2010 Vol. 36, No. 10

Display Method:
Numerical simulation on dynamic stability of pressure reducing regulator in integral bipropellant propulsion system
Chen Yang, Cai Guobiao, Zhang Zhenpeng, Xia Jixia
2010, 36(10): 1135-1139.
Abstract:
A finite volume transient model of a high pressure unloading pressure reducing regulator (PRR) with diaphragm, which is used in a integral bipropellant propulsion gas system, was established. Based on this, a modularization numerical model of a characteristic research system for PRR was established. Then aiming at the instabilities observed during testing operation, the influences of several structural and control parameter on the stability of PRR were clarified by a series of numerical simulation. Those measures which can improve the dynamic stability include:reducing the mass of valve spool, increasing the volume of high-pressure chamber or low-pressure chamber, increasing the damping coefficient of springy elements material, reducing the size of feedback orifice, increasing the stiffness of diaphragm. The comparison with the experimental and simulation results in earlier literature confirms the effectiveness and feasibility of some measures.
Approach of pilot modeling for predicting pilot control behavior
Tan Wenqian, A.V.Efremov, Qu Xiangju
2010, 36(10): 1140-1144.
Abstract:
During the process of aircraft design, the mathematical model of pilot control behavior characteristics is always used to predict aircraft flying qualities.This is one of the important methods to avoid pilot-aircraft adverse coupling. The pilot neural networks (NN) model was derived from experimental data obtained during pilot-aided tests using a special workstation. For a set of different aircraft dynamics configurations, which had different amplifications and different short period mode natural frequency, the pilot control behavior characteristics in the single-loop longitudinal pitch tracking task were studied based on neural networks model. The result shows that pilots have similar control behavior for similar aircraft dynamics configurations. Therefore, an approach used pilot control behavior of similar aircraft configurations to build a pilot model to predict pilot control behavior of new configuration was suggested. This pilot model-s precision was further calculated. And the result verifies applicability of this new approach for pilot predicting modeling.
GPS signal fast acquisition method aided by inertial information
Lin Heng, Zhang Qiusha, Yang Gongliu, Zhu Lufeng
2010, 36(10): 1145-1148.
Abstract:
The signal acquisition time affects the performance of global positioning system (GPS) receiver directly under high dynamic conditions. Based on the analysis of traditional acquisition method aided by external information, an improved fast acquisition method was proposed which was aided by inertial information and ephemeris supplied by GPS/inertial navigation system (INS) integrated navigation system. This new method was composed of coarse acquisition and fine acquisition,of which the implementation method and acquisition performance were analyzed. The acquisition algorithm was validated in efficiency by MATLAB/Simulink system-level simulation and Monte Carlo test. The simulation results show that when C/A code resolution is ensured and high carrier frequency resolution is obtained using this new method, the acquisition time can be reduced obviously so that the acquisition performance of high dynamic GPS receiver can be improved. Compared with the conventional GPS signal acquisition method, the total acquisition time can be reduced to 2%~3%.
Gyroscope aided feature matching method in vision navigation
Xu Chao, Fan Yaozu, Shen Xiaorong
2010, 36(10): 1149-1152.
Abstract:
In order to solve the problem of feature points mismatching when there is no camera platform in vision navigation, a gyroscope aided points matching method was proposed. The relationship between the output of gyroscope and the coordinate changes of features was built. The nearest cross-correlation method and bidirectional matching algorithm was adopted to perform the point matching and matching result verification respectively. The sub-pixel matching result was obtained by interpolation. The error sources of the matching method were analyzed. The effect of the gyroscope output and the focus length calculation errors among them was calculated. The experiment of real scene proved that, the proposed method has much improvement in accuracy over scale invariant feature transform (SIFT), and it also has a better practicability for it does not need any other equipment except the existing ones.
Lag-delay robust string stable control of platoon of automated vehicles
Gao Feng, Xiao Lingyun, Wang Jiangfeng
2010, 36(10): 1153-1157.
Abstract:
Based on the vehicle longitudinal lag-delay dynamics model, the string stability and the control strategies for the automated platoon of vehicles were analyzed and studied. The vehicle longitudinal lag-delay dynamics model was built under consideration of the time delay and time lag. The sliding model controller and proportion integration differentiation(PID) controller were proposed based on the constant time headway policy. Then, the analysis of string stability for the two controllers were conducted based on the string stable policy and the related string stable conditions were obtained. The comparative quantitative analysis and simulations- analysis demonstrates that the PID controller is more robust against the time delay and time lag.
