example, finding a more efficient way to integrate CNN and Transformer. In addition, the data set needs to be expanded to generate better results.10.7717/peerj-cs.1372/supp-1Supplemental Information 1Click here for additional data file.


The vehicle particle model was built to compare and analyze the effectiveness of three different collision avoidance methods. The results show that during vehicle high-speed emergency collision avoidance, lane change collision avoidance requires a smaller longitudinal distance than braking collision avoidance and is closer to that with a combination of lane change and braking collision avoidance. Based on the above, a double-layer control strategy is proposed to avoid collision when vehicles change lanes at high speed. The quintic polynomial is chosen as the reference path after comparing and analyzing three polynomial reference trajectories. The multiobjective optimized model predictive control is used to track the lateral displacement, and the optimization objective is to minimize the lateral position deviation, yaw rate tracking deviation, and control increment. The lower longitudinal speed tracking control strategy is to control the vehicle drive system and brake system to track the expected speed. Finally, the lane changing conditions and other speed conditions of the vehicle at 120 km/h are verified. The results show that the control strategy can track the longitudinal and lateral trajectories well and achieve effective lane change and collision avoidance. Over the past 20 years, the number of vehicles has been increasing , and theIn some scenarios, emergency braking cannot avoid accidents when faced with sudden obstacles. At this time, the lane change operation may avoid accidents . HoweverThere are two kinds of trajectory planning: online trajectory planning and offline trajectory planning. The heuristic search method represented by A* (A-Star) algorithm has the characteristics of efficiency and flexibility . AnotherSimulating the driver to control the vehicle to move along the desired trajectory through the control algorithm is the principle of trajectory tracking of the automated vehicle. Adaptive cruise control (ACC) was implemented based on fuzzy logic and controlled vehicle distance and vehicle speed, respectively, by Naranjo et al. . Some reHowever, In the aspect of longitudinal trajectory tracking control, most studies assume that the longitudinal speed is small and constant and take the heading angle as the only control quantity, which reduces the accuracy of trajectory tracking. Therefore, there is still some research space in the aspect of transverse and longitudinal cooperative control. In order to track the collision avoidance trajectory more accurately under high-speed driving conditions, a lateral tracking controller and a longitudinal tracking controller for cooperative control were designed. Moreover, multiobjective optimization model predictive control is used for lateral displacement tracking, which improves the accuracy of vehicle trajectory tracking.This paper has five chapters. In The principle of automatic emergency braking (AEB) is that the vehicle’s braking system is controlled by the electronic control unit (ECU) so that the vehicle can automatically brake to avoid colliding with pedestrians, other vehicles, etc. Additionally, the principle of automatic emergency lane changing is that the steering system and braking system of the vehicle are controlled by the ECU to avoid pedestrians and other vehicles. m is the mass of the whole vehicle; In order to evaluate and compare the effects of steering collision avoidance and braking collision avoidance, a vehicle particle model is established and analyzed. As shown in From tire physical properties and Newton‘s second law :(3)αxαx,It is assumed that the initial state of the vehicle before collision avoidance is There are three kinds of collision avoidance operations, including braking collision avoidance, lane change collision avoidance and braking + lane change combined collision avoidance. The system input and constraint conditions ) is substituted into the cubic polynomial (Equation (8)) to obtain the reference path of the cubic polynomial:The lateral acceleration constraints of the vehicle at the beginning and end moment of collision avoidance are taken into account in the quintic polynomial reference path, whose expression is the following formula.This reference path constraint is as follows.The rate of change in lateral acceleration at the initial and end moments of the vehicle is further considered for the planning of a hepatic polynomial reference path.b = 50 m, and vehicle lateral offset a = 3. 