To precisely diagnose the rotating machinery structural faults, especially structural faults under low rotating speeds, a novel scheme based on combination of empirical mode decomposition (EMD), sample entropy, and deep belief network (DBN) is proposed in this paper. EMD can decompose a signal into several intrinsic mode functions (IMFs) with different signal-to-noise ratios (SNRs) and sample entropy is performed to extract the signals that carry fault information with high SNR. The extracted fault signal is reconstructed into a new vibration signal that will carry abundant fault information. DBN has strong feature extraction and classification performance. It is suitably performed to build the diagnosis model based on the reconstructed signal. The effectiveness of the proposed method is validated by structural faults signal and the comparative experiments . The results show that the diagnosis accuracy of the proposed method is between 99% and 100%, the BPNN is less than 25%, and the CNN is between 70% and 95%, which means the verified, proposed method has a superior performance to diagnose the structural fault. Rotating machinery covers extensive mechanical equipment and plays an important role in industrial production. It generally serves in a complicated and harsh environment, and may experience faults caused by the environment . It is oStructural faults are the most common fault in rotating machinery. It not only causes direct baneful influences on performance of equipment and quality of products, but also it causes excessive stress on surrounding components (such as bearings and gears) and causes secondary failure . TherefoIt is a common method in rotating machinery fault diagnosis to analyze fault vibration signals and disclose fault characteristics by effective signal processing technology ,7. WhethIn frequency-domain analysis, characteristics of vibration signals in the frequency domain can be observed more easily by Fourier transform. In addition, explicit fault characteristics and diagnosis information can be acquired through frequency spectra of vibration signals . HoweverCompared with other machine faults, structural faults are prominent for changes of rotating frequency and changes of harmonic component. Moreover, vibration signals of structural faults are dynamic nonlinear system signals. Traditional time-domain analyses are mainly based on the hypothesis that the process of signal production is static and linear. Hence, they may make the wrong judgment if fault signals are dynamic nonlinear systematic signals caused by structural faults ,13. SomeWith the popularization of the artificial neural network, the fault diagnosis becomes more and more intelligent and accurate under the assistance of neural networks by its strong pattern recognition capability. Even though some studies have implemented a neural network-based fault diagnosis, the types of faults they can diagnose are specific fault states and are very limited . We haveDeep learning possesses considerable advantages in pattern recognition and it has been highly used in many fields ,21,22,23measuring vibration signals of the targeted rotating machinery ;decomposing the original vibration signal into several IMFs by EMD;calculating sample entropy of IMFs and screen the signals that contain many fault information;reconstructing the screened signals into new characteristic signals;implementing FFT to new characteristic signals, and then gain their frequency-domain characteristic signals;inputting the frequency-domain characteristic signals into the trained DBN and get the final diagnosis results.Procedure of the proposed method is shown in The rest part of this paper is organized as follows. Fault information in diagnosed signals shall be extracted before the training and use of the DBN in order to increase diagnosis accuracy based on DBN. This can be realized by combining EMD and sample entropy.EMD is an adaptive signal analysis and processing technique. In fact, it makes stationary processing of data sequences or signals. EMD has evident advantages in processing non-stationary and nonlinear data and has high SNR. Since vibration signals of different structural faults often have many similar characteristics on the waveform and frequency spectra, it is difficult to distinguish different types of structural faults. To extract fault information and improve the diagnosis accuracy, the diagnosed signal was decomposed into several IMFs by EMD.Instantaneous frequency at any one point of IMFs is meaningful. At any moment, signals can contain several IMFs. Composite signals are formed when IMFs overlap mutually.The decomposition process is introduced as follows.x(t) contains the following steps:Effective EMD process of one given signal x(t), including the maximum point (xmax(t)) and the minimum point (xmin(t)).(1) Find out all extreme points of the original signal eminx(t) of the minimum point and the upper envelope of maximum point emax(t) by using the interpolation method.(2) Form the lower envelope (3) Calculate the mean:(4) Draw the details:d(t) has a negative local maximum and a positive local minimum, it is not an IMF and screening shall be continued. In other words, all extreme points of d(t) shall be recognized and all above steps shall be repeated until meeting the given standards. If the screening process is accomplished successfully, the first IMF is extracted and it shall be subtracted from the original data. Next, repeat this process to get the next IMF until all IMFs are extracted.(5) If Each diagnosed signal can decompose several IMFs by the above EMD. However, only several signals that contain fault information have to be screened and reconstructed into new vibration signals for a more precise diagnosis. This was accomplished by sample entropy in this study. Sample entropy (SampEn) is an improved method to measure the complexity of time sequence based on approximate entropy (ApEn). It has been used in assessment of complexity of physiological time series and diagnosis of the pathological state. In this study, sample entropy can be used as the standard to judge how much fault information each signal contains.The calculation process of sample entropy is introduced as follows:N, which is expressed as The original data is set as a time series with a length of X(1), X(2), …, X(N − m + 1), and where X(i) = {u(i), u(i + 1), …, u(i + m)}.(1) Construct a group of m-dimensional vectors: d between vectors X(i) and X(j) as the one with the maximum difference in corresponding elements is: (2) The distance i:1 ≤ i ≤ N − m + 1}, a statistics on number of d < r is carried out when the allowable deviation is r, which is recorded as Nm(i). Meanwhile, the ratio between Nm(i) and the total distance is calculated, which is denoted as the equation below. (3) For each {i, which is denoted as the formula below. (4) Calculate the mean of all 1 to m + 1. Repeat Steps (1)–(4) to get:(5) Increase the dimension m by SampEn of this series is shown below.(6) Theoretically, the sample entropy N cannot be ∞. When N is a limited value, it is estimated that:Practically, Since sample entropy is an index that mainly assesses the complexity of the signal, it is inadequate for extracting essential fault information for precise diagnosis. For effective extraction of fault information, the sample entropies of different IMFs, which are decomposed by the EMD method from both the diagnosed signal and the normal state signal, have to be calculated. The ratio between IMFs of diagnosed signal and IMFs of the normal state signals was used as the reference to screen the signal containing many fault information.Through the empirical modal decomposition above, the original vibration signal is decomposed into several intrinsic mode functions. Each intrinsic mode function contains varying degrees of fault information. The sample entropy can screen IMFs that contain fault information. New vibration signals can be reconstructed by integrating these IMFs. The new signals have higher SNR than the original vibration signal and can increase the diagnosis accuracy effectively. In this study, the first three IMFs with the highest sample entropy ratios (farther from 1) were chosen from each group to reconstruct the new signals. New signals were used to replace the original vibration signal in a precise diagnosis. The extraction of fault information and the reconstruction of the vibration signal are shown in DBN is a probability generation model and a multi-hidden layer neural network formed by multiple restricted Boltzmann machines (RMB). The DBN model can extract features layer by layer from the original data through layered piling of RBM, which shows high-level expressions. The core of DBN is to optimize connection weight of the deep neural network by using the layer greedy learning algorithm ,26. FirsDBNs are composed of multiple RMBs. The structure of one DBN is shown in x and the first hidden layer are treated as one RBM, and the parameters of the RBM  are trained, and then fixed. By treating 1h as the visible vector, 2h as the hidden vector, and training the second RBM, the parameters of RBM can be obtained and then fixed. Afterward, the RBM composed of 2h and 3h is trained.To train the DBN, unsupervised pre-training based on RBM was performed first. Weights were initialized by the comparison divergence algorithm, which was followed by supervised optimized training. During supervised optimized training, it has to get a certain output from the input by using the forward propagation algorithm. Next, weights and offsets of the network shall be updated by the backward propagation algorithm. The training process of DBN is shown as follows. When training DBN, a layer-by-layer unsupervised method is used to learn the parameters. As shown in EMD was performed to experimental data under different states (labels). Signals containing abundant fault information were screened, according to sample entropy ratio and then reconstructed into new vibration signals. Frequency spectra and labels of these reconstructed signals were used to train the neural network. The training for the proposed model is shown in In this chapter, the proposed method was used to precise diagnosis of structural faults of rotating machinery. First, vibration signals of different structural faults shall be collected . The folThe rotating machinery simulator in It can be seen from In this study, the measured rotating speeds are 300, 500, 700, and 900 rpms, respectively. Acceleration sensors are used to measure the vibration signal in five directions. The vibration signal is stored by the data collector and converted into