For a spacecraft, its power system is vital to its normal operation and capacity to complete flight missions. The storage battery is an essential component of a power system. As a spacecraft spends more time in orbit and its storage battery undergoes charge/discharge cycles, the performance of its storage battery will gradually decline, resulting in abnormal multivariate correlations between the various parameters of the storage battery system. When these anomalies reach a certain level, battery failure will occur. Therefore, the detection of spacecraft storage battery anomalies in a timely and accurate fashion is of great importance to the in-orbit operation, maintenance and management of a spacecraft. Thus, in this study, based on storage battery-related telemetry parameter data  downloaded from an in-orbit satellite, a voltage anomaly detection algorithm for spacecraft storage batteries based on a deep belief network (DBN) is proposed. By establishing a neural network (NN) model depicting the correlations between each of the variables of temperature, current, pressure and charge/discharge times and voltage, this algorithm supports the detection of anomalies in the state-of-health of a storage battery in a timely fashion. The proposed algorithm is subsequently applied to the storage battery of the aforementioned in-orbit satellite. The results show the following. The anomalies detected using the proposed algorithm are more reliable, effective and visual than those obtained using the conventional multivariate anomaly detection algorithms. Compared to the classic backpropagation NN-based algorithm, the DBN-based algorithm is notably advantageous in terms of the model training time and convergence. Spacecraft telemetry data are real-time data acquired by sensors and transmitted to telemetry terminals via telemetry links; they are also the only data based on which ground management personnel determine and evaluate the working conditions and state-of-health (SoH) of a spacecraft. As the structure and function of spacecraft systems become increasingly complex, telemetry data-based system checks and state evaluations are becoming increasingly important. Storage batteries are important spacecraft components. As a spacecraft spends more time in orbit, its storage battery will experience a series of faults, such as performance degradation and output power decreases. In severe cases, these faults will render the power system unable to provide a normal power supply to relevant loads, thereby affecting the operation of the spacecraft. A statistical analysis of the collected data regarding 324 faults experienced by 227 satellites owned by countries outside China in the period from 1994–2014 found that 84 were direct power system faults, which account for 26% of the faults [Common storage battery faults include performance degradation, short- and open-circuit failures of single battery cells and failures caused by charge/discharge circuit faults . Amid thIn view of the important research and application value of anomaly detection in such fields as health management of important equipment , researchers have proposed various anomaly detection algorithms. Based on the working principle, overall, these algorithms can be categorized into six types ,3,4, namAs mentioned previously, spacecraft storage battery degradation is a typical of multivariate anomaly type. Considering that spacecraft systems are complex and often consist of multiple subsystems, their telemetry data are characterized by high volumes, high dimensionality, complex parameter relationships and the presence of noise disturbance. As a result, multivariate anomalies are more difficult to detect than conventional anomalies. Therefore, to detect anomalies in multivariate spacecraft telemetry data, it is often necessary to reduce their dimensionality and extract their features. On this basis, a statistical analysis- or classification-based algorithm is also required. Based on the working principle, currently, relevant algorithms for detecting multivariate anomalies in telemetry data are primarily categorized into four types, namely, subspace calculation-based, basic model error reconstruction-based, generative model estimation-based and structural graph-based algorithms .f and g), each reconstructed output iy. The specific forms of f and g vary between algorithms [f and g. These anomalies are reflected by two statistics, namely, the squared prediction error (SPE) statistic and the Hotelling SPE statistic is mainly used to calculate the total reconstruction error for each sample. The Hotelling Of the aforementioned four types of algorithms, the subspace calculation- and basic model error reconstruction-based algorithms are the ones most commonly used. A subspace calculation-based algorithm treats a multivariate time series as multiple independent samples distributed in a high-dimensional space. Based on a certain mapping rule, data samples can be embedded into low-dimensional spaces ,16. Thusgorithms . When ani et al.  applied i et al.  and Miaoi et al.  used theThe generative model estimation-based algorithms identify data points with low probabilities as abnormal points by establishing a generative model for the data. These algorithms have a solid basis in mathematical theory and are able to effectively reflect spatial and temporal relations in a time series if the estimates are accurate. Commonly used models include the vector autoregressive and state space models. Li et al.  used theStructure graph-based algorithms detect anomalies by establishing a graph structure for the properties in a time series and are able to simultaneously take into consideration the spatial and time-domain correlations between data. Idé et al.  defined The aforementioned classical multivariate anomaly-detection algorithms are unsuitable for spacecraft storage battery degradation. For dimensionality reduction and reconstruction algorithms, because Apart from the detection of spacecraft storage battery anomalies, relevant research has also studied the detection of anomalies in storage batteries in such objects as electric vehicles. This type of research shares the following common features. The detected anomalies are verified by static battery experiments under strict conditions. Additionally, the parameters are measured using high-precision sensors. These parameters include voltage, current, state-of-charge (SoC), temperature, capacity, internal resistance, number of cycles and time. Zhao et al.  measuredIn this study, based on the practical needs of spacecraft storage battery anomaly detection in combination with the characteristics of spacecraft telemetry data , the deep-learning approach is introduced into storage battery anomaly detection. A DBN is used to establish a neural network (NN) model depicting the correlations of multiple parameters  with voltage. When the storage battery voltage starts declining, there will be multivariate correlations in the model. By detecting these multivariate anomalies, degradation or faults can be detected in a timely fashion before a storage battery fails.Compared to the above studies, the main contributions of this study can be summarized in the following three aspects:(1) Based on the characteristics of telemetry data for spacecraft storage batteries , and in view of the practical needs for online storage battery anomaly detection and the evolutionary pattern of spacecraft storage battery systems, a system state anomaly detection algorithm based on the internal correlations between multiple storage battery parameters is proposed.(2) The deep-learning approach is introduced into storage battery anomaly detection. A DBN is used to establish an NN model depicting the correlations of multiple parameters  with voltage. When there is a significant decline in the SoH of a storage battery, there will be anomalies in the multivariate correlations in the model. By detecting these multivariate anomalies, degradation or faults can be detected in a timely fashion before the storage battery fails. Compared with the classic backpropagation NN-based algorithm, the DBN-based algorithm is notably advantageous in terms of its model training time and convergence.(3) The algorithm has been utilized to detect the anomalies in the state-of-health of an in-orbit satellite’s storage battery, and the results show that this algorithm outperforms the conventional multivariate anomaly detection algorithms in terms of reliability, effectiveness and visibility.First, the storage battery of the satellite, i.e., satellite X, examined in this study is introduced. Owing to the uniqueness of its orbit, the satellite X remains in the sunlit region for a relatively long period of time each year. In normal circumstances, when the satellite X operates in the sunlit region, the solar panels directly supply power to its loads, and its storage battery does not work and is only being charged by a weak current. Under this condition, the discharge current of the storage battery is basically zero, and the voltage of the storage battery remains basically unchanged. The solar panels and the storage battery supply power simultaneously only when there are enormous satellite loads. Under this condition, the voltage of the storage battery will decrease, and a charge current is generated. In less than one-third of the time each year, the satellite will frequently enter and exit the Earth’s shadow region. After entering the Earth’s shadow region, the whole satellite is powered by its storage battery. During this time, the voltage of the storage battery will continuously decrease, and the charge current remains zero during the discharge process. After the satellite re-enters the sunlit region, the solar array of the satellite starts charging the storage battery again, and the voltage of the storage battery also gradually increases. This process repeats continuously.The telemetry data for spacecraft storage batteries to which ground personnel have access to include the voltages, currents, discharge/charge times, and temperatures. However, ground personnel are unable to obtain battery capacity and resistance, which are parameters commonly used in the ground performance evaluation and degradation testing of storage batteries.The parameter extraction process is described as follows. First, the voltage of a storage battery is strongly correlated with such parameters as the charge/discharge currents, times and temperatures based on its working principle. Therefore, from the telemetry parameters, the aforementioned parameters are selected and recorded. Due to its orbital conditions, the spacecraft examined in this study will operate continuously in the sunlit region for a long period of time. During this process, the discharge current of its storage battery will basically remain zero, and its charge current is very small. Additionally, the voltage of the storage battery will remain basically unchanged. Therefore, the parameters of the storage battery when the satellite is in the sunlit region are meaningless and thus not selected. After the satellite enters the Earth’s shadow region, its storage battery will undergo charge/discharge cycles. Thus, the storage battery parameters in this process are extracted. As demonstrated in According to the research status at home and abroad, the most widely used model in the multi-parameter correlation training method is the back-propagation neural network (BPNN) method , which iThe BP neural network algorithm is relatively mature in terms of network theory and performance. Its outstanding advantage is that it has a strong non-linear mapping capability and a flexible network structure. The number of middle layers of the network and the number of neurons in each layer can be arbitrarily set according to specific conditions, and the performance differs depending on the structure. However, BP neural network also has some major defects, as follows: slow learning, even simple problems, generally require a great deal of iterative learning to converge; easy to fall into local minimum values and limited network promotion capabilities.In order to overcome the above defects, this paper uses the deep belief network (DBN) as a network model for anomaly detection. Compared with the general generalized neural networks, deep learning methods can learn the characteristic information inherent in data. The related literature has proven that deep learning methods have better