Capsule-based self-healing is increasingly being targeted as an effective way to improve the durability and sustainability of concrete infrastructures through the extension of their service life. Assessing the mechanical and durability behaviour of self-healing materials after damage and subsequent autonomous repair is essential to validate their possible use in real structures. In this study, self-healing mortars containing cementitious tubular capsules with a polyurethanic repairing agent were experimentally investigated. Their mechanical behaviour under both static and cyclic loading was analysed as a function of some factors related to the capsules themselves  or to the specimens . Their mechanical performances were quantified in terms of recovery of load-bearing capacity under static conditions and number of cycles to failure as a function of the peak force under cyclic conditions. Positive results were achieved, with a maximum load recovery index up to more than 40% and number of cycles to failure exceeding 10,000 in most cases, with peak force applied during cyclic loading at least corresponding to 70% of the estimated load-bearing capacity of the healed samples.  It is well-known that all cementitious materials tend to have defects, resulting from incorrect mix design or execution, shrinkage and other causes. Their low tensile strength, in combination with the presence of such defects, makes them prone to cracking. Because of the possible concurrent or subsequent action of cyclic loading, micro-cracks can propagate and coalesce into macro-cracks, ultimately leading to a reduction of durability or even collapse . This isCapsule-based self-healing has been proposed as a promising strategy to improve the durability and resilience of reinforced concrete infrastructures ,10,11,12Based on the above considerations and taking some of our previous experimental works as a starting point, the objectives of this study were to confirm the effectiveness of a capsule-based self-healing system using cementitious capsules and a polyurethanic repairing agent, to investigate the mechanical behaviour of the proposed system after pre-cracking under both static and cyclic flexural loading and to evaluate the influence of some capsule parameters and specimen configurations on the mechanical behaviour.In order to pursue these objectives, cement mortar prisms either with or without capsules were used. Cement mortar was selected as a prototypal cementitious material instead of concrete for several reasons. First, the polyurethane reaction does not depend on the mortar fraction and the aggregate-cement ratio, hence it is easier to evaluate its effect in a more homogenous matrix as the one offered by mortar. In addition to the fact that mortar is more homogenous than concrete, the main reason for its use is the possibility to do a fast and cost-effective screening of different self-healing techniques before upscaling for the use in concrete . For thiThe mechanical behaviour was investigated via three-point bending test in order to test the system under indirect tensile stresses and for the sake of comparison with the existing literature, it has been, so far, the most commonly employed test to assess the healing capacity of cementitious composites through the recovery of mechanical properties  under stOrdinary Portland cement ;3, Sinopia s.a.s., Torino, Italy);Calcium carbonate ;Hydroxypropyl methylcellulose .Cementitious tubular capsules were produced in accordance with previous researches ,41,42,43Demineralised water;Copolymer of ethyl acrylate (EA) and methylmetacrylate (MMA) ;Polyethylene glycol .The liquid compounds of the paste were:First, all solid compounds were manually mixed, while all liquid compounds were separately mixed together with an overhead stirrer . Then, the mixed powder compounds were added progressively to the homogenously mixed liquid compounds.The fresh polymer-modified cement paste was used to produce cementitious tubes according to two different manufacturing processes.In the first manufacturing process, already used in previous works ,41,42,43In the second manufacturing process, the fresh cement paste was rolled around an oiled bar with a circular cross section (diameter of 5 mm), until obtaining a smooth cementitious tube with a shell thickness of approximately 1.5 mm. The bar was removed only after setting and first hardening of the cement paste, i.e., after 24 hours storage in a moist environment with T ≈ 20 °C and RH > 95%. This allowed to keep a perfectly cylindrical shape of the tubes, unlike the extruded ones in which deformation of the cross section occurred during the first stages of curing because of their own weight. The total duration of curing in moist environment was of 7 days, after which curing was completed in air  over 28 days. At the end of curing, the tubes were further cut with a saw into smaller portions measuring about 60 mm in length.The mix design of the cement paste was slightly modified with respect to previous works in order to accommodate both the extrusion process and the rolling procedure see .In order to avoid penetration of water through the capsule shell during concrete mixing and hydration, all the cementitious tubes produced were further coated. First, a two-component epoxy primer  was applied by complete immersion of the tubes in order to prepare the surface. Subsequently, a layer of two-component epoxy resin  was applied to coat the capsule. The overall coating thickness was about 1 mm. The epoxy coating was applied to the internal surface of the tubes by injection in the case of the smaller capsules obtained by rolling (hence denoted as SI capsules). In the case of the larger capsules obtained by extrusion, the coating was applied either internally with the same procedure (LI capsules) or externally with a brush (LE capsules).After coating, one end of the tubes was sealed using an epoxy-based two-component thixotropic plaster , further coated with Plastigel. At this point, the healing agent was injected with a syringe until complete filling. Finally, the second end of the tubes was sealed in the same way as the other and both ends were covered with sand in order to improve the bonding with the surrounding matrix. Pictures of the capsules thus obtained are reported in The correct waterproofing and sealing of the capsules were issues of paramount importance, since a highly moisture-reactive substance was chosen as a healing agent. Namely, a commercially available polyurethane (PU) precursor  was used. It is a single-component resin that consists of modified polyisocyanates with additives that rapidly cures by reaction with ambient water yielding a polyurethane/polyurea foam. Its expansion rate depends on the backpressure exerted by the propagation of the resin into the structure to be sealed: wide cracks result in a high foaming factor, while narrow cracks in a low expansion rate and higher strength. Its viscosity range at 25 °C is 270–1,000 mPAs. The product is commonly used in the construction sector for stopping water inflow, water ingress in cracks and sealing of tunnel construction or of drill holes.3, were produced according to standard UNI EN 196-1. Ordinary Portland cement , tap water and normalised sand (grain size between 0.08 and 2.00 mm) were used, with a water-to-cement ratio of 0.5 and a sand-to-cement ratio of 3.Mortar prisms, with a volume of 40 by 40 by 160 mmReference specimens with no capsules (REF series) were produced along with self-healing specimens, in which the capsules filled with the PU precursor were embedded manually before casting, in fixed positions. Accurate control of the capsules position was achieved by gluing them on top of two thin nylon threads passing through the lateral faces of the mould, at a height of 10 mm from the bottom side of the specimen see .Different series of self-healing specimens were produced: the CEM_SI series contained two small-diameter capsules with internal epoxy coating, the CEM_LI series contained one large-diameter capsule with internal epoxy coating, and finally the CEM_LE series contained one large-diameter capsule with external epoxy coating. CEM_SI and CEM_LI specimens contained the same volume of healing agent (~ 0.6 mL) but had different geometric configurations since the healing agent was distributed in two capsules or concentrated in one capsule, respectively. Conversely, CEM_LI and CEM_LE specimens had the same geometric configuration, with a single capsule horizontally centred in the specimen cross-section, but contained a different amount of healing agent . For each series, 12 specimens were produced, for a total of 48 specimens.After casting, the moulds were covered with plastic foils in order to maintain a humid environment (T ≈ 20 °C). The samples were demoulded after 24 hours from casting and cured for two weeks still wrapped in plastic foils (T ≈ 20 °C). Then, a U-shaped notch  was created by means of wet sawing. In order to evaluate the effectiveness of the autonomous self-healing system, a controlled localised crack was first induced in the specimens using a mechanical pre-cracking procedure. At an age of 14 days from casting, all the specimens were pre-cracked via a crack-width controlled three-point bending test with a span of 10 cm using a 25 kN closed-loop servo-controlled MTS hydraulic press  equipped with a digital controller . It was possible to control the crack mouth opening displacement (CMOD) by using a strain-gauge-based displacement transducer  mounted on the bottom face of the specimen upon the notch. The test was conducted by imposing a CMOD rate of 1.5 µm/s. Upon reaching a maximum value of 800 µm, the specimens were unloaded at the same CMOD rate. The target value for the maximum CMOD was set at 800 µm in order to test the ability of the system to heal large cracks and in order to inhibit the influence of the autogenous healing, that could be significant for smaller cracks because of the young age of the specimens at pre-cracking. The CMOD and load were recorded throughout the execution of the test.Immediately after pre-cracking, the specimens were stored in a curing cabinet  for one week and then in the lab, with no temperature and humidity control, for another week. Two supports with a span of 10 cm allowed to keep the specimens in the same geometric configuration during pre-cracking, with their bottom face pointing downward. The duration of the curing cabinet conditioning definitely exceeded the time required for the PU to react with air humidity and form a rigid foam . This ensured that the healing agent released from the capsules during pre-cracking was fully cured at the time of successive testing. After 2 weeks from pre-cracking, the recovery of the mechanical properties was first evaluated by assessing the load-bearing capacity under static conditions.Half of the specimens from each series were statically reloaded following the same procedure described in peak) and reloading (Lreload) and as a function of the residual load-bearing capacity at the end of pre-cracking (Lunload). Its definition is reported in Equation (1):This allowed to evaluate the mechanical recovery through a load recovery index in accordance with common approaches reported in literature ,42,44,45The static reloading allowed also to subsequently define the parameters to perform the cyclic reloading procedure .After the static reloading of half of the pre-cracked specimens , the mecIn order to investigate the behaviour in cyclic conditions, the remaining specimens were reloaded through a force-controlled three-point bending test with the same span used for the pre-cracking and static reloading (10 cm) and using the same closed-loop servo-controlled hydraulic press. In order to measure the damage evolution during the cyclic loading in terms of increment of crack opening displacement (COD), an inductive displacement transducer , connected to the digital controller through a measuring amplifier , was mounted on the lateral surface of the tested specimen, just above the tip of the notch. It was not possible to mount the WI displacement transducer on the bottom face to measure the CMOD as in the pre-cracking and reloading setup because of the lack of space between the supports.max with a load rate of 50 N/s. Upon reaching Lmax, a sinusoidal loading with a frequency of 4 Hz was applied, where the peaks were set to Lmax and the valleys to a lower load value Lmin.The force controlled three-point bending test was conducted by first reloading