CN107958098A - A kind of bullet train based on spectrum analysis topples method for evaluating hazard - Google Patents

A kind of bullet train based on spectrum analysis topples method for evaluating hazard Download PDF

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CN107958098A
CN107958098A CN201711058298.1A CN201711058298A CN107958098A CN 107958098 A CN107958098 A CN 107958098A CN 201711058298 A CN201711058298 A CN 201711058298A CN 107958098 A CN107958098 A CN 107958098A
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wind
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CN107958098B (en
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严乃杰
李永乐
陈新中
向活跃
张志杰
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Southwest Jiaotong University
Railway Engineering Research Institute of CARS
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

Topple method for evaluating hazard the invention discloses a kind of bullet train based on spectrum analysis, it includes：Relative to the fluctuating wind spectrum computational methods of running train, the recognition methods of train admittance function, running train unsteady aerodynamic force computational methods and train response frequency-domain calculations and capsizing probability evaluation method；Running train fluctuating wind spectrum computational methods solve the problems, such as to calculate different speeds, traffic direction Train wind spectrum based on surface wind spectrum；Train admittance function recognition methods have identified the admittance function on different wind direction fluctuating winds；Running train unsteady aerodynamic force computational methods consider the contribution of down wind, beam wind to, vertical fluctuating wind at the same time；Train responds frequency-domain calculations and capsizing probability evaluation method, specify that the probability distribution of train extreme value response, has quantified the probability of happening that train topples.The present invention has calculated the train probability characteristics wind speed curve PCWC under different capsizing probabilities, can evaluate high wind effect Train safety in operation.

Description

A kind of bullet train based on spectrum analysis topples method for evaluating hazard
Technical field
The invention belongs to bullet train safety in operation analysis field, particularly a kind of bullet train based on spectrum analysis Topple method for evaluating hazard.
Background technology
Nearly ten years, bullet train is because its speed of service is fast, transporting power is big, safe, punctuality rate is high, comfort level is high And the advantages that energy-saving and environmental protection, it is developed rapidly in worldwide, China Railway High-speed construction is even more to be in the world Top standard.However, bullet train often travel on it is complicated across the wind environment such as river, over strait, high embankment, high mountain gorge, strong wind gobi Changeable area.Under high wind effect, car body can produce the roll moment around leeward siding track, which can cause side wheel pair windward Off-load, directly increases the danger of toppling of train.With the raising of speed, the reduction of the weight of train, body structure is more passivated Train it is more sensitive to beam wind.Therefore, it is necessary to the train operation security under acting on high wind is studied, research contents Relate generally to 4 aspects：1. determine the wind field characteristic around running train；2. calculate the aerodynamic force acted on running train； 3. simulate the train response under external load excitation；4. evaluate the train operational safety under high wind effect.
Fluctuating wind field around train is described usually using " fitful wind equivalent wind speed ", for example " Chinese hat ", use this Kind method can only obtain definite train extreme value response.However, wind loads have stochastic behaviour, under random load excitation Certain probability distribution is also obeyed in train response.Responded to obtain the train with random distribution nature, it is necessary to pass through pulsation Wind spectrum, coherent function simulation random pulse wind field.Train response analysis usually carries out, it is necessary to incite somebody to action continuous arteries and veins along the line in the time domain Dynamic wind field is separated into the wind field at finite point, has correlation between these discrete wind fields, due to discrete point enormous amount, along the line The calculation amount of simulation of wind is difficult to complete.On the other hand, relative to the fluctuating wind spectrum of running train and relative to still The fluctuating wind spectrum in face is different, when can draw up the fluctuating wind relative to running train using the fluctuating wind spectrum mould on train Journey, so can effectively reduce amount of calculation.
Running train aerodynamic force mainly includes Wind Loads Acting and wind loads (unsteady aerodynamic force), can pass through row Car aerodynamic coefficient, admittance function are calculated.At present, it is entirely to be caused by down wind fluctuating wind to generally believe wind loads , however, some researches show that beam wind to, vertical fluctuating wind also has material impact.Admittance function is fluctuating wind spectrum and pneumatic The transmission function of power spectrum, can be tested to obtain by wind tunnel test.Traditional recognition method thinks that the wind field in wind-tunnel is complete phase Close, the wind field actually in wind-tunnel is not perfectly correlated, it imitates the train aerodynamic-force under perfectly correlated wind field with reduction Should.Since correlation and the actual wind field of wind-tunnel wind field are there are notable difference, therefore, it is necessary to remove it is pneumatic in it is incomplete The reduction effect that related wind field is brought, and consider the aerodynamic force correlation in actual wind field.Admittance function is the letter on frequency Number, in a frequency domain using more simple.