Flight loads analysis of flexible aircraft under large deformations
Pan Deng, Wu Zhigang, Yang Chao
2010, 36(10): 1158-1161.
Abstract:
A flight loads analysis framework was devised to consider the geometrical nonlinear effect and the surface aerodynamic effect for flexible aircraft. The structure consisted of joined nonlinear Euler beams allowing arbitrarily large deformations, while the lifting surface model employed span-wise and chord-wise vortex ring lattice. The core algorithms were to dynamically modify the aerodynamic influence coefficient matrix by the surface lattice associated with deformations, and to iterate the computation until the deformations converged. The proposed method was applied to two models. The results for small deformations agree with the linear method, whereas for large deformations, a significant variation has arisen due to the surface aerodynamics. This approach proved to be more accurate than the conventional linear method under large deformations, and feasible for engineering analysis.
Preliminary experimental investigation on nitrous oxide/propane igniter
Wang Dong, Guo Hongjie, Liang Guozhu, Liu Yin
2010, 36(10): 1162-1165.
Abstract:
To investigate the ignition characteristics of nitrous oxide/propane, the torch igniter scheme of N2O/C3H8 was proposed initially. An igniter was designed and manufactured, and the experimental system was designed. The hot-tests under different condition of mass flow and excess-oxidizer coefficient show that the scheme is feasible, injector structure is reasonable, the spray quality and the excess-oxidizer coefficient are the key for successful ignition, and the igniter is able to generate multiple ignition and produce ignition torch successfully within the excess-oxidizer coefficient range 0.222~0.321. The experiment offers reference for the further study and establishes the foundation for achieving N2O/C3H8 motor ignition directly by this igniter.
Numerical simulation of atomization of liquid jet in supersonic crossflow
Liu Jing, Xu Xu
2010, 36(10): 1166-1170.
Abstract:
Liquid jet atomization in supersonic crossflow was simulated using Euler-Lagrangian method. Euler method was used for gas phase and Lagrangian method was used for liquid phase. The liquid influences were calculated by source items in gas equations. The atomization process was simulated using the hybrid atomization model. This model was improved according to the atomization mechanism and experimental results. The improved simulation results were compared with Taylor analogy breakup (TAB) model and Reitz wave model. The calculation results agree well with the experiment results. It is found that the advanced hybrid atomization model is much more suited for the current calculation than the other models.
Modeling and performance analysis of multiple-antennae communication channel for pilotless helicopter
Tan Zheng, Zhang Xiaolin
2010, 36(10): 1171-1175.
Abstract:
A statistical channel model for the pilotless helicopter multiple-antennae communication was derived based on the single-antenna aeronautical channel model. Characteristics of delay spread, Doppler spread and angular spread were discussed. Mask effect of fuselage and interference of the multiple-antennae were researched. An effective and accurate simulation model was derived from the proposed model. Simulation methods for delay power spectrum, spatial correlation, Doppler spectrum and mask effect of fuselage were presented respectively. Numerical simulations of single-antenna and multiple-antenna channel were carried out under three flying conditions: reroute, circled, taking off and landing. Good performance of differential space-time code was confirmed through simulation. The model is useful for the modulation/coding design of pilotless helicopter multiple-antennae communication system.
Statics analysis on the leg of water strider robot
Wang Shuhui, Wu Licheng
2010, 36(10): 1176-1179.
Abstract:
As a bionic robot of the water strider, water strider robot stays afloat and stride on water surface relies on surface tension provided by the legs. Statics analysis could be used to calculate the robot-s load capacity and then to define the criterions for designing the supporting leg. A static model of the supporting leg was built first and the surface-breaking condition, namely the condition for getting maximum surface tension, was analyzed. Then the methods for calculating the supporting force and the maximum allowed depth that the leg pushes the water were proposed respectively. Utilizing the proposed model and methods, the curves between surface tension and contact angle of several kinds of materials were figured by using of the Matlab program. The supporting force and the maximum allowed depth of the leg with several kinds of materials were calculated. The validity of the proposed models and methods were verified by comparing the calculation with some experimental values.
Improved immune algorithm and applications on function optimization
Sun Xuegang, Yun Chao, Cui Yihui
2010, 36(10): 1180-1183.
