Housing adaptations have been identified as an important environmental and prevention intervention for older adults, which may improve health and quality of life. The onset of disability in bathing can act as a warning for further disability in other activities and may therefore be a judicious time-point for intervention. The aim of this study was to determine the feasibility of conducting a Randomised Controlled Trial (RCT) of bathing adaptations, to evaluate whether they improve older adults’ perceived health status and quality of life, prevent further functional deterioration, and reduce the use of other health and social care resources. This study was conducted in preparation for a powered RCT.> 65 and referred to local authority housing adaptations service for an accessible flush-floor shower. Participants were randomised to either usual adaptations (3–4 month wait) or immediate adaptations (no wait). Outcomes were assessed at 3, 6 and 9 months and included perceived physical and mental health status, health and social care related quality of life, independence in activities of daily living (ADL) and bathing, and falls. Data on costs and the use of health and social care resources were collected during follow-up in order to inform a definitive health economic evaluation.Eligibility criteria were aged Sixty participants were recruited and randomised, 31 to immediate adaptations and 29 to waiting list control. Mean age was 77(SD8), 58% women and 58% living alone. Follow-ups were completed with 90, 85 and 72% at 3, 6 and 9 months respectively. Adaptations were delivered to 65% of participants within the requisite timescales as there were delays with some privately owned properties. There were improvements from baseline in both groups on all outcome measures following the completion of the adaptations.This is the first RCT of housing adaptations in the UK. We demonstrated the feasibility of using a waiting list control, subject to minor alterations to the timescales for privately owned properties. A powered trial would evaluate the impact on older adults’ quality of life and investigate the impact of waiting times on functional outcomes and health and care resource use.ISRCTN14876332 Registered 12 July 2016.The online version of this article (10.1186/s12889-018-6200-4) contains supplementary material, which is available to authorized users. People aged 65 and over spend more than 80% of their time at home  demonstrIn a review of national and international evidence, housing adaptations were identified as one of the ‘ten most promising’ prevention interventions for older adults . A housiThe Care Act 2014 has placed a duty on local authorities in England to provide services that prevent or delay the need for other health and social care services . AlthougFalls are the most common cause of injury related to deaths in people over the age of 75 in the UK, with up to 35% of people aged 65 and falling one or more times every year . The estResearch into the effects of housing adaptations has largely focussed on ‘minor’ adaptations (costing less than £1000)  such as The aim of this study was to determine the feasibility of conducting a powered randomised controlled trial of bathing adaptations for older adults. However, there are ethical issues in randomising participants to a control group without the provision of adaptations; this study therefore used routine waiting times in order to form a control group. This study is in preparation for a definitive trial, with health economic evaluation, which will evaluate the effectiveness of bathing adaptations on health and quality of life outcomes. A definitive trial will also evaluate whether expedited adaptations (i.e. shorter waiting times) are associated with better outcomes and increased cost effectiveness.This paper has been written in accordance with the CONSORT 2010 statement: extension to randomised pilot and feasibility trials .Specific objectives for this feasibility trial were: 1. To investigate whether the eligibility criteria were realistic; 2. To determine whether participants were willing to be randomised; 3. To calculate the attrition rate to inform a sample size calculation; 4. To determine whether the adaptations could be completed within the specified timescales; 5. To determine the suitability and participant completion of measures for use in a definitive trial; 6. To establish the feasibility and method of collecting information on costs of adaptations and health and social care resource use in order to inform a definitive health economic evaluation .This was a single centre feasibility RCT. The RCT was a parallel group, two arm trial with a 1:1 allocation ratio intervention (immediate adaptations): waiting-list control.The study was conducted in one city council in England with a dedicated Adaptations and Renewals Agency (ARA). The agency coordinates and manages major adaptations (costing over £1000) for public sector (council owned) and private properties where a Disabled Facilities Grant (DFG)  is beingParticipants were adults, aged 65 or over, referred by a social care occupational therapy team member for provision of an accessible showering facility. Exclusion criteria were: referral for an accessible showering facility plus one or more other adaptations , and priority ‘A’ referrals .Carers of participants were also approached for informed consent. We took a broad definition of ‘carer’ which was led by the participant and carer’s view of their role. This encompassed people who provided practical and/or emotional support, those who provided assistance with personal care and those who did not.The Housing Grants Construction and Regeneration Act 1996. Participants in both groups received this intervention; however they were randomised to either:Usual Adaptations Service (waiting-list control group) Those randomised to the control group received the usual routine service provided by the Adaptations and Renewals Agency. This involved allocation to a project officer to begin processing the DFG application (if applicable) and planning the accessible showering facility after a 3 to 4 month wait.Intervention (no waiting list) Those randomised to the intervention group were allocated to a project officer to begin processing the DFG application (if applicable) and planning the accessible showering facility immediately. Thus, they did not go onto the routine waiting list.The intervention was the provision of an accessible showering facility: a flush floor anti-slip walk in ‘level access’ shower . In circumstances where it was not possible to install a flush-floor (such as a high rise building) an easy access shower with a minimal access threshold was provided. The provision of the shower usually involved the removal of the existing bath, but could have been an alteration of a shower cubicle to make it more accessible. For publicly (council) owned properties the adaptation was paid for by the local authority; for private  properties a means tested Disabled Facilities Grant (DFG)  was usedThe main outcome for the study was to determine the feasibility of conducting a powered RCT. This was a composite of the feasibility objectives outlined above. We pre-specified our success criteria for proceeding to a main trial in the study protocol  as folloA further objective was to determine the suitability of the measures used and whether they appeared responsive to change following the adaptations. Participant and carer outcomes were assessed at 3, 6 and 9 months post-randomisation. We altered the original study protocol to add an additional follow-up at 9 months, as we wanted to follow-up any participants who may not have had their shower installed by the 6 month visit. Participant outcomes were: perceived physical and mental wellbeing, health and social care related quality of life, personal activities of daily living, independence in bathing, perceived difficulty in bathing, perceived risk of falling, falls, number of care support hours, health and social care service usage. The outcome measures were: Short-Form 36   EuroQol Carer outcomes were: health related quality of life, perceived physical and mental wellbeing and caregiver strain. The outcomes measures were: EuroQol EQ5D-5 L , Short-FFor a feasibility study, no formal sample size calculation is required. However, for this feasibility study the aim was to recruit between 40 and 60 participants (20 to 30 in each arm) to test the randomisation process and the feasibility of delivering the intervention in the proposed timescales. This sample size was decided upon as it is broadly consistent with the median sample size for UK feasibility trials which has been reported at 36 [www.sealedenvelope.com. Participants were individually randomised in random varying block sizes (sized in order to deliver the adaptations appropriately). Randomisation was stratified according to whether the property was publicly or privately owned. Randomisation was at a ratio of 1:1 (immediate adaptations to waiting list control). The allocation sequence was generated by www.sealedenvelope.com and members of the research team did not have access to it.Randomisation was generated online using a web-based randomisation programme Baseline assessments were completed prior to randomisation. Follow-up assessment visits were completed by a research assistant (MGD) who was blind to allocation. Incidents of un-blinding were recorded and are reported below.For feasibility outcomes, descriptive statistics were calculated based on analysis of the trial screening and recruitment log, follow-up rates, and routine adaptations data gathered by the Adaptations and Renewals Agency. Participant and carer outcome data was analysed by intention to treat, and participants were analysed according to their group assignment irrespective of whether they received the adaptation. Summary statistics, estimates of effect and confidence intervals were used. Effectiveness testing was not carried out as this is not appropriate for feasibility work .The trial opened for recruitment on 15th August 2016 and closed on 2nd March 2017. The final follow-up visit for the study was completed on 29th November 2017. Fig. Forty participants had a carer and 23 (58%) were recruited. Seventy percent of recruited carers lived with the participant compared with 50% overall. Carers were more likely to be recruited into the study when they were present on the initial research visit, some participants did not consent for the research team to make contact with the carers when they lived elsewhere stating that they did not want to overburden the carer. Eighteen carers were followed-up at 3 months (78%), 16 (70%) at 6 months and 13 (57%) at 9 months.The demographic characteristics and medical details of participants and carers are shown in Table Baseline measures are shown in Table It was possible to identify a pool of potentially eligible participants, between 11 and 12 per month. Eighty-three percent of those who were eligible consented to take part and were randomised. Our recruitment target was 40 to 60 participants in 8 months; we recruited 60 participants in just over 6 months. Overall attrition was low and was balanced between the groups. Eighty-five percent were followed-up at 6 months. The main reason for attrition was loss to follow-up as we were unable to make contact with six participants over the 9 month period due to moving or changing their contact details. Five participants withdrew between the 6 and 9 month follow-ups, the nine-month follow-up was added as a study amendment and participants were asked for further consent for this additional visit and five chose not to continue with the study. Overall, we vastly exceeded our pre-specified targets for identifying