the specimens up to a maximum load value Lmin and Lmax of the cyclic reloading were defined as a fraction of the average load-bearing capacity Lreload obtained during static reloading for each series. Specifically, Lmin and Lmax were set according to Equation (2):The limits Lreload obtained during static reloading. Testing the specimens cyclically with a cyclic peak value close to Lreload was meant to check their performances under severe conditions, in such a way to provide a first feedback on how this type of self-healing materials could behave during their remaining service life after they have produced their autonomous repair action. The number of cycles sustained until failure as a function of the maximum force applied during cyclic reloading was analysed as a representative parameter to describe their cyclic behaviour. Such settings were adopted in order to impose a high stress, equal to or higher than 70% of the expected strength of the healed material. Indeed, after release and curing of the PU in the crack, the material properties changed in correspondence of the most stressed cross-section with respect to their initial values. They depended not only on the mechanical characteristics of the hardened PU, but also on its crack filling ratio and interaction with the surrounding cementitious matrix. The flexural strength of the healed material could only be estimated experimentally based on the load-bearing capacity LAll specimens from each series , namely 12 specimens per series for a total of 48 specimens, were pre-cracked at an age of 14 days via a controlled three-point-bending test as described in During the controlled crack formation, first the load increased until reaching the peak value with a very low increase in terms of displacement because of the high stiffness of the intact material. After reaching the peak load, crack formation and subsequent propagation occurred, with progressive load decrease as a function of increasing CMOD due to the material post-peak softening behaviour. The specimens were unloaded upon reaching a CMOD of 800 µm, with a consequent small CMOD decrease due to recovery of the elastic deformation. While for the series without capsules (REF series) the softening phase had a continuous and gradual advancement, the self-healing series showed sudden load drops during this phase. These drops are attributable to the breakage of the capsules upon crack creation, being these drops accompanied with an audible acoustic energy release. These results are confirmed in literature, where the same behaviour was shown during crack creation using glass ,24,46 anIn all the specimens of the CEM_LI series, the drop was highly repeatable at a CMOD around 135 µm. In the case of the CEM_SI series, that contained two capsules per specimen, there were usually double load drops due to non-simultaneous breakage of the capsules. The first drop was always detected for a CMOD smaller than 215 µm. The highest scattering in the CMOD value corresponding to the load drop was shown by the CEM_LE series, for which such CMOD value did not exceed 240 µm on average: the higher scattering could be attributed to a higher variability in the coating thickness due to its manual application over the ridged surface of the capsule.It is worth recalling here that the capsules were positioned 10 mm above the bottom face of the specimens, while the CMOD measuring points were situated some millimetres below it because of the experimental setup adopted. Therefore, the actual crack opening at the capsule level in correspondence of the aforementioned load drops was surely lower than the corresponding CMOD value experimentally detected. This results in the possibility of using the cementitious capsules to trigger the healing also for cracks smaller than 135–240 µm. This range of crack size is particularly relevant from a durability point of view, as confirmed by the structural design codes, where the limit for the maximum acceptable crack width is fixed to no more than 400 µm, depending on the exposure conditions ,47,48.A further evidence of the relationship between the load drops, the acoustic emission and the breakage of the capsules was that they were followed by leakage of the foaming polyurethane released by the capsules in the crack see .The expansive foaming reaction is triggered by the capsule breakage, which makes it possible for the polyurethane precursor to get in contact with the humidity present in the air at the crack site and to start its polymerisation reaction. Such reaction induces gas formation and consequent expansion of the polyurethane precursor, that progressively passes from a viscous fluid state to a plastic foam and then hardened foam state. For equal conditions in terms of humidity, amount of reagent and relative contact surface, the expansion is governed by the crack width. It was possible to notice that in the case of the CEM_SI series containing two capsules, the PU leakage was most often visible both on the lateral faces and at the crack mouth, covering nearly the entire notch area. Despite that the amount of healing agent was the same, in the case of the CEM_LI series the PU leakage was mainly visible at the crack mouth, concentrated in the central part of the notch area in correspondence of the single capsule position. The CEM_LE series, containing 50% more healing agent with respect to the other two series, showed a behaviour in between, with the expansion zone mainly concentrated in the central part of the notch area in correspondence of the single capsule position, but with some visible leakage also from the lateral face. This releasing mechanism had consequences on the mechanical performance recovery which are dealt with in the following sections. peak, it should be pointed out that the presence of the cementitious capsules did not have a strong detrimental effect on the load-bearing capacity that the specimens could withstand. It is possible to assess the reduction of the load-bearing capacity Lreduction of the self-healing specimens with respect to the plain mortar specimens without capsules as:peak,REF is the average load-bearing capacity Lpeak calculated over the 12 specimens of the REF series and Lpeak,i is the average load-bearing capacity Lpeak calculated over the 12 specimens of each self-healing series. Respectively, the percentage reductions were equal to 8% for the CEM_SI series, 13% for the CEM_LI series and 6% for the CEM_LE series. This result showed that the flexural strength is not significantly influenced by the presence of the cementitious capsules, at least for the capsule proportion here used.Considering the peak load Lpeak and Lunload per each series and the percentage load reduction Lreduction of each self-healing series with respect to the reference series.After the pre-cracking and the complete curing of the PU in a controlled environment , half of the specimens  were selected to be reloaded in static condition to evaluate the self-healing efficiency in terms of strength regain. The specimens were selected based on a visual inspection in order to always have another specimen with a comparable PU release to be tested later in cyclic condition . reload ≤ Lunload) and then kept following the same softening branch of the pre-cracking phase. Conversely, the autonomously healed specimens showed a higher maximum load compared to the residual load-bearing capacity before healing (Lreload > Lunload). The load versus CMOD curves were sufficiently repeatable and highlighted a slightly less brittle behaviour if compared to the intact specimen behaviour. The possibility to improve the ductility as a side effect of the self-healing through polyurethanic agents is a positive aspect in order to prevent brittle failure in the remaining life and to sustain higher deformation in service conditions.Upon reloading, the reference specimens without capsules could only reach at max the residual load-bearing capacity after pre-cracking  while in the case of the CEM_SI and CEM_LE series respectively three and two specimens failed in the initial part of the procedure, before reaching the prescribed cyclic peak load. It is worth reminding that the latter was defined as 70% of their estimated load-bearing capacity after healing. Clearly, the estimation based on the results of the static reloading test was not very accurate in these cases.max) is reported for the specimen CEM_SI_4.For all the self-healing specimens that could undergo the cyclic reloading, a three-stage curve was detected. A typical example of it is reported in This three-stage behaviour is typically observed in plain or fibre-reinforced concrete under compressive, tensile and flexural fatigue loading ,52,53,54After an almost instantaneous crack opening displacement increase upon loading, there was a first rapid development denoted as flaw initiation, or Stage (I). In concrete, this stage involves the defects within the matrix; in the case of the self-healing system here studied, it most likely involved the defects at the interface between the PU and the crack faces and inside the PU foam, rather than the defects in the mortar matrix surrounding the crack, though it cannot be excluded that they also provided a contribution. It is worth noting that, in literature, tests conducted over pre-cracked fibre reinforced concrete under flexure lacked this stage, because the initial loading already caused the opening of the crack . So, theThe Stage (II) is a stable development stage that involves slow and progressive growth of damage, most likely concentrated in the bonding interface formed by the PU, and the progressive elongation and rupture of the foam cells. By comparison, in fibre-reinforced concrete this phase is mainly associated to the fibre/matrix bond deterioration ,57 and fFinally, the Stage (III) is the failure stage, in which damage develops unsteadily until fatigue failure occurs, with a complete failure of the bonding PU interface and detachment of the crack faces.The self-healing specimens were able to sustain a satisfactory amount of cycles before failure, both for the lower and the higher load levels. This result, compared to the performance of the reference specimens, strongly underlines the contribution of the autonomous self-healing system in restoring the mechanical properties of the damaged cementitious materials, especially in severe conditions of damage and also when cyclic loadings are involved, improving the resilience of the system during its remaining service life.In terms of number of cycles and maximum load level, the best performance was expressed by the CEM_LI series. On the other hand, it is important to point out that this result deeply depends on the estimation of the load-bearing capacity after self-healing that was made based on the static reloading data . unload): up to 15 times this residual capacity for the CEM_SI series, 10 times for the CEM_LI series and 5 times for the CEM_LE series  curves occurs and a progressive deviation from linearity as a function of the number of cycles is displayed. The latter is a typical feature of the Stage (III) and is evidenced for example in In this study, self-healing mortars were produced by incorporating cementitious tubular capsules filled with a polyurethane precursor. The capsules were manufactured according to two different procedures, by extrusion and by rolling of a polymer-modified cement paste, and were also characterised by different waterproofing coating configurations, size and distribution within the mortar specimens. Their self-healing effect was evaluated in terms of mechanical recovery under static flexural loading and number of cycles to failure under cyclic flexural loading. The results were not significantly affected by the capsule manufacturing procedure and by the sequence of application of the epoxy coating layers; conversely, the internal diameter of the capsules and their distribution within the specimen may have influenced the release of the polyurethane precursor upon pre-cracking and hence the final mechanical performance. In all cases, the mechanical regain was very satisfactory in comparison with the behaviour of reference plain mortars, both under static and cyclic loading. A maximum load recovery index in static condition of more than 40% and a maximum number of cycles to failure of more than 70,000 were observed, confirming the potential of the proposed capsule-based self-healing system for the purposes of improving the structures durability and mechanical performances.


