Quarter vehicle model is the simplest representation of a vehicle that belongs to lumped-mass vehicle models. It is widely used in vehicle and suspension analyses, particularly those related to ride dynamics. However, as much as its common adoption, it is also commonly accepted without quantification that this model is not as accurate as many higher-degree-of-freedom models due to its simplicity and limited degrees of freedom. This study investigates the trade-off between simplicity and accuracy within the context of quarter vehicle model by determining the effect of adding various modeling details on model accuracy. In the study, road input detail, tire detail, suspension stiffness detail and suspension damping detail were factored in, and several enhanced models were compared to the base model to assess the significance of these details. The results clearly indicated that these details do have effect on simulated vehicle response, but to various extents. In particular, road input detail and suspension damping detail have the most significance and are worth being added to quarter vehicle model, as the inclusion of these details changed the response quite fundamentally. Overall, when it comes to lumped-mass vehicle modeling, it is reasonable to say that model accuracy depends not just on the number of degrees of freedom employed, but also on the contributions from various modeling details. It is probably known that virtual development has become an integral part in vehicle development process due to the shortening of product life cycle in the automotive industry. Be it in the development of conventional vehicles or even in the research of state-of-the-art vehicle technologies like electric vehicle and hybrid electric vehicle –3, virtuThere are a number of vehicle models that are meant for vehicle dynamic simulation –6, coverOf the many lumped-mass vehicle models, quarter vehicle model is the most basic representation of a vehicle as it consists of only two DOFs, namely sprung and unsprung mass motions. However, the scenario for quarter vehicle model is an interesting one: on one hand, this model is widely used in researches involving vehicle and suspension analyses, particularly those related to vertical vehicle dynamics or ride dynamics. This is mainly due to model simplicity . On the This study provides some clarifications by focusing on the effect of adding various non-DOF-related modeling details on the vehicle response. In the study, four modeling details applicable to quarter vehicle model, namely road input detail, tire detail, suspension stiffness detail and suspension damping detail were identified and investigated. These acted as refinements to the otherwise linear and basic quarter vehicle model, and several enhanced models were compared to the base model through simulated responses. It was found that certain modeling details, like the road input detail and the suspension damping detail, are worth adding for improved accuracy, while others are not. These will be elaborated in the sections that follow.ms, mu are the sprung and unsprung mass values, zs, zu are the vertical sprung and unsprung mass displacements that represent the DOFs, their derivatives are the corresponding velocities and accelerations, zg is the vertical road input displacement, while k, c, kt are the dynamical representations of the system, namely suspension stiffness, suspension damping and vertical tire stiffness. The dynamical components of a quarter vehicle model are typically simplified, or linearized in this context: suspension stiffness is usually represented by linear or constant spring rate, suspension damping is usually treated as being linearly proportional to velocity, and the tire representation is usually assumed to have point contact with linear vertical stiffness but negligible damping. In general, this simplistic, lumped-mass, linear quarter vehicle model is the variant that is most widely used in vehicle-related studies.Quarter vehicle model is the simplest representation of a vehicle in dynamic analysis. It consists of the most essential DOFs that describe the movement of a vehicle, namely the sprung mass motion and the unsprung mass motion, all in the vertical translational direction. The lumped-mass approach in quarter vehicle modeling implies that there are only two inertial components which are the sprung mass and the unsprung mass, consistent to the two DOFs stated earlier. For a quarter vehicle model, the sprung mass represents loosely the quarter mass of vehicle body which includes all parts supported by the suspension system. Meanwhile, the unsprung mass comprises the masses of all parts of a single wheel station that are acted by the suspension. Due to the two DOFs, a typical lumped-mass quarter vehicle model is basically capable of representing the body bounce and wheel hop modes of movement of a vehicle. Mathematically, these motions can be described by the two equations of motion (Eqs  and 2)))2)) whicThe two-DOF quarter vehicle model has numerous applications. It is mostly used to study vertical vehicle dynamics, especially due to ground excitation which is the road input. This allows the common performance parameters, such as the root-mean-squared (RMS) sprung mass acceleration, dynamic tire load and suspension travel to be obtained for ride performance evaluation. Considering this, and also due to its fundamental nature, quarter vehicle model often finds its place in studies relevant to fundamental suspension concepts, such as controllable suspensions and a recently introduced new suspension element known as inerter. In fact, many well-known semi-active suspension control strategies, including Skyhook , GroundhObserving from all the applications above, it appears that the fundamental nature and the implied modeling convenience are the only reasons for the adoption of quarter vehicle model, but in so doing, the issue of modeling accuracy has to be tolerated or dealt with through control methods that are robust to uncertainties. This is the description of current scenario. The truth is, the use of quarter vehicle model in vehicle analyses has always received mixed views. The major supportive view is that this model is used due to model simplicity , 20. AccWhile the lack of accuracy for quarter vehicle model is probably true, this concern is unfortunately often accepted without further explorations. Lumped-mass vehicle models with greater DOFs usually receive decent attention in terms of model accuracy, as demonstrated by various dedicated validation studies –6. IroniIn this study, vehicle modeling details are taken to be the test subjects. Although the typical lumped-mass quarter vehicle model is highly simplified to the point that some features simply cannot be incorporated to the model, there are still various areas that can be enhanced by the corresponding modeling details. Referring back to the schematic model in The first description is related to road input. Among the four modeling details stated above, road input is the only detail that is external to quarter vehicle model. Strictly speaking, road input is not part of the model, but it is definitely part of the entire two-DOF system that is to be simulated. In fact, it is commonly known that there are three elements associated with a typical vehicle dynamic simulation, with vehicle and road being two of them . Road input is still included as one of the details, as it is the only direct input to a quarter vehicle system and is logically capable of affecting the output or vehicle response. For this study, a transient input emulating the scenario of a vehicle being driven across a bump was chosen as the road input. The most elementary but commonly used representation of this scenario is the step profile which was used in the base quarter vehicle model for reference. A possible enhancement can be achieved through the use of ramp profile as the road input detail. This detail is a much more realistic representation of a bump as it is highly reminiscent of an actual trapezoidal-shaped bump. For further illustration, the exact mathematical representation of both road profiles used in this study are shown in Meanwhile, for tire component, the usual modeling approach for a typical linear quarter vehicle model is to represent the vertical tire property by linear tire stiffness, assuming constant point contact with the road and also without tire damping. This formed the basis of tire modeling for the base model in this study for comparison with the enhancement. The tire detail is in the form of the addition of linear tire damping alongside the existing tire stiffness, similarly with constant point contact assumption. Actually, more involved vertical tire modeling using non-linear tire properties can possibly be added as part of the detail; however, the presence of tire damping in a quarter vehicle model is put into focus here as the expectation is that tire damping should have direct influence on vehicle response, particularly the unsprung mass response. In fact, tire damping is a subject that has received mixed views, with study that goes for its inclusion in vehicle modeling and study that mentions its insignificance . ConsideFinally, for suspension modeling of a quarter vehicle model, the suspension details consist of these two: the stiffness detail and the damping detail. These are seen as two separate details in this study. For suspension stiffness, the base model employed the common approach of using linear or constant stiffness value as the representation, while the enhanced model adopted stiffness detail in the form of non-linearity of the overall suspension stiffness contributed by the inclusion of suspension bushing property. In reality, the property of a physical suspension spring is generally linear, and the basic modeling approach of using linear stiffness value (constant spring rate) is probably sufficiently close. Consequently, instead of focusing on the rather insignificant non-linearity of the suspension spring, the overall non-linear stiffness due to inclusion of bump-stop and rebound-stop definitions was taken as the suspension stiffness detail. For clarity, the exact stiffness profiles adopted in the study are shown in With four modeling details in mind, the effect as well as the significance of these details on vehicle response can primarily be evaluated in the study by comparing