eligible participants, recruitment and attrition rates.The mean (SD) times to completion are shown in Table Table n = 13) compared to the waiting list control group (n = 15) and there were fewer falls overall in the immediate adaptations (n = 33) compared to the waiting list control (n = 65). Although there was one outlier in the control group who reported falling every day  there were fewer falls in the immediate adaptations group both including and excluding this data.Table With regard to carers, Table Table The average cost of the adaptations was £4878.46 across all participants, however, it was £4625.77 in the immediate adaptations group compared to £5131.15 in the control group a difference of just over £500. It is possible that overall costs were rising over time such that the contractors increased their prices for the work that was completed later (the waiting list control group). It is also possible that the additional works were added to the referrals in the waiting list control group during the wait, possibly due to deterioration. However, it could also be a chance finding due to the small sample size. All three issues may have been factors and warrant further investigation.We were able to collect the requisite data on use of health and social care services during the follow-up period which would inform a definitive health economic analysis alongside the EQ5D-5 L data. We demonstrated that the measures used and their collection methods would be suitable for roll out into a definitive trial. We collected a range of data on contacts with health and social care services including in-patient and out-patient visits, community and home appointments, this data for baseline and 3 months follow-up is included in Additional file The research assistant collecting outcome data was asked to report instances of un-blinding. They reported 15 definite instances at 3 months, ten in the immediate adaptations and five in the control group. They were also asked to make their ‘best guess’ and correctly guessed the allocation for 46/51 (90%) participants at 3 months. However, the CONSORT extension  states tWe found that it was feasible to conduct an RCT of bathing adaptations for older adults in collaboration with a local authority housing adaptations partner. We demonstrated a high level of participant engagement evidenced by rapid recruitment and low levels of attrition. It was possible to collect a complete set of outcome data across a comprehensive range of outcomes and collect the cost and resource use data which would be needed for a definitive economic evaluation. All outcome measures appeared responsive to change as improvements in all outcome measures were observed in both groups following the completion of the bathing adaptations; these indicative trends warrant further investigation in a powered RCT. However, there were difficulties in delivering the adaptations within the 3 month timescales for some privately owned properties and all housing association properties, this would necessitate changes to the timescales in a definitive trial and is discussed further.The principal strength of this study is that, to our knowledge, it is the first to use a randomised method to evaluate any type of housing adaptation in the UK and the first to evaluate major adaptations worldwide. The use of the routine waiting list as a control facilitated a comparison between those that had and did not have bathing adaptations; it would not be not be possible to randomise people to not have bathing adaptations for ethical reasons. This is also one of the first studies to focus specifically on the effects of an intervention to improve or maintain independence in bathing. Although there is an indication that bathing disability may be a precursor to further disability for older adults , there iAlthough there is a dearth of evidence for housing adaptations using randomised and experimental designs , our indCompared to other feasibility trials our findings on eligibility, recruitment, attrition, and the suitability of outcome measures are strong and are promising for a future, powered study. Recruitment rates were higher than expected and were in excess of the usual for clinical trials and rehabilitation studies at 83% of those eligible. The positive recruitment rate may be due to the 50% chance of expedited adaptations and the possibility of not going onto the routine waiting list; overall, participants expressed a preference for allocation to immediate adaptations. It is also likely that the lack of an ‘experimental’ treatment increased the acceptability of the trial; participants in both groups were due to receive the adaptation, therefore there was limited uncertainty as to what would happen to them if they entered the study. It is also possible that the high level of engagement within the local research team, which included the manager of the adaptations service, was a factor in the recruitment success. In the qualitative interviews participants reported that the face-to-face follow-up visits with the research assistant also encouraged study participation.Based on our findings we suggest that a powered trial is feasible. However, our target was to complete 70% of adaptations within the allocated timescales  and we aAlthough housing adaptations have been identified as one of the ten ‘most promising’ prevention services for older adults  there isData collection and analysis are complete, this is a results paper. The trial is registered ISRCTN14876332.Additional file 1:Health Economic Data Tables. Participant’s use of health and social care resources at baseline and 3 month follow-up. (DOCX 22 kb)


C60 molecules deposited on a WO2/W(110) substrate. The transition from a static state, where the molecules are rigidly bound to the surface by a coordination bond, to a state where the molecules are loosely bound to the surface by van der Waals force and rotate continuously, has been studied using scanning tunnelling microscopy (STM). The separation between the molecules and the surface increases by 1.2 Å across the transition. The transition from the static state into the rotating state takes place at 259 K. The energy of the spinning state with respect to the lowest energy state, having a single coordinated bond, can be obtained from the statistics of the molecules switching. The binding energy of the molecule in the spinning state can be easily altered by changing the polarity of the bias voltage applied between the STM tip and the surface. The binding energy decreases by 80 meV when the bias polarity of the sample changes from positive to negative with respect to the tip. The results are consistent with the Coulomb blockade model: when electrons travel from the surface to the C60 molecule, and then to the tip; charge accumulates on the molecule due to the Coulomb blockade. This increases the electrostatic interaction between the molecule’s charge and a corresponding image charge generated on the metallic surface.We report on a transition in a monolayer of  C60 molecules deposited on surface of WO2/W(110) using ultra-high vacuum STM3. The molecules were found in conducting and nonconducting states, and our results indicated that such changes were associated with the molecule acquiring or losing a single electron, i.e. C60 on the surface could be charge-neutral, or it could gain/lose one electron. This effect can be understood in terms of Coulomb blockade blocking electron transport from the surface to the STM tip via the molecule. We have also established that when such a change in the conduction state of the molecules occurs, the molecule can switch between different orientations at the surface4. The change between static and spinning states of the molecules takes place at the temperature of 259 K. In a monolayer of C60, the change takes the form of a phase transition, similar to the one in the C60 crystal8, where the molecules of an entire monolayer switch from a static state to a spinning state3. In this paper, we investigate the nature of the electronic bonds of C60 molecules positioned on the atomically flat substrate when the molecules undergo the phase transition from the static to the spinning state. We demonstrate that at a certain temperature the molecules become loosely bound to the surface and at once initiate their rotational movement. This change in the binding energy between the molecule and the surface is accompanied by the molecule acquiring a charge and this can be controlled via STM tip bias. Sending electrons from the tip into the C60 (positive sample bias) activates molecular rotation while reversing the current direction (negative sample bias) suppresses the rotation. The results can be explained on the basis of Coulomb blockade charging of the molecule, leading to a change in the Coulomb interaction force between molecule and substrate.The concept of constructing devices exploiting the electronic properties of single molecules is promising. Organic molecules deposited on insulating substrates in the form of single or fractional (incomplete) monolayers are very attractive systems for making progress in this direction. As the electronic properties of a single organic molecule on a surface are determined by the way it is bound to the substrate, the control of molecule-to-substrate interaction and atomic scale positioning on the substrate is of central importance. Due to the small mass and small moment of inertia, thermal movements of the molecules and thermally activated rotation of the molecules on the surface can hinder the operation of a single molecule device. This raises the importance of understanding the binding, movement and rotation of organic molecules on substrates. We have recently studied a monolayer of C60 molecules deposited on the WO2/W(110) surface forms one molecule thick nano-islands,  change of the STM tip which can be seen in the right panel of Fig. τ1 (τ2) of a molecule transitioning from state 1 (ground state) to state 2 and vice versa over a potential barrier separating the two states is determined by the number of attempts to overcome the potential barrier, i.e. Libron frequency fL:The average lifetimes U and U − ε are the heights of the potential barrier seen from the states 1 and 2 respectively. The difference in energies of the two states ε can be estimated from a statistical distribution of the residence time of the molecule in each state3. The difference in energies was estimated to be 18 ± 9 meV and does not depend on the bias which was used in the experiment. What is remarkable is that both potential barriers U and U − ε depend on the polarity of the bias. For positive bias, whereby electrons move from the tip to the molecule and then to the substrate, the energy of the potential barriers are some 80 ± 17 meV higher than in the opposing situation: negative bias, with electrons moving from the surface to the molecule and then to the tip. It is also notable that the energy of the molecule in the spinning state is not sensitive to the value of the bias voltage but rather to its polarity. The results shown in Fig. C60 molecules being located at a number of non-equivalent sites on the WO2 surface.Here, TC = 259 K) the molecules rotate faster than the time scale of the STM experiment2. The sub-molecular structure can no longer be resolved and the molecules appear in STM as perfect spheres Fig. K, we can establish a situation where fluctuations appear3 (see Supplementary video) and the C60 molecule typically switches between two states: the molecule being fixed on the surface, Fig. At high temperatures, above the temperature of the rotational phase transition  (indicated by the green line). Therefore, as the molecules start spinning at the surface they simultaneously