the csv format for subsequent processing. The sampling frequency is 10,000 Hz, the sampling time is 7 s, and the data length is 70,000. The original vibration signals and the EMD results are shown in It generally can be concluded from EMD results that the first IMFs among 10 decomposed IMFs have relatively dense images and may contain abundant fault characteristics. The rest of the IMFs have relatively sparse images and may contain few fault characteristics. However, this was inadequate to screen signals containing abundant fault information. To screen signals containing many fault information, sample entropy of each IMF shall be calculated.Parameters were set as follows before calculating the sample entropy: the dimension m and threshold r of the constructed samples were m = 2500 and r = 0.008, respectively. Due to the size of mass data in the original signal, it took a considerable long time to calculate sample entropy. In this study, 5000 sample points in the original signal were selected to calculate sample entropy, which could increase the calculation efficiency and shorten calculation time significantly. The ratio between sample entropy of IMFs of different structural faults and the sample entropy of IMFs of normal state can be expressed in In each group of IMFs, the first three IMFs with the highest ratio of sample entropy were used to reconstruct the new vibration signals, which are shown in Compared with the original vibration signal, the reconstructed vibration signals had fewer impacts from noises in view of images, and a higher proportion of fault information. Diagnosis based on reconstructed vibration signals can further increase the accuracy of precise diagnosis. To verify the validity of the proposed method, diagnosis results based on time-domain signal, diagnosis results based on frequency-domain signal, and diagnosis results based on the combination of frequency-domain signals, and the fault information extraction method were compared.First, parameters of the neural network were set uniformly.DBN size was set 100–50 (the explicit layer had 100 neurons and the hidden layer had 50 neurons).The number of iteration for samples was 100.The batch size was 160.Learning rate was 0.01.When only time-domain signals were used in the diagnosis, the following occurred.When only frequency-domain signals were used in diagnosis, When the diagnostic signal was a frequency domain signal, the diagnostic accuracy is very high at high rotating speeds (700 rpm and 900 rpm), but the accuracy of the precision diagnosis is very low at low rotating speeds (300 rpm and 500 rpm). According to above analysis, the most prominent common features of structural faults are changes of rotating frequency and its harmonic components. Different types of structural faults have very similar characteristics, especially under a low rotating speed. Therefore, the diagnosis accuracy based on frequency-domain signals was not satisfying under low rotating speed despite the overall diagnosis accuracy being improved significantly. Fault characteristics have to be further extracted and SNR of signals need to be increased in order to further improve the diagnosis accuracy.After the decomposition of the original signal by EMD and the selection of intrinsic mode function with high signal-to-noise ratio based on the sample entropy, the selected intrinsic mode functions are reconstructed into new vibration signals. The number of samples based on the reconstructed signals for each state is 100, the length of each sample is 1000, 80% of the total number of samples are randomly sampled for training, and the rest of the samples are used to verify the trained model. There are four types of states in this experiment , so the total number of training samples is 320, and the total number of test samples is 80. The structure of the deep belief neural network is , the number of iterations of the sample is 100, and the learning rate is 0.01. Based on the trained deep belief neural network, the diagnostic accuracy of the test samples is shown in During EMD processing of diagnosed signals, IMFs that contain abundant fault information were chosen according to the ratio with sample entropy of normal state and they were reconstructed into new vibration signals. The frequency-domain signals of these new vibration signals were used in diagnosis, which achieved very high accuracy under both high and low rotating speeds. The precise diagnosis was realized. DBN size was set 100–75 (the explicit layer had 100 neurons and the hidden layer had 75 neurons).The number of iteration for the samples was 50.The batch size was 160.The learning rate was 0.05.Diagnosis results.The diagnosis results show in DBN size was set to 100–100 (the explicit layer had 100 neurons and the hidden layer had 75 neurons).The number of iteration for the samples was 50.The batch size was 160.The learning rate was 0.02.Diagnosis results.The diagnosis results show in In the comparison experiment, the method of using the time domain signals only, the method of using frequency domain signals only, and the proposed method are performed. The fault characteristics in the time domain signal is difficult to express, which will result in low diagnostic accuracy when only using time domain signals for diagnosis. When only using frequency domain signals for diagnosis, although the diagnostic accuracy is greatly improved compared with the method of only using time domain signals, the faults of the structural faults often have similar characteristics and the diagnostic accuracy is not satisfied. In this paper, the method of extraction of fault information based on empirical mode decomposition and sample entropy is proposed to screen and reconstruct the vibration signals with high SNR for precision diagnosis, and the frequency domain signals of reconstructed signals are combined with a deep belief neural network, which has strong classification performance. This method can increase diagnosis accuracy significantly and realize a precise diagnosis of structural faults. This is because reconstructed vibration signals not only extract fault characteristics in original signals effectively, but also have extremely high SNR, which is conducive for increasing diagnosis accuracy greatly. The diagnosis accuracy was verified by changing the parameters of DBN.It can be known from the above diagnosis results that the proposed method still maintains extremely high diagnosis accuracy after parameters of DBN are changed. This method can adjust parameter settings according to different needs and realize a precise diagnosis.In order to compare the diagnostic accuracy of the precision diagnostic method with the diagnostic methods based on other neural networks, it is necessary to extract the fault characteristics for precise diagnosis before using the traditional neural network for diagnosis. Dimensional and dimensionless symptom parameters are capable of extracting the characteristics of vibration signals and are commonly used for mechanical condition monitoring. These parameters allow for more sensitive detection of mechanical faults and allow for distinguishing fault types . HoweverBack propagation neural network (BPNN) is the most common kind of neural network. It is a multi-layer feedforward network trained by error back propagation. The algorithm is called BP algorithm. The basic idea is the gradient descent method. Gradient search technology is used to minimize the error mean square error between the actual output value of the network and the expected output value . In thisThe convolutional neural network (CNN) is a multi-layer feedforward neural network. It is good at dealing with related machine learning problems of images, especially large images . It has In this study, the symptom parameters and their principal components are reconstructed into a matrix of image forms and then used as input to a convolutional neural network. When the symptom parameters are used as input, each state signal is divided into 12 segments, and a set of special feature parameters can be calculated, according to each segmentation signal. The number of each group of feature parameters is 12. The symptom parameters are rearranged and constructed into a 12×12 new pixel matrix as an input to the CNN neural network.To further verify the effectiveness of the proposed method, the results of the DBN network are compared with those of other neural networks (such as BPNN and CNN). The experimental data used are consistent with From the results in In this study, to realize accurate detection and recognition of structural faults of rotating machinery, a precise diagnosis method based on fault information extraction that combines EMD and sample entropy as well as DBN was proposed. Diagnosis results based on time-domain signals, diagnosis results based on frequency-domain signals, and diagnosis results based on the combination of frequency-domain signals and fault information were compared. It finds that diagnosis accuracy based on time-domain signals was unsatisfying because time-domain signals are difficult to express all features of signals. Therefore, the time-domain signals fail to detect and recognize structural faults. The most prominent common features of structural faults are changes of rotating frequency and its harmonic components. Therefore, diagnosis accuracy based on frequency-domain signals was increased significantly compared with that based on time-domain signals. Since different types of structural faults have similar features in the frequency domain, the diagnosis accuracy based on frequency-domain signals under low rotating speed is unsatisfying and has to be improved. When fault information was extracted by combining EMD and sample entropy, the original vibration signals were decomposed and signals with high SNR that contain abundant fault characteristics were selected and reconstructed into new vibration signals. Frequency-domain signals of these new vibration signals were used in diagnosis, which achieves high accuracy under both high and low rotating speeds. In other words, the proposed method can detect and recognize structural faults under different rotating speeds. It realizes precise diagnosis of structural faults. Moreover, an intelligent precise diagnosis system can be constructed based on the proposed method. This is conducive to realize the goal of early diagnosis of structural faults in practical production. Compared with BPNN and CNN, the method proposed in this study was superior to other methods in the precision diagnosis of structural faults in rotating machinery, and has the highest diagnostic accuracy.