Gold nanoparticles depending on their shape and mixtures of multiple shapes can exhibit peculiar optical properties, including the dichroic effect typical of the Lycurgus cup, which has puzzled scientists for a long time. Such optical properties have been recently exploited in several fields such as paint technology, sensors, dichroic polarizers, display (LCD) devices, laser applications, solar cells and photothermal therapy among others. In this article, we have demonstrated a simple room temperature one-pot synthesis of gold sol displaying a dichroic effect using a slow reduction protocol involving only trisodium citrate as a reducing agent. We found that the dichroic gold sol can be easily formed at room temperature by reducing gold salt by trisodium citrate below a certain critical concentration. The sol displayed an orangish-brown color in scattered/reflected light and violet/blue/indigo/purple/red/pink in transmitted light, depending on the experimental conditions. With minor changes such as the introduction of a third molecule or replacing a small amount of water in the reaction mixture with ethanol, the color of the gold sol under transmitted light changed and a variety of shades of red, pink, cobalt blue, violet, magenta and purple were obtained. The main advantage of the proposed method lies in its simplicity, which involves the identification of the right ratio of the reactants, and simple mixing of reactants at room temperature with no other requirements. TEM micrographs displayed the formation of two main types of particles viz. single crystal gold nanoplates and polycrystalline faceted polyhedron nanoparticles. The mechanism of growth of the nanoplates and faceted polyhedron particles have been described by an enhanced diffusion limited aggregation numerical scheme, where it was assumed that both trisodium citrate and the gold ions in solution undergo a stochastic Brownian motion, and that the evolution of the entire system is regulated by a principle of energy minimization. The predictions of the model matched with the experiments with a good accuracy, indicating that the initial hypothesis is correct. The outstanding optical properties of colloidal solutions of coinage metals have been known to mankind since ancient times ,2. MetalTo the best of our knowledge, the citrate-based protocol we are proposing here represents the easiest method to synthesize colloidal gold sol displaying dichroic effects without the use of any seed particles  or heatiGold (III) chloride trihydrate (99.9%), trisodium citrate dihydrate, polyvinyl alcohol (PVA) , polyvinylpyrrolidone (PVP) , dextran , were purchased from Sigma Aldrich  and were used as such. Milli-Q water was used in all the experiments.HAuCl4 = 2.0 mM and Ccitrate = 1.94 mM with a molar ratio R = Ccitrate/CHAuCl4 equal to 0.97.The basic principle of synthesis methodology was based on the ecofriendly protocol already developed in our lab with which we could easily synthesize gold nanowire networks and gold foam . In summ® 100 UV–Vis, Varian  and 1 and/or 2 mm quartz cells were used to measure the absorption spectrum or perform kinetic studies. TEM micrographs and electron diffraction patterns  were obtained using a TECNAI G2 F20 Transmission electron microscope  equipped with a Schottky field emission gun operating at an acceleration voltage of 200 kV and recorded at Ultrascan  CCD camera. SEM images and energy dispersive X-ray (EDS) measurements were obtained using FESEM ULTRA-PLUS (Zeiss) Scanning electron microscope .For these measurements, a small drop of solution containing gold nanocrystals was spread onto the surface of a silica wafer and was carefully mounted on an aluminum stub covered by carbon tape. No sputter coating was performed on the samples, which were then placed on the sample holder of the microscope and imaged using 10–20 kV accelerating voltage.Gold nanoparticles were mostly characterized by Cryo-TEM and UV–Vis Spectroscopy. UV–Vis Spectroscopy was performed on a CaryThe mechanism of metal growth was reproduced using a diffusion-limited aggregation (DLA) scheme, where randomly displaced nanoparticles stick together to form the final structures. In the simulations, a square lattice was considered as a domain and six initial seeds  were chosen. Cellular automata were used to reproduce the displacement of gold ions in the domain prior to deposition: the path of the ions was chaotic, and at each iteration, each ion was displaced randomly in the lattice. Upon contact with the seed, ions in the domain were incorporated into the aggregate according to the sticking probability 0), the absorption spectrum shows just one peak centered at 290 nm, which is compatible with the electronic spectra of chloroauric ions in combination with chloro-hydroxy species . Fr. Fr4- io values) . Citrate values) . In addi values) . All theLight scattering is typically very sensitive to the aggregation state of the sample, with the scattering contribution increasing as the particles aggregate to a greater extent. For example, the optical properties of metal nanoparticles change when particles aggregate and the conduction electrons near each particle surface become delocalized and are shared amongst neighboring particles . When thBoth nucleation and growth phases are heavily dependent on pH and its variation throughout the process because citrate ions and chloroauric ions experience pH-dependent speciation . These dIt is known that hydrogen ions are produced from the reaction between gold (III) species and citrate species, thus the redox reaction should clearly be predicted by pH variations over time. Therefore, we have conducted electrochemical experiments to monitor pH during the synthesis of gold nanoparticles. Initial pH values for the two starting solutions for each molecular ratio are reported in The chloroauric acid solution was added to the citrate solution and mixed for 5 s, as reported in the experimental section, and then the pH variations were monitored over time . Once ch- and HA, and consequently, the rapid change in their concentrations is reflected in a sustained lowering or loss of buffer capacity. The first two regions can be reasonably assigned to the induction period, which is ascribed to the initial stage when the nucleation is the predominant mechanism in place, although with slight concomitant nanoparticle growth. In support of this interpretation, the time elapsed until the end of the second region appears to be in good agreement with the behavior shown by the UV–Vis spectra. The pH monitoring also suggests that at the end of the induction period the nanoparticles grow quickly following the nucleation phase (third region). Furthermore, the abrupt variations observed in the third region suggest an activated grow mechanism.The behavior observed in the second region of the graph is probably associated with the buffer capacity of the citrate solution, which is opposed to the change in pH due to the redox reaction. The pH in the second region is almost steady and persists for a sufficient amount of time to guarantee the stabilization of the speciation of citrate and gold (III) chloride. In the third region, the trend changes drastically, probably due to the rapid consumption of AWe used a modified diffusion limited aggregation (DLA) scheme to reproduce the growth of multifaceted nanoparticles. DLA is a classical numerical method that allows the simulation of the aggregation and growth of structures from smaller elements ,60,61. I 0 and 1 . If sp isure (P) :(1)γ=∂G∂In crystals’ growth, the interfacial free energy may be approximated by the simple formula :(2)γ=12 We used an EM DLA scheme to reproduce the growth of nanocrystals. We launched several different simulations in which the shape of the seed was varied to examine whether the morphology of the final aggregate depends on the geometry of the originating nucleus. We used a point, an elongated, rectangular stripe, a square, a triangle, and a disk as a starting pattern. The raster plot of each of these initial seeds is reported in guration b. By enfial seed e. The nuWe used data from the simulations to examine how the numerical aggregates grow over time. We report in o sp=0.1 d, we obsUsing the energy minimization condition, we observed that the shape of the aggregate at the steady state of the process resembles the morphology of the originating seeds a,b. Diffgeometry . Using tical DLA . We measThe aim of the simulations was not to reproduce the shape of each of the particles that were formed by experiments exactly, but to develop a method that is capable of generating nanocrystals—i.e., particles with well-defined shapes and some internal correlation, resulting in structures with high symmetries. The technique, which is based on classical DLA, however, departs from the latter in that it introduces an energy optimization principle, described in the Methods and throughout the paper. This does not have any precedent in the literature for the numerical simulation of DLA aggregates. While this test campaign was not focused on optimizing performance, it is useful to put the results in context. The main conclusion suggested from experiments is that the entire process of growth can be divided into regimes. In the early stage of growth, the concentration of gold in solution reaches a critical value leading to the formation of stable nuclei. Once the nuclei have grown past a certain size, they become seeds, with a variety of different configurations, constituting the base for the successive particle synthesis, where the preferential absorption of ions to the aggregate determines particle growth. In this phase, because of the very small density of nuclei in solution, the relatively low amount of citrate, and low temperature, the growth is predominantly unidirectional—i.e., ions adhere to the aggregate along the preferential directions of growth. Unidirectional anisotropic deposition of ions onto the aggregate results in particles with regular shapes, high symmetries and crystal structures. The mathematical model that we have developed simulates the characteristics of real gold nanoparticles with accuracy, especially pertaining to particle shape, particle size and the dynamics of growth.In the model, the shape of the aggregate shows a very high sensitivity to the configuration of the originating seed. Thus, once the configuration of the seed is determined, the shape of the aggregate will bear a very close resemblance to the originating template at each instant of time. This is analogous to experiments, where the configuration of the nuclei governs particle growth after the initial induction phase. Low citrate content, low temperature, and the absence of possible external elements of interference are among the causes assuring that the energy minimization of the system is maintained throughout particle synthesis. Energy minimization, in turn, leads to unidirectional particle deposition and the formation of gold nanocrystals—i.e., structures with elevated orders, strong internal correlations and high degrees of symmetry. The ability of the algorithm to capture the dynamics of particle growth is relevant. In  diagram b. We theinhomogeneous variables—we can gain information on the process of growth by examining the shapes of the distributions. Notably, both distributions are skewed to the right, with a coefficient of skewness for the particle size distribution of about We examined the ability of the model to reproduce the shape of the size distribution of particles obtained under certain experimental conditions. position e. While In summary, we have demonstrated the synthesis of dichroic gold sol at room temperature by an ecofriendly route. We found out that the color of the transmitted light can be easily manipulated by the addition of a third molecule to the reaction mixture. Electron microscopy and UV–Vis spectroscopy have been used exclusively for characterization. At room temperature and using a very low amount of citrate, the morphology of gold tended to be non-spherical in shape and a variety of structures were developed in the reaction mixture. This opens new insights into the reduction mechanism of gold ions by citrate molecules.To analyze the aggregation mechanisms of the gold nanoparticles, we have developed a different formulation of classical diffusion limited aggregation (DLA) model that we have called energy minimization DLA (EM DLA) because it maintains the energy levels of the system at a lowest throughout the entire process of growth. The method, that does not have any precedent in the literature for the numerical simulation of DLA aggregates, was able to generate nanocrystals, i.e., particles with well-defined shapes, high internal correlations and high symmetries, similarly to the real particles obtained by experiments. The scheme also reproduced the size and the dynamics of growth of the gold nanoparticles.