move up and away from the surface and the bond between the molecule and the surface is altered. In the monolayer of C60 this takes the form of a well-defined phase transition at 259 K.In the first state, the molecule is static showing the sub-molecular features. This is the ground state as can be judged from the fact the molecule spends most of its time in this state. In the second state, the molecule spins faster than the time resolving capability of the STM. It, therefore, appears as a sphere in the STM image and the overall current through the molecule increases. The most surprising result was obtained when we measured the separation of the 11. This value is much greater than the difference between the bond lengths for the five well-defined static positions of the molecule. The bond lengths obtained from the DFT calculations2 are presented in the table presented in (Table h-h orientation) is set as a reference point and the bonds of the other four orientations are given with respect to the h-h ground state position. The difference in the C60-WO2/W(110) gap for the five orientations is of the order of 0.5 Å or less, significantly smaller than the difference in the separation between the molecules and the surface across the rotational transition at 259 K.The observed increase in the separation between the molecules and the surface of 1.2 Å is significant. It is in agreement with the difference in rotating and static molecule heights visible in the STM images and comparable with the difference in length between a coordinated and a van der Waals bond (0.9–1.2 Å)C60 molecule, the coordinated bond breaks and the molecule remains bonded to the surface via much weaker van der Waals forces, a schematic of this is presented in Fig. We have to conclude that during the rotation of the 12: the impedance from the molecule to the surface (Rms) and the impedance from tip to the molecule (Rtm). The resistance Rtm has to be much greater than the value Rms, for the STM to operate in a stable regime13. In this case one could achieve the conditions for the Coulomb blockade if the electrons flow from the sample to the tip (negative bias) but not in the opposite regime: electrons flow from the tip to the sample (positive bias). Under the conditions of the Coulomb blockade, the C60 molecule can acquire and retain an extra electron. Once the bias is reversed, the molecule remains uncharged at any tunnelling current value. The charged molecule will create an image charge in the metal, seen in Fig. D is the distance between the surface and the created charge. D can be estimated from DFT simulations (distance between molecule center and W atoms layer) and was taken to be about 8.7 Å. This results in an energy reduction of 414 meV. When the coordinated bond breaks and the molecule starts spinning, the change in D is ΔD = 1.2 Å. This results in a change in the energy barrier of ΔU = 50 mV, which is close to the experimental value of 80 meV. This deviation can be explained by 3 factors: (i) inhomogeneous charge distribution in a frame of the molecule14; (ii) there is some uncertainty in reference point of D; (iii) the electric field between the STM tip and the metal surface also contributes to the potential barrier. Therefore the results suggest that rotation state of the C60 molecule, which is realized at temperatures above that of the rotational phase transition, is different to any of the fixed binding states, as the energy of the spinning state is controlled by the bias of the tip and the direction of the current flowing through the molecule. The voltage controlling the switch between the static and the rotational states is around 1 V, the range convenient for typical electronic devices. The electronic impedance through the molecule is affected by the state of the molecule. This opens up the prospect of using such molecules on a surface as the core of an electronic current control device.The model is characterised by two impedance valuesC60 molecules on the surface. Once the coordinated bond breaks due to e.g. increased temperature, the molecule lifts away from the surface and it is then retained above the surface by a much weaker van der Waals force. In such a state the molecule is free to spin. The lifting of the molecule can be promoted or demoted by altering its charge. If the molecule is charged, it induces an image charge on the surface and this increases the energy binding the molecule to the surface and thus suppressed the transition from the bound state of the molecule to the spinning state. The charge of the molecule can activate the Coulomb blockade that is controlled by the direction of the current (into the surface or into the tip) and therefore controlled by the polarity of the bias voltage. Using the analogy of the Kugel fountain, this is similar to regulating the water pressure underneath the granite sphere: if the pressure is reduced, the sphere’s ability to go into the rotating state is suppressed. The observed difference in the potential barrier separating two adjacent in energy C60 molecule orientations, when the applied bias voltage changes polarity opens a way to control the rotation of the C60 molecules.One could consider the analogy with a Kugel fountain, see Fig. Vb = 1.2 V) is noisy and does not reveal the internal structure of molecules due to frequent switching of the molecules or their rotation. However, an STM image, presented in Fig. Vb = −1.9 V demonstrates prominent internal structure of C60 molecules, which corresponds to molecular symmetry.An STM image, Fig. C60 molecules deposited on a WO2/W(110) substrate from a fixed state, where the molecules are bound to the surface by a well-defined bond, to another state, where the molecules are loosely bound to the surface by van der Waals forces. The integrity of the monolayer of C60 molecules is not altered once the molecules transition to the loosely bound spinning state, but remarkably, the separation between the molecules and surface is increased by 1.2 Å across the transition. In the loosely bound state, the molecules start spinning around faster than the time resolving capability of the STM and therefore they appear in the STM as perfect spheres. In contrast, at low temperature, the molecules are bound to the surface in a static manner, and details of the sub-molecular orbital structure can be resolved with STM. The transition from the static state into the rotating state takes place at 259 K. The energy of the spinning state with respect to the lowest energy state having coordinated bonds can be obtained from statistics of the molecule’s switching. The binding energy of the molecule in the spinning state can be easily altered by changing the polarity of the bias voltage applied between the STM tip and the surface. The binding energy is reduced by 80 meV when the bias polarity of the sample changes from positive to negative with respect to the tip. The results are consistent with the Coulomb blockade model: when electrons travel from the surface to the C60 molecule and then to the tip, they produce an accumulation of charge on the molecule due to the Coulomb blockade. This increases the electrostatic interaction between the molecule’s charge and a corresponding image charge created on the metallic surface. The energy of this electrostatic interaction is consistent with the energy difference of the spinning state for positive and negative bias voltage polarity.We have studied the transition of C60 on WO2/W(110)1. The STM/STS experiments were performed using a commercial instrument from Createc, in an ultra-high-vacuum (UHV) system consisting of an analysis chamber (with a base pressure of 2 · 10−11 mbar) and a preparation chamber (5 · 10−11 mbar). An electrochemically-etched tip made out of tungsten single crystal with [100] crystallographic direction along the tip length, was used to record STM images in constant current mode. The voltage Vb corresponds to the sample bias with respect to the tip. No drift corrections have been applied to any of the STM images presented in this paper. A W(110) single crystal, prepared at the Institute of Solid State Physics RAS, was used as the substrate. An atomically-clean W(110) surface was prepared by in situ annealing at 1900 K in an oxygen atmosphere of 1 · 10−7 mbar, followed by a series of high temperature flashes at 2200 K. The sample was heated by electron beam bombardment and its temperature was measured using an optical pyrometer . The condition of the W(110) surface was verified by LEED and STM before oxidation. Once a clean surface was obtained, the sample was oxidised at 1600 K in an oxygen atmosphere of 1 · 10−6 mbar for 15 min. The quality of the resulting oxide structure was verified by Low Energy Electron Diffraction (LEED) and STM before the deposition of C60 molecules. C60  was evaporated in the preparation chamber isolated from the STM chamber at a rate of about 0.2 ML (monolayer) per min from a deposition cell operated at a temperature of approximately 700 K. Before evaporation, the C60 powder was degassed for about 8 hrs to remove water vapour. The total pressure during C60 deposition was in the 10−9 mbar range and the substrate was kept at room temperature. After deposition the sample was transferred into the STM and initially cooled down to 78 K before the temperature is raised in order to observe and conduct experiments relating to the rotational phase transition of the C60 molecules.The sample preparation and experimental conditions closely match that of our previous work with Supplementary Video


Stand‐off Raman spectroscopy offers a highly selective technique to probe unknown substances from a safe distance. Often, it is necessary to scan large areas of interest. This can be done by pointwise imaging (PI), that is, spectra are sequentially acquired from an array of points over the region of interest (point‐by‐point mapping). Alternatively, in this paper a direct hyperspectral Raman imager is presented, where a defocused laser beam illuminates a wide area of the sample and the Raman scattered light is collected from the whole field of view (FOV) at once as a spectral snapshot filtered by a liquid crystal tunable filter to select a specific Raman shift. Both techniques are compared in terms of achievable FOV, spectral resolution, signal‐to‐noise performance, and time consumption during a measurement at stand‐off distance of 15 m. The HSRI showed superior spectral resolution and signal‐to‐noise ratio, while more than doubling the FOV of the PI at laser power densities reduced by a factor of 277 at the target. Further, the output hyperspectral image data cube can be processed with state of the art chemometric algorithms like vertex component analysis in order to get a simple deterministic false color image showing the chemical composition of the target. This is shown for an artificial polymer sample, measured at a distance of 15 m. Illumination via laser light and collection of primarily backscattered Raman photons allow for a remote detection scheme, as long as free propagation of photons is possible. This makes stand‐off Raman spectroscopy a potent analytical solution for a variety of applications. The exploration of different materials located on planetary surfaces is one of the most prominent studied application possibilities, given its advantages in terms of accessibility of remote objects also when the rover is stationary.Hyperspectral imaging describes a wide range of increasingly used and constantly evolving techniques for chemical and structural analysis, which provides both spatial and spectral information for a given sample of interest.In this study, we compare the performance of two different stand‐off Raman imaging approaches: a pointwise or whiskbroom