75 m are compared under the cubic polynomial, fifth-order polynomial and hepatic polynomial planning. According to Equations (10), (13) and (16), the reference trajectories of different polynomials are drawn using Matlab, as shown in The lateral displacements under the constraints of vehicle longitudinal speed of 72 km/h, a longitudinal distance of the obstacle ahead The reference yaw rate and reference yaw angular acceleration for third-, fifth-, and seventh-order polynomials are compared, as shown in The MPC controller is used to track the lateral displacement. In this paper, the vehicle dynamics model considering two degrees of freedom of lateral and yaw is shown in Considering the real-time requirements of the controller, nonlinear model predictive control (NMPC) has not been adopted. The expression of the vehicle linear 2-DOF dynamic model is the following formula:The vehicle’s lateral displacement is the key quantity for trajectory tracking control, and its derivative  formula .(18)e˙ySince the transverse pendulum angle is small, it can be considered that This controller’s state volume is The coefficients areThe prediction model is discretized into the following formula.The coefficients are The prediction step is The system state volume can be expressed asThe output expression to the prediction step In order to improve the tracking accuracy, it is necessary to design the objective function and define the objective quadratic function :(24)J=kqLimiting the volume of control and its incremental and performance indicators to a certain range :(25)δminSolving the optimal front wheel steering angle by quadratic programming , the solThe optimal front-wheel steering angle of the vehicle isk, then enter the next control cycle and repeat the above steps to track the lateral trajectory.After inputting the optimal front wheel steering angle, the vehicle can obtain the vehicle state at time The choice of controller parameters and their effect on control performance are covered in detail in this section.The sampling time of the controller is 0.02 s, which is determined by the cycle update time of the ECU of the simulated vehicle. This guarantees that the controller has sufficient reference data to address the optimization issue. In addition, the sampling time should not be too long. Otherwise, the controller is unable to react quickly when interference occurs. The weight of the calculations will, however, grow if the sampling period is too short. The controller’s predictive step size is set to 30, which can ensure the accuracy and real-time performance of trajectory tracking. The predicted step size is too large while the vehicle speed is constant, which reduces controller sensitivity and trajectory tracking accuracy and wastes computation power. The controller will be too sensitive and cause vehicle instability and trajectory tracking failure if the predicted step size is too small. The tracking effect of the controller is not greatly affected by the control step size of the controller, but it should not be excessive. Generally speaking, we set the control step size to be between 10% and 20% of the predicted step size. Various weight coefficient choices will result in various control outcomes. For instance, raising The longitudinal velocity of the vehicle is variable in the vehicle body coordinate system. As shown in The purpose of the longitudinal acceleration decision is to determine the longitudinal acceleration to be used for closed-loop control based on the desired longitudinal velocity and the actual longitudinal velocity. The longitudinal acceleration decision equation is derived using the principle of preview longitudinal velocity in CarSim.In the formula, Next, the vehicle’s longitudinal driving mode needs to be arbitrated to decide whether to adopt acceleration, deceleration, or idle mode to follow the desired longitudinal speed. The switching logic of braking, driving, and idle modes of the vehicle is shown in After obtaining the arbitration results for the longitudinal driving mode, a vehicle inverse longitudinal dynamics model needs to be developed, and then the desired throttle opening in drive mode or the desired braking pressure in braking mode is obtained based on the desired longitudinal acceleration. The simplified structure of the inverse longitudinal dynamics model of the vehicle is shown in The longitudinal kinematic equations of the vehicle are as follows:Substituting the above equation into the driving equation yields the following:According to the formula, the expression for the desired engine output torque is obtained:The inverse engine model can be obtained by combining the engine MAP diagram as follows.From the previous formula, we can directly obtain the expected braking pressure :(37)PdesIn order to verify the control effect of the vertical and horizontal joint control strategy, MATLAB and CarSim are used. The vehicle model is built in CarSim, and the control