Abstract:
A novel eccentric dynamic immune clone algorithm (EDICA) was proposed based on the analysis of antibody behavior features in existed clone selection algorithm (CSA). Heuristic information implicates that descendant antibodies are always better than their parents during evolution, which derive an eccentric mutation strategy, and let the mutation center shift a proper distance along the direction which is from parent to descendant, antibodies may search towards optima more quickly. A dynamic mutation radial adjustment method was proposed with some introduced control factors. The search speed was accelerated by enlarged mutation radial at initial stage. Then the search granularity was gradually diminished so as to improve optimization precision at later stage. A hyper sphere chaos mutation strategy was adopted to avoid the adverse effects of anisotropy and ensure the ability to successfully find global optima. Experiment results show that the EDICA could not only accurately discover most optima of static function but also hit and follow optima of dynamic function with high precision.
On the high stress gradient and failure analysis of dovetail attachments
Wei Dasheng, Wang Yanrong
2010, 36(10): 1184-1188.
Abstract:
Studies reveals that high stress gradient exists near the edges of contact in dovetail attachment, of which the numerical solution to contact stress depends on finite element (FE) mesh density. So a set of FE models with different mesh of dovetail attachment were used to analyze the effect of FE modeling on improving the solving accuracy of contact stress. Then the effect due to elasticity and plasticity of materials was discussed. On the basis of elastic-plastic contact stress, a fracture model on the part with high stress gradient was established by means of fracture mechanics, which can be used to determine the direction of crack initiation and propagation and more to evaluate the structural strength and lives.
Structure selection and parameter set-membership identification for nonlinear systems
He Liqing, Sun Xianfang, Qiu Hongzhuan
2010, 36(10): 1189-1193.
Abstract:
Based on support vector regression and radial basis function (RBF) neural network, the set-membership identification for nonlinear systems with unknown-but-bounded noise was investigated. The relationships among the ε-insensitive parameter, noise bounds and the number of support vectors were deduced, and the method of determining the ε-insensitive parameter using the noise bounds was introduced. The algorithm of choosing the scale of RBF neural network via support vector regression was described, in which the Gaussian kernel function was taken as the radial basis function and the support vector as its center parameters. After the structure of the RBF neural network was determined, all the feasible weight vectors of the RBF neural network were found by the optimal bounding ellipsoid (OBE) algorithm and a class of feasible nonlinear models were formed which were consistent with the given noise bound series and the input-output data set. A simulation example shows that the proposed algorithm is effective.
Sliding mode control based on proportion allocation for over-actuated saucer-shaped aircraft
Zhang Youan, Wu Yinsheng
2010, 36(10): 1194-1198.
Abstract:
In order to avoid some actuators saturation in advance, a proportion control allocation strategy was proposed in over-actuated saucer-shaped aircraft under position limits. The proportion was defined by the lower and upper position limits of the actuators. With the strategy, the system with two inputs was changed into one with single input, and the appearance of some actuators saturation in advance was avoided. The actuator dynamics and the uncertainty of the aerodynamic coefficients of the system were considered. A sliding mode control law was designed. The weighting matrix of the pseudoinverse control allocation was determined by comparison between proportion control allocation and pseudoinverse control allocation. Simulation results show that the proposed method is right and effective.
Analysis on electrostatic levitation of lunar dust on the Moon's light side
Li Wen, Cui Yi, Wang Jun, Zheng Weilin
2010, 36(10): 1199-1202.
Abstract:
The electrostatic charging process of lunar dust particulate on the moon-s light side was modeled based on particle orbit theory and charging equation of space dusty plasma. Assuming a Maxiwellian distribution of photoelectron energies, the formulae of strength of vertical electric field as well as photoelectron density in a photoelectron sheath were derived. By means of the Newton-s law of motion and electrostatic force equation, the dynamic model of electrostatic levitation for lunar dust grain on the moon-s light side was derived. The dynamic behavior of levitating dust grain on the moon-s light side was numerically analyzed. The results show that the basic controlling parameters for the onset of levitation and dynamics of the levitating particulate are the solar elevation angle and dust grain radius. The electrostatic levitation of lunar dust occurs during sunset and sunrise above the lunar surface. The smaller the dust grain size, the higher the vertical displacement of dust grain due to electrostatic levitation on the same environmental condition.