imager (PI), where the HSI is created by scanning the laser point over the sample, and a direct hyperspectral Raman imaging (HSRI), where the HSI is created by stacking spectral snapshots on top of each other. The PI system employs a classical diffracting spectrometer, coupled to the telescope by an optical fiber with the laser point being scanned over the sample by means of an electronically controlled mirror. The HSRI uses a LCTF to select a specific Raman shift and collect a spectral image, while the laser illuminates the whole field of view (FOV) of the telescope or rather the camera.2In this study, two different optical setups were employed, which are displayed in Figure In both systems, a Q‐switched, frequency doubled (532 nm) Nd:YAG NL301HT laser  with a pulse energy of 50 mJ, a pulse length of 4.4 ns, and a repetition rate of 10 Hz was used as an excitation source. The beam profile is specified exhibiting a top‐hat beam profile in the near field and a near‐Gaussian profile in the far field with a beam divergence lower than 0.6 mrad.2.1For the pointwise stand‐off Raman system, the laser was aligned coaxially to a 6″ Schmidt‐Cassegrain telescope  for the collection of Raman scattered light using a motorized kinematic mirror mount , which allowed for the mapping of the laser onto the sample area. The backscattered Rayleigh light was filtered using a long pass filter , and the Raman photons were guided to an Acton standard series SP‐2750 spectrograph  via a round‐to‐slit fiber optical bundle cable consisting of nineteen 200‐μm diameter optical fibers . To match the F number of telescope and fiber bundle, a f = 50‐mm lens was used. Finally, the backscattered light was detected by a PIMAX 1024RB intensified charge‐coupled device (iCCD) camera . The outgoing laser pulse and the gate of the iCCD camera were synchronized so that the measurement window coincided with the maximum Raman signal. Data acquisition and mapping was automated using LabVIEW® .2.2The direct stand‐off imager Figure c employe2.3Vertex component analysis (VCA) was used for the evaluation of the generated HSI data cubes. VCA is a technique for unsupervised endmember extraction assuming the data is a linear mixture of pure components, also called endmembers.2.4Plates of different chemical composition and thickness were acquired from RS Components (United Kingdom), namely, polypropylene , polyethylene , polytetrafluoroethylene , and nylon . Pieces were cut out and glued together using small amounts of cyanoacrylate on the edges of the cut pieces. Sulfur (>99.98%) was obtained from Sigma‐Aldrich and for the spatial resolution experiments, polylactic acid plates were designed as samples containers on the computer and 3D printed afterwards.33.1−1 was assessed in dependence of the horizontal position of the illumination point. The resulting curve (black) shows a distinct fall off with increasing offset from the central point, reaching the 10% mark at a diameter of approximately 24 mm. To assess the FOV of the HSRI prototype, the same PP plate was used at 15 m distance as a target. A spectral image at 2,890 cm−1 was acquired, and the intensity was evaluated along the same horizontal axis Y as before. The HSRI configuration shows a broader intensity profile, mainly influenced by the emission characteristics of the laser beam. Normally, the FOV of a telescope and CCD chip combination is influenced by the focal length of the telescope, the stand‐off distance, and the size of the CCD chip itself. For the employed HSRI system, this surmounts to a theoretical FOV of approximately 110 m. Ideally, for the HSRI the laser beam has an ideal top‐hat structure also in the far field, which means the energy density within the beam is uniform. This leads to a uniform intensity distribution in aberration‐free optical systems, which enables the usage of the whole image without loss of SNR in less illuminated border regions. For the HSRI presented in this study, the effective FOV with adequate Raman intensity amounts to a diameter of approximately 70 mm.Illumination and FOV differ greatly between the two systems. Figure 2 and for the HSRI it is 3,848 mm2, a less than 10‐fold increase.In the PI system, the numerical aperture and the diameter of the fiber bundle limit the FOV. In contrast to the HSRI, the PI system with its fiber bundle with a numerical aperture of 0.22 and a diameter of 1.5 mm, the effective FOV is reduced to an area with a diameter of 24 mm. This means that the maximal useful area that can be illuminated for the PI is 452 mm3.2Spectra obtained with both systems were compared with spectra taken with a commercially available Raman microscope  with the same excitation wavelength of 532 nm used throughout this study. Again, a PP plate was the target of choice, and Figure −1 typical bands arising from the symmetric and asymmetric stretch vibrations of the methyl and methylene group can be found. Additionally, the bands attributed to the symmetric and asymmetric bending of the methyl and methylene group present in PP are visible between 1,260 and 1,500 cm−1 in the chosen spectral range. Both configurations of stand‐off Raman imagers show the same bands as the reference taken by the Raman microscope, and the spectral positions are in good agreement. The biggest difference in the shown spectra is their respective resolution. The Raman microscope uses a 600 gr/mm grating, which results in a spectral resolution of approximately 4 cm−1 with the spectrograph and camera built into the instrument. The PI system with a 300 gr/mm grating and a 750‐mm focal length f/10 spectrograph has the lowest spectral resolution of the compared systems with approximately 15 cm−1. The HSRI imager does not use a classical spectrograph as the dispersive element but the LCTF. Hence, the spectral resolution is a function of the width of the transmission curve, which is specified by the manufacturer to be constant over the complete visible range at 0.25 nm. This amounts to a mean spectral resolution of 7.4 cm−1 in the observed spectral range. Additionally, the relative intensities vary between spectrograph and filter systems. The tunable filter has lower throughput at shorter wavelengths, which becomes apparent when comparing bands at higher Raman shifts with bands at lower Raman shifts for the spectrograph and the filter configuration in Figure On the high Raman shift range from 2,840 to 2,950 cmThe tunable filter in the HSRI is mainly used because of the ability to perform direct imaging. Hence, in this system, it is important to evaluate the uniformity of the transmission window in terms of spectral position and spectral resolution over the FOV.−1 with spectral steps of 2 cm−1 was acquired, thereby oversampling the theoretical resolution of the HSRI of approximately 7 cm−1. PTFE shows several bands in this region, the two most important ones are the skeletal stretching at approximately 746 cm−1 and the symmetric CF2 stretching modes at approximately 1,380 cm−1.−1 shows higher intensity and narrow linewidth, it was chosen to be the indicator for spectral resolution and position accuracy of the filter. To assess these parameters, a fit of the band using a pseudo‐Voigt profile−1 by no more than 2 cm−1 with a standard deviation of 0.28 cm−1. An aggregation of extreme values at the edges of the image is observed. Similarly, the calculated FWHM ranges from 10 to 14 cm−1 in the inner circle, with considerable outliers at the edges of the image. These extreme values are due to the lower intensity of the exciting laser at the edges of the imaged area, reducing the SNR of the resulting spectra and preventing a regular fit for center position and especially for FWHM evaluation. Overall, the reported deviations of both center position and FWHM are within the expected error margin, given that the spectral resolution of the filter is specified to be around 7.5 cm−1. This means that adequate Raman spectra collection using the tunable filter is viable for the whole aperture given a strong enough laser excitationTo do this, a PTFE plate with an appropriate size was measured using the HSRI prototype. The region from 700 to 1,500 cm3.3−1  divided by the standard deviation between 3,090 and 3,200 cm−1 (baseline noise). When only one‐shot measurements are performed, spectra tend to be of low quality as can be observed in Figure To investigate the signal‐to‐noise performance of PI and HSRI, a PP plate was mounted at 15 m and measured with the systems. Both instrumentations work in a pulsed and time‐gated mode, meaning that after a laser pulse is emitted, a trigger signal is sent to the camera. After a set time delay of typical a few hundreds of nanoseconds (depending on the sample‐telescope distance), the gate of the intensifier is opened for 5 ns. This way, otherwise, interfering light sources can be suppressed, and the Raman signal from the sample can be maximized. The SNR in this study was calculated by using the mean intensity between 2,890 and 2,905 cm2) in order to calculate the SNR. As visualized in Figure 2 for the PI system. The HSRI uses an expanded beam to an effective diameter of approximately 100 mm, which leads to a power density 6.4 mW/cm2, a 277‐fold decrease compared with the PI system. The possibility of using lower laser power densities is beneficial for practical use of such stand‐off Raman systems, where moderate power density levels are sought after due to eye‐safety concerns in civil and also military applications. Since the intensity of scattered Raman photons is directly proportional to the input of laser power onto the sample, the much lower power density for the HSRI should cause a significant drop‐off in SNR. Instead, a comparable SNR performance of both systems was observed. This can be explained by the higher optical throughput of the optical system, for example, higher throughput of the LCTF compared with the spectrograph, on one side and a difference in detection efficiency of the iCCD cameras. The PIMAX 1024RB used in the PI imager has a quantum efficiency of about 7.5%, whereas the GenIII intensifier of the PIMAX4 1024HBf used in the HSRI has one of 45%, six times more. Additionally, the étendue, a measure for the gathering power of an optical system, which is equal to the source emitting area multiplied by the solid angle from which the light is collected, is different. Due to the small diameter of the single fibers used in the bundle, the PI has an étendue of 0.27 mm2 sr, whereas the HSRI can use up to the full sensor size of the CCD camera, amounting to an étendue of 1.09 mm2 sr. This is an increase of a factor of 4 and shows one of the downsides of fiber coupled stand‐off Raman instruments.Figure 2 at 15 m, the green and blue solid lines are the calculated time values for the respective prototype with the configuration used in this study. The dashed lines are calculated for a low spatial resolution for the PI and for a small number of spectral images for the HSRI. The dashed‐dotted lines represent the opposite situation, where high spatial resolution is needed for the PI system and a high number of spectral images are needed for the HSRI system. The semitransparent areas represent the possible or working span of both techniques  divided by the standard deviation of the baseline between 510 and 580 cm−1 (baseline noise). The concept of this study is depicted in Figure In order to highlight the importance of spatial resolution, samples with a sulfur feature of different sizes have been prepared by 3D printing polymer plates holding different sizes of cavities filled with sulfur powder. Square cavities with an edge length in the range of 1 to 4 mm and a thickness of 0.3 mm were measured at a distance of 15 m by employing 2‐s acquisition time per