between the base quarter vehicle model and several enhanced models with the addition of each detail individually. However, to ensure comprehensiveness, the study considered all possible cases involving single and combined addition of details. Following basic factorial design, with four factors to be investigated (modeling details) and each consisting of two states (with or without the inclusion of detail), a total of 16 combinations were possible for analysis. These possible cases, together with the description of the states of various modeling details, are summarized and stated in As observed from ® / Simulink®, to obtain 16 sets of vehicle response for subsequent analysis.In the study, the vehicle parameter values were extracted from the specifications of a generic vehicle available from a commercial vehicle simulation software. The vehicle data set refers to a general mid-sized passenger vehicle which can be treated as the typical vehicle representation in most situations. The parameter values relevant to quarter vehicle model are listed in After the completion of computation for all cases, the generated results were compiled for comparative analysis here. Results are in the form of vehicle response in time domain for front and rear quarter vehicle models. As a quarter vehicle model comprises two DOFs only, both sprung and unsprung mass responses are used as the basis for the few comparisons first mentioned in the preceding section. Apart from qualitative evaluation, comparisons are also made quantitatively by considering some derived result parameters. Considering the transient nature of the responses, particularly for sprung mass, several transient response parameters, namely rise time, peak time, maximum fractional overshoot and settling time are considered in the comparisons. In addition, three RMS result parameters commonly used for suspension performance evaluation in a typical study involving quarter vehicle model, namely RMS sprung mass acceleration, RMS dynamic tire load and RMS suspension travel, are also considered. The resulted data is presented in The first comparison involves the cases associated with the addition of individual modeling detail to the base quarter vehicle model, namely case 2 (road input detail), case 3 (tire detail), case 4 (suspension stiffness detail) and case 5 (suspension damping detail). By treating case 1  as the reference, this comparison provides information regarding the effect brought by the inclusion of each of these modeling details. Judging from the responses shown in While it is clear that road input detail has an effect on the simulated vehicle response, the same cannot be said for tire detail. With the inclusion of tire damping alongside tire stiffness, the effect due to tire detail is insignificant, at least for the sprung mass. Referring to the same figure, the sprung mass response (case 3) is almost identical to the reference (case 1). The effect due to tire damping is actually present in the unsprung mass, as can be seen from the huge increase in RMS dynamic tire load 185% in  which isMeanwhile, the effect of having suspension stiffness detail is a mixed one. For instance, the rear sprung mass response (case 4) is almost identical to the reference (case 1), but the front sprung mass response exhibits visible difference, judging from the increased overshoot  and alsoFinally, for suspension damping detail, the effect of having non-linear damping is comparable to that achieved by road input detail, as the use of non-linear damping can possibly change the fundamental characteristic of the responses. To illustrate, the rear sprung mass response (case 5) belongs to the over-damping response type, with no overshoot and extremely long rise time which are very different from the reference (case 1). For the front sprung mass, the under-damping response characteristic remains, but the response still exhibits lower overshoot with a much shorter settling time that hints at a much higher damping effect than the reference. The different front and rear response characteristics due to different damping profiles make it difficult to generalize the effect of suspension damping detail to a common trend. However, it can still be said that these observations have good correspondence with the general non-linear damping profile, with very high damping within the initial range of working velocity and much lower damping beyond that . It is tAs already mentioned, the effects due to the inclusion of tire damping and non-linear suspension stiffness are largely influenced by the types of road input, and they are probably better evaluated also with the much more realistic ramp road input apart from step road input. This calls for the second comparison which is among some selected cases with combined addition of modeling details. Specifically, cases 6 and 7 are put into focus in this comparison as they refer to the situations of having tire detail and suspension stiffness detail respectively, both with road input detail simultaneously. For meaningful comparison, case 2, with only road input detail present, is now the reference. The relevant results are displayed in the form of derived result parameters  instead The result parameter values in So far, the comparisons carried out have proven that the various modeling details do have effects on the response of a quarter vehicle model, although their magnitudes vary. However, strictly speaking, the analysis up to this point is limited to the quantification of the effect, and little is known regarding the portion of model accuracy contributed by these details. In this section, a comparison that is complementary to the previous ones is made in an attempt to determine the contribution of accuracy made by each of the four modeling details. This is carried out from a different perspective by using reverse deduction, that is, how much the response deviates from reference (most detailed representation) when each detail is taken away, obviously with the core assumption that the closer a model is to the physical representation, the more accurate the response will be. Consequently, this comparison involves cases 12, 13, 14 and 15 as they can be reversely interpreted as having the suspension damping detail, suspension stiffness detail, tire detail and road input detail omitted from the fully-featured model in case 16 which serves as the reference here. The vehicle responses for the said cases are shown in Based on the percentage differences of the result parameters, it is very clear that road input detail contributes most to the accuracy of the sprung and unsprung mass responses. In qualitative terms, with the removal of road input detail, the unsprung mass response is much sharper due to the harsh step road input, while the sprung mass response can have different characteristics depending on the front and rear non-linear damping profiles. Overall, the change in responses (case 15) relative to the reference (case 16) is of similar magnitude to the corresponding observation in earlier section ‘Evaluation based on individual detail’, so the finding here is basically consistent to the information from previous comparisons. By switching between the basic step road input and the refined ramp road input, the change in vehicle response remains fundamental regardless of the influences from other modeling details.The second largest model accuracy is contributed by the suspension damping detail, judging from the overall solid percentage differences stated in Meanwhile, both tire detail and suspension stiffness detail seem to contribute very little to the accuracy of vehicle response. For example, the omission of tire damping records only single-digit percentage differences for all evaluated result parameters . GraphicAt this point it is worth to make an overall evaluation. The importance or significance of a modeling detail is basically constituted by the magnitude of the effect brought by the detail as well as the accuracy contribution from it. Inferring from the outcomes of various comparisons up to this point, it can be said that road input is the most significant detail to a quarter vehicle model, as its presence changes the vehicle response very fundamentally and makes the greatest difference in terms of accuracy. Road input aside, suspension damping detail is also of similar significance as the detailed non-linear damping representation is capable of giving vastly different response characteristics, and this is both notable and consistent. Conversely, on the other side of thing, suspension stiffness detail and tire detail are much less significant when quarter vehicle model is concerned. The former’s presence, although capable of making a difference to the response, is only felt conditionally. More often than not, it gives no contribution to accuracy. Lastly, the latter, in the form of the addition of tire damping, is also very insignificant to quarter vehicle modeling as its presence has little effect and accuracy contribution, especially for sprung mass response which is usually the focus for ride-related studies employing this model. Together, these inferences give knowledge on significance to allow more informed decision to be made between the inclusion and exclusion of a particular detail in quarter vehicle modeling.In this section, additional evaluations are carried out regarding possible incremental modeling detail addition, as well as possible further refinements to the modeling details already introduced. For the former, the suspension damping detail is put into focus because it is acknowledged that there are many intermediate states between the linear and fully non-linear damping that are also commonly adopted, including the linear but asymmetrical damping  and the more involved piece-wise function modeling approach which are definitely worth being evaluated.For this further evaluation, the comparison is made among several suspension damping representations with increasing refinement. In total, four representations are considered: while the basic linear damping and the fully non-linear damping considering lookup table approach have already been introduced, two other damping representations, namely linear but asymmetrical damping and the two-piece, piece-wise damping modeling are considered here. These are the intermediate states that sit between linear and non-linear damping. For asymmetrical