predictive effects ,38. The The deep belief network  is a deeThe Restricted Boltzmann Machine  was origThe limitation of RBM makes it a more efficient training algorithm than the general Boltzmann machine, and the restricted Boltzmann machine is often used for different types of data generation models. Of course, its most important role is to serve as a learning module that forms a deep belief network. The RBM is a model based on the energy function. The joint configuration energy of the visible layer and the hidden layer is expressed as follows:Due to the special structural properties of the full connection between layers and no connection inside the layers of RBM model, the node states in the same layer are independent of each other, that is, when a visible cell state is given, the active states of the hidden cells are conditionally independent. Accordingly, when a hidden cell state is given, the activation probabilities of the visible cells are also conditionally independent.Therefore, given the activation state of the visible node Correspondingly, after the state of the implicit node is given, the visible node Here Pre-training process: The pre-training process is a process of initializing the connection weights and thresholds between the input layer and the hidden layer and between the hidden layers to obtain a better local optimal solution or even a global optimal solution. This process is implemented by an unsupervised greedy optimization algorithm for multiple restricted Boltzmann machines.The steps of the restricted Boltzmann machine training process are as follows: first, select a set of training sample inputs to the visible node to obtain This process is repeated iteratively until the error between the reconstructed value of the visible node and the true value reaches a certain precision. The relevant parameters are also obtained according to the error calculation gradient, and the update formula is as follows:) method  for traiThe RBM obtains the initial weights and thresholds between the input layer and the hidden layer and between the hidden layers of the deep belief network through such an unsupervised greedy learning method. The initial weights and thresholds between the hidden layer and the output layer of the deep belief network are generated by a random function.Fine-tuning process: After the pre-training process of the network is completed, the basic structure of the deep belief network can be constructed based on the initial parameters obtained. Then, add another layer of the BP neural network to store the target value of the sample data. The next step is to have a supervised learning of the deep belief network, which is to fine-tune the deep belief network. The fine-tuning process is the same as the conventional neural network parameter optimization process.However, in addition to selecting a high-performance deep belief network for the large amount of spacecraft telemetry data, efficient algorithms are also needed for the network parameter optimization. The traditional BP algorithm updates the parameter using the gradient descent method, that is, in the opposite direction of the gradient, the parameters are updated in a certain step size to make the loss function reach a minimum value. However, this method ignores the second derivative, and the final phase is linear convergence, and the convergence speed is slow. Therefore, it is suitable for optimizing the initial stage. By contrast, the Newton method uses the second derivative, and the final phase converges quickly and has good convergence, but it is not suitable for the initial phase. Therefore, the gradient descent method is often used in combination with the Newton method. However, the Newton method needs to calculate the Hessian matrix, which is the second derivative. The core idea of the Levenberg–Marquardt algorithm  is to reThe Levenberg–Marquardt algorithm is an improved Newton method and an algorithm for solving the optimal value of a function using non-linear least squares. The algorithm combines the relevant features of the Newton method and the gradient method. When the parameter u is small, the step size is equal to the step size of the Newton method, and when the parameter u is large, the step size is approximately equal to the step size of the gradient descent method. This method is not sensitive to over-parameterization, can effectively deal with the problem of redundant parameters, and reduces the possibility that the function falls into local minimum values. This algorithm can combine the advantages of Newton’s algorithm and the gradient descent method, and improve their insufficiency. The Levenberg–Marquardt algorithm is more advantageous for the optimization of neural network parameters for huge training samples.Algorithm goal: For function The specific steps of the algorithm are as follows:Step 1: Assume that the error precision is constant Step 2: Calculate the Jacobian matrix Step 3: Construct the corresponding normal equation Step 4: If Step 5: If t is time, and A storage battery voltage anomaly detection model is first established and trained based on a DBN. Then, based on the accumulated telemetry parameters of a storage battery, including charge/discharge currents, temperatures and times, the model can be used to continuously predict the charge/discharge voltages of the storage battery. Additionally, the predicted voltages can be compared with the measured voltages of the storage battery. Based on the difference between the predicted and measured voltages, the extent to which the voltage of the storage battery has declined can be determined, thereby realizing real-time diagnosis and provision of warning. Storage battery degradation is classified into four levels, 0, 1, 2 and 3. Level 1 corresponds to slight anomalies, i.e., when the voltage of the storage battery has just started degrading slightly. Level 2 corresponds to moderate anomalies, i.e., when the voltage of the storage battery has degraded significantly. Level 3 corresponds to severe anomalies, i.e., when the voltage of the storage battery has degraded severely. Naturally, level 0 corresponds to when the voltage of the storage battery is at the normal level. The definition of each level is provided as follows.The experimental data originated mainly from satellite X, as introduced in The experiment was conducted in a macOS environment on a MacBook Pro with a 3.1 GHz dual-core Intel i5 processor and 8 GB of memory. The code was written and compiled in MATLAB 2016b.This study aims to establish a complex mapping model for multiple storage battery parameters  and storage battery voltage for prediction purposes. In order to verify the prediction effect of the DBN neural network model proposed in this paper, this paper chooses to compare with the traditional BP-based neural network model. On this basis, the two parameter optimization methods of gradient descent (GD) and Levenberg–Marquardt (LM) are used to test the prediction performance. The models differed in the selected NN and optimization algorithm but shared the same network structure setting and training targets. Each model contained nine input layers , 15 hidden layers and 1 output layer . The tahn and purelin functions were selected as activation functions for the hidden and output layers, respectively. Additionally, the maximum number of iterations for NN training was set to 5000.MSE) and mean absolute error (MAE), which were calculated using the following equations:MAE was primarily used to calculate the mean loss for the test set. MSE was mainly used to enlarge the impact of outliers on the predicted value.In the selection of training and test data, the first 70% of the storage battery data for 2014 were used as the training set, and the remaining 30% as the test set to compare the algorithms. On the evaluation criteria for prediction performance, the three evaluation criteria of prediction error accuracy, iteration number and running time are mainly used. Among them, the prediction error adopts the mean square error  and gradient descent (GD), was also evaluated. −4) and MAE (0.0105) of the DBN model with the LM optimization algorithm outperformed those of the other models. This suggests that, for the normal dataset, the DBN model with the LM optimization algorithm was able to satisfactorily fit the multivariate correlations between the parameters of the storage battery. Thus, this model was selected as the storage battery voltage prediction model in this study.As demonstrated in The partial prediction results in 2014 data of the DBN model combined with the Levenberg–Marquardt method are shown in Based on the above DBN NN model trained on the 2014 telemetry data for the storage battery, to further examine whether there were signs of anomalies in the SoH of the storage battery in 2015 and 2016, the trained DBN model was applied to the 2014, 2015 and 2016 test datasets. The error between the measured and predicted values was used to characterize the storage battery degradation. The larger the error was, the more severely the storage battery degraded. Additionally, the long-term degradation trend of the voltage of the storage battery with time was also obtained from long-term observations. To visually display the detected anomalies more clearly, the predicted and actual results for 2015 and 2016 are enlarged in To examine its effectiveness, the storage battery degradation detection algorithm proposed in this study is compared with two classical multivariate anomaly detection algorithms, namely, PCA and LLE. The detection principle of these two classical algorithms is described as follows. At the offline training stage, normal historical telemetry data ribution ,43. WhenThe equation for the The equation for the SPE values in the stages when the voltage of the storage battery was normal and degraded, respectively). As demonstrated in SPE values between the normal and degradation stages. The SPE value is only relatively high in the later period of the degradation stage. Anomalies cannot be effectively detected by setting the control limit. In summary, the PCA algorithm is unable to effectively detect voltage degradation when there are large volumes of non-linear storage battery parameter data.SPE values in the stages when the voltage of the storage battery was normal and degraded, respectively. In T2 values in the stages when the voltage of the storage battery was normal and degraded, respectively. Similar to SPE and T2 values between the normal and degradation stages. The SPE and Based on the need to detecting anomalies in the SoH of storage batteries of the in-orbit spacecraft as well as the types and characteristics of the accessible telemetry parameters of spacecraft storage batteries, an approach is proposed in this study to characterize the evolutionary pattern of the SoH of a spacecraft storage battery based on the internal correlations between its multiple parameters. Additionally, a DBN model is proposed to learn and train for this evolutionary pattern. On this basis, whether there is an anomaly in the SoH of a spacecraft storage battery is determined based on the difference between the discharge voltage of the storage battery predicted by the DBN model and the actual observed voltage. The proposed DBN model is validated based on the actual telemetry data for the storage battery of a certain in-orbit satellite for a three-year period. It is found that the proposed DBN model can relatively accurately describe the internal correlations between multiple parameters of the storage battery . Furthermore, the proposed DBM model is able to provide the extent of the anomaly in the SoH of the spacecraft storage battery during the period almost one year before the storage battery fault occurred, as well as during the period when the storage battery fault occurred. The proposed DBN model significantly outperforms the conventional BP-based NN model in terms of training time and convergence. The above results show that the proposed DBN model-based voltage anomaly detection algorithm for spacecraft storage batteries is effective and of application value. This algorithm can provide excellent decision-making support for ground personnel to detect anomalies in the SoH of storage batteries of in-orbit spacecraft. Future work will focus on applying the proposed algorithm in the detection of anomalies in the storage batteries of other in-orbit spacecrafts with a view to further modify and improve it.