strategy is built in MATLAB. The emulation computer’s central processing unit (CPU) is AMD Ryzen 5 5600 H with Radeon Graphics 3.30 GHz, and its graphic processing unit (GPU) is an NVIDIA GeForce RTX 3050 Laptop GPU. Distance sensing is out of the scope of this work, and for the purpose of the experiments, an ideal distance sensor with zero lag is considered to be on board the automated vehicle. The simulation conditions are divided into two types: the first is the emergency lane change and collision avoidance of vehicles in a high-speed environment, and the second is the lane change in vehicles at different speeds. The quintic polynomial as the reference trajectory of lane change, longitudinal and lateral trajectory tracking control strategies are combined. Assuming that the vehicle is traveling at a speed of 120 km/h when t = 0, there is a stationary obstacle 90 m in front of the subject vehicle, and the subject vehicle must change lanes. After changing lanes, the vehicle keeps driving in a straight line. Then, another obstacle vehicle is found, the subject vehicle changes lanes again, and the subject vehicle keeps driving in a straight line after changing lanes. The collision avoidance scene is shown in The response of vehicle automatic emergency lane change collision avoidance is shown in As can be seen from The effect of the trajectory tracking control strategy at different vehicle speeds and the rationality of the controller parameter selection should be verified. The road adhesion coefficient is 0.7, and the speed is 72 km/h, 90 km/h, and 120 km/h, respectively. The vehicle travels 40 m on a horizontal road and then changes lanes. The quintic polynomial reference trajectories at different vehicle speeds are shown in From It can be seen from In the design of a lateral displacement tracking control strategy, not only the computational efficiency is considered but also the objective function, which is optimized by multiobjective optimization to achieve accurate tracking. The inverse longitudinal dynamics model is classical and easy to implement in longitudinal velocity tracking control strategy design.In order to demonstrate the advantages of the designed longitudinal and transverse joint control strategy, the effect of tracking the double lane change trajectory at different vehicle speeds compared to linear quadratic regulator (LQR) control is shown in It can be seen that the tracking effect of MPC+LST control is similar to that of LQR control at low speed, but as the vehicle speed increases, the tracking effect of LQR control is not as good as that of MPC+LST control at high speed. From the comparison of lateral displacement errors reflected in Aiming at the problem of vehicle dynamics control, lateral controllers and longitudinal controllers are proposed to track the lane change trajectory at high speed. Firstly, the vehicle collision avoidance particle model was built; the requirements of braking collision avoidance, lane change collision avoidance, and braking and lane change combined collision avoidance on the minimum longitudinal distance of the vehicle were analyzed. The results show that compared with braking collision avoidance, the requirement of lane change collision avoidance for longitudinal distance is significantly reduced, and the effect is more obvious with the increase in vehicle speed and the decrease in road adhesion coefficient. Then, the cubic polynomial, quintic polynomial, and hepatic polynomial are analyzed to comprehensively calculate the factors of efficiency, lateral acceleration, and trajectory smoothness. The fifth-degree polynomial is the final reference path. Next, the optimization of the lateral displacement tracking control strategy is to minimize the lateral position deviation, yaw rate tracking deviation, and control increment. The output of the multiobjective lateral MPC is the front wheel steering angle, and the longitudinal speed controller outputs the throttle opening or the brake master cylinder pressure. Finally, the simulation results show that the combined control of the optimized lateral control strategy and the longitudinal speed tracking control strategy can not only achieve more accurate tracking but also ensure that the vehicle will not roll and slip.Future research directions include: (1) The trajectory tracking controller studied in this paper simplifies the vehicle modeling, especially in the longitudinal speed tracking control. However, existing vehicle systems have strong nonlinearity. Therefore, research on the dynamic control of these aspects can be further intensified. (2) The trajectory planning can be based on the driving motive, which is not only for the self-vehicles but also for other traffic vehicles. (3) More constraints can be considered for the controller to conform to reality.