Estimating the Direction of Arrival (DOA) is a basic and crucial problem in array signal processing. The existing DOA methods fail to obtain reliable and accurate results when noise and reverberation occur in real applications. In this paper, an accurate and robust estimation method for estimating the DOA of sources signal is proposed. Incorporating the Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm with the RANdom SAmple Consensus (RANSAC) algorithm gives rise to the RAN-ESPRIT method, which removes outliers automatically in noise-corrupted environments. In this work, a uniform circular array (UCA) is converted into a virtual uniform linear array (ULA) to begin with. Then, the covariance matrix of the received signals of the virtual linear array is reconstructed, and the ESPRIT algorithm is deployed to estimate initial DOA of the source signal. Finally, the modified RANSAC method with automatically selected thresholds is used to fit the source signal to obtain accurate DOA. The proposed method can remove the unreliable DOA feature data and leads to more accuracy of DOA estimation of source signals in reverberation environments. Experimental results demonstrate that the proposed method is more robust and efficient compared to the traditional methods . In recent years, service robots with artificial intelligence technology have gained wide applications . In ordeChoosing the right microphone array structure is the prerequisite for proper estimate DOA, and Uniform Linear Array (ULA)  and UnifWith the popularization of the ESPRIT algorithm, the technique has been deeply studied by many researchers. The algorithms , which a(1) Since the array manifold matrix of UCA does not have Vandermonde matrix structure and UCA cannot be divided into two subarrays with the rotational invariance, it is not possible to directly estimate the DOA using the ESPRIT . Hence, (2) To further improve the performance of the DOA estimation, we propose an improved algorithm to obtain the optimal DOA estimation via the weighted average of each frame’s DOA estimation over the whole-time domain. However, under reverberant environment, only a fraction of frame’s DOA estimation is unreliable and useless. As a result, the final DOA estimation may exhibit poor accuracy and poor robustness in reverberate environment. To address the problem, we introduce the RANSAC algorithm  in orderThe rest of the paper is organized as follows. UCA is considered in this work and shown in The source signal’s elevation angle  problem . If therAmong the traditional DOA estimation algorithms, the high-resolution spectrum-based DOA estimation algorithms have become the one of the most common algorithms. The representative algorithms are the MUSIC and the ESPRIT. The MUSIC has high accuracy in DOA estimation, but its calculation speed is slow. The ESPRIT algorithm is faster than the MUSIC. It is important to estimate DOA of the source signal quickly in some real time applications such as robot sensing. Therefore, we choose the ESPRIT algorithm to estimate DOA of the source signals, but the accuracy of the ESPRIT in low SNR environment is low. In this paper, we propose a method to improve the accuracy of the DOA in such an environment.The ESPRIT algorithm uses the translation invariance of the sensor array in the estimation of source DOAs. Unlike ULA, UCA does not have the translation invariance. Hence, the ESPRIT cannot be applied to UCA directly. To solve this problem, the idea of phase mode excitation beamformer  is borroFor a continuous circular array, if a spatial harmonic function The discrete UCA shown in As all the modes are excited with reasonable strength, here we adopt the phase mode excitation beamformer From the condition in Equation (1), we can observe that Bessel function terms in Equation (9) are constants and can be calculated directly. Hence, a new direction vector can be obtained by a weight matrix that eliminates the Bessel function terms. The weight matrix is:From Equation (12), the beam space covariance matrix is:Assuming that the sixteen sensors on the UCA are evenly distributed on the circumference with To improve DOA estimations of source signals at low SNR, the idea of the combination of the ordinary and the conjugate data ,40 is boThe conjugate form of Equation (12) is:Here, We define the matrix SThe signal subspace of The diagonal elements of Since the environment contains noise, it can be seen from The source signals often contain noises and reverberation in real environments, the subspace Before we start to fit the DOAs, we observe that for multi-source signals, the same signal may be spread into different positions in dth reference signal, respectively. The source signal Generally, sound signals vary over time but they can be viewed as stationary in a short period of time, say within 10–30 ms . In thisThe eigenvectors that correspond to the same source signal in Because in the environments with noise and reverberation, the DOA estimation may be abrupt at low SNR. Straightforward usage of these DOAs may be not accurate enough. To solve the problem, the idea of RANSAC  is borroFor fined in  by:(21)hN frames DOAs.In each RANSAC iteration, for each group DOA, After the distance is calculated, we should consider how to choose the distance threshold The resulting largest consensus set that contains the most exact DOA parameter is obtained and the DOAs without unreliable parameters are determined. Assuming that there are sixteen sensors on the UCA are evenly distributed on the circumference with In this simulation, low SNR environment with reverberation is considered. It can be seen from the results shown in Algorithm 1: RAN-ESPRIT algorithm(1)Take multiple frames of source signals and perform step (2)–(6) for each frame;(2)Convert the UCA output signal to virtual ULA by Equation (12), and form the virtual ULA covariance matrix (3)Reconstruct the matrix (4)Obtain the signal subspace matrix (5)Partition (6)Compute the eigenvalues (7)Match the DOA of each source signal in each frame to get (8)Set parameters for adaptive RANSAC method: (9)Randomly select (10)Identify the threshold value (11)Update the number of iterations (12)If (13)Once the largest consensus is obtained, the subset of DOA of the group is determined. The optimal DOAs of each source signal are obtained by fitting the subset in each group.In summary, the RAN-ESPRIT algorithm is described as follows:Simulations have been performed to verify and analyze the proposed method in this section. The sixteen sensors on the UCA are evenly distributed on the circumference with parameter In this section, four methods are analyzed: (1) the proposed algorithm in this paper (denoted by Line 1); (2) UCA-ESPRIT algorithm  is fitteIt can be seen from the experimental results shown in Moreover, the experimental results for different SNR (without reverberation) have been reported in In the virtual space, the performance of four methods at different SNR (contain reverberation) is compared and the results are shown in In this section we discuss the estimation procedure of the DOA of source signal in the environment contained reverberation. In order to obtain 360° information from the sensor arrays, we choose the UCA to estimate DOA. Liu  proposesIn From Finally, we discuss the effects of the threshold used in RANSAC algorithm. While being very robust in dealing with data outliers, the RANSAC algorithm is affected by the threshold and is unstable. Hence it is important to choose the threshold appropriately. If a very high threshold is chosen, it is possible that we may mistakenly classify the outliers into the consensus set, and the accuracy of RANSAC decreases. If a very low threshold is chosen, it is possible that we are not able to get the optimal set. Comparing to In this paper, we converted the UCA into a virtual ULA and presented a modified method based conjugate matrix to improve accuracy of the conversion. Then, we proposed an accurate and reliable technique to estimate DOA of source signals based on RANSAC algorithm. Experimental results also show that the proposed approach is robust and efficient in the environments with noise and reverberation when compared with the other existing methods. In the real environment, there is a larger variety of source signals, with sources at a variety of distance from the array. We will conduct further research on this issue in our future work.