Seawater or brackish water desalination is largely powered by fossil fuels, raising concerns about greenhouse gas emissions, particularly in the arid Middle East region. Many steps have been taken to implement solar resources to this issue; however, all attempts for all processing were concentrated on solar to electric conversion. To address these challenges, a small-scale reverse-osmosis (RO) desalination system that is in part powered by hybrid photovoltaic/thermal (PVT) solar collectors appropriate for a remote community in the Kingdom of Saudi Arabia (KSA) was designed and its power requirements calculated. This system provides both electricity to the pumps and low-temperature thermal energy to pre-heat the feedwater to reduce its viscosity, and thus to reduce the required pumping energy for the RO process and for transporting the feedwater. Results show that both thermal and electrical energy storage, along with conventional backup power, is necessary to operate the RO continuously and utilize all of the renewable energy collected by the PVT. A cost-optimal sizing of the PVT system is developed. It displays for a specific case that the hybrid PVT RO system employs 70% renewable energy while delivering desalinized water for a cost that is 18% less than the annual cost for driving the plant with 100% conventional electricity and no pre-heating of the feedwater. The design allows for the sizing of the components to achieve minimum cost at any desired level of renewable energy penetration. Currently, the world population affected by water shortages is nearly 40% . The curhortages . Most of3 per day) of the worldwide capacity. Over the next 20 years it is predicted that the KSA will need to increase this output by 6 million m3 per day [3 of desalinized water [The Kingdom of Saudi Arabia (KSA) is the largest producer of desalinized seawater, with 17%  to supply fresh water. In remote communities that have periodic water shortages, small mobile desalination units are often used. There are two basic types of desalination: thermal and membrane. Globally, 68% of desalination is membrane-based, 30% is thermal, and the remainder uses other processes . Within RO operates by allowing the passage of water molecules, excluding salts and other impurities, through special membranes by applying high pressure. RO is the most common membrane process because of its low energy requirements and greater recovery percentage . RO desaThe goal of the research described herein is to optimize the integration of PVT for a small-scale desalination plant appropriate for a remote community in the KSA. The design uses a mix of PVT and conventional electrical power to drive RO desalination. The PVT thermal output can raise the feedwater temperature, thus reducing the viscosity and the power required for pumping, improving RO performance, and the PVT electrical output provides some of the RO power needs. Excess PVT electrical power may be stored in a battery for nighttime desalination, along with grid power as needed, to maintain continuous RO production. The following describes the structure of this paper. First, a detailed illustration of the methodology and the model used in this study is present in Although there are several PVT configurations, the type considered here is a flat-plate collector. The basic structure of this collector displays as a cross-section in Fluid circulates beneath a layer of standard PV cells, extracting heat from the cells and allowing them to operate at a lower temperature with higher electrical efficiency. There are ways to make such a structure favor the electrical or thermal output. For example, using an extra layer of glass on top of the PV cells increases the temperature and improves thermal conversion of the incident solar energy, but somewhat degrades electrical performance . Anotherllectors . The PVT model equations used to determine thermal and electric energy production are based on conservation of energy principles . The surThe quantity In this Equation, The collector heat removal factor is given by the following Equation, Beckman , Tiwari  Beckman , and Tiw Beckman . FinallyThe electrical power from the PVT panel is given byThe electrical efficiency of the PV/T panel is given by:Typical meteorological year (TMY) data for a specific location are used to provide hourly solar irradiation  the sun . The effA direct (open) configuration for the storage tank system is defined such that the water in the tank does not circulate through the PVT array. Instead, some of the brackish source water passes through the PVT array to gain heat and then flows directly to the storage tank. At night, or when the air temperature is too low, the source water bypasses the PVT array and flows directly to the tank. The total volume of feedwater entering and leaving the tank at each time interval is constant. The temperature in the tank therefore fluctuates according to the available solar energy. Auxiliary heating is used to maintain the tank temperature above a specified temperature The following energy balance equation utilized governs the tank and determines the tank temperature variations in time.The tank mass The useful heat from the PVT array that is passed into the tank The tank surface area is Making this substitution into Equation (12) and solving for 3/day. The RO modeling Equations described in [RO operates by forcing brackish water to flow through a membrane under high pressure. Water molecules pass through the membrane to form a flow of fresh water, while ions and other molecules are rejected with wastewater. Two high-pressure pumps are required to maintain constant pressure on the membrane, forming the RO electrical load age tank . A higheribed in , along wThe other significant load component for the system is the power required for pumping water through the PVT and tank from the reservoir source. There will be Referring to The PVT electrical output is split at each hour The total electrical load, Characterization of the battery storage includes the following three parameters: a maximum storage capacity Additionally, the battery charging and discharging at the same time is not allowable. At each hour, the dispatching proceeds based on Equations (19)–(22) and a few simple rules. If the electrical load exceeds PVT output, then all of the output is dispatched to the system and the battery satisfies as much of the remainder as possible, with grid power used as a last resort. If PVT output exceeds the load, then as much of the excess PVT power as possible is stored in the battery, and any remaining power is sold back to the grid.3/day of distilled water, a location for the TMY3 data, and four system parameters: Using the models for the PVT, thermal storage tank, RO, and electrical dispatching, a single dynamic model simulation for the system is constructed. The system is characterized by a fixed production level of 362 mThe PVT electrical output is only large enough to meet the full load during part of the day. At other times, either the battery or the grid power makes up the rest of the load. The battery and PVT array sizes chosen as such that the load (zero curtailed PVT power) can utilize all of the PVT electrical power output. Therefore, it is notable that expanding the size of the PVT system to function completely on renewable energy significantly adds to the system cost.To get a sense of average system performance, The system performance as illustrated by This section presents a model for total annual plant cost, represented as the sum of payment towards an amortized loan and annual operating costs (grid-power purchases plus maintenance). Both the loan payment and operating costs are functions of the PVT array size, the battery capacity, and the tank size. The up-front system capital cost functions as an investment repaid via a loan with a fixed interest. Operating costs are determined by simulating for one year. The full system capital cost is determined by the following components: PVT array, batteries, RO, storage tank, high-pressure pumps for the RO, and low-pressure pumps for moving water through the PVT. The PVT capital cost computes as the product of the number of panels with a per-panel price. Similarly, the battery capital cost is proportional to its storage capacity KSA encourages and offers incentives to effectively reduce this up-front cost burden, modelled here as a renewable credit projects . The entThe annual grid cost is found by running the dispatch model for the full year and summing all of the hourly grid energy purchases approach . The griInput the PVT array size, tank volume, and battery capacity.Compute the hourly PVT useful heat and electrical energy output, tank temperatures, and RO electrical demandOperate the hourly electrical dispatching simulation to determine system energy flows, grid purchases, etc.Determine the average renewable penetrationEvaluate the total system cost using Equations (21)–(25).The total cost viewable as a nonlinear objective function, which depends on the PVT array size, the tank volume, and the battery storage capacity. The total cost optimization over these variables, while keeping all other parameters  constant is a necessity. Furthermore, it is possible to perform cost optimization while constraining the average renewable penetration level. Evaluating the cost objective function requires the following steps.fmincon” package, which implements sequential quadratic programming to find the two PVT array dimensions, tank volume, and battery capacity to minimize cost with constraints on the renewable penetration. The cost objective function is optimized using Matlab’s “3/day of distilled water. The following sub-sections describe the performance of the individual system components in detail, along with the components of optimized cost.The cost function is minimized when the PVT supplies 70% of the total system electrical energy needs (70% penetration), with conventional grid power supplying the remaining 30%. In this case, the PVT array size is 10 panels in series  plotted in The non-linear cost objective function was minimized with constraints on the renewable energy penetration, which allows for identifying the level of penetration that produces the lowest cost, and it allows for a comparison of extreme cases (very