Despite the large demand for dental restoration each year, the design of crown restorations is mainly performed via manual software operation, which is tedious and subjective. Moreover, the current design process lacks biomechanics optimization, leading to localized stress concentration and reduced working life. To tackle these challenges, we develop a fully automated algorithm for crown restoration based on deformable model fitting and biomechanical optimization. From a library of dental oral scans, a conditional shape model (CSM) is constructed to represent the inter-teeth shape correlation. By matching the CSM to the patient’s oral scan, the optimal crown shape is estimated to coincide with the surrounding teeth. Next, the crown is seamlessly integrated into the finish line of preparation via a surface warping step. Finally, porous internal supporting structures of the crown are generated to avoid excessive localized stresses. This algorithm is validated on clinical oral scan data and achieved less than 2 mm mean surface distance as compared to the manual designs of experienced human operators. The mechanical simulation was conducted to prove that the internal supporting structures lead to uniform stress distribution all over the model. Oral problems, including dental caries or even tooth loss, are affecting about 2.5 billion people worldwide . With thIn the 1980s, With the rapid development of deep learning theory, neural networks started to be used in dental crown restoration design. In summary, the existing algorithms have significantly automated the design of crown restorations. However, it is still challenging to preserve anatomical morphological features such as developmental grooves and crests. Some of the studies only focus on occlusal surface reconstruction without close matching of the restoration with the adjacent teeth and the preparation, leaving the design process incomplete for clinical applications. Moreover, most existing studies lack biomechanical property optimization, potentially leading to localized stress concentration which reduces the working life.(1) A parametric statistical shape model (SSM) of the tooth was constructed based on a clinical dental scan data library which preserved the natural morphological characteristics of the occlusal surface. This model was deformed and matched to the patient’s oral scan to achieve an automatic crown design.(2) Different from the existing studies which only use tooth SSMs, a conditional shape model (CSM) was constructed in this work to model the occlusal and adjacency relationships between neighboring teeth, ensuring proper inter-tooth shape dependencies of the designed crown.(3) In addition to the crown body design, an automatic process was developed to closely fit the deformable crown to the preparation finish line, resulting in a crown model ready for subsequent CAM.(4) The internal support structure was optimized to prolong the working life and save the additive manufacturing material. The biomechanical simulation was performed to verify that the optimized support structure led to uniform stress distribution in all parts of the crown.To solve the above problems, an automatic full-crown restoration algorithm is proposed in this paper. The main contributions of this paper are as follows:This work addresses the problem of missing tooth crown design using the existing adjacent teeth as shape references, which are shown in (1) Conditional shape model (CSM) construction. Based on a library of clinical oral scan data, the deformable statistical shape models (SSMs) of different teeth were constructed. After that, the inter-teeth shape correlation between adjacent SSMs was modeled using the CSM approach.(2) Shape model matching with patient oral scan. First, the SSM of the neighboring existing teeth is matched to the oral scan. Then the missing crown model was created using the CSM, and the possible intersections between the crown and its neighboring teeth are automatically removed to ensure reasonable physical contact.(3) Crown fitting to the preparation. The preparation finish line is automatically identified and the bottom of the crown is deformed to closely fit to the finish line.(4) Internal supporting structure optimization. The porosity and direction of the internal supporting structure were optimized to ensure uniform stress distribution over the entire crown for the sake of prolonged working life and efficient material consumption.SSM  parametrTo construct the SSM of dental crown, a standard template was aligned to all other clinic oral scan models using the Thin Plate Spline Robust Point Matching (TPS-RPM)  method, From this, we can obtain a set of ideal data, each mesh has the same number of vertices, and the corresponding vertices in different meshes are located in the same anatomical position. To cancel the inter-subject variations in translation, rotation, and scaling, we used Generalized Procrustes analysis (GPA)  for the The singular value decomposition (SVD) of Eq. The parameter According to the proposed method, the SSMs are constructed for the missing tooth (described as “son model” in the following) and its adjacent teeth as a whole (described as “father model” in the following). Since the teeth perform important masticatory functions, the size and position of the missing crown mainly depend on its adjacent teeth. In other words, there is a high correlation between the shape coefficients of the two. We parametrically describe this relationship by building the conditional shape model (CSM) .The coefficients of the SSM of the son model Representations of rding to :μ=μS+ΣSWhen a set of SSM distribution coefficients of the father model After constructing the deformable models, in practical application, to obtain the set of shape coefficients of the father model, it is necessary to match the SSM of the father model to the patient’s oral scan model.According to Eq. The average model vertices of the father model can form a vector To improve the computational efficiency, the Iterative Closest Point (ICP) algorithm  was usedThe shape coefficients of the father model According to Eq. Then the results of the father model