Wind load, track irregularity load excitation under, the dynamic response of train system can be arranged by multiple degrees of freedom Car numerical model is simulated.It is whether train topples for evaluate train beam wind stability, rather than oversteps the limit, therefore, Non-linear Wheel Rail Contact can be simplified to linear contact, or directly ignore without considering.It in addition, there will be research to show, train The model free degree number, on train beam wind stability analysis result influence very little.Therefore, in train beam wind analysis of stability In analysis, simplified train model can be used, and ignore train nonlinear characteristic.
Toppling for train judges off-load rate usually using wheel, when side wheel reaches limit value to train to maximum off-load windward, Corresponding mean wind speed is critical wind velocity.The critical wind velocity that topples of train is the function on speed, initial wind angle, uses biography System time domain approach can obtain single critical wind velocity curve, i.e. feature wind speed curve (Characteristic Wind Curve, CWC).If consider fluctuating wind, the stochastic behaviour of track irregularity, and the uncertainty of other specification, it can obtain Feature wind speed curve under different failure probabilities (capsizing probability), i.e. probability characteristics wind speed curve (Probabilistic Characteristic Wind Curve, PCWC).The wind environment of Along Railway be it is continually changing, some region of wind speed, Wind angle can usually use specific probability distribution to describe, such as Weibull distribution.To whole Along Railway difference wind speed, wind direction Train capsizing probability integration under angle, can obtain high wind and act on the probability that Train topples along the operation of whole circuit.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of bullet train based on spectrum analysis danger of toppling and comment Valency method, based on probability analysis, determines train response extreme value probability distribution and capsizing probability, calculates under different capsizing probabilities Train probability characteristics wind speed curve PCWC, evaluation high wind effect Train safety in operation.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of bullet train based on spectrum analysis topples method for evaluating hazard, comprises the following steps：
Step 1：By wind tunnel test, different wind angles are testedWind angle of attack Train Wind Loads Acting aerodynamic coefficientUsing the train Wind Loads Acting aerodynamic coefficient of wind tunnel test, running train is calculated with the wind by the formula of derivation To unsteady aerodynamic force coefficient Ciu, beam wind is to unsteady aerodynamic force coefficient Civ, vertical unsteady aerodynamic force coefficient Ciw, and identify Go out admittance function χiξ0(f)；
Wherein,For initial wind angle, VtrFor speed, U is mean wind speed, For relative to the mean wind speed of running train；
According to theory deduction, ignore the influence of fluctuating wind cross-spectrum, train admittance function is identified by following formula：
Wherein,For aerodynamic force Fi(t) and pulsation wind component ξ (t) (ξ=u, v, w) cross-spectrum；χiξ0(f) it is to wait to know Other admittance function；ρ is atmospheric density, and H is train height, CiξFor train unsteady aerodynamic force wind load coefficient, Sξξ(f) it is Fluctuating wind ξ (t) is composed certainly in wind-tunnel, Jξξ(f) combine for wind component ξ (t) of pulsing in wind-tunnel and receive function, it is horizontal in wind-tunnel for reflecting To the reduction effect of endless total correlation wind field, calculated by following formula：
In above formulaL is train length；Cohξξ(y, f) is in the case of wind-tunnel medium spacing is y, and ξ is to fluctuating wind Coherent function；
Step 2：Vehicle numerical model is established, calculates wheel-rail contact force F under train steady state0；
Wherein, YD(t) motion vector is responded for Train Dynamic；For YD(t) first derivative；For YD(t) second order Derivative；MV、CV、KVRespectively train system quality, damping, stiffness matrix；FW(t)、FT(t) it is respectively wind loads, track Irregularity load vector；