damping, the damping effect can still be seen as linear, but it is a step forward with different damping rates for the jounce and rebound directions. Meanwhile, the piece-wise damping is another step further by approximating the non-linearity of damping profile using two-piece mathematical function for each direction, giving a semi-linear representation closer to the actual non-linearity. To clarify further, these two damping representations, together with the linear and non-linear damping already known, are illustrated in In this comparison, the two newly introduced damping representations are seen as incremental details and are referred to as cases 17 and 18 which is simply a continuation from the existing nomenclature. Case 17 refers to the addition of asymmetrical representation as the suspension damping detail while case 18 refers to the use of piece-wise modeling as the detail. Consistent to the incremental nature, the comparison is done in a sequential manner, following the order of no damping detail or linear damping (case 1), with asymmetrical damping as detail (case 17), with piece-wise damping representation (case 18) and finally with fully non-linear damping using lookup table representation as the detail (case 5). Because each is a step superior to the immediate previous one, the accuracy improvement can be determined for each successive incremental detail by evaluating the vehicle responses and the relative percentage differences which take the immediate previous case as the reference. The relevant results are shown in As expected, the sprung mass response changes with every incremental damping detail. Basically, it goes towards the direction of higher damping effect with every incremental step, and this is consistently observable for both front and rear responses. Correspondingly, because a quarter vehicle model has only two DOFs, the other mass, namely the unsprung mass, has response that is more oscillatory with the same successive damping detail increment. The justification for these observations is again the same as that described in previous comparisons. The basic linear damping (case 1) is linearized from the original damping profile and has a constant damping rate which is overall less as it averages the non-linearity. The asymmetrical damping (case 17) introduces slightly lower damping rate in jounce direction but notably higher damping rate in rebound direction, which is a more correct representation. For both piece-wise (case 18) and fully non-linear (case 5) representations, because of the division of each direction into two sections with the initial part having much higher damping, they are obviously the most correct representations in this comparison. Therefore, it is not surprising that in a general way, each increment in detail is loosely associated with higher damping effect. The more interesting observation here, however, is how close the vehicle responses are between cases 18 and 5. From Meanwhile, the second evaluation in this section evaluates the possibility of further refinements to the existing modeling details. Of the four modeling details that are present in the fully-featured quarter vehicle model in case 16, the suspension stiffness and suspension damping details, which involve the fully non-linear representations, are basically very well-defined. In contrast, for road input detail and tire detail, there is still some room for further refinement. For road input detail, within the context of transient event involving a vehicle hitting a bump, it is possible to have a closer-to-reality representation by adopting a smooth ramp profile based on sinusoidal definition, as in Judging from the results in Lastly, both cases 19 and 20, together with case 16, are compared against case 1 for an overall evaluation between these group of fully-featured quarter vehicle models  and the basic, linear quarter vehicle model. In general, improvement in model accuracy concerning vehicle simulation is desirable because it is expected that such model enhancement will eventually lead to superior vehicle suspension performance. In the design and development of controllable vehicle suspension, such as an active suspension system , the lesAs a final thought, while it is demonstrated that the inclusion of modeling details leads to improved accuracy in the predicted vehicle response, it is worth to discuss the difference between this and similar accuracy improvement brought by the use of vehicle models with greater DOFs. Basically, the inclusion of various vehicle modeling details increases the fidelity of the model within the same DOFs and brings the model closer to the physical representation. Meanwhile, adopting a vehicle model with greater number of DOFs opens the possibility for more features of a vehicle to be incorporated, which potentially improves the accuracy. These are two different approaches to more accurate vehicle modeling. Therefore, although the inclusion of modeling details does bring improved accuracy, additional DOFs, such as the roll, pitch, bending and torsional motions of the vehicle body, need to be incorporated when vehicle responses related to these motions are concerned. On the other hand, for purely vertical vehicle dynamic analysis or vehicle ride analysis, the use of a fully-featured quarter vehicle model with all the possible modeling details added means that meaningful quantitative vehicle analysis with a simple model becomes viable now.To sum up, the outcomes of this study have shown that various modeling details associated with a quarter vehicle model simulation do have effect on vehicle response, albeit to different extents. In particular, road detail changes the response fundamentally, damping detail affects the response significantly and consistently, stiffness detail similarly affects the response albeit only conditionally, while tire detail has rather insignificant effect. Interestingly, for non-linear damping modeling, the vehicle response due to piece-wise approximation approach is sufficiently close to fully non-linear representation approach, to the point that the former actually demonstrates a better compromise between significance and modeling convenience. Overall, a fully-enhanced quarter vehicle model with all the details added is a significant improvement compared to the base model. Looking at these outcomes, it is certain that the commonly adopted basic quarter vehicle model still has a lot of untapped potentials. In fact, a better trade-off between model simplicity and model accuracy can be readily achieved through the inclusion of the significant modeling details. Although this study does not reveal anything about the absolute or global accuracy of quarter vehicle model, it does convey an important message: that it is not all about the number of DOFs when it comes to vehicle modeling; it is also about the non-DOF-related details that are equally significant. By quantifying their significance, this study equips researchers the knowledge to decide the inclusion or exclusion of a modeling detail when using quarter vehicle model in their related work.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.


Molecular dynamics simulations of nanometric cutting on monocrystalline germanium are conducted to investigate the subsurface deformation during and after nanometric cutting. The continuous random network model of amorphous germanium is established by molecular dynamics simulation, and its characteristic parameters are extracted to compare with those of the machined deformed layer. The coordination number distribution and radial distribution function (RDF) show that the machined surface presents the similar amorphous state. The anisotropic subsurface deformation is studied by nanometric cutting on the (010), (101), and (111) crystal planes of germanium, respectively. The deformed structures are prone to extend along the 110 slip system, which leads to the difference in the shape and thickness of the deformed layer on various directions and crystal planes. On machined surface, the greater thickness of subsurface deformed layer induces the greater surface recovery height. In order to get the critical thickness limit of deformed layer on machined surface of germanium, the optimized cutting direction on each crystal plane is suggested according to the relevance of the nanometric cutting to the nanoindentation. In recent years, the accuracy and the dimension of ultra-precision machining have reached nanoscale along with the development of science and technology. A grasp of deformation mechanism in the material during nanometric processing becomes essential to achieve higher surface finishing and damage-free subsurface. Monocrystalline germanium, a group IV elemental semiconductor, has been widely used in the fields of solar cell, infrared optics, and so on. As it has the periodic ordered arrangement of diamond structure, which is similar to silicon, the anisotropy feature of germanium during nano-machining should be paid more attention to. In fact, the mechanism of subsurface deformation and material removal of single crystal is strongly influenced by the crystallographic orientation.A number of studies have been carried out to investigate the crystal orientation effects during the single-crystal machining. Komanduri et al. , 2 studiIn the present study, molecular dynamic simulations of nanometric cutting on germanium are conducted to investigate the subsurface deformation during and after machining. The cutting directions include several combinations of orientation and plane, and the structures in detail at the atomic level are disclosed and computed accordingly. The relationship between the structure of deformed subsurface and crystal orientation is observed and analyzed. In order to get the thinnest subsurface deformed layer, the machined directions on specific planes of germanium are suggested at the end of this study.The three-dimensional MD simulation model consists of the germanium substrate and a diamond tool, as shown in Fig. To investigate the effect of crystal orientation on the subsurface deformation in nanometric cutting, three typical crystallographic planes including the 010), (101), and (111) faces are designed as the machined surface and the cutting directions are shown in Fig. 0, (101),Many researchers have found that monocrystalline silicon underwent amorphization in nanometric cutting and