Digital holographic interferometry (DHI) radiation dosimetry has been proposed as an experimental metrology technique for measuring absorbed radiation doses to water with high spatial resolution via noninvasive optical calorimetry. The process involves digitally recording consecutive interference patterns resulting from variations in the refractive index as a function of the radiation-absorbed dose. Experiments conducted on prototype optical systems revealed the approach to be feasible but strongly dependent on environmental-influence quantities and setup configuration. A virtual dosimeter reflecting the prototype was created in a commercial optical modelling package. A number of virtual phantoms were developed to characterize the performance of the dosimeter under ideal conditions and with simulated disruptions in environmental-influence quantities, such as atmospheric and temperature perturbations as well as mechanical vibrations. Investigations into the error response revealed that slow drifts in atmospheric parameters and heat expansion caused the measured dose to vary between measurements, while atmospheric fluctuations and vibration contributed to system noise, significantly lowering the spatial resolution of the detector system. The impact of these effects was found to be largely mitigated with equalisation of the dosimeter’s reference and object path lengths, and by miniaturising the detector. Equalising path lengths resulted in a reduction of 97.5% and 96.9% in dosimetric error introduced by heat expansion and atmospheric drift, respectively, while miniaturisation of the dosimeter was found to reduce its sensitivity to vibrations and atmospheric turbulence by up to 41.7% and 54.5%, respectively. This work represents a novel approach to optical-detector refinement in which metrics from medical imaging were adapted into software and applied to a a virtual-detector system. This methodology was found to be well-suited for the optimization of a digital holographic interferometer. Radiation dosimetry is an umbrella term for a family of measurement techniques that quantify the amount of ionising radiation energy absorbed by an object or body. Radiation dosimetry is essential to many branches of science and industry and, in particular, healthcare for cancer treatment. As a radiation dose is defined as the amount of energy absorbed per kilogram of mass, one of the fundamental methods for its measurement is calorimetry, where the temperature change of the absorbing medium is measured and used to calculate the amount of absorbed energy. Conventional dosimetric calorimeters use thermistors embedded in absorption media to measure the temperature increase, but the inclusion of the sensors disturbs the propagation of the radiation field, necessitating the application of cavity-correction factors when calculating the absorbed dose . These cA proposed alternative to conventional calorimetry is a specialised type of optical interferometry known as digital holographic interferometric (DHI) calorimetry. Optical interferometry describes a family of metrology techniques in which interfering light waves are used to probe any physical parameter of a system that affects the path length of light travelling through it. In general, interferometers rely upon the use of two light fields: one that interacts with the sample of interest, and one that bypasses it. The beams are then superimposed and the resulting interference pattern is analysed to extract information about the parameter under investigation. Holographic interferometry describes an extension of interferometry in which interference patterns of two states are captured and then reinterfered experimentally or digitally in order to extract a two-dimensional map of optical path length difference with a subwavelength resolution. Due to its near-unparalleled sensitivity and noninvasiveness, interferometry is widely used in science and industry ,4,5.Holographic interferometry for radiation dosimetry was pioneered in 1971 by Hussman, who used a panchromatic sheet film to capture interferograms of a water cell before and after its irradiation with a high-intensity-pulsed 2 MV electron beam. Isodose contours and percentage depth dose curves were successfully reconstructed from these interferograms ,7. The tRecent developments in DHI dosimetry have shown the technique to be capable of generating absorbed dose maps with submillimetre spatial resolution, and have demonstrated its applicability to different types of radiation and diverse field geometries ,14. HoweThis paper describes the refinement and sensitivity analysis of a DHI calorimeter via the incorporation of medical-physics quality-assurance techniques into commercial optical modelling software. A virtual dosimeter mirroring the Cavan–Meyer prototype was created in the optical modelling program FRED , using its complex ray-tracing functionality to model interference phenomena. The aim of this research was to show that optical modelling software can be used to accurately simulate a DHI calorimeter, identify its major sources of error, and virtually test improvements to its design. The model, in conjunction with the quality-assurance protocols that were developed, found the major contributor to dosimetric uncertainty to be atmospheric turbulence causing fluctuations in air pressure, temperature, and humidity. The model was used to test improvements to the dosimeter, and it was found that miniaturisation of the dosimeter and equalisation of its path length largely mitigated the impact of environmental fluctuations on the measured dose.The virtual DHI dosimeter was modelled after the prototype lensless Fourier transform-type (LFT-type) interferometer developed by Cavan and Meyer in 2014 . In the Irradiation of the test cell with ionising radiation creates local variations in water temperature depending on the absorbed dose at each point. This leads to corresponding local variations in water density, thereby altering the refractive index and optical path length traversed by the object beam as it passes through the test cell, changing the interference pattern captured on the CMOS.k is the light wavenumber, s is the sensor to image distance, The intensity map of the interference pattern recorded on the CMOS is expressed by Reconstructed-object wave-phase maps can be extracted from acquired holograms of the test cell in both its unirradiated and irradiated states, and the interference phase between them is calculated by modulo The result, ence map .The continuous-phase difference map was then converted to a change in optical path length usingd, of the test cell was then calculated viaThe change in refractive index over the width, Temperature change ve index . The depThe commercial optical design software FRED was used to create a virtual model of the Cavan–Meyer prototype dosimeter. Each optical component was separately initialised according to its manufacturer-specified material, geometry, and coating parameters, and the optical elements were integrated into the model using the graphical editing interface in FRED, as shown in To test the ability of the system to resolve a simple dose distribution, two copies of the water-filled test cell were created. The first was a simple cube of water surrounded by a perspex box, with the refractive index of the water set to correspond to room-temperature  plugin created by Mitja et al.  was usedThe fencepost phantom was used to estimate the practical-resolution limit of the system. Holograms of the virtual-fencepost phantom were collected and reconstructed, and the resultant image was divided into its 20 constituent spatial-frequency regions. A 2D intensity profile was collected for each region by averaging the intensity of the pixels in each of its columns. These profiles were manually examined, and the practical resolution limit of the system was found to be the spatial frequency at which the line pairs could no longer be reliably counted.Finally, simulated holograms of the contrast-detail phantom were collected and reconstructed. The reconstructed images were manually examined using a calibrated reference display in order to determine which regions were distinguishable, providing a relative estimate of the contrast and detail resolution of the system depending on the dose and diameter of the visible areas.The following environmental-influence quantities were identified for modelling and implemented via FRED’s scripting functionality: atmospheric turbulence, atmospheric drift, heat expansion, and mechanical vibration. These were grouped into long-timescale fluctuations (atmospheric drift and heat expansion), which cause homogeneous systematic errors in measured dose and affect the comparability of measurements acquired under different conditions, and short-timescale fluctuations , which cause blurring of the acquired holograms and random defects in measured doses across the test cell.T (P (Pa),The atmospheric refractive index was calculated via the Edlén equations , which ff is the vapour pressure of water in ambient air (Pa).Finally, the impact of atmospheric humidity is factored into the final refractive index,To assess the impact of atmospheric drift on dosimetric uncertainty, mean values  was then calculated for each atmospheric parameter.The average ambient laboratory temperature was determined to be To model heat expansion in the prototype dosimeter, FRED’s scripting interface was used to obtain the spatial coordinates of each optical element. With the origin taken to be the centre of the test cell, each component was then translated according to the following heat-expansion formula:A reference interferogram of the unirradiated test cell was collected with no perturbation of the optical elements to represent the Atmospheric turbulence, resulting from fans, air conditioning, and other draughts, is responsible for short-timescale local disruptions in atmospheric temperature, pressure, and humidity, which cause blurring and dosimetric error in the captured interferograms. In order to simulate its effect, the beamline of the interferometer was divided into 9 regions, as shown in These were each populated with cubic atmospheric voxels of 2 mm side length as shown in quations –10)) we) weμ) anImages of the fencepost, slant-edged, and contrast-detail phantoms were captured in order to assess the impact of atmospheric turbulence on the resolution of the dosimeter system.The impact of mechanical vibrations on dosimetric uncertainty was also assessed. The amplitude and frequency of displacements induced by common sources shown in  were fouThe time-averaged hologram-acquisition method outlined in Two refinements to the dosimeter were tested in order to determine whether they were capable of alleviating uncertainties introduced by environmental fluctuations.The original dosimeter configuration had very unequal path lengths, with object- and reference-beam lengths of 401.28 and 1235.19 mm, respectively. According to interferometric theory, this contributes to errors caused by homogeneous changes in the atmospheric refractive index or geometric path length, since each optical path is differentially altered