Step 3：Determine Surface Winds Over characteristic, including：Mean wind speed U, down wind turbulence intensity Iu, beam wind is to turbulence intensity IvWith vertical turbulence intensity Iw, down wind turbulence integral scale Lu, beam wind is to turbulence integral scale Lv, vertical turbulence integral scale Lw, ground down wind fluctuating wind is from composing Su(f), ground beam wind composes S certainly to fluctuating windv(f), the vertical fluctuating wind in ground composes S certainlyw And ground pulse wind coherent function Coh (f),u(Δy,f)；
Step 4：Calculate vehicle velocity VtrWith initial wind angleUnder running train down wind fluctuating wind from composing Su′u′(f)、 Running train beam wind composes S certainly to fluctuating windv′v′(f), the vertical fluctuating wind of running train composes S certainlyw′w′(f), movement is further calculated Fluctuating wind on train, which is combined, receives function Jξ′ξ′(f)；
Suu(Δ y, f)=Cohu(Δy,f)Su(f)
Wherein, Ruu(Δ y, τ+τ ') represents ground pulse wind down wind correlation function, Suu(Δ y, f) represents ground with the wind To fluctuating wind cross-spectrum, f is frequency, and τ is time interval, and τ ' is fluctuating wind freeze-off time, and Δ y is ground point beam wind to spacing； Ru′u′(Δ η, τ) represents train fluctuating wind correlation function, and Δ η is to put spacing on train；Su(f) for ground down wind fluctuating wind certainly Spectrum, Cohu(Δ y, f) is ground pulse wind coherent function；Su′u′(Δ η, f) is running train down wind fluctuating wind cross-spectrum；Using Same method, obtains on running train beam wind to fluctuating wind cross-spectrum Sv′v′(Δ η, f), vertical fluctuating wind cross-spectrum Sw′w′(Δη, f)；
Svv(Δ y, f)=Cohu(Δy,f)Sv(f)
Wherein, Rvv(Δ y, τ+τ ') represents ground pulse wind beam wind to correlation function, Svv(Δ y, f) represents ground beam wind To fluctuating wind cross-spectrum；
Sww(Δ y, f)=Cohu(Δy,f)Sw(f)
Wherein, Rvv(Δ y, τ+τ ') represents the vertical correlation function of ground pulse wind, Svv(Δ y, f) represents the vertical arteries and veins in ground Dynamic wind cross-spectrum；
Further calculate the fluctuating wind on running train and combine and receive function Jξ′ξ′(f)；
Step 5：Pass through the mean wind speed relative to running trainRunning train down wind fluctuating wind composes S certainlyu′u′(f)、 Running train beam wind composes S certainly to fluctuating windv′v′(f), the vertical fluctuating wind of running train composes S certainlyw′w′(f), admittance function χiξ0(f)、 Running train down wind unsteady aerodynamic force coefficient Ciu, beam wind is to unsteady aerodynamic force coefficient Civ, vertical unsteady aerodynamic force system Number Ciw, calculate running train Wind Loads ActingAnd calculate wind loads on running train and composeTrack irregularity Traffic spectra
Wherein,For running train Wind Loads Acting, AW(f) matrix to be made of aerodynamic coefficient, admittance； For wind loads matrix,For track irregularity load matrix；SW(f) it is pulsating wind spectrum matrix, SX(f) it is rail Road irregularity spectral power matrix；
Step 6：By Wind Loads ActingWind loads are composedTrack irregularity traffic spectraIt is loaded into On train numerical model, mean wind load Train static displacement vector Y is calculatedS, Train Dynamic response spectraFurther The wheel under the mean wind load effect of calculating windward side is calculated to off-loadWheel composes off-load dynamic response
KVYS=FS
Wherein, KVFor train system stiffness matrix, YSFor mean wind load Train static displacement vector；FSFor mean wind load Vector；AW(f) matrix to be made of aerodynamic coefficient, admittance；Respectively aerodynamic force, track are uneven Along exciting power spectrum matrix；SW(f) it is pulsating wind spectrum matrix, SX(f) it is track irregularity spectral power matrix；For Train Dynamic response spectra；H (f) responds transmission function, H for train system*(f) associate matrix for being H (f)；
Step 7：Extreme value type I Geng Bell distribution is obeyed according to the extreme value of Gaussian process, calculate corresponding mean wind speed U, Initial wind angleThe probability that Train topples