nanoindentation by MD simulation and experimental study , 10–14. a × 30a × 30a (a = 5.657 Å) and with a periodic boundary condition. After relaxation at initial 293 K, germanium is heated to 4500 K slowly, which is much higher than the melting temperature of monocrystalline germanium in MD simulation so that the germanium presents liquid state. After that, the workpiece is cooled to room temperature (293 K) quickly for imitating the quenching and then relax the model for a while. Thus, the stable amorphous germanium is modeled. As the time span is limited in simulations, the cooling rate can be high enough to get amorphous germanium. In addition, the temperature mentioned above is calculated in the simulation and cannot be compared with the real condition directly. The melting temperature of germanium in MD simulation with Tersoff potential is about 3300 K  direction on the (010) surface, the serious deformation is observed in the region beneath the tool, which is proved to be amorphous structure. Previous study showed that a large area of phase transformation from diamond cubic structure to β-tin-Ge was obviously observed in the subsurface region of nanoindentation on the (100) plane by MD simulation . HoweverWhen the cutting direction is along the [101] direction on the (010) plane, most of the germanium atoms neighboring beneath the tool present amorphous state. Unlike the subsurface deformation with the cutting direction of [010], the bct5-Ge structure is observed under this high-pressure region, as shown in Fig. According to the preceding analysis, the machined region forms an amorphous layer with a certain depth. The transformed region extends mainly along the mulation , 24. AllFigure Figure Figures , on the 1 plane. The thickness of deformed layer and the surface recovery height when cutting on various lattice planes are measured in this study. Since the machined surface is not flat because the form of three-dimensional tool would print as the cut mark, the thickness of deformed layer is defined as the distance from the lowest position of the surface, namely, the middle of the cut mark, to the deepest location of the deformed layer in workpiece. Assume the bottom of the tool contact closely to the materials, the surface recovery height is defined as the distance from the bottom of the tool during cutting to the middle position of cut groove after machining. In order to obtain the details of subsurface deformation when cutting along different orientations, the thickness of deformed layer and surface recovery height of machined surface are measured from 17 equally spaced cross sections of machined surface, which are perpendicular to the cutting direction.Figure  surface . During Generally, the controllable surface recovery is highly desirable in the ultra-precision machining in order to ensure that the machined surface is as close to the designed forming as possible. In nanometric cutting, processing in the nanometer range and extremely high surface accuracy are needed. The uncontrollable surface recovery may be fatal to the surface integrity, which would be counterproductive to the goal of achieving controllable nanometric cutting. Therefore, less deformed layer on machined surface is required so as to get the high surface accuracy when cutting on monocrystalline germanium in nanoscale directly.Usually, nanoindentation is used to study the mechanical properties of materials in nanometer scale, such as nano-hardness and phase transformation under stress , 22, 24.Generally, the thicknesses of subsurface deformation are different from each other with various combinations of cutting crystal plane and orientation in nanometric cutting of monocrystalline germanium because of its anisotropy. Thus, a large number of simulations or experiments may be needed for investigating the relative depth of subsurface deformation with cutting directions, which is time-consuming. According to the analysis above, the relative depth of subsurface deformation when nano-cutting along different directions on the monocrystalline germanium can be obtained from the transformed phase distribution of the subsurface with nanoindentation on the same crystal plane with a spherical indenter, instead of extremely large numbers of simulations or experiments on nanometric cutting. That is, the larger extending range of transformed phase on the subsurface around a certain direction in nanoindentation, the greater thickness of deformed layer would occur with nano-cutting along the same direction on the same crystal plane of germanium. Thus, it helps to select the appropriate cutting direction considering the demands for the thickness of deformed layer in nanometric cutting of monocrystalline germanium. For example, in order to get the machined surface with the thinnest thickness of deformed layer in nanometric cutting, the cutting directions of 100 on the (010) crystal plane, 010 on the (101) crystal plane, and Compared with the CRN model of amorphous germanium, the RDF and coordination number distribution show that the machined surface of germanium presents the similar amorphous state.The subsurface deformed structures of germanium after nanometric cutting tend to extend along the 110 slip system. The surface recovery height increases with the increment of thickness of subsurface deformed layer on machined surface.The thickness of subsurface deformed layer on the machined surface varies with different cutting orientations. According to the analyzed relevance of subsurface deformation in nanometric cutting to nanoindentation, nanometric cutting along the 100 direction on the (010) crystal plane, 010 direction on the (101) crystal plane, and The MD simulations of nanometric cutting on the (010), (101), and (111) planes of monocrystalline germanium are carried out in this study. The CRN model of amorphous germanium is established to contrastively analyze the structure of germanium on the machined surface. The anisotropic behaviors in subsurface deformation are investigated and the conclusions are as follows:


There are a great variety of joint types used in nature which can inspire engineering joints. In order to design such biomimetic joints, it is at first important to understand how biological joints work. A comprehensive literature review, considering natural joints from a mechanical point of view, was undertaken. This was used to develop a taxonomy based on the different methods/functions that nature successfully uses to attach dissimilar tissues. One of the key methods that nature uses to join dissimilar materials is a transitional zone of stiffness at the insertion site. This method was used to propose bio-inspired solutions with a transitional zone of stiffness at the joint site for several glass fibre reinforced plastic (GFRP) to steel adhesively bonded joint configurations. The transition zone was used to reduce the material stiffness mismatch of the joint parts. A numerical finite element model was used to identify the optimum variation in material stiffness that minimises potential failure of the joint. The best bio-inspired joints showed a 118% increase of joint strength compared to the standard joints. E/ρ) and strength-to-weight (σ/ρ) ratios. However, joining is a key issue in the mechanical design of composite parts due to the structural discontinuity that joints cause. This can be a source of unreliability, a factor critical in the aerospace and automotive sectors. Adhesive bonding is a popular method for joining dissimilar materials because this can produce joints with higher structural efficiency, excellent fatigue life, a particularly small weight penalty and more uniform stress fields than alternatives such as fastening or riveting. Additionally, corrosion between the dissimilar materials is prevented [In recent years, the use of composite materials in automotive and aerospace industries has shown an upward trend due to their good stiffness-to-weight  propeller blades. World-leading manufacturers of integrated propeller systems use CFRP-to-steel joints to attach the CFRP blade to the steel hub. Applications range from regional airliners  and military airlifters  to marine hovercraft (Textron Systems’ Landing Craft Air Cushion (LCAC) hovercraft). Additionally, composite structures are used in piping systems with applications in a wide range of industries , where composite materials are an attractive alternative to metals considering the extreme environments that the piping systems are exposed in for onshore or offshore applications . Since jBiomimetics uses ideas from nature to inspire engineering solutions. In the context of joining, nature has developed a wide range of solutions for joining of many different materials and geometries, which have the potential to inspire more robust and efficient joints in engineering applications. This paper expands the conference proceedings published in , includicomprehend and analyse the functions and the structure of biological joints;identify the features that may be transferred from biological to engineering joints;devise the most favourable joint configuration that will highlight the identified features by considering the available technology and materials;use the available technology, materials and the devised joint configuration to design optimised mechanisms for the specific engineering application.The biomimetic design approach cannot consist of just copying the designs of nature because of the significant differences between natural and engineering materials. Thus, several biomimetic design reviews exist, focusing on a variety of engineering challenges where nature has provided inspiration ,18,19,20To understand how to optimise biomimetic engineering joints, first it is important to understand how biological joints “work”. Thus, This section contains a review of natural joints. Both effectively rigid joints and joints which provide relative motion between parts are considered. The findings from the review are discussed in Joining methods found in nature have been classified into five different groups depending on the different joining method used: Network structures, transitional zones of stiffness, bridging connections, hooks and adhesive joints. Examples for each of these types of joint are described below.Network structures use complex geometric arrangements in order to join materials. Two examples are described here: root