according to its length. A new dosimeter configuration was created in FRED with equal length (610.25 mm) reference and object beam paths, as shown in The second option for dosimetric improvement was miniaturisation, which theoretically mitigates uncertainties introduced by intrabeamline fluctuations by reducing the length of the reference and object paths. A FRED model of a miniaturised dosimeter with equal reference and object path lengths  was created, as per the schematic shown in A sample experimental hologram a and assReconstructed dose maps of the simulated irradiated phantom were generated for each of the atmospheric refractive indices shown in shown in  to obtaiAccording to these simulations, the combined drift of all atmospheric parameters generated an average dose defect of The spatial-resolution characterisation protocols described in The calculated MTF system under each of these uncertainty regimes is displayed in As expected, the system with no simulated uncertainty had the best spatial resolution, with a best-case estimate of 34 lp/mm, and a practical estimate of 14 lp/mm. Both the MTF-derived and fencepost-derived limiting resolution estimates indicate that atmospheric turbulence was a more significant source of error than mechanical vibration.Contrast-detail plots are displayed for each of the uncertainty regimes in The uncertainty contributed by atmospheric drift and heat expansion were reassessed using a dosimeter configuration with equalised path lengths. Maps of the dose defects generated by each uncertainty simulation are shown in The dose defects generated by atmospheric drift and heat expansion on the equalised dosimeter were 96.9% and 97.5% lower than those found using the original dosimeter configuration. This indicates that equalising the lengths of the reference and object beam paths reduces the impact of long-timescale changes in atmospheric refractive index and ambient temperature. This finding is consistent with interferometric theory, which states that the defect should tend toward zero, as the difference in path length is reduced .The slanted-edge, fencepost, and contrast-detail phantoms were imaged using the miniaturised system with no environmental perturbations, with simulated atmospheric turbulence, and with simulated mechanical vibrations. The miniaturised dosimeter performed better than the original configuration in all spatial-resolution tests. The MTF-derived estimate for the limiting resolution of the miniaturised dosimeter was improved by 29.4% when no environmental perturbations were applied, and by 29.4% and 27.3% for the system subject to atmospheric turbulence and mechanical vibrations, respectively. The fencepost test, which incorporated the effects of phase unwrapping and dose reconstruction, found the spatial resolution with no perturbations to be 28.6% better than the original dosimeter. The resolution of the system under the influence of simulated atmospheric and mechanical perturbations was improved by 58.4% and 41.7%, respectively, by miniaturisation.Finally, the contrast-detail plots showed the same trend, wherein more dose regions were visible in the reconstructed images of the CD phantom acquired with the miniaturised system compared with those acquired with the larger setup. These results indicate that miniaturisation of the dosimeter yielded a consistent improvement in contrast-detail resolution.This work showcases an approach to optical-detector refinement and sensitivity analysis that combines methods from medical imaging with the modelling capability of commercial optical design software. This approach was undertaken using a prototype DHI radiation calorimeter as a case study.A virtual detector was created in Photon Engineering’s optical design program FRED, and a number of simulated phantoms analogous to those used in medical-imaging quality-assurance testing were integrated into the model to characterise its performance and dependence on environmental influence quantities. Variation in atmospheric parameters, ambient temperature, and displacement due to mechanical vibration were simulated through perturbation of the optical model, and the system’s performance was probed under these uncertainty regimes in order to establish the degree and nature of error introduced by each one.The spatial resolution of the ideal detector was estimated via MTF calculation to be 34 lp/mm, and by imaging a fencepost phantom to be 14 lp/mm. These were reduced to 22 and 7 lp/mm when the effects of mechanical vibrations were simulated, and 17 and 5 lp/mm when atmospheric turbulence was simulated, indicating that atmospheric turbulence had more serious impact upon the spatial resolution of the dosimeter. Long-timescale fluctuations in the atmospheric refractive index and ambient laboratory temperature were found to introduce average dose defects of These virtual quality-assurance tests were repeated on two dosimeter configurations that were proposed as potential improvements to the prototype: a configuration with equalised reference and object path lengths, and a miniaturised configuration. It was found that these improvements alleviated the dosimeter’s dependence on the simulated environmental influence quantities. Equalising the dosimeter’s path lengths reduced the dose defects generated by simulated atmospheric drift and heat expansion by 96.9% and 97.5%, respectively, signifying a large improvement in dosimeter performance. Similarly, miniaturising the dosimeter improved the MTF-estimated spatial resolution by 27.3% and 29.4% for the system undergoing simulated mechanical vibration and atmospheric turbulence, respectively. Similarly, spatial resolution as estimated by fencepost analysis was improved by 54.5% for the system with simulated atmospheric turbulence, and 41.7% for the system undergoing simulated vibrations.The sensitivity of interferometric systems to small changes in an experimental setup, and the reconstruction steps needed to physically interpret their raw output, make the experimental optimisation of interferometric optical detectors difficult. This simulation-based approach to detector refinement has proven advantageous for analysing detector performance and probing its sensitivity to different environmental influence quantities. Simulating fluctuations in each influence quantity separately allowed the nature and degree of their impact to be assessed in isolation. This provided valuable insight into which improvements would be the most beneficial for refining the prototype and, using QA-inspired virtual phantoms as a surrogate for the endpoint of absorbed dose to water, made it possible to test targeted alterations with the aim of reducing the DHI dosimeter’s dependence on different environmental influence quantities.The next step in this research is to carry out rigorous experimental verification of the virtual-detector model. Physical phantoms will be developed and incorporated into the interferometer prototype, and identical tests will be carried out experimentally and virtually in order to establish equivalence between modelled and physical results. As the original experiments conducted by Cavan were carried out using an Ir-192 brachytherapy source, it is a priority for future work to reproduce these experiments both physically and via our model dosimeter in order to establish correspondence between the physical and virtual systems’ response to clinical-dose distributions. Additional testing will be carried out using high-energy X-rays generated via synchrotron in order to probe the system’s sensitivity to different radiation-delivery modalities. Once this is achieved, our quality-assurance methodology can be used in conjunction with the model to incrementally refine the detector prototype, with the goal of reducing its uncertainties to clinically acceptable levels.


The implementation of an innovative and sustainable professional pharmacy service in routine care requires substantial resources borne by the pharmacy owner. Although a community pharmacy is a business setting, few studies have examined cost as a potential barrier to widespread implementation. Implementation costs, as the cost impact of an implementation effort, can be significant and hamper the decision to invest from the provider perspective. Traditional financial planning tools can be used to analyse and support business decision to implement a service by assessing the net impact of a new service on the provider’s budget. This study aimed to estimate the implementation costs and the break-even point of an interprofessional medication adherence program for chronic patients in Switzerland. The program combines motivational interviews, medication adherence electronic monitoring and feedback reports to patient and physicians.We used a 3-step approach: (i) micro-costing analysis: identification of implementation activities, quantification and valuation of required resources. Implementation costs, including service support costs and direct delivery costs, were analysed according to the implementation phase ; (ii) break-even analysis: estimation of the required number of patients to follow up with to ensure that the generated revenue exceeded the total cost; and (iii) univariate sensitivity analyses.The estimated total cost of the installation phase was 8481 CHF, more than half of which represented the cost of the equipment. Direct delivery costs were 666 CHF per patient per year, with 68% of this value associated with the cost of workforce time. According to the Swiss national reimbursement system, a minimal of 16 [10–27] patients was required to cover the implementation costs of the installation phase. This break-even point decreased to 13 patients in the initial and full operation phases.These estimates lead to a better understanding of the real cost of implementing a professional pharmacy service in routine care. In a Swiss context, the current medication adherence support fee-for-service system allows pharmacists to reach the break-even point. Such information is important for community pharmacists to guide their implementation strategies. The replication of similar analyses in other settings and countries is paramount. In 2011, the World Health Organization (WHO) and the International Pharmaceutical Federation (FIP) officially adopted changes in the practices of community pharmacists from the delivery of medicines to a collaborative, person-centred care process –7 and con = 32) [n = 104) [n = 762) [Medication nonadherence is endemic and decreases the cost-effectiveness of chronic treatments –13. In 2n = 32) . Moreoven = 104) . Finallyn = 762) . Other fn = 762) –23.Despite these encouraging developments, the implementation of professional pharmacy services in routine care faces certain challenges –26. AmonThe literature often focuses on the direct service delivery costs, and rarely includes service support costs, or it values at best the initial staff training. However, the implementation of a sustainable, innovative service requires substantial resources to organise, engage and integrate the pharmacy in a novel philosophy of practices and business strategy. To be financially feasible and viable, the