spectral snapshot (20 accumulations), 140‐ns gate delay and 5‐ns gate width using the HSRI system. The influence of spatial resolution was explored post measurement by choosing a central pixel inside the feature and averaging adjacent pixel spectra to decrease the spatial resolution. Then, the SNR was calculated through the maximum band intensity between 478 and 482 cm3.4−1 are shown. The effects of polymer thickness and reflectivity can then be observed in Figure −1 reflects the laser beam intensity distribution, except for the area blocked by the PE. In the case of PE, which is thicker and less transparent, a drop‐off in intensity can be observed. For the nylon, however, which is of the same thickness as the PE, a stronger signal is obtained, which is attributed to the fluorescence of the material, which results in an elevated baseline. The signal at 2,850 cm−1 is very intense for all polymers, except for PTFE, exhibiting the CH stretch vibration at this spectral region. The HSRI approach usually leads to large datasets, which in most cases is not informative for the user nor required to solve the given analytical problem. Hence, efforts are made to simplify data interpretation by using a variety of algorithms to deconvolute and classify the recorded data in order to facilitate the extraction of the required information needed to provide a meaningful result. Linear unmixing algorithms are commonly used for hyperspectral datasets, when the presence of pure pixels can be assumed. Among these methods, VCA is advantageous because the VCA algorithm competes with state‐of‐the‐art methods while exhibiting a computational complexity between one and two orders of magnitude lower than the best available method.4−1 for the central position and better than 4 cm−1 for the FWHM of the PTFE band at 746 cm−1. This proves the viability of the filter as a dispersive element for direct Raman imaging. The excitation beam has to be expanded in order to illuminate the whole scene for the HSRI, which leads to significantly lower power density at the sample. For the tested scenario, the difference in power density amounts close to 277‐fold increase with the PI imager. Nevertheless, the HSRI setup shows similar SNR values over the same measurement time, although the PI system would benefit substantially from a better matched fiber bundle‐spectrograph matching.In this study, a comparison of a pointwise stand‐off Raman imager and a direct hyperspectral Raman imager in terms of achievable FOV, signal to noise, spectral and spatial resolution, and total measurement time is reported. The investigated prototypes differ in maximal possible FOV, which for the PI is limited by the numerical aperture of the optical fiber coupling the telescope with the spectrograph and for the HSRI by the FOV of the telescope and CCD size. The HSRI exhibits a FOV of roughly 70 × 70 mm, which is nearly 10 times more than the FOV of the PI. The stability of the spectral resolution of the tunable filter over the open aperture was investigated and determined to be better than 2 cmA significant contributor to the time needed for data acquisition is the size of the area to be investigated. A bigger FOV helps with screening larger areas faster. Inversely, the higher the spatial resolution of the imager has to be, the more time a mapping instrument would need, because the diameter of the excitation laser beam would need to be small and the number of mapping points would substantially increase. Spatial resolution is better suited for the HSRI, because the whole FOV of the collection optics can be used with a spatial resolution defined by the pixel size of the CCD chip. In time‐gated configuration like stand‐off applications, the required time is proportional to the repetition rate of the laser and inversely proportional to the number of accumulations, which holds true for both configurations.In summary, two stand‐off Raman imagers were constructed and compared, one relying on mapping of the excitation laser beam, the other directly imaging the scene for single Raman shifts in order to create a HSI cube. The HSRI instrument showed better suitability for large area scanning, especially if a small number of spectral snapshots are required and offers a smaller electric and mechanic footprint, making it the better choice for mobile applications in the field.Fig S1. Total measurement time over image size at a target distance of 15 m. Rspat means spatial resolution of the PI, nspec is the number of spectral images for the HSRI.Fig S2. Comparison of stand‐off HSRI spectra and reference spectra collected with a Horiba LabRAM confocal microscope. All spectra were baseline corrected and normalized for better comparability. Nylon showed significant fluorescence during the measurement with the HSRI, so the characteristic of the Rayleigh filter is visible in the spectrum.Fig S3. a) Example spectra of the PTFE plate at 15 m distance. b) Example of a Voigt profile fit for the band at 746 cm‐1. c) Spatial distribution of the central position of the PTFE band over the whole image. d) Spatial distribution of the FWHM of the PTFE band over the whole image. The black circle indicates the area of illumination by the laser beam.Click here for additional data file.


R2 should not be used to assess the predictive capability of a model, before introducing a method for calculating predicted R2, which is then used to assess the models. It is found that a linear model with the resonant frequency peaks as predictors cannot be used to predict elongation at failure or reduction in area. However, linear models did demonstrate better predictive capabilities for Young’s modulus, yield strength, and especially ultimate tensile strength.There is a need to qualify additively manufactured parts that are used in highly regulated industries such as aerospace and nuclear power. This paper investigates the use of resonant ultrasound measurements to predict the mechanical properties of Ti-6Al-4V manufactured by selective laser melting using a Renishaw AM 250. It is first demonstrated why  Highly regulated industries such as aerospace and nuclear need to be able demonstrate that parts manufactured using additive techniques achieve satisfactory performance when compared to parts made by more established processing routes.The use of additive manufacturing is rapidly increasing, with an estimated increase in the value of parts produced of 32.4% in 20172 is a method of non-destructive evaluation (NDE) that measures the acoustic resonance of a part over a certain spectrum, and compares the resonant frequency peaks of the part to a training library of parts in order to classify the measured part using the Mahalanobis-Taguchi System3.Process compensated resonant testing (PCRT)et al.4 described a “strong correlation” (R2 = 0.8384) between one of the resonant frequency peaks and the 0.2% yield stress of Ti-6Al-4V parts manufactured using metal injection moulding (MIM); the resonant frequency peaks were measured using PCRT equipment. Sidambe proposed that a linear model using a single resonant frequency peak as the predictor could be used to make predictions about the 0.2% yield stress. They then used their model to predict the 0.2% yield stress of a test population, and found that the error between predicted and experimental results was less than 10%. It should however be noted that error of 10% appears to be greater than the maximum difference observed between the experimental results in their test population.Sidambe The aim of this study was to investigate whether the shift in resonant frequency peaks could be used to make predictions about the mechanical properties of Ti-6Al-4V parts manufactured using selective laser melting (SLM), with a view to using this technique to non-destructively evaluate additively manufactured components.R2, and the lasso (variable selection) are presented for the reader who is unfamiliar with those concepts. This is followed by a description of the method used for creating the statistical models. The experimental results are then presented, followed by the results of the statistical models and a discussion of those results. The final part of this work gives the authors’ conclusions about the usefulness of resonant frequency data in predicting tensile properties.This article starts with an explanation of the experimental method used for obtaining the tensile test data (response variables) and the resonant frequency data (predictors). Next, a brief introduction to the statistical concepts of leave one out cross-validation (model selection), predicted 2 cross section FCE type A cylindrical fatigue specimen detailed in BS EN 6072:20105. To enable the parts to be machined to final size before mechanical testing, extra material was included by adding an offset of 0.5 mm to all surfaces in the CAD model. The parts were designed around a fatigue geometry to support another element of work under this grant, however tensile tests were used in this part of the work due to significantly narrower distribution of results obtained by tensile testing than by fatigue testing.A batch of 60 mechanical test blanks was additively manufactured using a Renishaw AM 250 selective laser melter. The AM 250 uses a 50 ms pulsed ytterbium fibre laser of wave length 1060 nm. As these parts were primarily intended for fatigue testing, the part geometry was based on the 12.5 mmFollowing creation of the 3D CAD representation of the test geometry the file was processed using Materialise Magics. Specimen samples were located on the build plate as indicated in Fig. The parts were manufactured using a 30 μm layer thickness, and a meander scan strategy with a 67° hatching direction rotation between layers. The laser power, exposure time, point distance, and hatch distance values are given in Table Evacuate the chamber.Heat to 350 °C in 1 hour.Hold at 350 °C for Heat to 850 °C in 1 hour.Hold at 850 °C for 1 hour.Turn-off heating and allow to furnace cool.Turn-off the vacuum pumps once the temperature was below 100 °C.The parts were removed from the build plate using EDM prior to annealing to enable resonant testing in both the as built and annealed conditions. The annealing heat treatment, which was performed in a vacuum furnace, was:The resonant ultrasound testing was performed using a system provided by Vibrant GmbH , which was designed for PCRT. The measurement system included a piezoelectric driver for inducing the resonance and two piezoelectric sensors for measuring the resonance. The driver and sensors were brought into contact with the part by placing the part in a purpose built jig that was provided with the measurement system see Fig. . The priet al.2. The driver and sensors were controlled by the instrument manufacturer’s data acquisition system, which was in turn connected to a personal computer (PC) running the manufacturer’s Quasar/Galaxy software. The Galaxy software analyzed the sensor data to identify the resonant frequencies of the part. When a peak could not be identified during data collection the software issued a warning message, in which case the scan was repeated for that part. This would sometimes enable the identification of all peaks, but would other times still lead to incomplete results, in which case the scan was repeated for a third and final time.Resonance ultrasound measurements were taken from the parts in the as built state and after annealing. The frequency scanning ranges were selected by the RUT instrument manufacturer as being from 500 Hz to 226.5 kHz for the as built parts, and from 500 Hz to 600.5 kHz for the annealed parts. The measurement of 8 resonant frequency peaks was selected by the instrument manufacturer for parts in the as built state and 17 for after