structures where the soil and plant components have very different mechanical properties and tree joints where the elements being attached have the same material properties.Roots are the first structure that develops in a growing plant. Root networks provide an ingenious anchorage and stability system ,23, and pinus radiata. They concluded that, despite the brittleness of the cellulose constituent of the natural wood composite, the failure mode of the tree joints was ductile. From an X-ray tomography study conducted on the branch-trunk joint [The idea of a continuous fibre flow pattern from one part of the joint to the other can be found in abundance in tree joints. The non-articulated joints that exist in trees have to withstand a combination of static and dynamic loads, including self-weight, snow and wind loading. Burns et al.  tested bnk joint , three kThe embedded design consists of a cone-shaped branch end that is embedded and enclosed in the main trunk. This type of joint has the advantage of increasing the effective joint load transfer area and thus reducing the stress acting on the joint interface. Moreover, any interfacial cracks are forced to grow in mode II (shear) rather than in mode I (tension) and thus the toughness is increased. The 3D fibre lay-up is made from trunk fibres that extend forward and laterally to the joint and thus they fully enclose the branch, leading to a “ball and socket” joint configuration. Finally, fibre density variation leads to the creation of an iso-strain condition in the joint by reducing the elastic modulus mismatch between the fibres aligned with the branch and trunk directions. Burns et al.  used theThe attachment of dissimilar materials is a major challenge due to the high levels of stress concentration that arise at their interface. As an alternative to geometric complexity, microstructural changes within the joint can give changes in stiffness across the interface to alleviate this stress concentration. Such transitional zones of stiffness are typified by the tendon-to-bone attachment and the mussel anchoring system described below. Another example is the hard jaws of marine polychaete worms, which anchor to soft cuticles and the ligaments at their base . The jawThe tensile modulus of tendon in the direction of the muscle force is 200 MPa while it buckles in compression. By contrast, bone has a tensile modulus of 20 GPa in both tension and compression . To avoiFour discrete types of tissue can be recognized in the tendon-to-bone insertion site under an optical microscope . These aTwo major factors contribute to the tissue stiffness increase from the tendon to bone material. Firstly, the linear increase in mineral concentration in collagen fibres stiffens the partially mineralized collagen fibres ,43. Secomytilus edulis mussel thread depends on the nature of the substratum [One of the main defence mechanisms of mussels is their anchoring system, which is achieved by byssus threads . Byssus bstratum . The adhbstratum .The byssus thread consists of two mechanically district regions; the proximal region, which is highly extensible and wrinkled, and the less extensible and smooth distal region . Each reWhile the above examples have been concerned with more-or-less rigid joints, there are many situations in anatomy where relative movement between components is needed, particularly but not always associated with locomotion. These joints typically use bridging connections, for example ligaments, to provide the joining mechanism. But as well as movable joints, there are immovable joints which also use bridging connections to form the joint. The following examples from the human anatomy illustrate the range of solutions that nature provides in these situations. There are three primary types of joints in the human body, fibrous , cartilaginous  and synovial (freely moveable) .Fibrous joints have collagen fibres that span the space between the parts. A gomphosis is an immovable fibrous joint attaching tooth roots to the alveolar sockets in the jaw bones. The fibrous periodontal ligaments bridging the gap consist of connective tissue of collagen fibres .Sutures are another form of immovable fibrous joint that connect two stiff skeletal components to each other via a thin layer of a dense fibrous connective tissue , and thus provide flexibility to accommodate growth, respiration and/or locomotion ,55,56,57The nail is an opalescent window through to the vascular nail bed . AnchoriA syndesmosis is a partially movable type of fibrous joint connecting two bones together by an interosseus membrane (ligament that holds two bones together) . SyndesmCartilaginous joints are partly moveable joints, where the bones are connected to each other by pads of either fibro cartilage or hyaline cartilage . There aSynovial joints are highly movable joints and they are the most common classification of joints within the human body . They alThe most well-known biomimetic example inspired by nature itself is the invention of Velcro fasteners . It was evarcha arcuate [In legged insects/animals the main way to obtain reaction forces, and thus locomotion, on various substrates is by the attachment organs. This plays a more significant role when animals move on steep, vertical or even inverted substrates, where adhesive forces are needed to prevent them from falling down . Gecko T arcuate ) to adhe arcuate ,107.These attachment organs can be classified into claws, hairy pads and soft smooth pads ,109. ClaInsect wings have to withstand a combination of bending and torsional deformations during flight. Wing deformability is of significant importance for the flight performance of insects and can define their flight capabilities ,126. WooAccording to Fauziyah et al. ,139, draThe literature survey above has described a range of different natural joints, divided into different joining methods. A theme common to a wide range of systems is how nature uses structural and material complexity to ensure effective anchorage and stress dissipation in the joint site. Parallels between different natural joints can be found related to this theme.There are many examples where nature uses complex architecture, taking advantage of the way that it can build in complexity from the bottom-up generation of structures. Such complexity can serve to increase the structural efficiency of the joint and reduce the material investment, since this comes with a biological cost. The majority of the material serves other functions apart from the load-carrying requirement . Thus, iThe root and tree network structures typify an obvious structural complexity, with the root structure serving both a joining function and providing a mechanism to draw water and nutrients from the soil. Looking at the gecko lizard, it relies on a complex hierarchical structure for the adhesive properties of its feet. Structural complexity is similarly found in the tendon-to-bone attachment with bony spicules radiating in all directions to facilitate load transfer. Even on a larger scale, tendons and ligaments take advantage of structural complexity by not forming an isolated attachment onto a bone, but instead blending several overlapping attachment sites to produce more stable anchorage . In AchiAn additional strategy is to introduce geometric complexity in the form of scalloping at the interface to increase the bonding between tissues. This approach is used for both the dentino-enamel junction and the tendon-to-bone attachment .A closely related way of increasing joint efficiency in nature is to use microstructural or material complexity, again using the sophisticated generation routes available for natural materials.The tree trunk branch offers a botanical example of such an approach, using variations in fibre density to give an iso-strain condition in the joint. Moreover, the transition zone solutions used in tendon-to-bone and mussel attachments take this material complexity further by using significant changes in local material composition and microarchitecture to ensure a smooth load transition and shock-loading capability. Similarly the dentino-enamel junction uses a mineral content gradient to increase the interfacial strength .Both natural and man-made structures require joining of materials with severe property mismatches. There are two options in engineering to avoid interfacial failure in these circumstances. Firstly, the interaction energy can be increased across the interface. This is achieved by surface treatment (primers and coupling) of the metal adherends prior to bonding  or throuIn summary, a biomimetic solution using a transitional zone of stiffness offers the potential to provide a robust and efficient joint for engineering situations where there is a large material stiffness mismatch. The challenge is to take these ideas from nature and to adapt them to practical engineering joints. This is what the next section aims to do.The idea of a transitional zone of stiffness between dissimilar materials used by natural joint designs is applied in this section to adhesively bonded single-lap, double-lap and hybrid joints. The aim is to evaluate the hypothesis that using the bio-inspired design strategy of a transitional zone of stiffness across the overlap length of GFRP to steel joints can increase the strength of the joints.The present study was triggered by the positive results obtained in previous work by the authors, where a numerical investigation of carbon fibre reinforced plastic (CFRP) to steel single lap joints (SLJ), using materials with linear elastic properties in the numerical models, was carried out . The prol/t) less than 5, the scarf joints showed a 65% to 150% increase of joint strength compared to the single-lap joints. However, when l/t was around 10, the failure strength of the single-lap joints exceeded that of scarf joints.One way to achieve the stiffness variation in the overlap region of engineering joints is to gradually decrease the stiffness of the metal part of the joint by perforating it. The concept of reducing the stiffness of a steel plate using perforations was firstly proposed and patented by Unden and Ridder . RelatedThe novelty of the present study is that a numerical finite element model is used to identify the optimum variation in material stiffness which maximises the strength of the joint. The assumption is that such an approach can be realised in practice