aligned to the patient’s oral scan model can be obtained as follows,The son model matching with the shape of the father model,To further improve the alignment accuracy, the TPS-RPM alignment algorithm was used to align Finally, the intersection-removing algorithm was used to ensure that there was no unreasonable intersection between the crown and its adjacent teeth. Specifically, the vertices of the crown were looped through, and those located inside the adjacent teeth were moved outward along the direction of the normal vector until all vertices did not need to be adjusted. Finally, the face intersection was detected to ensure reasonable contact between the crown and its adjacent teeth.The above steps ensure a clear occlusal surface with anatomical features and a harmonious external surface with the morphology of its adjacent teeth . HoweverAs shown in To fit the bottom of the crown to the finish line of preparation, the sign distance function (SDF) was used to control the crown deformation. The SDF is defined as the distance from a point in space to the surface with a positive interior and negative exterior, and the surface is expressed as the 0-equivalent surface of the SDF. First, the mesh of the crown and the preparation were converted into 3D voxels separately and combined into one whole. The SDF values at the vertices of the voxels were calculated, as shown in Nowadays, additive manufacturing (AM) is increasingly used in the CAM of the dental crown. Compared to the traditional computer numerical control (CNC) technique, AM is more flexible for producing complex structures thus facilitating the manufacturing of complicated support structures inside the object. In this work, skeletonized internal supporting structures of the crown are designed to improve the biomechanical properties and to save the materials for additive manufacturing.The supporting structure is designed using the triply periodic minimal surfaces (TPMS) method that we previously proposed for generating porous structures . To effeSpecifically, firstly, the initial TPMS-based structure is obtained according to the input crown model and the loading conditions. The initial porosity is 60%, and the wall thickness is set within  mm. Note that the parameters can be adjusted according to the applications. Secondly, a function representation-based optimization formulation is defined to minimize the compliance of the porous shell structure. The bottom of the crown is rigidly fixed to prevent any lateral movement, while disregarding the frictional forces. Additionally, we impose the constraint of vertical pressure exclusively on the occlusal surface of the crown. Thirdly, the aforementioned two-step optimization strategy is exploited to optimize the topology and the geometry, respectively. Finally, we obtain the optimized porous structure of the crown with continuous geometry changes and smooth topology changes that have reasonable stress distribution. In the final processing, an outer shell is added to wrap the porous structures. The default thickness of the shell is set to 0.6–1 mm according to the precision of 3D printers.To verify the proposed method, we choose the first molars as the missing teeth for crown design, since the first molars have the highest damage rate according to the statistical surveys . Twenty Previous to the automatic crown design, the SSMs of the target crown (for the first molars) and its adjacent teeth are constructed. It can be seen from To observe the shape variation modeling ability of the SSM, different shape coefficients were adjusted to produce deformed shape instances. To construct the CSM, we take the mandibular first molar SSM as the son model, and its five neighboring teeth as a whole SSM as the father model. Then the dependence between the shape coefficients of the two SSMs was constructed as a CSM.To verify the constructed CSM, we actively changed the shape coefficients of the father model and generated the corresponding son model using CSM. Similarly, the CSM of the maxillary first molar was established.The proposed crown design method was used to test 20 oral scan data randomly selected from our database of maxillary first molar and mandibular first molar, respectively. All the test data were not included in the model training dataset. The first molar and its five adjacent teeth are manually cropped from the organ scan for algorithm validation.To quantify the accuracy of crown design, we used the manually designed crown by experienced designers as the reference standard. The Chamfer Distance (CD) between our result model and the expert designed to quantitatively assess the accuracy of the SSM matching,A randomly selected part of the test results is shown in The quantitative test results are shown in The internal supporting structure of the crown was optimized using the proposed method. The obtained internal porous structure is shown in To verify the biomechanical property of the optimized internal supporting structure, finite element simulations were conducted for the designed crown with porous internal structures. The crown material was assumed to be nickel-chromium alloy, with Young’s modulus 214 GPa and Poisson’s ratio 0.3. A nodal load of 0.5 N was applied to the occlusal surface with fixed support conditions to the bottom surface of the model as shown in In this paper, we propose an automatic design algorithm for crown restoration by matching the conditional shape model of the target crown and its adjacent teeth. The missing crown with realistic occlusal surface morphology was automatically generated and fit to the finish line of the preparation. The geometry of the internal supporting structure was optimized to yield uniform stress distribution. As a proof of concept, our biomechanical simulation proves that the porous optimization resulted even stress and strain distribution over the entire crown. We will further validate this advantage with real crown mechanical test in future study. In future work, we will continue to expand the data sample library and automate the identification of missing tooth positions since this method still relies on manual specification of the target teeth location.