The improved split Hopkinson pressure bar (SHPB) was used to study the dynamic mechanical properties and failure characteristics of surrounding rock in deep rock mass engineering that is under high stress and affected by blasting excavation and other dynamic disturbances. In a three-dimensional high static load and frequent dynamic disturbance test, the preload high axial pressure and confining pressure are used to simulate the high crustal stress of deep rock, and the effect of small disturbances on the rock is simulated by the low impact load. The results show that there are two types of dynamic stress-strain curves of deep rock: an elastic-plastic curve and plastic-elastic-plastic curve. The curves consists of five parts: the compaction stage, micro-crack steady development stage, micro-crack unstable propagation stage, fatigue damage stage, and fatigue failure stage. Reductive phenomena of constringent strain after dynamic peak stress appear because of the different degrees of rock damage. Moreover, these phenomena include two conditions, namely, whether rebound occurs or not. The impact resistance of rock is strongest when the ratio of the confining pressure to axial pressure is optimal, and the dynamic average strength of rock and accumulative impact times decrease with the increase of the preloaded axial compression and increase with the increase of the preloaded confining pressure. Both the dynamic deformation modulus and dynamic peak stress decrease with the increase of the accumulative impact time, while the maximum strain and the dynamic peak strain increase. The corresponding rebound strain as a whole first increases and then decreases with the increasing impact times. For deep rock, tensile failure and single-bevel plane shear failure are the main failure modes, and pull-compression mixed friction failure is the auxiliary failure mode. Additionally, the lumpiness of broken rock decreases with the increase of the preloaded axial compression and increases with the increase of the preloaded confining pressure. The demand for mineral resources is increasing gradually with the rapid development of the world economy and industrial technology. The exploitation of deep resources is unavoidable because mineral resources are non-renewable, especially metal mineral resources. However, the mechanical properties and failure characteristics of deep rocks are different from those of shallow rocks because deep rocks exist in the complex environment of high earth temperature, high karst water pressure, and high crustal stress, and they are also affected by blasting excavation and other dynamic disturbances –3. RightIn recent years, the problem of dynamic mechanical properties of rocks in the deep complex mechanical environment has attracted the attention of experts in the field of rock mechanics. A large number of experimental studies have been carried out, and the results can lay the foundation for the study of dynamic properties and failure characteristics of deep rocks. To research the dynamic impact strength of deep rock in different complex mechanical environments, the improved split Hopkinson pressure bar (SHPB) has been used by scholars to carry out the dynamic impact disturbance test. The dynamic triaxial compressive strength of rocks under low confining pressures increases with the increase of strain rate and increases linearly with the increase of confining pressure when the only influencing factors considered are high strain rate and low confining pressure –8. The dThe surrounding rock is affected by frequent blasting excavation disturbance in deep rock engineering, especially in the mining process of deep mineral resources. Therefore, the three-dimensional high static load and frequent dynamic disturbance test was carried out, and its engineering background is the Dongguashan Copper Mine. The Dongguashan Copper Mine is located in Tongling City, Anhui Province, China. Because the extractive depth of the Dongguashan Copper Mine has already reached one kilometer, the deep surrounding rock of extracted ore drift produces an intricately destructive phenomenon under intensively high static stress and blasting disturbance –33. In tThe serpentine specimens used in the test were drilled from the wall rock of extracted ore drift in the Dongguashan copper mine, 900 m underground. The Dngguashan mine is a mine in China, located in Tongling city, Anhui province. Scholars are welcome to conduct academic research in mines. In this paper, only rock samples are taken from the mine, and there is no interest conflict. Test sampling has been approved by Dongguashan copper mine, therefore, no special permission is required for this research activity". To ensure homogeneity, a compact-structure cylindrical core with no obvious micro-cracks should be selected in the first place. According to the test requirements, the samples were made with two cylindrical dimensions of 50 mm×50 mm or 50 mm×100 mm, i.e., a height-diameter ratio of 1:1 or 2:1. In the meantime, all test specimens were polished carefully at both ends to make sure that the no parallelism and the no perpendicularity were both less than 0.02 mm. The rock samples with a height-diameter ratio of 2:1 are used for the triaxial compression test, while the rock samples with a height-diameter ratio of 1:1 are used for the three-dimensional high static load and frequent dynamic disturbance test.The loaded structural representation of the improved SHPB test system is shown as The main content of the experiment is to pile a certain confining pressure upon the specimen beforehand and then impose higher axial static load. After stabilization of the foregoing load, the axial impact load of definite strength is applied to the specimen frequently until the specimen exhibits macroscopic destruction. It is necessary to keep the values of the confining pressure and axial compression constant throughout the entire test, and the test loaded mechanical model is shown in To determine the values of the pre-loaded confining pressure and axial compression, the British Instron 1346 type electro-hydraulic servo testing machine was utilized to conduct the triaxial compressive strength test of serpentine. The test specimen was made into a cylinder with a diameter of 50 mm and a height of 100 mm. The test results are shown in Before the impact test, the rock sample is not installed between the incident bar and the transmission bar, and the first impact occurs when the incident bar is in contact with the transmission bar at the same cross-section. At this moment, the stress equilibrium between the incident, transmitted, and reflected waves can be verified by the stress wave signal. n in the previous diagram represents the number of impact disturbances.Due to the differences of confining pressure and axial compression, the test is divided into 16 groups. Dynamic stress-strain curves can reflect the features of the dynamic deformation of rock, so only two groups of typical dynamic stress-strain curves are listed in As shown in The general characteristics of the dynamic stress-strain curve of serpentinite subjected to frequent impact disturbance under three-dimensional high static load are further analyzed, and this can be divided into an elastic-plastic curve and plastic-elastic-plastic curve according to the curve form, as shown in OA, AB, BC and C; plastic-elastic-plastic curves include five stages: OO1, O1a, ab, bc and c. Each stage shows that the rock samples have undergone different deformation characteristics.According to the morphological changes of two types of dynamic stress-strain curves, elastic-plastic curves include four stages: OO1 stage): This section of the dynamic stress-strain curve is convex, and the strain increment decreases with the increase of stress. When the preloading axial pressure is small or the rock sample is about to undergo macroscopic failure, the OO1 stage appears under impact load. One reason is that the small axial pressure of preloading cannot completely close the micro-cracks in the specimen. Another reason is that a large number of new cracks in serpentinite are generated before the macroscopic failure. In the initial stage of impact load, new cracks are compacted, and this causes the dynamic stress-strain curve to be convex.Compaction stage (OA stage or O1a stage): This section of the dynamic stress-strain curve develops in an approximately straight line, and the corresponding deformation modulus is the largest. This suggests that the rock at this stage is in the elastic deformation stage. When the micro-cracks in the rock are constant or exhibit steady development, the rock can be approximately considered to have the greatest impact resistance and the greatest difficulty of deformation under the impact compressive stress at this stage.Micro-crack steady development stage (AB stage or ab stage): This section of the dynamic stress-strain curve exhibits nonlinear development, and this curve increase trend gradually becomes slow. At the same time, the deformation modulus decreases gradually. This suggests that the rock at this stage is in the plastic deformation stage. When the micro-cracks in the rock are unstable, they can be instantly extended and penetrated, and the macroscopic failure of rock is caused under certain conditions. However, a single impact cannot make the micro-cracks in the rock specimen break through instantaneously because the dynamic disturbance impact stress is small. A single impact only acts as a disturbance and causes a state of unstable development.Micro-crack unstable propagation stage (BC stage or bc stage): This section of the dynamic stress-strain curve shows a dramatic declining trend. This phenomenon indicates that the impact compressive stress is in the unloading stage, and the serpentine specimen is in a state of damage. Both elastic deformation and plastic deformation occur in rocks. Rock damage accumulates with the increase of the number of impact disturbances. When the stress unloading is completed, even if there is no macroscopic failure of the rock, the internal structure of the rock has also changed. It is believed that the rock’s impact resistance is reduced at a macro level.Fatigue damage stage (C later stage or c later stage): The specimen is macroscopically damaged in this stage. When the rock is not damaged, it is considered to be in an incomplete failure state. According to the different failure degrees of rock, the stress-strain curve shows two types of situations.Fatigue failure stage (CD stage or cd stage): The phenomenon of stress-strain curve rebound is that the strain decreases as the stress decreases. The reason is that, when the pre-loaded axial pressure does not cause the rock sample to become completely broken, there is a certain amount of elastic energy still stored in the specimen with fewer disturbance impacts. The elastic force stored in the rock sample is greater than the disturbance impact stress when the disturbance impact stress is in the unloading stage. The rebound phenomenon of the dynamic stress-strain curve is due to the small amplitude rebound of specimen deformation and the small amplitude reduction of dynamic strain.