total revenue generated by the implementation of the service must at least cover the total cost of its implementation. Hence, traditional financial planning tools can help to analyse and support the business decision to implement a service by assessing the net impact of a new service on the provider’s budget . The breThis pragmatic study aimed to estimate implementation costs and the break-even point (in terms of the number of patients to follow up with) based on a real-world activity of the interprofessional medication adherence program for chronic patients.http://www.xe.com, 11/13/2018). The initial staff training and investment, as well as the equipment, were amortisable over a 5-year amortisation period.This analysis assessed the costs of a community pharmacy to implement the program. Because it focused on the implementation costs from the provider’s perspective, patient and societal costs were not considered. We performed a micro-costing analysis that included three steps , 38: (i)The identification of the relevant activities and the quantification of required resources were based on the experience of the Community Pharmacy of the PMU, University of Lausanne (Switzerland) . The cosDuring the installation phase, the initial pharmacist training focused on (1) knowledge of medication adherence and (2) motivational interviewing skills. First, the pharmacist attended a 10-h adherence course organised into 5 modules: (i) introduction to medication adherence, (ii) theoretical frameworks of medication adherence, (iii) medication adherence interventions, (iv) structure of medication adherence interviews, and (v) case studies. Second, the pharmacist was trained in motivational interviewing during four 4-h sessions . Then, dIn the analysis, we considered a day of internal training per each new pharmacy technician during the installation phase. The objectives were to train technicians on the handling of EMs, the secure uploading of EMs data and counting tablets. Moreover, during the initial and full operation phases, the technicians participated in the same education internal meetings along with the pharmacists. Initial training costs were amortised over 5 years.In the installation phase, the pharmacist-technician duo needed two days to prepare and organise the delivery of the service. This time included the development of the planning process, the writing of procedures and the preparation of support material. To ensure the quality of the service and the fidelity in its delivery, the service is ISO certified at the Community Pharmacy Center of the PMU and all procedures are written and made available to the team at any time. The cost of support material was estimated by expert opinion, including patient leaflets and information and education material. In the initial and full operation phases, these efforts decreased but were still considered.http://www.sispha.com). The cost of this annual licence was considered during all three phases of the implementation process.According to Swiss law, a community pharmacy who offers a professional pharmacy service must have a privacy room or area that allows confidentiality for a face-to-face interview with the patient. Based on this fact, we assumed that pharmacists already had this space (including a computer) available for the medication adherence program, hence their acquisition costs were not considered in the analysis. As part of the equipment, we included the cost of the licence for a secure web platform to collect electronic patient data . This licence also comprises the implementation and technical support, including coaching meetings to guide the pharmacist during the interview and to edit the report for the physician and the nursing team  [The average duration of the follow-up per patient was estimated at one year in accordance with PMU data  . The freThe variable costs associated with the delivery of the service included the pharmacist time  and the technician time (EMs handling). Since 2011, the Community Pharmacy Center of the PMU routinely collects all time, except for coordination. Thus, we used these established median durations . HoweverHealth insurance in Switzerland effectively reimburses the medication adherence program for all polypharmacy patients, defined as people who are simultaneously prescribed at least three chronic treatments and who are referred by their physician to their pharmacist because of a history or a risk of poor adherence. Therefore, in this analysis, we decided to include the costs of three EMs per patient. The EM unit cost was annualised to consider a battery life of two years, including the cost of the hardware required to read EMs data.http://www.vd.ch). This scale defines a salary level per profession (classes ranging from 1 to 18) according to professional experience (grades ranging from 0 to 26). The annual gross salary for a mid-career professional corresponded to class 11/grade 13 for a community pharmacist and class 4/grade 13 for a pharmacy technician. According to the finance department at the PMU, a multiplier coefficient (22%) was applied to consider social security contributions and reflect the full cost to the employer. Finally, the number of annual working hours used corresponded to the usual number of effective working hours in Switzerland .The hourly labour costs for health professionals were estimated by expert opinion based on the Swiss salary scale in the canton of Vaud (http://www.pharmasuisse.org/de/). The total annual cost was divided by the mean opening hours in the canton (57 h per week in the “RoKA” report).We considered the opportunity cost  of the interview private room/confidentiality area used for the delivery of the service. To estimate the hourly cost of this space, the size of the room was fixed by expert opinion to ten square metres. The cost per square metre included the annual rent, maintenance and utility fees, derived from the annual cost survey on Swiss pharmacies in 2014 . We estimated the break-even point using Microsoft Office Excel 2007 software.The BEA formula can determine the volume of services  needed to ensure that the generated revenues exceed the costs  see Fig. The “prUnivariate sensitivity analyses were performed to assess the impact of the uncertainty generated by estimated parameters . This uncertainty takes into account the risk management of the activity (e.g. longer interview time with complex patients). Only the parameters estimated to have the greatest impact on the model output were assessed:25, IQR75) [(i) the professional delivery time using interquartile ranges  ;(ii) the pharmacist and technician labour costs using +/− 20% of the base case values to account for the impact of professional experience level;(iii) the number of EMs per patient using one and four EMs for the minimum and the maximum scenarios; and (iv) the doubling of trained professionals to ensure a full-time capacity to deliver the program.In the installation phase of the implementation process, the total cost was estimated at 8481 CHF, more than half of which represented the cost of the equipment . We assume that this time will decrease and stabilise in the medium term with routine program delivery , providiWith our assumptions and the current national reimbursement system model, a minimum of 16 patients must be follow up with to ensure a profit for the pharmacy, with a range from 10 to 27 according to scenarios assessed in sensitivity analyses. In real life, some patients may stop the follow-up before one year, and the frequency of interviews will depend on the patient’s needs. Is this number realistic in terms of inclusion and follow-up rates? The patient inclusion process into the medication adherence program depends on several factors, which are specifically linked to the setting: the needs of the targeted population of patients, the state of the interprofessional collaboration, and the pharmacists’ ability to include patients. First, about 50% of chronic patients do not take their medications as prescribed . Each prIn our model, only one full-time equivalent (FTE) pharmacist and one FTE technician followed up with the entire cohort of patients. However, the management of 16 patients only represents a 7% FTE for pharmacists and a 4% FTE for technicians (9 and 5% respectively for 27 patients). In the context of a pharmacy, this implies a solid management and planning of staff resources for each basic and advanced activity. Strategically, we recommend training at least two pharmacists and technicians to ensure a turnover in case of absence. Assuming an amortisation over 5 years, the doubling of trained professionals had a minimal impact on the break-even point . With a fourth chronic medication or more, the pharmacist can charge an additional polymedication check fee (48.60 CHF every 6 months). Although the number of tablets can affect adherence , these rThe estimates or our analysis is not generalizable per se as it is context-dependent. However, the BEA equation see Fig.  can be aSome methodological considerations should be noted when interpreting these findings. BEA is a simplistic representation of reality. Although the estimated parameters are based on the experience of the PMU and expert opinions, BEA assumed a similar variable cost for all patients. However, the pharmacy faces a variety of patients, leading to a range of variable costs in the type and extent of nonadherence issues, frequency of visits, number of EMs, duration of interview and duration of follow-up. For instance, at the PMU, patient retention in the program is longer in patients with more serious nonadherence issues than in patients with less serious issues. This repartition is nevertheless unknown in the community and different in each pharmacy setting. Prospective studies should assess this variability in real life. The major unpredicted event that occurs in the IMAP program is when patients do not show up and the visit is rescheduled. We have not taken this uncertainty into account in our model as extra-cost because the pharmacist is directed to another clinical activity when this situation happens.This pragmatic analysis can be used as a template to estimate the implementation costs and assess the economic feasibility and viability of a professional pharmacy service from the provider’s perspective. In a Swiss context, the implementation in community pharmacies of the described interprofessional medication adherence program for chronic patients treated with at least three medications seems to be profitable; the current medication adherence support fee-for-service system allows pharmacists to reach a break-even point with at least 13 patients. These findings are important to community pharmacists in deciding whether to implement the service and can guide their business plans and implementation strategies. The replication of similar analyses in other settings and countries is paramount for a better understanding of the feasibility and implementation costs of medication adherence programs, as well as other advanced services, in routine pharmacy care. Implementation research can also aims to optimize the service design and process to reduce its cost.