annealing. Further details about the instrument manufacturer’s process for selecting the resonant frequencies can be found in Sloan 6. The samples were machined by the testing company prior to performing the tensile testing. The machined sample dimensions are according to specimen 4 of figure 8 in ASTM E86 for test specimens with a gauge length four times the diameter .To assess the mechanical properties of the samples, fifteen parts were sent to Exova Ltd  for room temperature tensile testing according to ASTM E8R2. R2 is the ratio of variability in the response variable that can be explained by the model to the total variability in the response variable. The total variability in the response variable is measured by the total sum of squares (TSS). The variability that can be explained by the model is equal to the TSS less the residual sum of squares (RSS)  , where yR2 is often seen as being relatively easy to interpret, as it always takes a dimensionless value between 0 and 1, with 0 indicating no fit whatsoever, and 1 indicating a model with a perfect fit to the data. However, a significant problem with R2 is that the measure improves in the presence of over-fitting. Over-fitting occurs when the model complexity is increased in an attempt to reduce the residual error that is due to noise. Unfortunately, by reducing the residual error for the training set, this can increase the error when making predictions. For example, consider an experiment to measure the thermal expansion of a material over some range where the expansion is actually a linear function of temperature (l = 8.64 × 10−6 ⋅ T + 1), but where the length measurement is subject to a Gaussian error. Table R2 value of 0.9447, indicating an excellent fit.Due to the Gaussian noise in the measurement of the length, the residual error can be reduced by over-fitting. Figure R2 value of 0.9996, indicating an almost perfect fit.However, the polynomial model Eq.  has an RR2 measure, the polynomial model would appear to be better. But it is important to note that whilst the polynomial model is indeed a better fit for this training data, if this model is used to make predictions of sample length based on temperature, then on average the linear model will perform better. For example, the observed value at 30 °C is 1.000419 m. The polynomial model predicts a mean sample length of 1.000424 m at 30 °C. The linear model predicts a mean length of 1.000264 m at the same temperature. The true mean length of the underlying model used in the simulation at 30 °C is actually 1.000259 m. So whilst some repeat measurements at 30 °C may be closer to the value predicted by the polynomial model, on average the measurements at 30 °C will be closer to the value predicted by the linear model.Using the et al.7 for some examples) that can be used to assess the ability of a model to make predictions and help the designer to avoid over-fitting; one class of methods is cross-validation. In cross-validation the training data is first split into groups. Then all but one of the groups are used to fit the statistical model. The excluded group is then used as a test set to assess the performance of the fitted model. The excluded group is then returned to the training set, and the process repeated with a different excluded group. This process continues until all groups have been used as the test set once. If the training data is split into groups of one, the method is referred to as leave-one-out cross-validation (LOOCV).There are a number of available statistical techniques  and the value predicted by the model fitted using the set excluding the value being predicted t}yˆ(i)) . The PREyi) and the mean value of the response variable excluding the samples from the same group as the sample currently being predicted  of the model to the error of the null model. Following this definition of R2, the predicted R2 can be defined using LOOCV, which replaces the numerator with the PRESS of the model, and the denominator with the PRESS of the null model . The lasso (Eq. λ). This extra term is the lasso penalty, which has the effect of reducing the coefficients towards zero. This effect will be greater the larger the value of the tuning parameter. If the tuning parameter is equal to zero, the equation reverts to the standard equation for multiple linear regression.In the case of a polynomial model with over-fitting, the over-fitting can be reduced by reducing the order of the polynomial without affecting the number of predictors used in the model. In the case of a multiple linear regression, LOOCV still enables the assessment of model over-fitting, but this then leads to the question of how select the predictors to remove from the model to reduce the over-fitting. There are a range of variable selection techniques that can be used, but the method used in this work is the lassoasso Eq.  introducTo analyze whether the resonant frequency data could be used to predict the tensile properties of the samples, multiple linear regressions were fitted to the frequencies of the resonant peaks (predictors) and each tensile property (response variable). The predictors were taken to be either the set of measured resonant frequencies for as built condition or the annealed condition. Given that the training set size was only 15 and there are 8 predictors (resonant frequencies) for the as built condition, and 17 predictors for the annealed condition, variable selection was performed using the lasso.10 in the R programming language. The near-optimum tuning parameter is determined by calculating the lasso for a range of discrete values, and using LOOCV to calculate which value of λ gives the lowest estimate of test MSE. 1000 different values of λ between 103 and 10−3 were tested in descending order, as given by  multiple linear regressions and the multiple linear regressions with the lasso were calculated using the as built predictors. As the number of annealed predictors is greater than the training set size, only the multiple linear regressions with the lasso were calculated using these predictors.11 specifies minimum values in the Z-direction for additively manufactured Ti-6Al-4V of 855 MPa for ultimate tensile strength (UTS), 765 MPa for yield strength at 0.2% offset, and 5% elongation at failure. It can be seen from Table The results of the room temperature tensile testing are presented in Table The measured resonant frequency data for the as built state can be found in Table R2 are presented in Tables R2 of each model for comparison to the other model statistics. The prediction accuracies are presented graphically in Fig. The number of coefficients (predictors) used in each of the fifteen models, along with the estimated test MSE, and the predicted R2 values less than zero. Two of the models using the lasso have reduced to the null model with no non-zero coefficients, and the remaining two models that use the lasso have predicted R2 values of just 0.14 and 0.02.The results for all six models indicate that a multiple linear regression using resonant frequency peaks cannot be used to make predictions about elongation at failure or reduction in area. The two ordinary least squares models have predicted R2 values of −1.06 and −0.54. The equivalent model for predicting ultimate tensile strength performed better, having a predicted R2 value of 0.18. For the models built using the as built predictors with the lasso, the predictive accuarcy was increased for all three tensile properties, with the model for ultimate tensile strength again demonstrating the greatest predictive accuracy. For the Young’s modulus, the yield strength, and the ultimate tensile strength, the multiple linear regressions that gave the lowest prediction errors were those using the annealed frequency peaks with the lasso. Of these three tensile properties, the Yield strength model predictions had the greatest error, with only a modest improvement over the null model (For the Young’s modulus, the yield strength, and the ultimate tensile strength, the models have varying levels of predictive capability. The ordinary least squares models using the as built predictors for the Young’s modulus and the yield strength performed worse than the null model, having predicted The models for predicting the ultimate tensile strength had the lowest error of all the multiple linear regressions. The model using the annealed predictors achieved R2 is greater than the value of predicted R2. For some of the models the values of the two measures of R2 are sufficiently close that the same interpretation of predictive ability would be reached from either measure. For example, the model to predict UTS using the as built predictors with the lasso has an R2 of 0.78 and a predicted R2 value of 0.71. It is quite possible that both of these results could be read to suggest that the model has some predictive capability. Similarly, the model to predict the reduction in area using the annealed predictors with the lasso has an R2 value of 0.12 and a predicted R2 value of 0.02. Again it is reasonable to assume that both of these results would be interpreted in the same way: this model has no predictive ability. However, for the ordinary least squares model using the as built predictors to predict reduction in area, the R2 value of 0.69 could be understood to say that the model does have some predictive use, whereas the predicted R2 value of −1.65 clearly indicates that no predictive use should be made of the model. This final example illustrates why the authors believe that predicted R2 should be used in place of R2 when considering the ability of a statistical model to make predictions.It should be noted that for all of the models that have at least one non-zero coefficient that the value of R2 should not be used to measure the ability of multiple linear regressions to make predictions, as low residual error between model and training data does not necessarily translate to low prediction error when used with test data. The predicted R2 value has been introduced, which is calculated using leave-one-out cross-validation, and is a more useful measure of the prediction accuracy of a statistical model. The calculated value of predicted R2 has been used to assess the predictive ability of a series of linear models using resonant frequency peaks to predict the mechanical properties of samples built using selective laser melting.It has been demonstrated that The statistical results indicate that the resonant frequency peaks as measured in the samples either in the as built or the annealed states can be used to make predictions about the ultimate tensile strength of the samples. It should be recognized that although these two linear models were able to explain the majority of the variability in the measured values of UTS, the residual errors are not insignificant when compared to the limited scatter in the measured UTS.R2 value of 0.54 using the annealed resonant frequency data does suggest the possibility that a different type of model could potentially make useful predictions about Young’s modulus using resonant frequency measurements.The linear models were less able to accurately predict the measured value of Young’s modulus than the UTS. However, a predicted There is very limited evidence to support the conclusion that resonant frequency measurements can be used with a linear model to predict yield strength. There is no evidence that a linear model can use resonant frequency data to predict either elongation at failure or reduction in area. It is slightly disappointing that the models were unable to make useful predictions about elongation or reduction in area, as these were the properties that were found to have the most variability in the mechanical testing results.