(1) Stress-strain curve rebound stage (DF stage or df stage): The stress-strain curve does not rebound when the rock sample is completely broken under the disturbance impact load. The reason is that the elastic force stored in the rock sample begins to release before the maximum strain is reached during the impact unloading process, which causes the disturbed impact stress to be greater than the elastic force in the rock sample during the entire unloading stage. When the pre-added axial pressure is too high, macroscopic failure of the rock sample will occur. At this time, the role of disturbance impact is mainly to induce elastic energy release from the serpentinite specimen. The dynamic stress-strain curve does not rebound because the disturbance impact stress is greater than the stored elastic force in rock sample throughout the entire impact disturbance stage.(2) Stress-strain curve no-rebound stage , the results indicate that the coefficient k1 decreases with the increasing confining pressure. When the confining pressure exceeds a certain value, the reductive rate of accumulative impact times may be increased on the condition of increasing confining pressure. The coefficient k1 shows a decreasing trend in the mass with the increase of axial compression. That is to say, the increase rate of accumulative impact times may decrease due to the increasing axial compression.In Figs Based on the above analysis, the accumulative impact times were affected separately by confining pressure and axial pressure when the rock is under the condition of three-dimensional high static load and frequent impact disturbance. The accumulative impact times decrease as the axial pressure increases, and the accumulative impact times increase as the confining pressure increases. To analyze the influence of confining pressure and axial pressure on the accumulative impact times at the same time, the ratio of confining pressure to axial pressure was selected as a parameter variable to further analyze the change relations of the accumulative impact times, as shown in From There is no definite stipulation regarding dynamic mechanical characteristic parameters at home or abroad. Therefore, for further study on the dynamic mechanical properties of rock, the typical dynamic stress-strain curves are selected to conduct analysis of the characteristic parameters. In this test, the defined schematic diagram of dynamic parameters of dynamic stress-strain curves after each impact is shown as E1, E2, E3, and Ed are the secant modulus, second category of the secant modulus, deformation modulus of the loading section, and dynamic deformation modulus, respectively; σd is the peak stress, while σd50 is half of the peak stress; εd is the peak strain, while εd50 is the corresponding strain of half of the peak stress; α is the angle between the tangent of half of the peak stress and the ε-axis; and εmax, εz, and εt are the maximum strain, final strain, and rebound strain, respectively.According to With the increase of impact times, the dynamic deformation modulus of serpentinite exhibits a gradually decreasing trend under three-dimensional high static load and frequent dynamic disturbance. Thus, the change law of the dynamic deformation modulus is as shown in Under the state of three-dimensional stress, although the confining pressure impedes a rock’s development of transverse deformation and enhances the resistant ability of rock to external impact load, internal micro-cracks of rock always go through a process of germination, extension, closure, and connection. All of these lead to perpetual accumulation of internal damage because of three-dimensional high static load and frequent dynamic disturbance. With the increase of impact times, the resistant ability of rock to external impact load decreases under the same stress status, i.e., the dynamic deformation modulus of rock exhibits a reductive trend.n is a positive integer; σAS is the dynamic average strength of rock samples; σPsi is the dynamic peak stress that was obtained in the impact disturbance test, and the subscript i is the number of impacts.To research the influences of confining pressure and axial compression about resistant ability to impact disturbance, average values of dynamic peak stress are defined as the dynamic average strength of rock. The calculation formula of the defined "dynamic average strength of rock" is as follows:To verify the rationality of the defined dynamic average strength, the law of its variation with the accumulative impact times is first analyzed. The dynamic average strength of rock samples was defined, and its variation rule with the number of impacts was analyzed, as shown in Based on the above definitions, the relationship between the dynamic average strength and preloading axial and confining pressure was studied. It can be seen from Based on the above analysis, the dynamic average strength of rock under three-dimensional high static load and frequent dynamic disturbance was affected separately by confining pressure and axial pressure. The dynamic average strength of rock decreases as the axial pressure increases, and the strength increases as the confining pressure increases. To analyze the influence of confining pressure and axial pressure on the dynamic average strength of rock at the same time, the ratio of confining pressure to axial pressure was selected as a variable parameter to further analyze the change relations of the dynamic average strength of rock, as shown in As shown in With the increase of impact times, deep rock’s dynamic peak strain of the variational trend is similar to the trend of maximum strain, namely, both of them show an increasing trend. The trend line of dynamic peak strain also presents two different conditions from Rock exhibits the phenomenon of rebound at the later time of dynamic stress-strain curves in this test, which indicates that rock has elastic properties and elastic deformation under three-dimensional high static load and frequent dynamic disturbance. In the frequent impact disturbance test, the failure features of the specimens in the confining pressure device failed to be observed directly during the impact disturbance process. However, the failure features of the specimens can be identified indirectly by the change trends of the incident, reflected and transmissible voltage time history curves, which can be detected in the process of impact disturbance and can reflect the dynamic mechanical characteristics of specimens, as shown in As shown in The mechanical condition of rock and the interior defect of the rock structure can be reflected by the ultimate failure mode of rock. There are many factors influencing the failure characteristics of rock, and preloading axial pressure, confining pressure and frequent impact disturbance are the most important influencing factors. Those can be obtained by analyzing the influencing factors of the failure mode of rock under three-dimensional high static load and frequent dynamic disturbance. By analyzing the pictures of the damaged rock blocks after the test, it can be found that the tensile failure and the single-bevel plane shear failure are the main failure modes and that the pull-compression mixed friction failure is the auxiliary failure mode when testing the deep rock under three-dimensional high static load and frequent dynamic disturbance, as shown in The broken rock appeared to be shaped like an arc or a long ribbon when the broken rock block was large. The shape can be determined by analyzing the shape of the broken rock block, as shown in As shown in It was found that there is a layer of rock powder adhered to the fracture surface of the specimen, and there is more rock debris mixed in the broken rock blocks. This feature can be obtained by further analysis of the broken rock blocks of the serpentinite specimen, as shown in In the three-dimensional high-static load frequent impact disturbance test, the main factors affecting rock failure characteristics are preloaded axial pressure and frequent impact disturbance. It was found that the broken rock block was smaller when the preloading axial pressure was larger by analyzing the ultimate failure lumpiness of the rock, as shown in In the three-dimensional high-static load frequent impact disturbance test, the main factors affecting rock failure characteristics are the preloaded confining pressure and frequent impact disturbance. It was found that the broken rock block was larger when the preloading confining pressure was larger by analyzing the ultimate failure lumpiness of rock, as shown in With the Dongguashan Copper Mine as the engineering context, the test program was developed. The improved split Hopkinson pressure bar (SHPB) was used to study the dynamic mechanical characteristics and failure mode of deep serpentinite under three-dimensional high static load and frequent dynamic disturbance, and the main conclusions are as follows.There are two types of dynamic stress-strain curves of deep rock under three-dimensional high static load and frequent dynamic disturbance: an elastic-plastic curve and plastic-elastic-plastic curve. The curve can be divided into five stages—the compaction stage, micro-crack steady development stage, micro-crack unstable propagation stage, fatigue damage stage, and fatigue failure stage—and the curves exhibit reductive phenomena of constringent strain after the dynamic peak stress because of the different degrees of rock damage. Moreover, these phenomena include two conditions, i.e., whether they rebound or not.Both the dynamic average strength of rock and accumulative number of impacts decrease with the increase of preloaded axial compression and increase with the increase of preloaded confining pressure. When the ratio of confining pressure to axial pressure is optimal, the specimens have the strongest resistance to external impact load.Both the dynamic deformation modulus and dynamic peak stress decrease with the increase of the accumulative number of impacts. However, the maximum strain and the dynamic peak strain increase with the increase of the accumulative number of impacts.The phenomenon of rebound appears at the later time of dynamic stress-strain curves, and this is because the rock produces elastic deformation under impact load. The corresponding rebound strain as a whole first increases and then decreases with the increasing number of impacts.For deep rock under three-dimensional high static load and frequent dynamic disturbance, tensile failure and single-bevel plane shear failure are the main failure modes, and pull-compression mixed friction failure is the auxiliary failure mode. The lumpiness of broken rock blocks decreases with the increase of preloaded axial compression and increases with the increase of preloaded confining pressure.