Novel evaluation method of time base distortion of nonuniformly sampling data acquisition systems
Liang Zhiguo, Meng Xiaofeng
2010, 36(10): 1203-1206.
Abstract:
By using both the time base differential non-linearity and integral non-linearity,a novel method to evaluate the time base distortion is presented, which deal with the nonuniformly sampling data acquisition systems. By using sinusoidal stimulating, and then re-sampling the data to create sub-series of each sub-A/D converter, through curve-fit results of sub-series sinusoidal waveforms, the phase difference between two sub-series was obtained. The time difference corresponding the phase difference is the sampling time delay between two sub-A/D. Their consistency is the time base distortion of nonuniformly sampling systems, which can be expressed in time base difference non-linearity and time base integral non-linearity. In simulation test, the correctness of the method was validated. In practical experiment on a digital storage oscilloscope, the feasibility of the method was proved. The method above can be use to evaluate the time base distortion of nonuniformly sampling data acquisition systems.
Modeling of emergency management in altitude simulation testing with Petri net and its application
Ma Feng, Qiu Wanhua
2010, 36(10): 1207-1212.
Abstract:
An emergency management workflow strategy was constructed for altitude simulation testing, and a Petri net model of the strategy was modeled. The model mainly comprises an urgency stop program and a crisis stop program. The urgency stop program is aimed to ensure safety of the tested engine and the testing facilities, simultaneously, is got attention to quickly stop, so it is basically composed of some stages in series. But the crisis stop program is targeted for a quick response, therefore, its various stages is principally in parallel. By analyzing the model, it was demonstrated that the model is reachable, sound, with free choice, well-structure, and S-coverable characteristics. According to the Petri net model, an emergency management for an aero-engine in altitude simulation testing was trained, and the response time was obtained in each stage. Key stages that effect the response time of emergency management were found in the crisis stop program of emergency management operation by analyzing the time data. In the follow, it was found that maximum benefit come from a compromise between ensuring safety of tested engine, testing facilities and the response time according to emergency event level in the urgency stop program. Modified emergency program and training effectively reduced the emergency response time in the key stage.
Glass forming ability and thermal stability of Zr-Al-(Ni-Cu) alloys
Zhang Jing, Zhang Tao
2010, 36(10): 1213-1216.
Abstract:
Glass forming ability (GFA) of Zr-Al-(Ni-Cu) alloys with different Ni and Cu element contents was studied by injection copper mold casting method. Structures of the as-cast alloys, sliced along the cross-section, were identified by X-ray diffraction (XRD). Thermal properties of the bulk metallic glasses (BMG) were analyzed by differential scanning calorimetry (DSC). Results reveal that the critical diameters for glass formation of the ternary Zr-Al-Ni and Zr-Al-Cu alloys were highly improved by the coexistence of the similar elements (elements with similar atomic sizes and chemical properties) Ni and Cu in the quaternary Zr-Al-(Ni-Cu) alloys. For the Zr65Al7.5Ni10Cu17.5 alloy, which is the best glass former in the studied alloy system, BMG rod of 7mm in diameter was successfully synthesized. It is suggested that the significant improvement of GFA is attributed to the increase in the entropy and the decrease in free energy of the Ni and Cu substituted alloy systems.
Influence of boron and carbon on the shrinkage defects of TiAl alloys
Gao Yong, Yang Lili, Zheng Lijing, Zhang Hu
2010, 36(10): 1217-1220.
Abstract:
Alloys whose nominal compositions were Ti-47Al-2Cr-2Nb, Ti-47Al-2Cr-2Nb-0.8B and Ti-47Al-2Cr-2Nb-0.1C were vacuum induction skull melted. Ingots were produced by pouring the molten alloys into a room-temperature graphite mold. Chemical compositions of ingots obtained were analyzed respectively. Microstructure as well as shrinkage cavity and porosity were also investigated with stereo microscope and scanning electron microscope (SEM). The results indicate that Ti-47Al-2Cr-2Nb alloy shows an intense columnar-growth tendency, and shrinkage porosity distributes dispersedly in the center zone around axis of ingot. Microstructure is refined and the columnar-growth tendency is weaken with the addition of 0.8% boron (atomic fraction). Shrinkage porosity becomes more concentrated to form a cavity in the center zone of ingots, and the density and size of micro porosity also decrease. However, the addition of 0.1% carbon (atomic fraction) doesn-t result in any apparent effects in terms of shrinkage porosity or microstructure compared to ingots without any additive.