low and very high penetration). Each cubic meter of purified water produced by the RO system requires a certain amount of electrical energy, depending on the feed-water temperature. In terms of economic cost, the PVT and additional hardware increase the portion of the annual cost due to payment towards the capital. The benefit for PVT, however, is the lower operating costs, as the PVT reduces the RO electrical energy needs and supplies 70% of that electrical energy. In this research, a theoretical approach to building a low energy cost desalination system powered by renewable energy is an optimistic proposal. The research contributes to the knowledge in the design of a low-cost desalination system and that building this in remote areas in the Mediterranean region is beneficial. In particular, this work presents a design for optimizing the integration of PVT into small-scale desalination. This is appropriate for a remote community in KSA, such that the PVT electrical output and conventional grid power will satisfy the electrical load for the plant and the excess PVT electrical power may be stored in a battery for nighttime desalination, along with grid power as needed to maintain continuous RO production. The PVT thermal output can raise the feedwater temperature, improving RO performance. The energy demands for RO reduces by preheating the feed brine. The non-linear cost objective function minimizes with constraints on renewable energy penetration. When the PVT supplies 70% of the total system energy needs (70% penetration), the cost decreases. The dynamic modeling for this study indicates that the optimal PVT, hot water tank, and battery capacities are


Accurate estimation of 3D object pose is highly desirable in a wide range of applications, such as robotics and augmented reality. Although significant advancement has been made for pose estimation, there is room for further improvement. Recent pose estimation systems utilize an iterative refinement process to revise the predicted pose to obtain a better final output. However, such refinement process only takes account of geometric features for pose revision during the iteration. Motivated by this approach, this paper designs a novel iterative refinement process that deals with both color and geometric features for object pose refinement. Experiments show that the proposed method is able to reach 94.74% and 93.2% in ADD(-S) metric with only 2 iterations, outperforming the state-of-the-art methods on the LINEMOD and YCB-Video datasets, respectively. The pose of an object contains vital information to mimic how humans describe the position and orientation of real-world objects appeared in their vision. Making accurate estimate of the object pose favors not only robotic pick-and-place applications  but alsoTraditional pose estimation methods can generally be divided into two categories: feature-based methods ,3,4 and Thanks to the rapid development of powerful graphical processing units (GPU), the data-driven techniques have made a great leap in pose estimation ,9. RecenAs an attempt to solve the above-mentioned problem, this paper proposes a pose estimation system which contains a pose estimator and a novel iterative refinement process, where the former roughly makes a pose estimate and the later revises the estimated pose to obtain better estimation result by iteratively updating the input data of the pose refinement network in both geometry and color. Because the refinement process uses basic image processing techniques, it is very simple for implementation. Although the pose refinement network mainly depends on geometry features, color features can be helpful for further improvement. Experimental results show that the performance of the proposed pose estimation system reaches 94.74% and 93.2% in accuracy with average distance of model points (ADD) metric, outperforming state-of-the-art methods on the LINEMOD ,29 and YThe rest of the paper is organized are follows: The entire pose estimation process  containsFurther robustness of pose estimation can be obtained with the availability of depth data. In fact, the depth of a target object is helpful to perform 3D localization and detect texture-less objects for pose estimation. For approaches ,31 usingx, y) in the cropped depth map generates a 3D point  in the point cloud as follows:x, y), s is the camera scale factor, and  are the camera internal parameters.When an image with 640 × 480 resolution is captured by the camera, object detection is applied to label the target object in the image. According to the detection result, we then generate a mask by applying the method in  where thIn this step, the features are gathered and described in a higher-level manner before being sent into the following pose estimator. Both the cropped image and the corresponding point cloud data are separately taken as the inputs of two independent neural networks to generate color embedding and geometry embedding, respectively. The cropped image is normalized and then fed into a Pyramid Scene Parsing Network (PSPNet)  for geneIn the pose estimation stage, the rotation matrix and the translation matrix are estimated in this step based on the dense data. In the forward process of propagation, the input dense data pass through a CNN to generate a quaternion rotation matrix, a translation matrix, and a confidence value given the target object. Since we built our method upon DenseFusion , we use f asn is the total number of the pixel positions projected from the chosen point cloud, and in is the number of the projected points which lie within the bounding box region. If f is greater than 0.8, we launch the following image modification and embed the modified image into color embedding at the last step of the refinement process. Otherwise, the previous color embedding is used for the next iteration. The stage of pose refinement is an iterative refinement process which learns how the pose is gradually varied to narrow the gap between the prediction and ground truth. In fact, the residual of the predicted pose is learned by iteratively setting the current transformed point cloud as the new input data of the refinement network. That is to say, the geometry embedding is changed based on the predicted pose during the iterative process. Compared with the structure of DenseFusion , we extebI indicating the current pose projection. The resulting image oI iscI is the cropped image, “G(x) is a two dimensional Gaussian blur function with zero mean. The logical AND and NOT operators are implemented with OpenCV open source functions “CV.bitwise_and” and “CV.bitwise_not”. Although there is a binary mask generated in the data acquisition stage, it is our goal to utilize the available source in the inner network and maximize the use of the predicted pose for improving the performance of the pose refinement process.The image modification is a process that blurs the entire region except the ROI. The purpose of this modification is to reduce the redundant factor of the color embedding. This is because the color embedding of the cropped image is a high-dimensional vector containing the gradient of color at each pixel position. If we blur the surrounding region of ROI, the amount of the redundant gradient can be suppressed in the feature embedding process, resulting in a better pose refinement performance. To accomplish the task, image processing is applied to the cropped image. In order to evaluate the proposed pose estimation system, we conduct our experiments on Intel (R) Core(TM) i7-7700 @ 3.6GHz and a NVIDIA GeForce GTX 1080 graphic card. The well-known LINEMOD and YCB-Video datasets  are chosThere are two metrics for performance evaluation in this paper, i.e., the average distance of model points (ADD)  and the In the test of AUC on the LINEMOD dataset, the proposed method reaches 94.79%, which is slightly better than 94.49% of DenseFusion. According to the experiment in , we plotThe advantage of the proposed method is that we improve the pose refinement process by adding an image modification based on both geometric and color components. In addition, the image modification step of the proposed method includes only basic openCV functions which bear a low computational cost. Specifically, the execution time of the image modification step is around 24 ms per frame. We believe that there is room for improvement if the codes can be executed on GPU. There are, however, the limitations of the proposed method, which lie in the 2D projection process and the parameter setting of mask-generating in the image modification step. The former indicates that the initial estimated pose has to make a proper 3D-to-2D projection close to the ROI region for the following mask-generating process. Otherwise, the blurring process will incur negative impacts to the generated color embedding since the important color features are suppressed. Moreover, 2D projection process needs a careful selection of the launch time of the image modification in the training process. The later indicates the need of an adaptive kernel size selection for generating the mask in the pose refinement process. If the projected point cloud is not sufficiently dense enough, the kernel size of morphology opening has to be adaptively increased for hole filling process. It is our plan to remove these limitations by adopting learning techniques in the future.We developed a novel iterative pose refinement process that utilizes the predicted pose to update both the color and geometric embedding for obtaining better performance on object pose estimation. Since the color embedding for pose estimation contains high-dimensional information extracted at the local region of an image, our method aims at reducing the image redundant factor so that the embedding data can suppress the interference of surrounding objects. Thus, the proposed method can reduce estimation error when the color of surrounding objects is similar to that of the target object. Experimental results show that the proposed method outperforms the state-of-the-art DenseFusion method in both ADD and AUC metrics. Moreover, the design of the proposed refinement network only utilizes the available data of the inner network. This makes the proposed method flexible to support other designs for object pose estimation.