The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric. Mechanical state estimation of a vehicle is a field of interest. A vehicle is considered a rigid body, and its state of motion is represented by 4 mathematical objects: two of them represent its position and velocity, and the other two represent its orientation, and angular velocity. This paper is focused on the estimation of the angular state, composed of orientation, and angular velocity.Although there are other mathematical tools used for estimation , the KalThe orientation of a system is represented by the rotation transformation that relates two reference frames: a reference frame anchored to that system, and an external reference frame. A thorough survey of attitude representations is provided in Reference . The parspecial orthogonal group SO(3) has dimension three, ideally we would seek for a continuous and non-singular representation expressed by 3 parameters. However, since 1964 we know that “...it is topologically impossible to have a global 3-dimensional parametrization without singular points for the rotation group” [Having in mind that the n group” . Knowingn group” ,11,12.Quaternions are 4-dimensional entities, but only those having unit norm represent a rotation transformation. This fact implies a problem in applying the ordinary Kalman Filter, so different approaches have emerged. Since a quaternion is of dimension 4, one tends to think at first on a n Filter . Given tn Filter  and was n Filter ,11,12. Ion step” .This paper presents a new viewpoint on the problem of attitude estimation using Kalman filters when the orientation is represented by unit quaternions. Noticing that unit quaternions live in a manifold  is different from the product denoted by (⊗) in reference [complex conjugate quaternion. Note that if Quaternion product is defined by Equation  which preference . Given tEach rotation transformation is mapped with a rotation matrix Note that Quaternions representing rotations have the formThis means that quaternions describing rotations live in the unit sphere of When dealing with the Kalman filter, the distribution of a random variable Definition 1 (Homeomorphism).A homeomorphism is a function f is a bijection,f is continuous,its inverse function If such a function exists, we say that X and Y are  homeomorphic.Definition 2 (Manifold).A n-manifold Definition 3 (Chart).A chart for a manifold with φ a homeomorphism. Traditionally, a chart is expressed as the pair This definition makes sense when our random variables are defined in the Euclidean space. But how do we define the covariance matrix of a random variable living in a manifold like ours? How can we define the covariance for unit quaternions if Given these definitions we can continue our reasoning.Orthographic (O), the Rodrigues Parameters (RP), the Modified Rodrigues Parameters (MRP), and the Rotation Vector (RV). The first three are what we know as stereographic projections . The last one is a projection called Equidistant. But all four are charts defining a homeomorphism from the manifold In Reference  it talkseference , all fouWe should notice that having ested by . This is product:q=q¯∗δq¯,After reviewing these concepts, we can define the covariance matrix of a distribution of unit quaternions.Given a unit quaternion At some step of the Kalman filter, we will have a distribution of unit quaternions defined in a Definition 4 (Transition map).Given two charts with  transition map. Being that For the present case, let us consider two unit quaternions These two quaternions define the charts That is to say, first we take the point Note the equivalence of expressions (18c) and .In this section we present the models adopted for the Manifold Kalman Filters (MKF), and we display the resulting algorithms.t is defined by an orientation, encoded with a unit quaternion The state of the system at a time Our unit quaternions For example, if we measure an acceleration The vector t will be denoted as We can predict the value of the random variables that describe the state of our system through the following motion equations: We will assume that we have sensors giving measurements of angular velocity x at a time t, having included measurements up to a time t, having included measurements up to a time t.We will assume that the measurements arrive at discrete times The following subsections present the developed Kalman filters: one version based on the EKF and another version based on the UKF. The EKF is based on the linearization of the non-linear models to calculate the predicted covariance matrices. That is, the EKF approximates non-linear functions using their Jacobian matrices. To apply the EKF, our functions must be differentiable. On the other hand, the UKF is based on a deterministic sampling to approximate the distribution of our random variables. We select a minimal set of samples whose mean and covariance matrix are those of the state distribution. Then, they are transformed by the non-linear models, and the resulting set of points is used to compute the means and covariance matrices necessary to perform the Kalman update. This second approach does not need the functions to be differentiable.In this section we present the EKF-based estimator: the Manifold Extended Kalman Filter (MEKF). We offer here the main results of the more detailed derivation given in A measurementThe state prediction at time The measurement prediction at the same time is given byAt this point, we compute the Kalman gain Knowing that the Kalman update (41) could produce any point in the big O notation to describe the limiting behavior of the error term of the approximation as To update the covariance matrix we need to consider its definition . We wantAfter the final computation we obtain the fouralent to  in whichIn this section we present the UKF-based estimator: the Manifold Unscented Kalman Filter (MUKF).A measurement The first step in the UKF is to create the augmented j-th sigma point, Then, we obtain the matrix  in Ref. :(52a)Xi can use ), Xjv is in Ref. . Namely,After this, we use the obtained mean quaternion Our best estimation for the orientation at this time isNote that setting This section presents the results of the simulations used to measure the accuracy of each estimator. Simulations are chosen instead of real experiments because a real system entails an uncertainty in the measurement of the true attitude: the attitude that is used to compare with that estimated by the algorithms. There are sources of error ranging from a miscalibration of the measurement system to a possible bias in the “true attitude” produced by another attitude estimator, which makes it problematic to define an adequate metric to measure the accuracy of the algorithms. For this reason, the authors consider that using a simulation is more reliable to avoid possible biases in the results due to said sources of error. Others have performed similar types of tests ,17. HoweWe perform our comparison through a simulation in which we do have an absolute knowledge of the attitude of the system: a true oracle exists in a simulation. Therefore, we can compare the real orientation with the attitude estimated by the algorithms having fed them only with simulated measurements that we obtain from such known orientations. We will extract our performance metrics from a wide set of orientation trajectories in order to obtain statistically conclusive results.We try to answer three questions with the simulation test. The first question is, is there a chart for which we get a greater accuracy in attitude estimation? The second one is, what algorithm produces the most accurate attitude estimation, the MEKF or the MUKF? The last question stems from the fact that previous algorithms on attitude estimation, such as the Multiplicative Extended Kalman Filter, did not contemplate updating the distribution from one chart to another as done at 47b) in the MEKF. However, their estimators performed well ,7,12. Thb in the Although a simulation has been used to compare our algorithms, these have also been tested with a real IMU. In the We have already described a quaternion ecalling , this anAngle Finally, Being that the lower the better, the value of To compute the performance metrics we will need to generate a large number of simulations. Each independent simulation will consist of three steps: initialization, convergence, and estimation.In the initialization step we set up the initial conditions accordingly to the chosen simulation parameters. This includes generating the initial unit quaternion In the convergence step we keep the system in the initial orientation ed using  and (24)T(qt) in  is obtait trough k steps does not depend on the simulation time step Finally, in the estimation step we generate a random but continuous orientation sequence using a Wiener process for the angular velocity: ed error . After einterval .In this section we present the results of the simulations. The algorithms are tested for update frequencies t, and the simulation parameters depicted in Although the algorithms have been developed allowing a different Tsim, dtdtsim, and R represent an imprecise sensor (The parameters The results of the simulation are presented in We observe that there is no chart that is especially advantageous. All things being equal, we would opt for the RP chart. For this chart it is not necessary to worry about the domain since it maps We note that the MEKF performs the same or better than the MUKF. This differs from the usual experience, in which the UKF outperforms the EKF in traditional non-linear estimation applications. The fact that the charts resemble the Euclidean space near the origin see  might beWe can observe that there is almost no difference between using the “chart update” and not using it. The concepts used in this paper have helped us to understand the mechanisms of the MKF, and ultimately to arrive to the concepts of “multiplicative update”, and of “covariance correction step” with the There is no chart that presents a clear advantage over the others, but the RP chart has some characteristics that motivate us to prefer it.The MEKF is preferable to the MUKF due to its lower computational cost and its greater accuracy in orientation estimation.The “chart update” is not necessary for the MKF in practice.We have used concepts from manifold theory to define the expected value and the covariance matrix of a distribution in a manifold. In particular, we have defined the expected value and covariance matrix of a distribution of unit quaternions in Then, the MEKF with the RP chart and without applying the “chart update” is our best attitude estimator according to the adopted performance metric. This algorithm resembles the conventional “Multiplicative Extended Kalman Filter”, but we have obtained the MEKF without having to redefine any aspect of the classic Kalman filter.