Wherein,For mean wind speed U and initial wind angleCapsizing probability under operating mode；For dynamic extreme value Respond and beWhen accumulated probability distribution；klTo take turns to off-load rate limit value；Wheel under being acted on for mean wind load is to subtracting Carry；FD(t) for fluctuating wind, track irregularity effect under wheel to off-load；v0For intersection of the stationary Gaussian process in zero-mean Rate；It is poor for wheel-rail contact force extreme value response criteria；
Step 8：Adjust initial wind angleScope is in [0,2 π], mean wind speed, and scope is [0, Umax], UmaxFor train Restricted driving wind speed, is recalculated from step 3, until initial wind angle reaches 2 π, mean wind speed reaches Umax, obtain different be averaged Wind velocity U, initial wind angleTrain runs capsizing probability curve；
Step 9：Consider corresponding initial wind angleLower mean wind speed U probability of happeningInitial wind angleHair Raw probabilityCalculate mean wind speed U and initial wind angleTrain capsizing probability under composite condition It is final to calculate the capsizing probability run along fixed vehicle speed Train
Step 10：It is fixed value p to take failure probabilityf, vehicle velocity V is selected from the capsizing probability curve that step 8 obtainstr, just Beginning wind angleUnder wind velocity U of topplingc, train probability characteristics wind speed curve is obtained, for as guarantee high wind effect Train The reference frame of safe operation.
Compared with prior art, the beneficial effects of the invention are as follows：Train response extreme value probability distribution is determined and topples general Rate, has calculated the train probability characteristics wind speed curve PCWC under different capsizing probabilities, can evaluate high wind effect Train fortune Row security.
Brief description of the drawings
Fig. 1 is the flow diagram of evaluation method of the present invention.
Fig. 2 is running train wind field in the present invention, Surface Winds Over relation schematic diagram (three-dimensional view).
Fig. 3 is running train wind field in the present invention, Surface Winds Over relation schematic diagram (top view).
Fig. 4 is running train wind vector figure in the present invention.
Fig. 5 is ground in the present invention, train parting spectrogram.
Fig. 6 is that wind-tunnel Wind Field combines and receives function in the present invention.
Fig. 7 is the admittance function (horizontal mechanical mobility) of the method for the present invention identification.
Fig. 8 is the admittance function (lift admittance) of the method for the present invention identification.
Fig. 9 is the admittance function (horizontal mechanical mobility) of conventional method identification.
Figure 10 is the admittance function (lift admittance) of conventional method identification.
Figure 11 is train aerodynamic-force spectrum (cross force) in the present invention.
Figure 12 is train aerodynamic-force spectrum (lift) in the present invention.
Figure 13 is the lower response spectra of middle orbit irregularity of the present invention, fluctuating wind excitation (under track irregularity acts on).
Figure 14 is the lower response spectra of middle orbit irregularity of the present invention, fluctuating wind excitation (under fluctuating wind acts on).
Figure 15 is failure probability curve under different speeds in the present invention.
Figure 16 is PCWC under different failure probabilities in the present invention (initial wind angle is 90 °).
Figure 17 is PCWC (speed 70m/s) under different failure probabilities in the present invention.
Embodiment
The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.Present invention incorporates opposite In the fluctuating wind spectrum computational methods of running train, the recognition methods of train admittance function, running train unsteady aerodynamic force calculating side Method, train response frequency-domain calculations and capsizing probability evaluation method, fluctuating wind, track irregularity excitation are applied in the form of traffic spectra To train system, running train response spectra is calculated, based on probability analysis, train response extreme value probability distribution is determined and topples general Rate, calculates the train probability characteristics wind speed curve under different capsizing probabilities, evaluation high wind effect Train safety in operation.