Bayesian inference is increasingly popular in clinical trial design and analysis. The subjective knowledge derived from an expert elicitation procedure may be useful to define a prior probability distribution when no or limited data is available. This work aims to investigate the state-of-the-art Bayesian prior elicitation methods with a focus on clinical trial research. A literature search on the Current Index to Statistics (CIS), PubMed, and Web of Science (WOS) databases, considering “prior elicitation” as a search string, was run on 1 November 2020. Summary statistics and trend of publications over time were reported. Finally, a Latent Dirichlet Allocation (LDA) model was developed to recognise latent topics in the pertinent papers retrieved. A total of 460 documents pertinent to the Bayesian prior elicitation were identified. Of these, 213 (45.4%) were published in the “Probability and Statistics” area. A total of 42 articles pertain to clinical trial and the majority of them (81%) reports parametric techniques as elicitation method. The last decade has seen an increased interest in prior elicitation and the gap between theory and application getting narrower and narrower. Given the promising flexibility of non-parametric approaches to the experts’ elicitation, more efforts are needed to ensure their diffusion also in applied settings. The frequentist inference paradigm has been the main statistical approach to the design and analysis of clinical trials since the 1940s [However, the improvements in statistical computing methods and the introduction of the Markov Chain Monte Carlo (MCMC) algorithm have facilitated the spread of the Bayesian methods, also in the field of clinical trials .The prior distribution is a key element of Bayesian inference and represents the information about a parameter of interest that is combined with the likelihood to yield the posterior distribution. The prior information may be derived from either expert beliefs (subjective prior) or relevant empirical data (objective prior) ,4. Especially when few data are available to estimate the likelihood, for example in clinical trials in rare diseases  and poorMoreover, it is interesting to consider that, the development of user-friendly interfaces, as SHELF (SHeffield ELicitation Framework)  or MATCHThe SHELF software carries out elicitation of probability distributions for uncertain quantities from a group of experts. Each expert provides a small number of probability opinions corresponding to points on a cumulative distribution function. The SHELF tool fits a range of parametric distributions displaying them in the form of fitted probabilities and percentiles. For multiple experts, a weighted linear pool of the subjective distributions can be calculated . Another useful tool provided in the literature is MATCH, which provides a web-based interface for the SHELF routine with the aim of being more user-friendly, including also features for the conduction of the elicitation process remotely .The elicitation process is usually performed by asking the experts to report a few summaries of treatment effect, generally medians, modes, and percentiles of the probability distribution. Some authors assessed that the role of a facilitator is fundamental in the elicitation process. The facilitator translates some percentiles, defined by experts, into a probability distribution. This process is generally based on parametric distributions  . This taThe elicitation approach accounts for the subjective expert’s uncertainty about the treatment effect under investigation, and the consequences of this uncertainty in final inference can be investigated using sensitivity analysis techniques . Quantiles information about expert beliefs is generally easier to elicit than moments . ProbabiQuantiles information are widely adopted, to fit prior probability distributions, not only in a parametric but also in the semiparametric and non-parametric setting; for example, it is possible to ask the expert the quantiles  of the subjective prior distribution. These points may be plotted, and it is possible to smooth a distribution function drawn through them using a semiparametric or non-parametric representation of the expert’s opinion ,21.In a parametric setting, the elicitation process assumes that experts’ opinion may be represented by a good note family of probability distributions identified by hyper-parameters. Thus, the elicitation consists of the definition of appropriate values for hyper-parameters to represent the experts’ belief .It is widely assessed that the main limit of a parametric approach is to constrain expert belief into a pre-specified distribution . TherefoThis work is aimed to investigate the state-of-the-art of Bayesian prior elicitation methods, focusing on the discrepancy between the available methodological approaches in the statistical literature and the elicitation procedures applied within the clinical trial research. In this general framework, another issue is the identification of the main research topics and the definition of the peculiarities of papers using parametric and non-parametric approaches in a clinical trial concerning identified research themes. A tool that automatically allows classifying the overall elicitation literature could reduce the manual text classification burden and characterise topic patterns over the time.A search on the Current Index to Statistics (CIS), PubMed, Scopus, Embase, and Web of Science (WOS) electronic databases, finalised to identify all papers dealing with prior elicitation and published from 1 January 1980 to 1 November 2020, was performed. The search string “prior elicitation” was used. This search string is very general to ensure that all relevant results would be included in the final analysis. The pertinent articles were identified after duplicate removal. The overall prior elicitation literature and the articles pertaining to the prior elicitation in the clinical trial have been screened by reading the title and abstract. Summary statistics were reported to describe the corpus of papers pertinent to the prior elicitation theme. ® [The prior elicitation-relevant articles have been classified in those published in “Probability and Statistics” journals  according to the Journal Citation Reports®  classifiAs for articles concerning drug clinical trials, the frequencies of published papers have been reported according to publication time and prior elicitation methods, in parametric and in not (or semi) parametric settings. Methodological approaches to the prior elicitation currently used in clinical trial literature have been described, evaluating the main characteristics of parametric and non-parametric approaches adopted in trial design and analysis distinguishing by type of outcome considered in the study.For a general comparison purpose, available methods for expert elicitation in the overall pertinent prior elicitation literature have been also reported and described. A text mining (topic model) analysis has been conducted to automatically identify the main topics characterising the overall publications on prior elicitation. The literature on clinical trials could constitute a limited subset of the total literature on prior Elicitation. For this reason, this subset was used as a validation set by classifying the documents manually and comparing the outcome of the manual classification with the automatic one. Topic modelling is an unsupervised machine learning technique that is capable of automatically clustering word groups (topics) and similar expressions that best characterise a set of documents . The titles and abstracts of prior elicitation pertinent papers have been pre-processed. Punctuation, stop words, white spaces, and numbers were removed. Redundant words  were also removed. All words were converted to lowercase.Once the text corpus has been cleaned, a Document-Term Matrix (DTM) has been created. A DTM is a matrix, reporting documents (articles) by rows and words by columns; a generic element of DTM is the word counts. To detect topics, a Latent Dirichlet Allocation (LDA)  analysisThe method aims to infer the latent topic structure given the words and document. LDA recreates the documents in the corpus by adjusting the relative importance of topics in documents iteratively using a Gibbs sampler algorithm . Gibbs sampling works by performing a random walk. The starting point of the walk is chosen at random; for this reason, it may be useful to discard the first steps (burn-in period). Overall, 10,000 iterations have been considered in the computation, and 100 draws have been discarded as burn-in. A total of five Markov chains with different starting points were generated. The number of topics has been chosen following the maximisation criterion of the Deveaud measure . The metThe algorithm has been validated on the clinical trial pertinent articles. Furthermore, the overall accuracy has been calculated, comparing the manual and automatic classification.The convergence of the LDA algorithm has been evaluated showing the Log-Likelihood in correspondence of the first 500 iterations. If the Log-Likelihood estimate stabilises after the first iterations, then the convergence is deemed acceptable .Once the algorithm has been validated, the distribution of the publication topics identified by the algorithm on the prior elicitation literature has been characterised according to the year of publication and the field of application .Computations have been performed using R 3.3.2  System w® classification [A total of 3725 articles have been found performing the literature review. Among them, 470 articles are identified as pertinent to the Bayesian prior elicitation theme . Of thesfication .As per the temporal pattern of the prior elicitation literature, it is possible to observe that, until 2010, there is a greater number of publications in the statistical literature compared to other research areas; the pattern is reversed starting from 2009 to November 2020 .Concerning the clinical trial research setting, it is possible to observe that 42 articles out of 470 deal with this research argument. Moreover, according to temporal trends, an increase in the number of publications concerning clinical trials is observed over time; 2 articles between 1992 and 2000, 10 in the period comprised between 2001 and 2008, 15 between 2009 and 2016, and 15 between 2017 and 2020.Considering continuous and time to event outcomes, Normal or Log-Normal priors are the preferred distributions for the elicitation procedure in 22 research articles. Survival endpointsThe Normal prior distribution is used in several fields of application:The Gaussian distribution is a used solution to define priors on hyper-parameters for a survival function assuming a Weibull time to event shape relation . The autIn several cases, log-hazard ratios are also modelled as a normal distribution. Histograms representing the prior beliefs of each investigator were constructed and interpolating the Log Hazard ratio with a Gaussian distribution ,62. ThisThe poling of the expert opinion may be performed by calculating the average of the height of the prior distributions for each parameter value (average pooling) or computing a geometric mean of the original densities (logarithmic pooling). Both techniques allow for different weights to be given to each opinion depending on the clinician’s experience in the area under study .Models hyperparametersThe normal approximation of experts’ opinion is also implemented to model parameters of Bayesian logistic regression. The method models the response as a Bernoulli random variable assuming the regression coefficients as a mixture of three normal distributions reflecting increase, decrease, and no substantive