using a steel perforation pattern a or a no1GFRPE = 20 GPa. The Young modulus of the steel material was taken as 200 GPa and the Poisson ratio as 0.28. The proposed solutions offered a transitional zone of stiffness in the overlap region (OL) of the metal part to reduce the material stiffness mismatch at the joint site. Different sets of variable stiffness functions were investigated to optimise the material stiffness variation, identifying the stiffness function which minimises potential failure of the joint. The stiffness E(x) of the metal part was varied as a function of the position x along the OL of the joint, from a minimum value of ESmin at the left end, to a maximum value of ESmax at the right end of the joint. The value of ESmax was held fixed at 200 GPa, while ESmin was chosen to take values of 10, 20, 40, 70 or 100 GPa. The variation within the overlap between these extreme stiffnesses at the two ends was described using parabolic and s-shaped functions, with parameters a and b defining their shape as described in detail in the Materials and Methods Section below. It is believed that, in practice, non-linear scarf joints can be more reliable than the perforated steel configuration when the minimum stiffness of the steel (ESmin) has to reach very low values (ESmin/ESmax less than 10%).ux was applied to the steel end of the model together with a lateral restraint.The composite part of the joints was modelled as a unidirectional GFRP material with material properties given in x within the overlap region between the extreme stiffnesses at the two ends was described using parabolic and s-shaped functions as defined by Equations (1) and (2), respectively.cx is the overlap length equal to 75 mm. The locations with x = 0 and cx = 0.075 correspond to the left and right end of the overlap length, respectively. The parameters a and b defining the shape of the curves were spaced logarithmically. These stiffness variations were chosen for their simplicity to investigate the effect of the transitional zone of stiffness on the joint strength. Future research should include approaches such as topology optimisation to identify the best stiffness variation case. a and b. The user subroutine “USDFLD“ in Abaqus was used to implement this stiffness variation. For comparison, reference joints were modelled with the same configurations but without any stiffness variation.The stiffness variation as a function of position ESmin and b shape parameter are plotted and compared with the reference configuration without stiffness variation in the OL. The horizontal axes are separated into three parts, each section describing one of the joint configurations. The horizontal axes show the minimum stiffness (ESmin) as a percentage of the maximum stiffness (ESmax) in the steel part of the joint within the reduced-stiffness overlap length, corresponding to the different values of ESmin considered. Thus a value of ESmin/ESmax equal to 50% corresponds to ESmin equal to 100 GPa, while a 10% value relates to calculations where the steel was reduced down to the stiffness of the GFRP adherend (20 GPa) at the end of the overlap region. A set of curves giving the variation of strength with stiffness reduction are given for the chosen range of values of the parameter b defining the shape of the variation in stiffness through the OL. For comparison with the proposed bio-inspired joints, the maximum loads of the “REF” reference joints  are included on a defining the stiffness variation.s-shaped stiffness variation functions give higher (or similar) joint strengths compared to parabolic stiffness variation functions with the same stiffness range. SLJs with the stiffness in the overlap varying from 10 to 200 GPa  and following the s-shaped function with a = 1 show a 32% increase of the maximum load compared to the reference joints. On the other hand, there is a 118% and 100% strength increase for DLJs and hybrid joints comparing to the reference joints, respectively, for the optimum stiffness variation. These increases in strength for the GFRP-to-steel joints are comparable with measured increases of 175% for perforated CFRP-to-steel joints [From l joints  and betwl joints . Similarl joints , althougESmin/ESmax equal to 10%; 1GFRPE = ESmin) and following the parabolic stiffness distribution for different values of the b shape parameter. Both the reference and bio-inspired joints show a linear response until the maximum load is obtained. As the b shape parameter increases, the joints fail at a higher load , bio-inspired joints showed a 118% increase of joint strength for the best case.The strength increase depends significantly on the form of stiffness variation within the overlap region.The potential for increased strength is greater in the double lap and hybrid joints, compared to the single lap joint.A numerical investigation of bio-inspired joints with a transitional zone of stiffness between GFRP and steel adherends has been undertaken to show the potential of such joints in engineering. An optimisation procedure was carried out to identify the material stiffness variation within the steel overlap region which gives the joint with the highest strength. According to the results, the follow conclusions can be drawn:


The segmentation of a high spatial resolution remote sensing image is a critical step in geographic object-based image analysis (GEOBIA). Evaluating the performance of segmentation without ground truth data, i.e., unsupervised evaluation, is important for the comparison of segmentation algorithms and the automatic selection of optimal parameters. This unsupervised strategy currently faces several challenges in practice, such as difficulties in designing effective indicators and limitations of the spectral values in the feature representation. This study proposes a novel unsupervised evaluation method to quantitatively measure the quality of segmentation results to overcome these problems. In this method, multiple spectral and spatial features of images are first extracted simultaneously and then integrated into a feature set to improve the quality of the feature representation of ground objects. The indicators designed for spatial stratified heterogeneity and spatial autocorrelation are included to estimate the properties of the segments in this integrated feature set. These two indicators are then combined into a global assessment metric as the final quality score. The trade-offs of the combined indicators are accounted for using a strategy based on the Mahalanobis distance, which can be exhibited geometrically. The method is tested on two segmentation algorithms and three testing images. The proposed method is compared with two existing unsupervised methods and a supervised method to confirm its capabilities. Through comparison and visual analysis, the results verified the effectiveness of the proposed method and demonstrated the reliability and improvements of this method with respect to other methods. The ultimate goal of remote sensing is to mirror, elucidate, quantify, and describe surface patterns to contribute to the understanding of the underlying phenomena and processes . In recePartitioning an image into spatially contiguous and relatively homogeneous regions, also known as image objects or segments, is a key step of the GEOBIA approach ,7. The rThe existing strategies for evaluating segmentation quality can be divided into five categories: subjective evaluations, system-level methods, analytical methods, supervised evaluation methods, and unsupervised evaluation methods . The mosSupervised evaluation methods, also referred to as empirical discrepancy methods or relative evaluations methods, are designed to quantitatively measure the dissimilarity between segmented images and manually segmented reference images to assess the performance of segmentation algorithms. In other words, these methods attempt to determine how different the segmented image is from the ground truth, which is derived from expert interpretation ,14. SeveUnsupervised evaluation methods, also referred to as empirical goodness methods or stand-alone evaluation methods, evaluate the performance of segmentation algorithms without the need of reference images. Unsupervised evaluation judges segmented images with certain quality criteria that were established according to human perception . As the Many unsupervised approaches for remote sensing images have been presented in the literature. Stein and De Beurs used complexity metrics to quantify the semantic accuracy of image segmentations of two Landsat images . ChabrieIn previous studies, the global intra- and inter-segment indicators were combined to assign an overall goodness score to the segmentation in most unsupervised evaluation methods. However, the design of effective indicators, reasonable combination strategies, and operation domains remain challenging for unsupervised methods. This study proposes a novel unsupervised evaluation method that can overcome these difficulties. Based on characteristic criteria, spatial stratified heterogeneity and spatial autocorrelation serve as the indicators that are calculated on a spectral-spatial feature set. These indicators are then combined into a single overall evaluation metric for scoring and ranking multiple segmented images. Different from previous studies, this paper makes the following contributions: (1) it captures a feature set to describe image objects in both the spectral and spatial domains; (2) designs a new composite evaluation metric that accounts for spatial stratified heterogeneity to measure intra-segments; (3) devises a reasonable indicator combination strategy based on the Mahalanobis distance; and (4) validates the evaluation method using results from multiple segmentation algorithms targeting different types of landscapes.The remainder of the paper is organized as follows: An optimal image segmentation result is supposed to satisfy the principle that maximizes intra-segment homogeneity and inter-segment heterogeneity. According to the characteristic criteria of unsupervised evaluation methods discussed in The majority of the existing unsupervised evaluation methods in the literature attempt to use the original spectral features as the basis for calculation, which is effective if each primitive object has a uniform spectrum . Howeveri and j are pixel indexes of the raw image, x is the