Basic theories according to the present invention is as follows：
First, running train wind-field model
Based on Taylor " turbulent flow freezes " it is assumed that when mean wind speed is much larger than fluctuating wind speed, it is believed that fluctuating wind speed exists Not changed in certain time, spatial dimension, i.e., interior in fluctuating wind freeze-off time τ ', whirlpool does not have enough time also developing, It just experienced distance, delta x under the carrying of average wind.Based on this, fluctuating wind cross-correlation function R on ground can be useduu(Δ Y, τ+τ ') represent fluctuating wind cross-correlation function R on running trainu′u′(Δ η, τ) (as shown in Figure 2 and Figure 3), i.e.,
u(xk′,yk′, t+ τ) and=u (xm,ym, t+ τ+τ ') and=u (xj,yj-Δy,t+τ+τ′) (1)
Ru′u′(Δ η, τ)=E [u (xj,yj,t)u(xj,yj- Δ y, t+ τ+τ ')]=Ruu(Δy,τ+τ′) (2)
Wherein,
Suu(Δ y, f)=Cohu(Δy,f)Su(f) (4)
Then, it is relative to the fluctuating wind cross-spectrum of running train：
S in above-mentioned formulau(f)、Cohu(Δ y, f) is composed certainly for fluctuating wind on ground, coherent function；Δ η is 2 points on train Spacing；Su′u′(Δ η, f) is fluctuating wind cross-spectrum on running train.There is no analytic solutions, it is necessary to pass through for integration in above-mentioned formula Numerical computations solve.Using same method, beam wind can be obtained on running train to, vertical fluctuating wind cross-spectrum Sv′v′(Δη, f)、Sw′w′(Δη,f)。
By the numerical method, any type of surface wind spectrum, coherent function, can calculate mean wind speed U, initial Wind angleAnd vehicle velocity VtrUnder running train wind spectrum.Itd is proposed than what Cooper was proposed based on von-Karman spectrums, Wu Mengxue Based on Kaimal spectrum running train wind spectrum, the method is no longer composed by surface wind, coherent function type is limited.
2nd, running train Aerodynamic Model
Work as vehicle velocity VtrAngle with mean wind speed U isThe instantaneous wind speed that then running train " impression " arrives is (such as Fig. 4 institute Show)：
Running train Wind Loads Acting is：
By theory deduction, if considering the contribution of down wind, beam wind to, vertical fluctuating wind at the same time, running train is non-fixed Normal aerodynamic force can be expressed as：
Wherein,
In above-mentioned formula, i=S, L represent cross force, lift；If take Vtr=0,Then obtain the non-of static train Unsteady Flow expression formula, available for the aerodynamic admittance function for identifying static train model and testing.
3rd, admittance function identifies
According to theory deduction, ignore the influence of fluctuating wind cross-spectrum, train admittance function can be identified by following formula：
In above formula,For aerodynamic force Fi(t) and pulsation wind component ξ (t) (ξ=u, v, w) cross-spectrum；χiξ0(f) it is to treat The admittance function of identification；Jξξ(f) combine for wind component ξ (t) of pulsing in wind-tunnel and receive function, it is laterally endless in wind-tunnel for reflecting The reduction effect of total correlation wind field, can be calculated by following formula：
In above formulaL is train length；cohξξ(y, f) is in the case of wind-tunnel medium spacing is y, and ξ is to fluctuating wind Coherent function.
Remove the J of endless total correlation wind field in wind-tunnelξξ(f) after, then running train unsteady aerodynamic force is calculated, it is necessary to consider Combining for actual wind field receives function Jξ′ξ′(f), it can be integrated and tried to achieve by the coherent function of running train wind field, i.e.,：
4th, the train system equation of motion
Train system is made of 1 car body, 2 bogies, each have laterally, it is vertical, sidewinder, nod, shake the head 5 from By spending.Train, which responds, can be divided into STATIC RESPONSE, dynamic response, and the equation of train mot io n under quiet, dynamic load function is respectively：
KVYS=FS (16)
In above-mentioned formula, YSFor mean wind load Train static displacement vector, YD(t) motion vector is responded for Train Dynamic； MV、CV、KVRespectively train system quality, damping, stiffness matrix；FS、FW(t)、FT(t) it is respectively mean wind load, fluctuating wind lotus Carry, track irregularity load vector.