change in the response . Moreover, the Gaussian priors have been considered also to define the hyperparameters for an adjusted hierarchical model for the miscounting count predictions of the Poisson and negative binomial models. The parametrisation has been proposed and applied to a large randomised controlled trial on Chronic Obstructive Pulmonary Disease . The autStudy designThe Normal distribution has been also proposed in multi-stage trials to elicitate a prior for the treatment effect estimation and then calculating the probability that the trial will produce a favourable outcome; the decision to proceed with a larger trial has been translated in a prior probability distribution incorporating the information provided by a smaller trial . The treThe normal prior elicitation is also considered for the Bayesian clinical trial design. Recent research evaluates the prior impact on the observed data model by introducing the effective current sample size (ECSS) prior approach. Special emphasis is put on the robust mixture, power, and commensurate priors defined on a normal and beta parametrisation .The Gaussian random variable is considered in literature also to perform a prior elicitation for a survival function in the context of a Bayesian clinical trial planning . The autTreatment effect estimationAnother application of this prior parametrisation is used to elicitate the mean change score in a rare disease trial once the consensus among the experts has been reached . The stuIn other cases, continuous outcomes, defined on log scales, are modelled eliciting experts’ opinions with normal distributions . IndividAdditionally, cost data, typically highly skewed, are elicited using Log-Normal transformation . The resMultivariate distributions and mixture of priorsIn several cases, the overall prior distribution is developed by a weighted mixture of the single expert priors . The mixA Bayesian method has been proposed and applied to a colon cancer trial where the expert information is used to perform a variable selection procedure . A bivarIn the CHARM clinical trial, the log-hazard of cardiovascular death has been modelled via Multivariate Normal distribution . The anaThe bivariate normal parametrisation has been also considered, in a two-stage phase I–II clinical trial design to optimise dose–schedule regimes where a flexible Bayesian hierarchical model has been used to account for the relation among patients subgroups and treatment regimens .Other parametric distributions are considered in the literature for the continuous outcomes, for example, surgical learning curve parameters (first procedure and plateau level) are obtained averaging different experts’ opinion, using a power–law function .The inverse gamma distributions served, instead, to model the accrual rate monitoring in a clinical trial. The posterior predictive accrual distribution has been obtained combining prior information on the accrual rate, provided by experts or historical data, with the information known up to the monitoring time point .In another case, Laplace’s and Jeffreys’s priors are elicited to estimate a competing risks model with covariates . LaplaceLaplace’s distribution is a continuous probability distribution also note as a double exponential because its density can be seen as the association of two densities of exponential laws. Laplace’s law can also be obtained from the difference of two independent exponential variables with the same parameter . This diThe Jeffreys prior instead is a non-informative prior distribution. In agreement with the Jeffreys rule, a prior distribution is uninformative if its density function is proportional to the square root of the determinant of the Fisher information matrix ,78.Generally, prior probability distributions for binary outcomes are elicited in terms of Beta priors ,46,56,58SHELF elicitation procedureThe SHELF elicitation procedure is a widely used approach to elicitate Beta event rate in a clinical trial  and is tIn the roulette method, the expert provides probabilities of the treatment effect lying in a particular “bin” by allocating “gaming chips” to that bin. The method provides a graphical representation of the provided expert beliefs .Another research underlines the feasibility of a SHELF elicitation procedure for the evaluation of drug safety or efficacy in a hypothetical early-stage trial. A beta prior has been considered for the elicitation of the expert’s opinions .A sequential update of the experts’ opinion is also reported in veterinary trials by using a SHELF elicitation procedure on the beta event rate. This research has demonstrated the usefulness of probabilistic elicitation for evaluating the diversity and strength of experts’ beliefs concerning the efficacy of systemic antibiotics as dry cow therapy .This software is often used for the computer-based elicitation procedure; the distributions are interactively elicited by showing to the experts the priors obtained through the software. Other elicitation procedures are based on (1) informal discussion (2) structured questionnaires (3) Structured interviewing with poling of opinions .Dose-response curvesIn some cases, a normal distribution has been assumed on parameters characterising the dose-toxicity curve in Phase I clinical trial . A phaseThe Log-Normal and Normal prior parametrisation has been used also to develop generalised priors for different Bayesian Dose–Response parametric models .A parametric distribution is also adopted in the literature for categorical endpoints by using the log transformation of odds ratios modelling binary data using elicited Normal priors . OpinionHistogram approachA total of eight articles ,53,61,70Graphical visualisation of the expert opinion in histogram defined on parameters of a log-hazard function is a possible approach used to perform elicitation of the expert opinion. The method is flexible leading to define hazard regression coefficient with parametric distributions also allowing for non-parametric adjustments using more general copula combinations of marginal distribution . IndividStudy design and power prior approachThe use of historical information to define the prior distribution in a non-parametric context is a method recently used in the literature . InformaThe approach is widely used for the design and analysis of clinical trial data. The method is useful for handling problems related to a lack of exchangeability between the historical and current data, and the risk that prior information overwhelms the clinical trial data information .In a sequential clinical trial, for example, a power prior approach is considered to weight the prior information together with the ESS (Effective Sample Size) approach is used to set the maximum desired amount of information to be shared from historical data at each step of the trial . The ESSRecently, some efforts are evidenced in the literature to incorporate, in the study design phase, the alternative procedure to the prior definition. The method is tailored on a phase IIA trial and represents a Bayesian counterpart of a Simon two-stage design using historical data and semi-parametric prior’s elicitation methods .Dose findings in early phase trialsNon-parametric approaches are also considered to find a maximum tolerated dose in Phase I clinical trials using the Continual Reassessment Method design and proposing a suitable informative prior distribution on the relationship between outcome data and covariates ,84. In aPhase II-III trial. The prior elicitation has been applied (16 studies) to the trials for an efficacy assessment within phase II or III trials . The priIn other cases, different hypotheses are defined on the informative prior parameters ,62. DiffEarly Phase I-II. Seven studies implemented the prior elicitation in early phases trial for the safety assessment ; the greThe analysis was performed on textual data of 470 articles. Two topics were selected for analysis because the maximum value of the Deveaud metric is 2.3 and has been reached in correspondence of two topics. Among the most frequent words , the redThe features pertinent to each topic are shown in The first one, here in after referred to as applied topic, is more related to the empirical application of the prior elicitation methodsThe second topic, here in after referred to as theoretical topic, seems to be related to the theoretical implications of the prior elicitation procedureObserving the predictions of the LDA algorithm according to publication year  it is poMoreover, comparing LDA results about trial articles with the overall pertinent literature on prior elicitation, it is possible to observe a greater proportion of applied papers in trial pertinent literature, and evidence that a consistent part of theoretical literature is allocated in not pertinent articles .Study findings indicate that starting from 2010, it is also possible to observe a spreading of the prior elicitation techniques in research fields different from the theoretical statistics. This aspect may be related to the recent increase in the popularity of the Bayesian methods in a general setting and the clinical trial research .The increase in popularity of Bayesian methods in a clinical trial involves a need for statisticians to define tools useful for the definition of robust and defensible informative prior distributions .Empirical data may be used to define such priors (objective prior) whenever possible. However, in some cases, the limitations in data availability may preclude the construction of a data-based prior. In this situation, an expert elicitation procedure may be a solution used to define prior distributions .In clinical trial publications, parametric distributions are mostly employed in applied settings. Semi-parametric or non-parametric priors are poorly used within this field, confining them mainly to the theoretical field. This aspect concerns especially less diffused approaches involving non-parametric methods for prior elicitation method. The reason behind the limited application of the non-parametric methods is surely related to the computational effort associated with the definition of a prior distribution which is more flexible and adaptable to the expert opinion but, in several cases, leads to obtaining posterior distributions difficult to be expressed in the closed-form .It is important to consider that, in some research contexts, the translation of the experts’ opinions into a pre-specified family distribution may be considered a limitation because many different distributions may be more suitable to the experts’ opinions generally expressed in quantiles .In recent years, not only parametric but also non-parametric methods to the elicitation of expert opinion are treated especially in the theoretical literature.However, in clinical trial research, the conventional parametric methods are the more adopted procedures to the elicitation of expert opinion, leaving non-parametric methods predominantly in a statistical field.Given the potential of prior elicitation to a better decision on making, more efforts are needed to ensure diffusion of the prior elicitation facilities, not only in theoretical statistical research but also in applied clinical trial settings, both at the design and analysis stage.The prior elicitation methods are recently appealing not only to statistical literature but also in other research settings. It is possible to observe that the methods are increasingly used in general literature and clinical trial research.However, in this framework, conventional parametric methods are more popular in clinical trial research. The non-parametric approaches are, in several cases, treated specially in the theoretical literature which is mainly focused on a statistical argumentation.