Saccharomyces cerevisiae, damaged proteins are retained within the mother cell, resulting in an ageing mother while a new daughter cell exhibits full replicative potential. The cell-specific features determining the ageing remain elusive. It has been suggested that the replicative ageing is dependent on the ability of the cell to repair and retain pre-existing damage. To deepen the understanding of how these factors influence the life of individual cells, we developed and experimentally validated a dynamic model of damage accumulation accounting for replicative ageing on the single cell level. The model includes five essential properties: cell growth, damage formation, damage repair, cell division and cell death, represented in a theoretical framework describing the conditions allowing for replicative ageing, starvation, immortality or clonal senescence. We introduce the resilience to damage, which can be interpreted as the difference in volume between an old and a young cell. We show that the capacity to retain damage deteriorates with high age, that asymmetric division allows for retention of damage, and that there is a trade-off between retention and the resilience property. Finally, we derive the maximal degree of asymmetry as a function of resilience, proposing that asymmetric cell division is beneficial with respect to replicative ageing as it increases the lifespan of a given organism. The proposed model contributes to a deeper understanding of the ageing process in eukaryotic organisms.Accumulation of damaged proteins is a hallmark of ageing, occurring in organisms ranging from bacteria and yeast to mammalian cells. During cell division in  Cell division, growth and death are fundamental features of any living organism. During its life cycle, a cell produces a set of functional components such as proteins or other metabolites, which will ultimately allow the cell to divide, giving rise to a newly born daughter cell. However, due to inherent imperfections in the cellular machinery over time, cells are slowly deteriorating causing essential intracellular functions to perish. At the very end of a cell’s lifespan, age-associated damage builds up consistently impairing the ability of the cell to divide and survive, which eventually culminates in cell death. In environments with a sufficient amount of food, damage will be formed as a consequence of cell growth. This causes the partitioning of damage between the progenitor and progeny during cell division to be an important function.Saccharomyces cerevisiae (S.cerevisiae). The number of divisions before cell death is a measure of the age of a single yeast cell, which has been studied substantially by means of experiments2, and it is called the replicative life span (RLS). The asymmetric division of the budding yeast results in a large ageing mother cell with a finite RLS and a new small daughter cell with full replicative potential3. Replicative ageing in yeast is characterised by the accumulation of age-related damage that is selectively retained within the mother cell compartment at each division4. This retention of damage is required to rejuvenate daughter cells and thereby maintain viability in populations over time. The described mode of division resembles the division observed in multicellular organisms, characterised by the separation of the soma and the germ cell lines5. However, the details behind the interaction of the involved systems and their effects on ageing are still largely unknown. To elucidate the interplay between the various constituents of these processes, theoretical approaches are often implemented in addition to experimental methods.An asymmetric distribution of cell mass after division constitutes a vital part of ageing in the yeast 12. One of the first models showed that even simple unicellular bacteria undergo ageing as a means to cope with damage6. This finding suggested that the phenomenon of ageing precedes eukaryotes and has evolved numerous times as it occurs in multiple organisms. A model of damage accumulation showed the importance of asymmetric partitioning of damage through retention in the symmetrically dividing fission yeast Schizosaccharomyces pombe (S.pombe) and in the asymmetric budding yeast S.cerevisiae as it increases the fitness of the population at both low and high damage propagation rates7. A model of ageing in the bacteria Escherichia coli (E.coli) showed that under the examined conditions the cell lineage was immortal due to its low rate of formation of damage8. A follow-up model quantified the importance of a deterministic (as opposed to a stochastic) asymmetric distribution of damage upon cell division11, also further concluding that asymmetric partitioning of damage increases the overall fitness of the population. An additional study in yeast proposed that the ratio between maintenance and growth is critical when determining the benefits of symmetric and asymmetric division9. Furthermore, damage repair has been identified as a better strategy in terms of coping with damage compared to asymmetric segregation10. Most recently, it was demonstrated that asymmetric segregation of damage in E.coli is deleterious for the individual cell, but it is beneficial for the population as a whole12. In general, these models include the five key properties cell growth, formation of damage, repair of damage, cell division and cell death to a varying extent. Further, a commonly implemented methodology consists of conducting simulations in order to draw conclusions about the effects of the accumulation of damage on a population level.Hitherto, multiple qualitative mathematical models of the accumulation of damage have been developedIn this study, we take advantage of thorough mathematical analysis in combination with simulations coupled to cell growth data of single cells, in order to obtain a detailed description of the constituent parts. Moreover, we address new synergistic effects of the formation of damage, repair of damage, retention and cell size, as well as the conditions under which ageing occurs.resilience to damage, corresponding the difference in volume of an old and a young cell. The implemented mathematical analysis provides a deep understanding of the interplay between the fundamental constituent forces such as damage formation, repair, retention and cell size summarised in a theoretical framework describing the conditions determining if a given cell will undergo replicative ageing, starvation, immortality or clonal senescence. This framework allows us to examine ways of altering the rate of repair and formation of damage as strategies to increase the age tolerance of a single cell. Under the assumption that a minimum amount of functioning proteins is required for the cell to live, we find that asymmetric cell division enables retention of damage and that symmetrically dividing organisms cannot retain damage. Also, we show that there is a trade-off between resilience to damage of the individual cell and the capacity to retain damage. Under the same assumption, we derive the maximum degree of asymmetry that a cell can divide with as a function of the resilience to damage of the individual cell. Finally, we show the evolutionary benefit of asymmetric cell division and high damage resilience in the context of replicative ageing.Here, we present a comprehensive replicative ageing model on the single-cell level. The model which includes all five key properties is validated by cell growth measurements of the increase in cell area over time for individual young and old cells. Using a mathematical methodology called non-dimensionalisation in combination with the experimental data we introduce the concept of P) and damaged proteins (D) is continuous. The continuous part, which is described by a coupled system of ordinary differential equations (ODEs)  Eq. , is gove13. In the model, the growth of the cell is assumed to be exponential: “μ ⋅ P”. The growth rate μ is constant as it is assumed that an abundance of substrate is available for each cell, which would occur in a microfluidics system with continuous inflow of nutrient rich media  corresponds to the size of the daughter cell. The size proportion in the fission yeast S.pombe or E.coli is S.cerevisiae divides asymmetrically with 27. The retention value all damage being retained while no retention is given by mass conservation over generations . The introduction of these new states which are proportions of their respective thresholds results in the removal of the two threshold values Ddeath from the model. Similarly, the time t measured in hours [h] is non-dimensionalised by introducing the variable τ defined as τ = μ ⋅ t. A summary of all the dimensionless components of the model is presented in Table To by-pass the estimation of the parameters which can not be measured and to scale down the number of parameters, we non-dimensionalise the model. To this end, all the states and the time variable are scaled in a way such that the variable, states, and parameters of the resulting model lacks physical dimensions. This in turn simplifies the comparison between the various model components . Typically, this is given by measuring the cell area obtained by time-lapse microscopy imaging31. In the context of the dimensionless model, the corresponding output can be written as τ is the dimensionless time. This indicates that the damage resilience quotient Q corresponds to the increase in size of an old cell compared to a young cell. Assuming that a daughter cell born with no damage has accumulated almost no damage at the point of budding (i.e. D ≈ 0), its dimensionless area is y ≈ 1 as cell division occurs when P = 1. An old mother cell undergoes cell death when D = 1 and hence the volume of this cell at the point of cell death is y = 1 + Q. Accordingly, the damage resilience quotient should be Q ≈ 2.5. It is of interest to note that damage resilience is embedded in the proposed modelling framework for describing replicative ageing and that it is independent of the specific dynamics assumed in the model. As the property is introduced by the non-dimensionalisation procedure, the formulation of the ODE’s is independent of the damage resilience parameter. In other words, using the proposed non-dimensionalisation the property of resilience to damage will be introduced independent of the assumptions made on the forces cell growth, formation and repair of damage.As each cell consists of intact proteins e D Fig. , it is r10 . These images are taken of both young and old yeast cells , which accounts for the model complexity, the presented model  value of the fit and the 32, for the models to describe replicative ageing they should satisfy the criteria that RLS ∝ Q independent of the rate parameters that are selected. Thus, by picking parameters giving rise to a finite RLS, an increase in Q while keeping the remaining parameters fixed should increase the life span, while a decrease in Q should decrease the life span. The simulations show that our model together with the model by Erjavec et al.7 satisfy this criteria which the model by Clegg et al.10 does not, and hence our theoretical description captures this important aspect of replicative ageing in yeast  how much damage can a mother cell retain, (2) how does the capacity to retain change throughout the life time, (3) what factors limit the amount of damage a mother cell can retain at cell division and (4) how does the degree of asymmetry in the cell division affect the capacity to retain damage.Assuming that the minimal amount of intact proteins that a cell is required to have after cell division is sion Eq. .5\documeThree main conclusions can be drawn from the upper constraint on the retention of damage. Firstly, the capacity to retain damage is inversely proportional to the amount of damage that the cell contains, i.e. Secondly, the capacity to retain damage is inversely proportional to the degree of resilience, i.e. s = 1/2, the upper limit vanishes  and asymmetric (s = 0.64) cell division (with and without retention) under low (Q = 2.5) and high (Q = 3.0) resilience to damage  Thath Fig. . (III) Tath Fig. . (IV) Reath Fig. . (V) Asyath Fig. .Q emerges which is essential to the replicative ageing of a single cell where an increase in resilience greatly prolongs the life span  system and allowed to sediment in the main channel. Fresh CSM media was supplied to the cells through the other channel. The experimental setup is further described in Welkenhuysen et al.49. Imaging was performed on a Leica DMi8 inverted fluorescence microscope (Leica microsystems). The microscope was equipped with a HCX PL APO 40x/1.30 oil objective (Leica microsystems), Lumencor SOLA SE (Lumencor) led light and Leica DFC9000 GT sCMOS camera (Leica microsystems). Cell growth was recorded at 1 frame in bright-field at 20 ms exposure every 5 minutes. Only daughters who have been budded of from the mother cell in the PDMS system were observed for their first divisions. Analysis of cell area was performed with the ImageJ distribution FIJI50.The yeast cells  were inoculated in 5 ml of complete synthetic medium media containing 1.7 g/l yeast nitrogen base, 5 g/l ammonium sulfate, 670 mg/l complete supplement mix supplemented and 4 % glucose from freshly streaked (2-4 days old) plates and incubated in a shaker at 3051. The system of ODEs for the various models have been solved using the built-in solver ode45 which uses an adaptive "Runge-Kutta-Fehlberg"-method of order 4 and 552. The model validation have and the numerical identifiability analysis have been conducted using the optimiser lsqnonlin. The structural identifiability analysis of the three competing models have been obtained using the Mathematica software developed by Karlsson et al.53. A detailed description of the numerical implementations of the algorithms used for generating the results can be found in the Appendix (See Supplementary material SAll the numerical results, except for the structural identifiability analysis, were generated using MatlabSupplementary Information.