Concrete creep has become one of the major problems that threatens concrete structural development and construction. However, a reasonable and accurate calculation model for numerical analysis is the key to control and solve the creep deformation of concrete. To better describe the concrete nonlinear creep damage evolution rule, the visco-elasticity Plasticity Rheological Theory, Riemann Liouville Theory and Combined Model Theory are quoted, and the Able dashpot is used to reconstruct fractional-order soft-body composite elements to propose the expression of the stress-strain relationship of the elastomer, visco-elasticity plasticity body, and Viscoplasticity body, considering the evolution of the concrete compression damage process. A nonlinear creep damage constitutive model of concrete, based on fractional calculus theory, is conducted, and the parameters of the specific calculation method of the model are given. The influence of stress level σ, fractional order n and material parameter α on the concrete creep process is determined by a sensitivity analysis of the model parameters. The creep process and deformation amount of concrete in practical engineering can be effectively controlled by the results of the proposed sensitivity analysis. The research results can be used to provide guidance and reference for the safe construction of concrete engineering in actual practice. Concrete creep refers to the phenomenon in which concrete deformation increases with time under long-term external load . Creep dCreep strain has a linear relationship with applied stress in the case of low stress levels (less than 30% compressive strength). However, creep presents an unstable phenomenon as time and stress increase in the case of high stress levels (between 30% and 80% compressive strength); that is, it presents a nonlinear relationship, which is found in concrete creep theories and experimental research ,5,6,7. AThe nonlinear creep process of reinforced concrete columns was simulated considering the high stress conditions by Bažant and Tsubaki . A simplSome strain in creep is related to the corresponding instantaneous stress state, and also to the previous stress state, which is illustrated by a large number of concrete creep phenomena. The fractional derivative, based on time parameters, is an arbitrary order time differential operator, which can fully reflect the course of the function change over time ,23. FracTo better describe the concrete nonlinear creep damage evolution rule, Fractional Calculus Theory and Rheological Model Theory have been quoted to propose a non-linear creep damage constitutive model of concrete using Able dashpot to replace Newton dashpot and the concrete damage evolution rule. The rationality and applicability of the conducted constitutive work was verified. Finally, the calculation method and sensitivity analysis of the conducted model parameters provide a reference for safe construction and the long-term stable operation of concrete engineering.t > 0, Re(n) > 0.There are many fractional order calculus definitions, among which the creep characteristics of concrete are defined and described by Riemann Liouville theory ,30. Thisn (n > 0) is the fractional order, n, and d is a differential operator. The ideal solid stress-strain relationship follows Hooke’s law.The Riemann Liouville fractional order differential form is defined as.The ideal fluid stress-strain relationship follows Newton’s viscous law.Ideal solids and ideal fluids are idealized models, which can only be used for approximate calculations in practical engineering. Concrete is a material between an ideal solid and an ideal fluid, and a software element  can be uThe constitutive equation based on the fractional derivative  is estabIn current research, the basic rheological mechanics models include elastomers, the viscoelastic body, the visco-elasticity plasticity body, the viscous body and the viscoplastic body. The rheological properties of materials can be described by the combination of strings and parallelism among them. The combined model has been widely used in the creep simulation research of asphalt, rock, polymer materials, concrete, and other materials because of its visualization and intuition capabilities ,34,35.The typical concrete compression and creep process consists of three stages: deceleration creep, steady creep, and accelerated creep. In the current study, the elastic-visco-elasticity plasticity-viscoplastic creep model  is used to describe the instantaneous and isovelocity creep of concrete. However, when concrete reaches the yield limit, the creep curve will exhibit accelerated unsteady characteristics. At this time, the MSSB model cannot describe the nonlinear creep characteristics of concrete, and it can only be studied by nonlinear theory. In this paper, the creep constitutive Equation based on the fractional derivative is constructed by using the Able dashpot, instead of the Newton dashpot in the MSSB model to accurately describe the three stages of deceleration creep, steady creep and accelerated creep. The constitutive model combination is shown in The small damage produced is neglected during the deceleration creep and steady creep stages, and only the damage caused by the accelerated creep stage is considered in the concrete indoor creep test.The concrete damage evolution in the accelerated creep process is consistent with the change in the exponential function.To derive the constitutive equation, the main hypothesis conditions are given.Stress-strain relationship of elastomer.Stress-strain relationship of visco-elasticity plasticity body.The visco-elasticity plasticity body is represented in parallel with the elastomer element, the Able dashpot and the friction element. The stress on the friction element is expressed by Based on the above constitutive models and assumptions, the stress-strain relationship between elastomers, the visco-elasticity plasticity body, and the viscoplastic body are derived as follows.The total stress on the visco-elasticity plasticity body can be obtained from the combined model theory.When Equation (11) can also be expressed as follows.Laplace transformation of Equation (12).Laplace inverse transformation of Equation (13).(3) Stress-strain relationship of viscoplastic body. The viscoplastic body is expressed in parallel with the friction element by the Able dashpot. The stress When According to the theory of fractional calculus ,36, the During the creep test process, especially in the accelerated creep stage, the creep rate of the concrete specimens increases continuously until failure, which is caused by the expansion of internal damage and crack development in the concrete. Therefore, the viscosity coefficient is no longer a fixed value, but rather is a variable that decreases with the increase in the degree of damage. The damage variable is a negative exponential function  that conCombining the above three parts, the strain and nonlinear creep damage constitutive model of concrete, based on fractional calculus theory, is obtained asThe parameter t is the creep time t, where When the creep curve has an unloading curve, the three parameters nloading . The exp, and A nonlinear regression analysis method  can be uThe parameters 3. The experimental curves are shown in Uniaxial compressive nonlinear non-linear creep and residual strain tests of normal concrete with deep storage nuclear waste were carried out by Narintsoa Ranaivomanana, et al. . The speAs shown in et al.’s  experimeNarintsoa Ranaivomanana et al.’s  experimeCompressive nonlinear creep and residual strain tests on C40 concrete specimens under different stresses were carried out by Can Tang et al. . The conUnder stress of 16.9 MPa and 25.7 MPa, the instantaneous creep occurred first and then the isometric creep, and the creep was velocity first increased and then decreased, as shown in Can Tang et al.’s  test curσ, n, and α are the main factors affecting the concrete creep in the concrete creep damage constitutive model; these parameters are obtained by analyzing the experimental data curve and the theoretical curve. Therefore, the sensitivity analysis of the model parameters will be carried out by the control variable method in this section to study the influence of the above model parameters on concrete creep. The model parameters are as follows: Parameters Parameters The concrete creep deformation is greatly affected by the stress level, and the creep deformation will be increased as the stress level increases. However, stress has no obvious effect on the creep velocity. The higher the stress level, the greater the instantaneous deformation in the elastic stage, and the shorter the time required to enter steady state creep at a constant velocity. In addition, the form of the concrete creep curves is gradually changed to the exponential type as the stress level increased. When the stress level exceeds a certain level, a sudden change will occur. At this point, micro-cracks will occur, eventually causing macro-crack penetration failure. This is consistent with Narintsoa Ranaivomanana et al.’s test  of how hIn order to analyze the sensitivity of the fractional order, the control variable method is used to ensure that other parameters remain unchanged. The fractional order is gradually increased from 0.1 to 0.6, and a series of creep curves with different orders are obtained, as shown in From α, as shown in α increases, the sooner the accelerated creep phase begins, and the greater the creep velocity will be. The power index is the main factor that influences creep velocity. The larger the power exponential value, the more prone the concrete will be to accelerated creep.Considering the change in the damage variable in a viscoplastic body, the control variable method is used to obtain the creep curves under different α, by changing the value of The classical rheological model and the Fractional order theory are introduced to inform the concrete nonlinear creep damage constitutive model after the results of the above research. The conducted constitutive model is a viscoelastic-plastic model. It is assumed that the damage in the deceleration creep stage and in the stable creep stage is neglected, and only the damage in the accelerated creep stage is considered. Also, the accelerated creep rate conforms with changes in the exponential function charge in the indoor concrete creep tests. In practice, the above two assumptions may not be agreed with each other. Therefore, the concrete fractional nonlinear creep damage constitutive model derived from this assumption differs from the actual situation. However, the concrete specimen damage data contributes little to the constitutive equation in either the initial stage or the stable creep stage in the actual uniaxial