In order to obtain comprehensive assessment of the factors influencing fatigue life and to further improve the accuracy of fatigue life prediction of welded joints, soft computing methods, including entropy-based neighborhood rough set reduction algorithm, the particle swarm optimization (PSO) algorithm and support vector regression machine (SVRM) are combined to construct a fatigue life prediction model of titanium alloy welded joints. By using an entropy-based neighborhood rough set reduction algorithm, the influencing factors of the fatigue life of titanium alloy welded joints such as joint type, plate thickness, etc. are analyzed and the reduction results are obtained. Fatigue characteristic domains are proposed and determined subsequently according to the reduction results. The PSO-SVRM model for fatigue life prediction of titanium alloy welded joints is established in the suggested fatigue characteristic domains. Experimental results show that by taking into account the impact of joint type, the PSO-SVRM model could better predict the fatigue life of titanium alloy welded joints. The PSO-SVRM model indicates the relationship between fatigue life and fatigue life influencing factors in multidimensional space compared with the conventional least-square S-N curve fitting method, it could predict the fatigue life of the titanium alloy welded joints more accurately thus helps to the reliability design of the structure. Welded components have been widely used in the engineering equipment field under static or dynamic load circumstances because of their advantages of good connectivity, light weight and ease of use. Due to stress concentration however, the welded joint becomes one of the weak links of the structural reliability of the product. This causes great hidden dangers to the safety and normal work of the structure.Currently, three popular fatigue life analysis methods of welded joints have been proposed, which include S-N curve method, local stress strain method and fracture mechanics method . CompareThermodynamics entropy has been used for fatigue life prediction for a long time. For example, a damage metric based on the second law of thermodynamics and statistical mechanics was presented . The proMeanwhile, from the perspective of information entropy, the principal author’s team has proposed an evaluation model of aluminum alloy welded joint low-cycle fatigue data based on information entropy . In ordeIn the finite element stress calculation the results are affected by mesh size, which causes inconsistency in calculations for different structures. In order to address this problem, structural stress based on the line force is first defined in the nodal force based structural stress method.yF is the vertical stress in the weld toe, xM is the moment around the weld toe. The normal structural stress at each node is defined asm is the crack propagation exponent in the conventional Paris law, taking on a value of about 3.6 , in order to prevent the particle from being too fast to miss the optimal solution. The algorithm ends when the maximum number of iterations is achieved or the specified accuracy requirements are met.The velocity of each particle SVRM  is a supb is the threshold. The optimization problem to be solved by SVRM could be described by Equation (19), where c is the penalty coefficient used to control the complexity of the model, training error rate and generalization ability, m is the number of training samples:The principles of SVRM can be described briefly. For nonlinear regression, a nonlinear function is used to map training data into a high-dimensional feature space and linear regression is carried out in the high-dimensional feature space. The regression estimation function is set as Formula (18), where ia and i*a are range multiplier, The dual form of the optimization problem could be obtained as Equation (20):Generally speaking, the most commonly used kernel types in SVRM includes linear, polynomial, radial basis function (RBF), sigmoid and pre-computed kernels. Since only one parameter needs to be determined in RBF and it has global performance similar to other kernel functions, RBF is chosen as the kernel function of SVRM here.C, the other is the kernel width parameter C controls the complexity of the SVRM model and the penalty level for the wrong samples. If C is too large, the prediction accuracy of SVRM in training phase is very high, but in testing phase is very low; if C is too small, it is difficult to obtain satisfactory prediction accuracy. The parameter C, too large value will lead to an “over-learning” problem, and too small value will lead to an “under-learning” problem. Therefore, in the SVRM training process, it is particularly important to choose the appropriate parameters for the penalty factor C and kernel function width There are two parameters to be optimized when using RBF as the kernel function, one is the penalty factor assifies  and an iassifies . In this1c, 2c), weight factor The reduction results show that besides the equivalent structural stress range, the joint type influencing factors also play a very important role in determining the fatigue life of titanium alloy welded joints.(2)The fatigue characteristic domain could be determined according to the reduction results of the entropy-based neighborhood rough set theory.(3)A PSO-SVRM model for fatigue life prediction of titanium alloy welded joints is established in the determined fatigue characteristic domain. Experimental results indicate that compared with the traditional least squares method, the proposed PSO-SVRM model could better predict the fatigue life of the titanium alloy welded joints.Entropy-based neighborhood rough set theory is used for analysis of the fatigue life influencing factors of titanium alloy welded joints and the PSO-SVRM model is constructed for fatigue life prediction of the titanium alloy welded joints. The following conclusions can be proposed:Future work will be concentrated on other determination methods of fatigue characteristic domain and further validation of the PSO-SVRM model as more fatigue test samples become available.


The boundary layer height (BLH) determines the interface between the lower and the free atmosphere, and it is a key variable in numerical simulations and aerosol and environmental pollution studies. This article proposes a novel method in conjunction with numerical regularization to analyze the climate characteristics of the marine boundary layer height (MBLH) using 2007–2011 GPS-RO data from the COSMIC mission. The MBLH corresponds to the smallest gradient, which is calculated using the numerical regulation method where the regulation parameters are determined by the double-parameter model function method. The results reveal the relationship between the MBLH and ocean currents for the first time. A low MBLH is associated with cold seasons and seas where cold ocean currents prevail whereas a high MBLH is related to warm seasons and seas where warm currents prevail. This correlation was validated by comparing the obtained results with different occultation data including atmprf and echprf, which also showed that atmprf is more sensitive to convective cloud top capture. To test the credibility of the results, the standard deviation was used to express the MBLH confidence level. The results show that the standard deviation of the MBLH was highest in low latitudes and lowest in the middle and high latitudes. Furthermore, we analyzed the trends in interannual MBLH variations, which display significant seasonal variations and spatial distributions that correspond with the current and subsolar point. Finally, we conducted a case study in the South China Sea, and identified a distinctive seasonal change and interannual decline in MBLH. The physical processes that take place in the marine atmospheric boundary layer mostly occur at the sub-grid scale ,2, whereIn many recent studies, the data used to detect the boundary layer height include radiosonde data ,5,6, varGPS radio occultation observation technology utilizes the radio waves’ additional phase delay and amplitude change in the atmosphere, which is caused by the interaction of electromagnetic waves emitted from high and low orbit satellites. Furthermore, it can also obtain the bending angle profile of the radio waves due to the atmospheric refraction gradient. Assuming local spherical symmetry of the Earth’s atmosphere, we can know that the bending angle and refractivity have a one-to-one mapping relationship (Equation (1)), and the nonlocal refractive index can be obtained via Equation (2). In the process of obtaining the bending angle and refractivity, we found that the former was more advantageous than the latter when calculating the ABL height. First, the bending angle data is obtained directly from the original, observed optical path length, which has relatively limited observational error characteristics and is more sensitive to the vertical distribution of meteorological elements in the atmosphere. Second, it offers an alternative to calculating the refractivity profile using the Abelian inverse integral. Thus, it avoids diffusion of the bending angle observation error on the refractivity, which is a side effect of a poorly posed Abelian integral, and circumvents the unnecessary error caused by the Abelian weak singular kernel in the process of numerical discrete calculation. So, the COSMIC occultation bending angle data can be reliably used to characterize global MBLH climate change.Given that the boundary layer height  plays a role in improving weather forecast accuracy, climate prediction, and air quality research ,11,13,14Unlike the BLH on land, which exhibits significant diurnal fluctuations, the MBLH changes relatively slowly over space and time because the ocean serves as its underlying surface. Essentially, the strong mixing of seawater makes the physical properties of the surface uniform. In addition, due to its massive heat capacity, even if a large amount of heat from the sun is absorbed, the temperature of the underlying surface, which forces the boundary layer to rise, does not change significantly . DrasticIn this work, we used the numerical differential regularization method combined with COSMIC occultation bending angle data to analyze the trends in MBLH due to climate change in the global ocean. We begin by introducing the data and methods used in our research, then we demonstrate the global distribution of MBLHs, their seasonal variation, and interannual variation characteristics and finally, we summarize our findings.https://cdaac-www.cosmic.ucar.edu/cdaac/index.html), and included 2007–2011 atmprf, echprf, and sonprf products. The atmprf data is a product provided by COSMIC. It assumes that the atmosphere is dry air and provides dry temperature values from the ground to 0.2 hPa. The echprf data is obtained by interpolating the data on the ECMWF high-resolution grid onto the occultation profile, including the pressure profile, temperature profile, water vapor pressure profile, refractivity profile, and bending angle profile. The sonprf data is obtained by interpolating National Center for Atmospheric Research (NCAR)’s radiosonde data onto the occultation profile, and includes temperature, pressure, humidity and refractivity profile data. The global distribution of GPS-RO profiles is shown in In this study, we employed GPS radio occultation (GPS-RO) data from the COSMIC mission. The data was obtained from the COSMIC RO Data Analysis and Archive Center BA(ziThe matrix expression of Equation (4) is:However, if the observation data in Equation (3) has high-frequency components, the vertical gradient of bending angle will have large errors. Therefore, in order to overcome the ill-posedness of Equation (4), we transformed the solution into a problem that requires the objective functional minimum value to be solved as follows:In this paper, a double-parameter model function method ,24 was uThe objective function The damped Morozov deviation equation is:Substituting Equation (9) into Equation (8):For the sake of simplicity, let Let By putting the The numerical regulation method, in combination with the atmprf and echprf products from CDAAC, were used to comprehensively analyze the seasonal variation characteristics of the height of the global ocean boundary layer.  seasons , which pTwo primary modes and the time coefficients of global MBLH were analyzed by Empirical Orthogonal Function (EOF). As shown in We estimated the global MBLH using GPS-RO profiles from the FORMOSAT-3/COSMIC satellites using a new numerical differential regularization method to analyze and compare the MBLH based on three CDAAC products—atmprf, echprf, and sonprf. Compared with the central difference method, this new method can better filter high-frequency noise to obtain more accurate results, but with high computation cost. The annual variation characteristics of MBLH were studied using this method, and we found that the average MBLH is closely correlated with cold and warm ocean currents. The MBLH is relatively low in the sea area near cold ocean currents, and relatively high in the sea area near warm ocean currents. We also investigated and compared the seasonal variation characteristics of MBLH obtained by atmprf and sonprf. The results show that the seasonal variation in the MBLH is related to the north-south movement of solar direct points and the distribution of ocean currents, which was also verified through EOF decomposition of the global MBLH. The comparison between atmprf and echprf demonstrates that atmprf is more sensitive to convective cloud top capture. Finally, the interannual changes in parts of the South China Sea indicate that the MBLH exhibited a downward trend from 2007 to 2011.The numerical regularization method proposed in this work is suitable for fitting functions of discrete data, and can effectively avoid data errors, thus providing stable and reliable results. With further work on the modification of this method, we expect the MBLH found by the method proposed in this paper could be incorporated into climate models to significantly improve the accuracy of future climate forecasting.