Detection of Australian southeast forest fire using HJ satellite
Li Jiaguo, Gu Xingfa, Yu Tao, Wei Bin
2010, 36(10): 1221-1224.
Abstract:
By detecting forest fire happened in Australian southeast from remote sensing imagery to demonstrate the application ability of HJ-1B satellite in disaster. After analyzing the character of HJ-1B IRS B07 system parameters and data trait, a normalized forest fire index, Ku, was constructed. Pixels are potential fore fire points where Ku are greater than 0.40. Cloud dazzling points and surface high-temperature points are the main noises disturbing the fire point detection. MODIS 250m spatial resolution band 1 and band 2 were used to get normalized difference vegetation index(NDVI) for the lack of HJ-1B data earlier than the fire happened date and its results are suitable for the forest fire detection. The compare of detection results by HJ-1B and moderate-resolution imaging spectroradiometer(MODIS) fire product, MOD14, shows that HJ-1B is better than MOD14 on presenting fire spatial structure for the reason of its higher spatial resolution, 300m.
Change estimation of damage with acoustic emission nonlinear behavior model
Wang Hongwei, Luo Hongyun, Han Zhiyuan, Zhong Qunpeng
2010, 36(10): 1225-1228.
Abstract:
An acoustic emission nonlinear behavior model which consists of acoustic emission (AE) cusp and review model was established, which can estimate the changed time at which the state of 16Mn steel was changed from elastic deformation to yield deformation. Firstly, some preliminary changed time at which the state of 16Mn steel plate specimen might be changed from elastic deformation to yield deformation was estimated with AE cusp model. Next, all preliminary changed time was rechecked by the review model, and the analytical changed time from elastic deformation to yield deformation of 16Mn steel was obtained. The experiment results show that the analytical changed time which was estimated by acoustic emission nonlinear behavior model was ahead of the actual time which was estimated by the load-time curve. Therefore, the acoustic emission nonlinear behavior model is helpful to monitor the safety and reliability of 16Mn steel structure on line.
Bias and scale factor drift modeling methods for accelerometers
Huang Xiaokai, Chen Yunxia, Kang Rui
2010, 36(10): 1229-1233.
Abstract:
Engineering data modeling methods and their application features were summarized, Combine with the accelerometer bias and scale factor drifting law of experimental measurements in storage conditions, bias time series analysis method and scale factor regression methodology were established respectively, and the detailed steps were also given. The bias and scale factor data of a certain accelerometer was given at last, and the drift values have been predicted via the presented method. The relative error between the prediction values and the measured data was small enough compared with the given acceptance level 10%, which shows the efficiency of the presented methods. The drift models reflect the bias great randomness drift feature and scale factor variation tendency description in true situation, and the accelerometer bias and scale factor drift models can not only be used in parameter exploration and drift compensation, but also provide long term stability assessment technique for the accelerometer bias and scale factor.
Standardization benefits assessing model of complicated production development program
Hu Qianhong, Chu Hengzhi, Liang Defang, Lü Juan
2010, 36(10): 1234-1238.
Abstract:
To quantify the benefits of standardization calculation,highlight the important role of standardization, the accounting method of the standardization work weight was determined, and the standardization work system and benefits index system were established. By analyzing the characteristics of the standardization of complex product development program, studying deeply on the mathematic model of standardization benefit assessing method, preparing the questionnaire survey of total benefits and collecting related data, mathematic model of standardization benefit assessing method for complicated production development program was established. Mathematic model of assessing method for complicated production development program in aviation areas was built by this method. Real data collected from China’s aviation program was used to validate veracity of assessing method.
Effect of temperature on corrosion and scaling of galvanized steel pipe in simulated geothermal water
Wu Kunhu, Li Weiping, Liu Huicong, Zhu Liqun
2010, 36(10): 1239-1243.