Grooving is widely used to improve airport runway pavement skid resistance during wet weather. However, runway grooves deteriorate over time due to the combined effects of traffic loading, climate, and weather, which brings about a potential safety risk at the time of the aircraft takeoff and landing. Accordingly, periodic measurement and evaluation of groove performance are critical for runways to maintain adequate skid resistance. Nevertheless, such evaluation is difficult to implement due to the lack of sufficient technologies to identify shallow or worn grooves and slab joints. This paper proposes a new strategy to automatically identify airport runway grooves and slab joints using high resolution laser profiling data. First, K-means clustering based filter and moving window traversal algorithm are developed to locate the deepest point of the potential dips . Subsequently the improved moving average filter and traversal algorithms are used to determine the left and right endpoint positions of each identified dip. Finally, the modified heuristic method is used to separate out slab joints from the identified dips, and then the polynomial support vector machine is introduced to distinguish out noises from the candidate grooves (including noises and true grooves), so that PCC slab-based runway safety evaluation can be performed. The performance of the proposed strategy is compared with that of the other two methods, and findings indicate that the new method is more powerful in runway groove and joint identification, with the F-measure score of 0.98. This study would be beneficial in airport runway groove safety evaluation and the subsequent maintenance and rehabilitation of airport runway. Since the early 1960s, grooving has been increasingly used on airfield pavements and roadways to improving tire-pavement friction through efficient water-run-off and prevent airplanes or vehicles from accidents . The purPast studies indicate that groove dimensions can be automatically measured using point laser ranger-based profiling equipment and 3D laser imaging sensor-based instruments ,13,14,15Currently there are four methods for the potential dip identification ,12,14,16The determination of the two endpoint positions of grooves is critical for the computation of groove dimension. Previous studies indicate there are three methods for the determination of two endpoints of grooves ,12,13,14Although the groove identification algorithm in ProGroove can identify out grooves and joints, the unsatisfactory results are obtained. The authors of  presenteIn summary, current studies on groove identification and measurement still have three limitations: (1) they cannot avoid the presence of fake grooves or noises in the process of attempting to find more true grooves; (2) they may miss some grooves and joints if these thresholds are inappropriately set, and the number of identified grooves and joints has a large variation or fluctuation with the change of parameter settings; (3) they cannot exactly localize the slab joints in the scenarios that have more identified dips within a possible range of next slab joint if the heuristic method is used to determine the slab joint location. To address these issues, the more promising and powerful algorithms should be investigated. To accomplish this goal, the point laser-based profiling equipment developed by the U.S. Federal Aviation Administration (FAA) is employed to collect grooving data on a full-scale runway. Subsequently the slab joint and true grooves are separated out from the identified dips that are produced with the K-mean clustering method and moving window traversal method. Finally, the identification and measurement results from the new method is compared with the algorithm in the ProGroove software  and Li’sFAA point-based laser profiling equipment was developed to conduct the rapid measurement of surface elevation profiles on airport runways, in which an accelerometer and vertical distance sensor are used to measure true changes in concrete or bituminous pavement elevation. With the high-power point laser system, this profiling system can work at highway speeds during daytime and nighttime and maintain data quality and consistency. That means the profiling data can be acquired at any time of the day, regardless of lighting conditions. Even though this system has been designed to accommodate all dynamic and static conditions incurred during normal driving conditions, it cannot collect data on wet runways in rainy days. In addition, the contaminants on runway surface should be cleaned off before data collection, i.e. removal of rubber deposits, removal of sand, dust, mud, etc. It is strongly recommended parking the profiling system either indoors or under certain type of shelter in case of inclement weather since it is not dust-proof and water-tight.When the profiling system is used for data collection, its parameters or settings should be properly configured, and then the user can open the collection screen and start data collection. The collected data can be plotted in real time in the main widow. The collected data (.dat file) are saved to the designated directory for post-processing. Airport runway surveys are usually conducted at after midnight without any traffic interruption. Typically, each single measurement or pass needs about two minutes depending on airport runway length and the driving speed. The total time for accomplishing the entire runway survey needs about 40 to 60 min depending on the number of measurements or passes.In previous studies, a four-stage method is proposed for automated groove measurement and evaluation, in which runway grooves can be identified out with Li’s method . HoweverIdentification of runway grooves is dependent on the elevation difference between the raw grooving data and the low-pass filtered data (termed the base curve). A potential dip or candidate groove can be determined if the corresponding elevation difference are greater than a prescribed threshold. Two key problems need to be addressed for the identification of potential dips: (1) the determination of the base curve; (2) the selection of the threshold. For grooving data, the generation of base curve is susceptible to impacts of narrow and deep dips, which would lead to the elevation difference at dips are less than the actual dip depths. This phenomenon would bring in the difficulty in identifying shallow or worn grooves if the threshold is given. To solve this issue, K-means clustering based filter is proposed and used to determine the base curve.The basic idea behind the new filter is to partition n observations into k clusters or groups in which each group belongs to the cluster with the nearest mean ,20. In tx2,⋯,xn) a can be (1)Assign an initial set of 3-means (2)Assign each observation to the cluster whose mean has the least squared Euclidean distance, as mathematically described in Equation (1):(3)Calculate the new means to be the centroids of the observations in the new clusters, as mathematically described in Equation (2):The implementation proceeds by alternating between two steps (2) and (3), and is converged when the within-cluster sum of squares for the chosen set of grooving data are minimized. Finally, the three clusters and their centroids can be determined, as mathematically described in Equation (3):The new grooving data can be calculated by using raw grooving data to subtract base curve, as mathematically described in Equation (4): In previous studies, a prescribed threshold is used to identify the potential dips. Usually true grooves may be not successfully identified out if the given threshold is too large, while more fake grooves or noises would be introduced if the given threshold is too small. Accordingly, the selection of threshold is critical for the accurate identification of potential dips. To address this issue, moving window traversal algorithm is proposed to locate the deepest point within each potential dip across the window length (BL). Practically the moving window length is dependent on groove space. For each point The calculation of dip dimension is dependent on the three elements of a dip, namely the deepest point, left endpoint, right endpoint. Therefore, the following task is to find out the two endpoints of a dip once the deepest point is located.In this study backward traversal technique is used to locate the left endpoint of a dip. Its implementation starts at the deepest point of a dip until the traversed gradient is no smaller than zero, and simultaneously the current pixel value is larger than the corresponding pixel value of the auxiliary curve. The calculation of gradient of a point can be mathematically described in Equation (6):Similarly, the forward traversal technique is used to find the right end point of a dip, starting at the deepest point of a dip until the traversed gradient is no larger than zero and the current pixel value is larger than the corresponding pixel value of the auxiliary curve. Once the deepest point inside dips and the two endpoints of dips are determined, dip dimension can be computed based on the procedure specified in the FAA Advisory Circular No. 150/5320-12C [Groove volume, an important statistical index associated with wet pavement safety, is initially proposed to describe the drainage capacity of measured grooves. Grooving volume equals to the sum of elevation difference between the base curve and raw grooving data for all points inside each groove, as the right plot in The identified dips consist of true grooves, slab joints, and other noises . Therefore, true grooves should be distinguished out from the identified dips firstly before they are used for airport runway safety evaluation. This goal can be implemented in two phases: (1) use the modified heuristic method to separate out slab joints from the identified dips, in which the naïve Bayesian classifier is introduced; (2) use the polynomial support vector machine to distinguish true grooves with noises. Finally, the slab-based groove performance evaluation can be performed.To separate out slab joints from the identified dips, the naïve Bayesian classifier is introduced to modify the heuristic method in this study. Its implementation can be described using Naïve Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of feature values, where the class labels are drawn from some