coordinate of the current pixel to be filtered, I is the intensity value and The feature representation should be a good fit to the human visual perception of the objects. Given within-object variation or a complicated texture, the original intensity values from remote sensing images are not suitable for direct use as spectral features. A bilateral filter is applied to extract the spectral feature to remove such within-object variation while maintaining the boundary information. The bilateral filter is a non-linear, edge-preserving and noise-reducing filter for images that can smooth an input image while preserving its edges. The bilateral filtering kernel pression :(1)WijGu,v are significantly different, suggesting high inter-segment heterogeneity. The Global Moran’s I  in the The most commonly used distance metric is the Euclidean distance. However, the Euclidean distance is sensitive to the scales of the variables involved. The Euclidian distance assumes that each variable of the data point is equally important and all variables are measured in the same units. The scale problem that is inherent in Euclidean distance can be solved by defining dissimilarity measures with the Mahalanobis distance , which iThis paper presents three existing segmentation evaluation methods for comparison. Two of the methods are composite unsupervised measures and follow the characteristic criteria that include two metrics to measure the intra-segment uniformity and inter-segment disparity. These methods, and how they combine the two metrics, are summarized in E, is built, which additively combines both the layout entropy The first method is an entropy-based evaluation method proposed by Zhang et al. . This meT and the heterogeneity part D, where the former is modified from the h, The second measure is the so-called g et al. . Two meti et al. :(10)T(I)The Adjusted Rand Index (ARI) is a supervised evaluation method proposed by Huber and Arabie , which iThe notations E and ARI on the segmentation results from two segmentation algorithms to compare both the various parameterizations of one segmentation method as well as fundamentally different segmentation techniques.This paper implements the evaluation methods The multi-resolution segmentation (MRS) algorithm is based on the fractal net evolution approach (FNEA) . The MRSMean-shift segmentation (MSS) is a robust and adaptive clustering algorithm that uses non-parametric density estimation . MSS shihttp://www.outex.oulu.fi).To compare the difference between the feature set and original image used as input data for the proposed evaluation method, two synthetic images, named S1 and S2, respectively, were created for testing . These oThe reason for using the synthetic image is that its ground truth is available, and the reference segmentation results conform to reality. Therefore, the experimental results can accurately reflect the difference between the original image and feature enhanced image by comparing them with the ground truth. In addition, the effectiveness of feature set is further validated by remote sensing images.To verify the effectiveness of the proposed method in remote sensing image segmentation, a study area was selected in the northern part of the Beijing central zone, China . The study area includes abundant urban landscapes. A WorldView-3 scene of this area that was acquired on 3 September 2014 was used as the experimental data. The image contains information in the NIR, red, green, and blue spectral bands. The spatial resolution of the image was increased from 1.6 m to 0.4 m using the Gram-Schmidt pan-sharpening method  for a beIn the experiments of testing the effectiveness of feature set, three types of base images were involved: original images, feature enhanced images and the ground truth. Reference segmentation boundaries were overlapped on these base images where the indictor In the experiments of verifying the effectiveness of the proposed metric produced . The othBased on the original images, feature enhanced images and ground truth, the proposed evaluation method was performed on the reference segmentation of testing images. The evaluation results can be seen in the As indicated by  metrics . SpecifiBoth MRS and MSS segmentation were performed at 20 scales, ranging from level 1 (over-segmentation) to 20 (under-segmentation) to assess the effectiveness of the proposed measure across the remote sensing images. Two segmentation results of each testing image, corresponding to scale 2 and scale 19, are displayed in The changes in the The The combined indicators were further evaluated by comparing existing evaluation methods to assess the effectiveness of the proposed method, as presented in Specifically, for T1 and T3, the value of The variation tendency of To quantitatively compare the performance of In addition to determining the optimal parameters, the Visual analysis was applied for further comparison of the two segmentation methods based on the roof c, which the roof d. The obfs in T3 b are not(1)In the experiments, (2)As a significant indicator in geostatistics, the introduced spatial stratified heterogeneity can successfully indicate the intra-segmentation property, as demonstrated by (3)The effectiveness of the (4)n, the computational complexity described using big O notion is OThe main factor that affects an evaluation method’s use of computational resources is the number of segments. Analyzing each evaluation method with an input-data size Several issues need to be further discussed. (1)Although the spectral-spatial feature used in the proposed method is advantageous for representing real objects, the method of constructing feature models and the choice of extractors still could be optimized. In addition, the strategy used to stack the spectral and spatial features involves simple combination. A more sophisticated strategy could be developed that might extract features more efficiently and accurately.(2)Scale is important for the interpretation of remote sensing images and is an important parameter of the segmentation algorithms. This paper only focuses on the optimal choice of the scale parameter in segmentation quality evaluation. The universality and robustness of the proposed method should be verified for the other segmentation parameters.(3)The experiment only tested three sub-images from the same WorldView-3 scene. However, in practices of GEOBIA, it is necessary to evaluate the integrated image segmentation results, which may consume a large amount of computing resources. Thus, to increase efficiency, small and randomly selected sub-images could be used as samples to evaluate the segmentation results of a large-scale image.Future studies should address the following aspects:A novel unsupervised method is proposed for evaluating the segmentation quality of VHR remote sensing images. This method uses a multidimensional spectral–spatial feature set as the feature image, which is captured from a raw image using a bilateral filter and a Gabor wavelet filter. Based on this integrated feature set,


As excess water is discharged from a high dam, low frequency noise  is generated and propagated in the surrounding areas, causing environmental hazards such as the vibration of windows and doors and the discomfort of local residents. To study the generation mechanisms and key influencing factors of LFN induced by flood discharge and energy dissipation from a high dam with a ski-jump type spillway, detailed prototype observations and analyses of LFN are carried out. The discharge flow field is simulated and analyzed using a gas-liquid turbulent flow model. The acoustic response characteristics of the air cavity, which is formed between the discharge nappe and dam body, are analyzed using an acoustic numerical model. The multi-sources generation mechanisms are first proposed basing on the prototype observation results, vortex sound model, turbulent flow model and acoustic numerical model. Two kinds of sources of LFN are studied. One comes from the energy dissipation of submerged jets in the plunge pool, the other comes from nappe-cavity coupled vibration. The results of the analyses reveal that the submerged jets in the plunge pool only contribute to an on-site LFN energy of 0–1.0 Hz, and the strong shear layers around the high-velocity submerged jets and wall jet development areas are the main acoustic source regions of LFN in the plunge pool. In addition, the nappe-cavity coupled vibration, which is induced when the discharge nappe vibrates with close frequency to the model frequency of the cavity, can induce on-site LFN energy with wider frequency spectrum energy within 0–4.0 Hz. By contrast, the contribution degrees to LFN energy from two acoustic sources are almost same, while the contribution degree from nappe-cavity coupled vibration is slightly higher. As a majority of high dams built in recent decades or projected in China have been with the features of high water head, big flood-discharge capacity, deep narrow valley and large flood-discharge power, issues such as energy dissipation and scour protection, vibration control for hydraulic structures, atomization protection and aeration in cavitation protection, have received considerable attention and abundant technological achievements have resulted ,2,3,4. RJapanese scholars have carried out some research on the flow-induced LFN. Because Japan is a densely populated country and many hydropower stations are located closed to residents’ living quarters, the hazards of LFN were first observed in Japan. Most research has been focused on the LFN induced by the oscillating nappe, which is formed when the flood is discharged through a weir, and its adverse impact on the surrounding buildings and inhabitants. The induced LFN can produce squeaking noise of doors and windows in the surrounding areas and cause psychological problems of inhabitants such as insomnia, dysphoria and chest congestion ,8. In adThe engineering objects in these past studies have the common characteristics of low water heads, small flow rates and simple flow regimes, and the LFN is induced by relatively continuous nappe. As for the hydraulic projects with high water heads, large flow rates and complex flow regime which dissipate energy by ski-jump type spillways, the previous theories cannot be directly applied. Moreover, LFN energy still can be observed on site in the conditions