compression creep tests. The constructed concrete creep damage model is more able to meet the needs of actual working conditions and tests that consider accelerated creep stage damage as the main research object. In addition, the constructed concrete creep damage model parameters have specific physical significance in this paper, and the entire concrete creep process in practical engineering can be reflected and described by the proposed model, which has certain engineering practical and reference values.To better describe the concrete non-linear creep damage evolution rule, and better solve the concrete creep in concrete engineering, Fractional Calculus Theory is introduced to inform a concrete nonlinear creep damage constitutive model. The conducted constitutive model is verified and analyzed for sensitivity by means of the concrete creep test. The following conclusions may be drawn:The Visco-elasticity Plasticity Rheological Theory, the Riemann Liouville Theory and the Combined Model Theory are quoted to propose the stress-strain relationship expressions of the elastomer body, the visco-elasticity plasticity body, and the viscoplastic body. The nonlinear creep damage evolution equation of the concrete fractional order is conducted with consideration of damage evolution, and the parameter specific calculation method in the constructed model is given.The constructed concrete creep damage constitutive model in this paper is validated in high stress and different stress situations that involve uniaxial compression creep; data from the residual strain tests of Narintsoa Ranaivomanana et al.  and Can σ, material parameter α, and fractional order n, are analyzed. The results show that σ and n are positively correlated with the concrete creep deformation and rate. The creep deformation and rate will increase as σ and n increase. α is related to the time at which the concrete enters the accelerated creep stage, and the larger the value of material parameter α, the earlier the concrete will enter the accelerated creep stage.To determine the influence degree of the model parameters, the sensitivity analysis of the main influence parameters in the concrete creep damage constitutive model, including


We suggest a concept design of a SAW-based microaccelerometer with an original triangular-shaped console-type sensing element. Our design is particularly optimized to increase the robustness against positioning errors of the SAW resonators on the opposite sides of the console. We also describe the results of computer simulations and laboratory tests that are in a perfect agreement with each other and present the sensitivity characteristics of a manufactured experimental design device. In recent years, micromechanical sensors found a variety of applications ranging from aerospace, vehicle and automotive industry to consumer goods such as personal navigation tools, smartphones, video cameras and many other devices with embedded micro-electromechanical systems (MEMS) . CurrentOne of the key applications of micromechanical sensors are inertial integrated navigation systems that currently find an increasing number of applications in various mobile vehicles. Recent progress in the microelectronic technology provides the opportunity to design and to manufacture such devices as solid-state accelerometers (SSAs) that are currently of urgent demand for multiple civilian and military applications, such as biomedical wearable and implantable devices , industrHowever, the majority of commercially available silicon microaccelerometers (SMAs) are not solid-state in the true sense. Generally, they utilize discrete elastic suspensions that provide the necessary degrees of freedom for inertial masses that, in turn, require that the microoscillating system is installed with a high precision of 0.1–1 μm. These conditions reduce both the vibrostability and the shock resistance of SMAs while requiring high-tech manufacturing technology .simplicity of the sensing element kinematic scheme;high-level design integrity ;lack of extra discrete elastic suspensions;minimal use of conventional planar microelectronic technologies, thus minimizing the SSA production cost.In contrast, a specific class of devices and systems that employ the surface acoustic wave (SAW) properties in piezoelectric crystals is largely free of these limitations and thus its utilization in perspective microaccelerometer design is largely promising ,15,16,17The conceptual SAW microaccelerometer design incorporates two main parts, namely a micromechanical sensitive element (SE) and an electronic signal-converting circuit. The experience in the development of SAW transducers ,19 indicg is applied, the console exhibits elastic deformation that is proportional to the applied acceleration.The IDT 2 induces two reciprocally directed running acoustic waves that are next reflected from reflectors 1 thus forming a standing wave. On each side of the sensitive console, using the method of photolithography (which is widely used for the production of SAW devices), the structure of the SAW resonators is produced see . The conOn the opposite sides of the console, SAW resonators are located, formed by the IDT 3 and reflectors 4. When subjected to acceleration, the beam undergoes bending deformations and, as a result, stretches and contracts the opposite surfaces of the console. The resulting surface stresses change the elastic modulus and the density of the material in the surface layer, as well as its geometric dimensions. During stretching deformations, the SAW propagation time along the surface of the console increases both as a result of its geometric elongation and due to the decrease in its phase velocity, the variations of which are determined by the change in the elastic modulus. On the opposite side of the plate, compression deformations occur, leading to the opposite change in the SAW propagation time.The characteristic frequencies of the resonators are determined by the distance between the reflectors, their dispersion properties, and the SAW propagation velocity. The characteristic frequency of the unperturbed resonator  and IDT  thus yieThen, the characteristic frequencies of the resonators The overall operational scheme of the SAW accelerometer is shown in y-axis. One end of the console was clamped firmly. The simulation results of the influence of the applied linear acceleration on the characteristics of SE of SSA on SAW with triangular shape of console are shown in Next we designed a 3D model of the described SE using OOFELIE: Multiphysics. Isotropic quartz was chosen as the console material, while W/Ni/Mo alloy was chosen as the inertial mass material. External acceleration application was defined as uniformly distributed gravity acceleration that was directed along the b(x) is chosen such that the SAW propagation velocity is constant along the console. Triangular-shaped console design is a solution that provides the equal bending resistance. The equation that relates the variable width of the console with the longitudinal coordinate and relevant expressions for internal stresses σ(x) as well as relative deformations ε(x) is given by [In order to maintain equal distributions of normal stresses on any cross-section of the console, a variable console width given by .(6)b(x)m2 >> m1 leads to the ansatz m1 = 0. According to Equation (6), in order to provide the uniform distribution of the relative deformations along the console, its side faces should converge in the center of a loading mass.Assuming The simulation results of a linear acceleration influence on the characteristics of the SAW SSA with a triangular-shaped SE console are given in Next, a series of experimental tests have been performed with a prefabricated console element to confirm its characteristics predicted previously by computer simulations only .After subtracting the obtained function from the experimental data, the noise component has the form shown in The characteristics of the noise obtained are presented in Next, the calibration of the experimental design with the triangular shape of the sensitive element was performed in the gravitational field of the Earth and its main characteristics were investigated. The graduation was carried out on an original two-axis rate-table design  described in detail  as depicCalibration was performed along the two horizontal axes, so the rotation was performed around axes x and z with 10° angular resolution, see Finally, the output characteristic for the same axes was obtained. The acceleration was first increased from –g to g and next was reduced back to –g, thus testing the reproducibility of the sensitive element’s reaction to external acceleration.x-axis, that is, measuring the acceleration along the z-axis, back-and-forth acceleration change induces a hysteresis-shaped effect in the sensitivity characteristics. Thus the reproducibility of the results for x- and z-axes is significantly different (As shown in ifferent . BesidesThese results were next compared against the results of laboratory tests of an accelerometer prototype . The accExperimental data that are shown in Direct comparison of the simulation results and laboratory tests provides a perfect match. The sensitivity of the accelerometer is about 14.62 kHz/g, as obtained by both lab tests and computer simulations, while the relative standard deviation between the experimental data and the computer simulation results did not exceed 3% for the entire acceleration range shown. A nearly perfect match of the results indicates that even rather simplified models that do not take into account material anisotropy and piezoelectric effects may provide a very good characterization of the modeled finite element.SAW-based accelerometers possess a number of significant advantages, such as high resistance to vibration and shock, low cost and simplicity of production. The suggested SAW SSA demonstrates improved characteristics due to the optimization of the SSA console shape design that is more robust against technological SAW-resonator disposition errors compared to the rectangular shape design. Obtained results were compared with the experimental data and demonstrated a perfect match that indicates high accuracy of the applied simulation technique. Both experimental and simulated data show that the sensitivity of an accelerometer is close to 15 kHz/g, which is approximately one-half of the sensitivity of a similar design based on a rectangular console ,17. TakiThe keynote advantage of the SAW-based accelerometers is the absence of any moving parts in their design, which could potentially make them extremely shock, vibration and temperature resistant. Recent literature data based solely on the results of computer simulations predict potential values up to several-dozen g ,24, whil