finite dataset ,22,23. TThe identified dips falling inside the possible range of the next joint can be divided into two classes: the groove or noise In practice, the identified dip depth, width and volume belongs to a continuous dataset, so a typical assumption is that the continuous values associated with each class are distributed according to a Gaussian distribution. For instance, the training feature In Equation (7) there is interest only in the numerator, because the denominator does not depend on classes In addition, the percentage of the cases where the joints fall or not in the PLRoNG is examined based on the twenty concrete slabs. In this study the NSL equals to the mean (4.46 m) of the measured slab lengths in fields, and SLTR (0.054 m) equals to two times the standard deviation. The findings indicates the chosen twenty slabs all fall in the PLRoNG since the maximal and slab lengths are 4.51 m and 4.41 m, respectively. Once slab joints are distinguished from the identified dips, the following task is to separate out noises and true grooves using Support Vector Machine (SVM) based on the three variables or vectors namely dip depth  is used to replace Assume the optimal Lagrange multiplier is {As a result, the category that contouring box belongs to can be determined based on Equation (19). If the sign of The FAA AC No. 150-5320-12C provides standard groove configuration and the tolerable range in depth, width, and spacing for the entire airport runway or each PCC slab [One small section of the grooving data, made of 100,000 discrete points, are chosen to illustrate the implementation of automated groove identification, measurement and evaluation. The chosen grooving data provided by FAA has been in service for several years, with a length of approximately 95 m, as shown in The implementation of groove measurement and evaluation is organized as follows: (1) the potential dips are identified out with the three approaches namely the algorithm in ProGroove software, Li’s method, and the newly proposed method. The comparison results are analyzed based on identification results; (2) the slab joints are distinguished from the identified dips using the modified heuristic method, and then the true grooves are separated out from the candidate grooves using polynomial SVM method. In this study the identified dips include true groove, slab joint, and other noises, whilst the candidate groove contains true groove and other noises; (3) the slab-based groove performance is evaluated, and the corrective measures can be taken on each concrete slab to improve runway skid resistance.To position the potential dips along runway grooving data, the K-means clustering based filter and moving window traversal algorithm are initially used to locate the deepest point of each potential dip. Each deepest point that is identified represents one potential dip. Subsequently, adaptive forward and backward traversal algorithms are used to find the left and right endpoints of each identified dip based on the location of the deepest points that are identified. Once the locations of the three elements  of a dip are determined, each potential dip dimension can be computed. The number of identified dips and from the three methods are summarized in As mentioned above, the identified dips with the three methods contain true grooves, slab joints, and other noises. To analyze the groove dimension distribution on each PCC slab and perform slab-based groove performance evaluation, the slab joint should be determined first.According to the heuristic method used in the paper , the slaIn this experiment, the number of identified joints with the algorithm in ProGroove software is about 319, which is 298 more than the ground truth. Accordingly, the algorithm in ProGroove software is inappropriate for slab joint identification. In light of joint locations, all the slab joints at the test section are identified with the proposed algorithm, and the identified joint locations correspond to the joint locations in field. Li’s method fails to detect two joints. As a result, the newly proposed method is more suitable for the slab-based groove performance evaluation.Once the slab joint is determined, the subsequent work is to separate out noises or fake grooves from the candidate grooves on each individual slab, and the polynomial SVM is used to achieve this goal. To quantitatively describe identification results of candidate grooves, three evaluation metrics namely precision, recall, and F-score are presented in this study . For eacOnce the TP, TN, FP, and FN are determined, three evaluation metrics can be calculated, as described in Equations (20)–(22). Generally, the larger the evaluation metrics is, the better the performance of the test algorithm is. An ideal or robust algorithm would have values of all evaluation metric approximating to one:The goal of the test algorithm is to be the precision and recall close to 1.0. However, the three methods produce the lower recalls when compared with their respective precisions. To conduct groove performance evaluation on each individual slab, it needs to report the statistical groove information for each individual slab based on classification results of grooves and joints. The measured groove dimension  and the three-evaluation index  with the proposed approach are summarized in According to the FAA AC No. 150-5320-12C guideline, there are no slabs that conform to the guideline requirement. For Slab3, although the percentages of grooved depths larger than 4.76 mm is over 90% and that larger than 6.35 mm is over 60%, the percentage of groove depths larger than 7.94 mm is more than 10%, which do not meet guideline requirement. For other slabs, the percentages of groove depths larger than 6.35 mm are less than 60%, which do not meet guideline requirements. To make grooves on each slab meet the FAA guideline requirement, part of grooves on each slab need to be corrected, as illustrated in The corrective activity aims to increase groove depths at test runways except for the Slab No 3, and to ensure groove depths are above the low limit of acceptable range. If the slabs after maintenance have the standard groove configuration, all evaluation indices comply with the FAA standard, which means the groove performance on this section is able to conform to the FAA guidelines once the 21 slabs (exclusive of Slab No 3) are maintained with corrective measures. Accordingly slab based evaluation method is able to provide airport authority with the slab number and also the percentage of slabs that need corrective actions. 3, which is computed as the product of the lower limit of groove depth by the design value of groove width. The design value of groove volume is 40.32 mm3, which is computed as the product of the standard groove width by the standard groove depth. However, groove depth cannot efficiently reflect the drainage ability of the test grooves. For instance, if two grooves have the same depths, they should have the same performance in accordance with the FAA groove evaluation guideline, but actually the two grooves could have the different drainage capacity due to the different groove volumes. As a result, the groove volume-based evaluation method is initially proposed for groove performance evaluation in this paper. 3), for Slabs No. 14, 16, 18–20, and 22, indicating the test runway grooves are not efficient for rapid discharge of the rainy water on the pavement surface during wet weather. Before any corrective measures are taken, the groove depths should be investigated. If the groove depth distribution does not meet the FAA guideline requirement, the corrective measures are taken to increase groove depth. If the groove depth distribution satisfies the guideline requirement, the cleaning work should be taken to sweep away the surface debris or loosened aggregate inside grooves and to ensure runway surface grooves have the good drainage ability during wet weather.Note that the measured groove volume is less than the acceptable volume value (30.23 mmIn this study a new methodology for automatic groove identification, measurement, and evaluation is proposed. First, experimental data are collected using the FAA point laser-based profiling equipment. The K-means cluster filter and moving window traversal algorithm are developed to identify the deepest point of each potential dip, and then the backward and forward transversal methods are used to position the left and right endpoints of the potential dip. Once the three elements of a dip are determined, the dip dimension is computed. Subsequently, the modified heuristic method is initially used to separate out slab joints from the identified dips, and the polynomial SVM is proposed to distinguish out the true grooves from the candidate grooves. The groove identification results with the new method are compared with that of the algorithm in ProGroove and the Li’s method, findings show the new method is more powerful in groove and slab identification, with the precision of 1.0, the recall of 0.96, and the F-measure of 0.98. Eventually, slab-based groove dimension performance can be evaluated in accordance with the FAA Advisory Circular AC 150-5320-12C. In addition, the groove volume-based evaluation approach is also proposed in this study, which would be beneficial in complimenting the existing runway groove performance methods. Runway pavement engineers can use the evaluation results as basis to take corrective measures on slabs with poor groove performance. Even though the new method produces the better precision and recall in groove identification than other existing methods, computation cost is expensive in k-means clustering, and usually it would take a longer time than other methods to process the same amount of data. Moreover, the point laser profiling instruments only collect one line-of-sight profile, which cannot reflect the entire runway groove information due to the limited quantity of profiles. In the future the line-scan imaging data can be used in lieu of point laser-based profiling system to conduct full runway measurement. To increase the computational efficiency, a new filter can be developed to replace the k-mean clustering-based filter in this method. The method presented in the paper can also be extended to the longitudinal or transverse groove performance evaluation for highway applications.