Abstract:
Steel pipe corrosion and scaling is a universal problem in the geothermal water environment. Scanning electron microscopy (SEM), energy dispersion spectrometry (EDS) and X-ray diffraction (XRD) were used to study the corrosion and scaling behavior of galvanized steel pipe in a simulated geothermal water environment with different temperatures. Results indicate that there are two kinds of microcosmic appearance ("ball" like and "needle" like) on the surface of galvanized steel pipe in the forepart of experiment. The shape of corrosion and scaling crystals is different at different temperatures. The main components of corrosion and scaling products are Zn(OH)2,ZnO,CaCO3 and MgCO3, and they could restrain the further corrosion of galvanized steel pipe in the geothermal water. The area of corrosion pit of galvanized steel pipe is small at 50℃, and which is big at 65℃ and 80℃. The corrosion and scaling of galvanized steel pipe accelerates as the temperature increases.
Operation mode design of multi-FOV star sensor
Ye Shenglong, Wei Xinguo, Fan Qiaoyun, Zhang Guangjun
2010, 36(10): 1244-1247.
Abstract:
Two operation modes, namely high precision operation mode and high update operation mode, were designed in view of the characteristics of the multi-filed of view(FOV) star sensor. The central timing controller accomplish its operation mode configuration according to the instructions and starts image acquisition and processing module in the appropriate timing. With the timing characteristics of operation mode, the multi-FOV image fast centroid extraction in two operation modes was achieved by designing in field programmable gate array (FPGA) three centroid extraction modules, which implement simultaneously with their own corresponding image acquisition modules. The operation mode configuration and data update rate were tested on the experimental platform which was designed based on FPGA, with IBIS5-A-1300 of Cypress as the image sensor. Results show that the star sensor can be configured and switched normally and flexibly through the instructions, and that the data update rate is up to three times of that of the traditional star sensor.
Improved 3-D real-time trajectory planning algorithm for UAV
He Pingchuan, Dai Shuling
2010, 36(10): 1248-1251.
Abstract:
It is of vital importance to plan trajectory for unmanned aircraft vehicle (UAV) completing missions in battlefield. A method to address the real-time problem of low-altitude UAV 3-D trajectory planning in realistic battlefield was proposed. Simplified threat models of battlefield were constructed, and an algorithm based on sharing niched genetic algorithm (NGA) was developed by defining the contrast of gene to change gene-s inheritance characteristic. The improvement made superior genes easy to transmit to the next generation, targeted to accelerate the NGA converging to the global optimum and improve real-time performance of NGA. The algorithm was used to 3-D trajectory planning for UAV in virtual battlefield environments while the 3-D digital terrain space was coded by gridding with constant interval. Experimental results show the effectiveness of the proposed algorithm, and prove it meets the real-time requirement of UAV trajectory planning on-line.
Searching and tracking ground target UAV flight control system design
Wang Yang, Liu Wei
2010, 36(10): 1252-1255.
Abstract:
According to a high aspect ratio and V-shaped empennage unmanned aerial vehicle (UAV), a flight control strategy based on searching and tracking ground target was researched. A control method was designed with which a single-axis camera detecting system eliminated vertical error and UAV heading control loop eliminated horizontal error on field of view. By simulating and analyzing the UAV-s motion state and using six-degree-freedom nonlinear equations, an adaptive proportion integration differention (PID) controller was designed. And the designed algorithm was applied to the experiment of ground target tracking. The simulation and flight experiment results indicate that the UAV-s dynamic performance is well realized under the influence of sudden wind and other large disturbance. The designed control system effectively inhibits the coupling influence of the UAV-s attitude control channel to the optical axis control channel and meets the requirement of the flight missions.
Analysis of depth testing model for thin board specimen in pulsed thermography
Wan Kai, Ma Qishuang
2010, 36(10): 1256-1260.
Abstract:
Pulsed thermography (PT) is always considered as a quantitative testing approach in infrared thermal imaging. One of its main models called temperature-contrast function (TCF) method is usually found invalidated in defect depth measurement when meets a thin sample. To exhibit the existing fault during TCF modeling, one-dimensional finite analytical solutions were used to carry out calculations instead of the approximate solution adopted in original TCF model under an ideal impulse excitation. Two kernel parameters, named as peak temperature-contrast time (PCT) and peak temperature-contrast slope time (PST), were detailedly analyzed both in temperature-contrast curve and its derivative line. Comparison was made in their detecting abilities. The results show that PCT is governed by background-s depth, not by test point-s depth, so this parameter isn-t suitable for a quantitative test; and PST is also manifested to have service restriction in a depth ratio between the two points (test point/reference point). The upper limit of this depth ratio (approximately 0.5) was obtained by a criterion equation as a theoretical reference when PST was chosen in applications.