with single discharge orifice opening or several nonadjacent orifices opening, although the continuous nappe does not exist. Therefore, new research should be done on the generation mechanisms of LFN induced by flood discharge from the high dam by ski-jump type spillways and resulting energy dissipation.In order to reveal the generation mechanism and key influencing factors of LFN induced by flood discharge and energy dissipation from high dams with ski-jump type spillways, a multi-sources generation mechanism is put forward based on the prototype observation results, vortex sound model, turbulent flow model and acoustic numerical model. Two kinds of sources of LFN are studied. One comes from the energy dissipation of submerged jets in the plunge pool and is studied through a vortex sound model and turbulent flow model, the other comes from nappe-cavity coupled vibration and is studied based on the finite element method coupled boundary element method (FEM/BEM). Analyses on the degree of contribution of the multiple sources to the LFN energy are also made according to the prototype observation results. The results in this study should provide reference data, a theoretical basis and an assessment method for the environmental harm from LFN induced in flood-discharge engineering of high-dams equipped with ski-jump type spillways.The Jinping First Stage Hydropower Station is an important controlling cascade built on the downstream main stream portion of the Yalong River. The station consists of a water-retaining structure, flood discharge and energy dissipation structures and a power generation system. The water-retaining structure is a concrete double-curvature arch dam with the maximum height of 305 m, which is the highest in the world . The totSince Jinping First Stage Hydropower Station began to discharge floodwater, Tianjin University has organized frequent prototype observations of LFN. The on-site LFN observation equipment consists of an infrasound microphone, multi-channel digitizer and computer. The infrasound microphone operates in the frequency range of 0.1–300 Hz with a sensitivity of 150 mv/Pa. The multi-channel digitizer connects the microphone with the computer, which supplies power to the microphone and saves the data at high speed. The digitizer has a built-in GPS, so it can work well in the open air.The observation points are distributed along the river valley from the dam area to the downstream location which is approximately 1.25 km away from the dam body. The number of observation points is 12 in total p only contain the vorticity variable eduction , G can bIn the acoustic theory, the acoustic wave equation can be expressed as:The acoustic Helmholtz equation can be deduced from taking the Fourier transform of the Equation (7) and be expressed as:i’ in the equation denotes the i-th node and the subscript ‘a’ indicates that the items in the equation is about acoustic system.When using the acoustic FEM, the acoustic matrix equation for finite element analysis can be written as:i-th order acoustic modal shape of the cavity; Acoustic mode is a unique property of the air medium ,24, whicFurthermore, the acoustic direct BEM can be used to calculate the acoustic field distribution in the cavity . The velPast studies have indicated that the ent flow ,27. Its d Orszag , can sim Nichols  in 1975  Nichols . So the Basic equations of turbulent flow:Gas-liquid VOF equation:The numerical turbulent flow model established is a 1:1 scale simplified arch dam of Jingping, as shown in As for the boundary conditions, the upstream inlet of the reservoir and the downstream outlet of the plunge pool are set as the pressure inlet and pressure outlet, respectively. The top boundaries of the model and the both sides of nappe area are set as air pressure inlets with the normal atmospheric pressure. Other boundaries are set as no-slip wall. The time step size of unsteady flow calculation is set to 0.001 s. The calculation is considered to be completed when the deviation of mass flow rates between inlet and outlet is less than 0.1%.The analyses of the LFN generation mechanisms have been separated into three parts. The multi-sources mechanisms are introduced basing on the prototype observation. Then two kinds of mechanisms have been analyzed. One comes from energy dissipating submerged jets in the plunge pool and is studied through vortex sound model and turbulent flow model, the other comes from nappe-cavity coupled vibration and is studied based on finite element method coupled boundary element method (FEM/BEM).The spatial distribution of the LFN along the downstream area is analyzed. The relation between the observed LFN intensity and flood discharge capacity is analyzed. The amplitude of LFN is found to not increase in direct proportion to Q. A parameter is set as P/Q for further analyses, where P is the root mean square (RMS) of the LFN amplitude. The PSD curves of LFN are calculated to analyze the frequency-domain characteristics. It is found that LFN data observed with different flow regimes has different characteristics. The results of prototype observation indicate that LFN is induced during flood discharge and multi-sources generation mechanisms make contribution to induce the LFN. In this study, we propose that the LFN are induced by two kinds of sources. One comes from energy dissipation of submerged jets in the plunge pool, the other comes from nappe-cavity coupled vibration. In this section, the former source will be analyzed first.The calculation of turbulent flow is validated by the flow regime, nappe trajectory distance and water-entry velocity. Due to the space limitations, only the numerical results of several typical discharge conditions are shown, such as Conditions 2 and 6.In this study, free surface of water in the flow field is determined by air volume fraction of 0.6. The trajectory distance and water-entry velocity of the discharge nappe are the key parameters in the safety problem for hydraulic structures. The theoretical equation for nappe trajectory distance, which has considered internal turbulent diffusion, aeration and the influence of air resistance , can be In actual calculation, the bucket angles . The VFF of energy dissipation field should be analyzed. The correlation between vortex motion and far-field sound pressure can be revealed and the location of effective acoustic source region of the LFN can be estimated by analyzing VFF. The VFF data have been extracted from numerical simulation and analyzed in time and frequency domain. The PSD curves in The analyses in 3, and the velocity of sound (The 3D finite element model of the cavity behind the nappe jets in Condition 6 has been established through ANSYS software, basing on the cavity shape simulated in The modal frequency of first order is 0, which is the rigid modal. According to In this section, the LMS Virtual. Lab Acoustics software is adopted to analyze vibration response of the cavity. The boundary element model is formed through importing the finite element grid model into the acoustic module. As it can be seen in Furthermore, 30 prediction points have been set in different location of the cavity to evaluate the acoustic field of the cavity behind the nappe jets, as it can be seen in The frequency response functions of acoustic pressure and acoustic pressure level data of all these points has been overlapped in The multi-sources mechanisms of LFN generated in the flood discharge and energy dissipation of ski-jump type of a high dam have been revealed by the analyses above. In this section, the contributions of different mechanisms to the LFN energy of prototype will be calculated. The LFN energy consists of the energy caused by submerged jets in plunge pool and nappe-cavity coupled vibration. The equation can be expressed as:In In this study, the results of prototype observation indicate that LFN is generated during the flood discharge and energy dissipation of a high dam with a ski-jump type spillway. The LFN intensity attenuates at different rates in different distances away from the dam. The LFN observed in the conditions with adjacent orifices opening has wider energy distribution and several peak frequencies within 0–4 Hz, which indicates that multi-sources generation mechanisms make contribution to induce the LFN during the flood discharge of Jinping First Stage Hydropower Station.The generation mechanism for LFN induced by submerged jets has been studied basing on the numerical simulation of the turbulent flow. The VFF data is extracted from the numerical results and analyzed in time and frequency domain. The comparison between the data of VFF and prototype observation indicates that the LFN induced by submerged jets only contribute to 0–1 Hz LFN energy on site, and the strong shear layers around high-velocity submerged jets and wall jet development area are the main acoustic source regions of LFN in plunge pool.The generation mechanism of LFN induced by nappe-cavity coupled vibration is analyzed by FEM/BEM method. The results of acoustic modal and acoustic field calculation reveals that the coupled vibration of nappe-cavity contributes not only to the acoustic power that within 0–1 Hz, but also to the power higher than 1 Hz, which explained the acoustic power with frequency within 1–4 Hz observed in prototype observation.The results in this study suggest that both kinds of LFN generation mechanisms have approximate contribution degrees, while the contribution of nappe-cavity coupled vibration is a little higher. We conclude that two kinds of mechanisms contribute to the LFN induced by flood discharge and energy dissipation of the ski-jump type spillway of a high dam. One is the mechanism of vortex of submerged jets in plunge pool, and the other is the mechanism of nappe-cavity coupled vibration. In additions, the conditions with more adjacent orifices opening uniformly have been found effective to reduce the LFN intensity according to the results of prototype observation. Therefore, we suggest more adjacent orifices to be opened uniformly in a certain discharge capacity during the operation period of the dam. Nevertheless, the mathematical model to exactly calculate the LFN pressure has not been proposed. Further investigations should focus on the quantitative forecast of the LFN induced by flood discharge and energy dissipation of the ski-jump type spillway of a high dam.