To design a soft robotic fish with high performance by a biomimetic method, we are developing a soft robotic fish using piezoelectric fiber composite (PFC) as a flexible actuator. Compared with the conventional rigid robotic fish, the design and control of a soft robotic fish are difficult due to large deformation of flexible structure and complicated coupling dynamics with fluid. That is why the design and control method of soft robotic fish have not been established and they motivate us to make a further study by considering the interaction between flexible structure and surrounding fluid. In this paper, acoustic fluid-structural coupling analysis is applied to consider the fluid effect and predict the dynamic responses of soft robotic fish in the fluid. Basic governing equations of soft robotic fish in the fluid are firstly described. The numerical coupling analysis is then carried out based on different structural parameters of soft robotic fish. Through the numerical analysis, a new soft robotic fish is finally designed, and experimental evaluation is performed. It is confirmed that the larger swimming velocity and better fish-like swimming performance are obtained from the new soft robotic fish. The new soft robotic fish is developed successfully for high performance. With the development of interdisciplinary sciences, including the science of electronic information and biological technology, biomimetic robots have made a lot of irreplaceable contributions in human life , 2. ManyIn order to fulfil some special work in the complicated or unknown environment accurately and reliably, the biomimetic robotic fish should be designed as soft as the real fishes, and the actuation strategy using a soft structure is needed due to the obvious advantages of smooth propulsion, high safety, and high mobility. It has been proven difficult to reproduce the fish-like smooth propulsion by using conventional rigid mechanisms, causing a relatively complex and unreliable propulsion structure with low efficiency and mobility , 9. A soWhen designing a soft robotic fish, it must consider a surrounding fluid. The fluid increases the system mass, stiffness, and damping and changes the dynamic characteristics of the soft robotic fish. The fluid-structural coupling analysis considering the interaction between the flexible structure and the surrounding fluid is performed in the design of dynamic behaviors of the soft robotic fish. Most of fluid-structural coupling problems involve a fluid without significant flow, and the main concern in the fluid is pressure wave propagation. The acoustic fluid-structure coupled method considering the sound pressure can thus be utilized to solve these coupling problems and predict their dynamic responses. According to the coupling analysis using finite element method (FEM), Ai and Sun  studied In the present research, the fish's body and/or caudal fin (BCF) propulsion is focused. PFC can be constructed to a simple structure with high energy conversion efficiency and large displacement response and is utilized as a soft actuator to develop a BCF-propulsion prototype. In the paper, the acoustic fluid-structural coupling using FEM is applied to predict dynamic responses of the soft robotic fish in the fluid. Through the coupling analysis, a new soft robot structure is proposed, and a well-established experiment is performed to evaluate dynamic behaviors with the coupling method. From the results, it is confirmed that the new soft robotic fish with larger velocity and better fish-like swimming performance is achieved by the established coupling method. The new high-performance soft robotic fish is developed successfully.Ex and Ey are the tensile modulus in the X and Y directions, respectively, vxy and vyz are Poisson's ratio, d33 and d31 are the piezoelectric constants, V is the voltage, W is the distance between the electrodes, and P is the driving load.In this study, macrofiber composite (MFC) , one of When MFC combined with a thin elastic plate, the bending deformation generated due to resonance. The characteristics of bending deformation were utilized to design the soft robotic fish with BCF propulsion. The carbon-fiber-reinforced polymer (CFRP) was adopted as the thin elastic plate in the research.The biomimetic approach has been used to design the soft robotic fish in the unknown or complicated environments. Through mimicking the real fish, the concerned functions of the soft robot can be classified into two types: moving like a fish and looking like a fish, described in In the research, the main research purpose is to develop the high-performance soft robotic fish by a biomimetic method. The design method based on numerical analysis is presented. It takes into account the interaction between the flexible structure and the surrounding fluid. In this paper, the FEM approach was used to deal with the acoustic coupling problems through ANSYS software. Acoustic elements, four degrees of freedom (DOF): three for optional displacement and one for pressure, accomplished the required fluid-structural coupling. A consistent matrix coupling was set up between structural and fluid elements in which strongly coupled physics caused no convergence problems.FS is zero,  SOLID186 elements, and 3-D FLUID30 elements were used to model the fluid domain and coupled interface. As shown in In the coupling analysis, the driving load of 3 Hz ranging from −500 V to +1500 V in sine waveform was applied. The simulation results on the displacement of the caudal fin end based on different parameter arrays are described in The bending mode frequencies of the new robot model in the fluid are shown in The bending mode frequencies of the prototype in the fluid are shown in The corresponding bending propulsion modes are shown in Sw of the fish was widely used to evaluate the swimming performances of the robotic fish [Sw, related to velocity V, frequency f, and body length L, could be expressed byThe new prototype also could realize the basic swimming motion such as the straight-ahead motion. The swimming velocity is described in tic fish . Sw, relSw of the fish described the distance fish moved per tail beat. It was generally about 0.6 for high performances with good flexibility and mobility [Sw was sufficient to describe the performance related to the swimming motion of the real fish by biomimetic approach [Sw of the new soft robot. It was decreasing with the increased frequency in the certain range. Maximum Sw was about 0.75 occurred at 1 Hz. At 2 Hz, Sw was close to 0.6, much closer to the value of real fishes. The new soft robotic fish had better fish-like propulsion performance near the main propulsion mode.mobility . It meanapproach .  FigureSw. By comparison, the new soft robot had better fish-like propulsion performances on maximum swimming velocity by using speed  and Sw. The maximum velocity of the new soft robot was improved by more than one order of magnitude. And Sw was enhanced by at least 3 times. It could be considered that the new soft robotic fish had higher propulsion performance similar to those of real fishes than the conventional soft robotic fish.wS. The maximum velocity of the new soft robot was improved by more than one order of magnitude. And Sw was enhanced by at least 3 times. It could be considered that the new soft robotic fish had higher propulsion performance similar to those of real fishes than the conventional soft robotic fish.By comparison, the new soft robot had better fish-like propulsion performances on maximum swimming velocity by using speed  and By controlling the amplitude of input voltage on soft actuators, the soft robot could obtain the turning motion. The soft robot in  was takeIn the research, the soft robotic fish was composed of two soft actuators for propulsion. When the input voltage signals on both left and right MFC actuators had the same voltage amplitude and were distributed in opposite directions from each other, the straight-ahead motion was realized on the soft robotic fish. Based on these input voltage signals on both MFC actuators, the straight-ahead motion of the soft robotic fish was generated and the corresponding propulsion modes are presented in In order to realize the turning motion of the soft robotic fish, the asymmetric signals were applied based on the conditions of the straight-ahead motion. Through controlling input voltage signals for bias voltage between two soft actuators, the turning motion could be obtained due to the asymmetrical output from actuators. When the voltage amplitude on the left actuator was larger, the motion of turning right was obtained. On the contrary, the motion of turning left occurred. Based on these asymmetrical signals, the motion of turning right was achieved and corresponding propulsion modes are described in For the motion of turning left, the applied approach of input voltages was contrary to that of turning right motion. The voltage on the left actuator was in the range of −500 V~+500 V, and the voltage on the right actuator was ranged from −500 V to +1500 V. Based on these asymmetrical input voltages, the turning left motion was achieved and the corresponding propulsion modes are presented in Based on the controllability of input signals, swimming motions such as turning motion could be achieved. To validate the turning motion control of the soft robot, the corresponding experiments on robot prototype in  were perThrough applying the asymmetrical signals on both actuators, motions of turning right and turning left were achieved successfully. Based on the trajectory of turning motion and corresponding time, the turning velocity was determined, and the maximum turning velocity was about 27 deg/s by using square waveform.According to the control method of input voltage signals on both actuators, the turning motion was also achieved on the new soft robot prototype. To describe the turning motion of the new soft robot, the input voltage signals with 15 Hz in square waveform shown in Based on these asymmetrical input voltage signals, the turning motions of the new soft robotic fish were achieved. Figures In this paper, a new soft robotic fish using PFC was designed through the fluid-structural coupling analysis based on biomimetic approach. Through the experiment evaluation, it was confirmed that the better fish-like swimming performances were achieved successfully by the new soft robotic fish. The new soft robotic fish with high performance similar to those of real fishes had been developed successfully. In addition, the turning motion control of the soft robotic fish was established by controlling the input signals on both actuators. The turning left motion about 53 deg/s and turning right motion about 51.6 deg/s were achieved through the new soft robotic fish at the place where the maximum swimming velocity occurred.


To quantitatively evaluate maxillary complete dentures fabricated from polylactic acid (PLA) using fused deposition modelling (FDM) technology.A digital maxillary complete denture was prepared based on a standard maxillary edentulous plaster model. The PLA pattern was printed by a FDM machine, with 5 repetitions, while another 5 wax patterns were printed as control group, using a high accuracy three-dimensional (3D) wax printer. The patterns were scanned with a 3D scanner. A light-body silicone film was made after each denture pattern had been totally seated on the plaster model, and was scanned to determine its thickness, which reflected the 3D space between the plaster model and the tissue surface of the denture pattern. The overall area was separated into four parts: primary stress-bearing area, secondary stress-bearing area, border seal area and relief area, and the average deviation of these four parts were measured. The values were analyzed by independent t-test.The overall mean value and standard deviation of space between PLA denture patterns and plaster model was 0.277 ± 0.021 mm, while that of the wax denture patterns was 0.279 ± 0.045 mm, which showed a good fit overall. No statistically significant (𝑃 > 0.05) difference was observed between the PLA patterns and wax patterns.The adaptation of the PLA pattern of maxillary complete denture printed by FDM technology is comparable to that prepared by wax printer, and can satisfy the accuracy requirements. Over the past 30 years, digital technology has come to be widely used in the field of oral medicine. Complete dentures have always posed some problems in traditional prosthodontic treatment, and computer-aided technology is an emerging method for fabricating complete dentures. At present, most digital systems for complete denture production adopt a method of milling a base into which commercial teeth are inserted. –3 HoweveThree-dimensional (3D) printing technology, also known as additive manufacturing technology, which became available in the 1980s, uses a method of layer-by-layer stacking to combine materials to a physical object based on a 3D digital model. In recent years, 3D printing technology has increasingly been applied in the field of prosthodontics, dental implants, orthodontics, surgery guidance, etc. , 5 CompaFDM technology uses high temperature to heat and melt various types of material for deposition modelling. This technology appeared in the late 1980s, and is now widely used for building models in the medical, aerospace, and light industries, etc. –12 FurthThis study aimed to evaluate the adaptation of the PLA pattern of maxillary complete dentures printed with an FDM machine, in a quantitative manner, to lay the basis for further clinical applications.The 3D data of the standard edentulous maxillary plaster model and dentition plaster model were obtained using a 3D scanner  and saved in stereolithography (STL) format. These data were imported into reverse engineering software . The dentition part of the dental model and the corresponding parts in contact with the denture base of the edentulous model were cut and merged into a complete denture by filling the space between them with triangular mesh data in order to form the thickness of the complete denture. In this way, the complete denture design was formed  and saveThe complete denture dataset was imported into the supporting software of the FDM 3D printer . Then, after adjusting the printing angle  and settThe tissue surfaces of the denture patterns were filled with light-body silicone rubber  and each pattern was completely seated onto the plaster model; then a load of 5 kg was applied to the pattern for at least 5 min. The operation was completed in a temperature (20°C)-controlled room and the process from injecting the silicon rubber to placing the pattern onto the plaster model was controlled to be within 1 minute. After complete polymerization, the space between the denture pattern and plaster model was filled with silicone. The pattern was removed and the silicone film could be seen attached to the plaster model. The plaster model covered with the silicone film was scanned using the same optical scanner and the data were exported as an STL file (2 groups × 5).The data above were imported into Geomagic software. To analyze the printing error, the scanned data of the printed patterns were registered to the corresponding CAD data, using the multipoint registration command. After registration, a 3D deviation analysis command in Geomagic software was used to measure the deviation between the two data mentioned above (scanned patterns and their CAD data) with the CAD data as the reference and the scanned data as test. The deviation was calculated using average value and Root Mean Square value (RMS). The average value represent the overall error of printing deviation, but this error is the result of positive and negative counteraction, so the RMS  is used to eliminate the influence of positive and negative signs when it squared the error, which can better reflect the discreteness of the experimental result errors.For quantitative evaluation of the adaptation of the denture pattern, the data of plaster model (without any silicon film) was registered to the data of plaster model with the silicon film using the best-fit alignment command, where the axial plane of the plaster model, that is, the area not covered by silicone film was set as the common area for data registration. So that the thickness of the silicone film was measured by 3D deviation of the surfaces inside the denture marginal line of the data of plaster model with and without silicon film, which represents the space between the plaster model and tissue surface of the denture pattern. The measurements were separated into 4 distinct areas: primary stress-bearing area, secondary stress-bearing area, border seal area and relief area, and the average deviations were recorded to represent the internal adaptation of the corresponding area. Color surface maps were created to generate a visual display of the adaptation of the denture base with the cast overall and in 4 distinct areas. .The space between the 2 digitally produced denture patterns was compared using an independent sample t-test. P values equal to or less than 0.05 were considered to be statistically significant. All statistical tests were performed in IBM SPSS Statistics 19 software As shown in t-test (P > 0.05).As shown in In recent years, many digital complete denture systems have been devised, in which the most common method for fabricating complete dentures is to mill a resin base with individual sockets for each tooth and then manually bond commercial teeth to the milled sockets of the denture.  There arIntegrated manufacture of complete dentures can effectively avoid the above problems. Integrated multicolor printed dentures are the ideal, but to date, the strength, aesthetics, abrasion resistance, and biosafety of the print processes and materials cannot meet the clinical demands of complete dentures. Therefore, the PLA pattern is printed as an indirect production of complete dentures in this study. The pattern was used to fabricate complete dentures and can also be used for clinical try-in before fabrication. When it is used to manufacture complete dentures, the pattern needs to be fully seated on the plaster model, combined with conventional technology, such as pack and press or injection molding, to form the matrix of the denture. Then the pattern is removed; the commercial teeth (as selected during the design process) are inserted and fixed in the matrix to replace the teeth in the pattern. Special attention is required when using pack and press technology, as the pattern needs to be softened or melted prior to removing it, due to the undercut of the plaster model. PLA material can be soften in water at 100° C allowing PLA patterns to be used with pack and press technology. Finally, the base resin materials are used to fill in matrix to form the base of the denture. However, adaptation of the tissue surface, the accuracy of the polishing surface morphology, and artificial tooth positioning should be evaluated.Although the polymerization shrinkage of denture base fabricated by the traditional techniques can not be avoided, while the milled denture has less deformation that is an obviously advantage of CAD/CAM technique, the shrinkage of traditional denture base is very low due to the continuous improvement of the base resin material. Studies  had showThe most important issue is whether the pattern can be accurately seated on the plaster model, because inaccurate seating could lead to a series of errors in jaw position and occlusion problems. So, this experiment was designed to evaluate the printing accuracy and adaptation of PLA pattern. In this study, we printed the same data five times to verify the stability and repeatability of the technology, and found that the average standard deviation and RMS of the PLA pattern (in comparison with its CAD data) was 0.016 mm and 0.143mm, which was comparable with the precision of the wax pattern printed using expensive printing equipment. This provided evidence of the high stability and repeatability of FDM printing, and supporting its routine use in clinical practice. The average standard deviation of PLA patterns was positive, indicating slight swelling, while that of wax patterns was negative, indicating slight shrinkage. These errors may be related to the calibration parameters of the printer, emphasizing the need to calibrate the printer regularly.The adaptation of denture patterns directly determines the effect of the final denture fabricated in the laboratory; hence, in this study, we quantitatively evaluated the adaptation by measuring the space between the tissue surface of the denture pattern and the plaster model. The average standard deviation  showed nThe accuracy of printed wax patterns of complete dentures has been reported previously. Hu et al.  printed In this study, the infill percentage was set to 0% to reduce the shrinkage of the material and to shorten the printing time, as compared to a 100% infill percentage. The infill percentage is used to change the interior solidity of the 3D print; 0% is completely hollow and 100% is completely solid. Moreover, a zero-fill structural pattern can easily be softened in boiling water and taken out to manufacture the final complete denture. Compared with wax patterns, the time for producing a PLA denture pattern was greatly shortened (about 1 h) and the cost was greatly reduced, and there was less deformation when seating it on the plaster model or during try-in on the alveolar crest. As compared with the traditional manual method, the CAD&FDM protocol can reduce the time-consuming manual laboratory procedures and improve the production efficiency of complete denture patterns.However, there are still some limitations in the process of printing a PLA pattern using an FDM machine: The angle at which the denture pattern is placed for printing will have a certain impact on the printing accuracy. The unsupported mode was used to achieve surface smoothness of the pattern, but the hanging part, which has no support, will be prone to more errors. In order to reduce the printing errors and ensure the success of the printing progress, the denture was placed vertically, and the postdam area was set downwards during printing ; howeverA 0.8-mm diameter nozzle was used to shorten the printing time to about 1 hour for printing a maxillary complete denture pattern. If higher accuracy is required, for instance to show more details, a smaller diameter nozzle can be used, but the printing time may be extended. However, the printing process that does not require manual intervention, and can therefore save valuable labor hours, thus still offering a technical advantage over the manual approach. In future, final complete dentures based on this technology should be clinically evaluated, establish its usefulness in dental practice.In this study, the adaptation of a maxillary complete denture pattern printed by FDM technology, was found to be comparable to that produced using the wax printing method. Used together with CAD software for producing a pattern of complete dentures, it can replace the traditional manual approach and improve the functional suitability of the final complete denture. The PLA pattern printed using an FDM machine can be a low-cost substitute for manufacturing complete dentures and the process satisfies accuracy requirements.S1 DatasetThis table contains a summarized table and detailed data of printing accuracy and the deviation between the denture pattern and plaster model.(XLSX)Click here for additional data file.