Consider each phase difference taken turns to track irregularity under synchronization, then track irregularity excitation can be expressed as：
YTj(t)=[yw(t+τj),zw(t+τj),φw(t+τj)]T(j=1,2,3,4) (20)
Wherein, KT、CTRigidity respectively corresponding with track irregularity, damping matrix；YT(t) it is track irregularity matrix.It is each Wheel can be expressed as the phase difference between track irregularity：
In above-mentioned formula, YT(t) it is track irregularity matrix；YTj(t) it is vectorial to track irregularity for jth wheel；
Under wind loads, track irregularity effect, the dynamic response power spectrum of train is：
H (f)=[- MV(2πf)2+CVi2πf+KV]-1 (23)
Wherein,
In above-mentioned formula, AW(f) matrix to be made of aerodynamic coefficient, admittance；Respectively gas Power, track irregularity exciting power spectrum matrix；SW(f)、SX(f) it is respectively fluctuating wind, track irregularity spectral power matrix；For Train Dynamic response power spectrum；ET(f) serve as reasonsThe diagonal matrix of composition.
5th, response evaluation
Fluctuating wind, track irregularity are generally stationary Gaussian process, and corresponding train response is also the steady height of zero-mean This process.Therefore, based on Poisson it is assumed that wheel-rail contact force extreme value FDmaxAccumulated probability be distributed as：
In above formulaWherein,
Then the wheel-rail contact force extreme value under fraction p is：
When windward side wheel maximum off-load rate exceedes critical value kl, then it is assumed that train topples：
F in above formula0For the wheel-rail contact force under train steady state.
In the case of given wind speed, initial wind angle, speed, the probability that toppling occurs in train can be expressed as：
Calculate the train capsizing probability under different wind speed, initial wind angle.Finally, train topples along what railway was completely run Probability is：
The symbol definition that table 1 is referred to herein
The feasibility and advantageous effects of the method for the present invention are verified below by instantiation.Use near surface Kaimal Spectrum is composed as target, and with reference to wind tunnel test data, simulation running train aerodynamic force is composed, and with typical China Railway High-speed train Exemplified by, analysis high wind effect Train capsizing probability, obtains the PCWC under different capsizing probabilities.
1) running train wind field
Down wind, beam wind are to, vertical near surface Kaimal spectrum：
In above formula：For reduction frequency；LξFor integral length scale；σξFor weathercock of pulsing It is accurate poor.Down wind, beam wind are as shown in table 2 to, the relation of the integral length scale of vertical fluctuating wind, standard deviation, wherein, σ1It is mark Poor, the Λ of standard1It is integral length scale parameter.In order to truly reflect near surface wind field, take hereinLu= 40m.Using Davenport coherent functions, attenuation coefficient takes 7.By taking down wind fluctuating wind as an example, under friction speed ratio, on ground Wind composes (speed ratio 0) and running train wind spectrum is as shown in Figure 5.As seen from the figure, running train wind spectrum and surface wind spectrum energy point Cloth significant difference.
2 fluctuating wind parameter of table
2) admittance function identifies
According to the static train aerodynamic-force model of derivation, while consider the influence of down wind, beam wind to, vertical fluctuating wind, By wind tunnel test, the admittance function of Chinese Typical Representative High Speed Railway Trains is tested, and calculates and connects combining for wind-tunnel Wind Field By function, as shown in Figure 6.As seen from the figure, combining for wind-tunnel Wind Field receives function much smaller than 1, shows incomplete phase in wind-tunnel Wind field is closed to act on train aerodynamic-force with significant reduction.Pass through analysis, the performance of toppling of the phase of admittance function to train Do not influence, therefore, the imaginary part of admittance function can be ignored, cross force, the amplitude of lift admittance function under typical wind angle As shown in Figure 7, Figure 8.Conventionally only consider the influence of down wind fluctuating wind, the admittance function identified such as Fig. 9, figure Shown in 10.Found by contrasting, the admittance function that new method, conventional method identify is there are significant difference, and not Tongfang To fluctuating wind admittance function there is also notable difference.
3) running train aerodynamic force is composed
Pick up the car speed 70m/s, wind speed 25m/s, and the running train wind being calculated spectrum is updated to the running train gas of derivation In dynamic model, and consider the admittance function identified, running train unsteady aerodynamic force spectrum can be obtained.Using same Method, running train tradition gas is updated to by the admittance function that conventional method (only considering down wind pulsation wind effect) identifies In dynamic model, running train aerodynamic force spectrum can also be calculated.The aerodynamic force spectrum such as Figure 11, Figure 12 that two methods are calculated Shown, as seen from the figure, there are significant difference for the running train aerodynamic force spectrum that two methods are calculated.In theory, if actual wind Field is identical with wind-tunnel wind field, then the running train aerodynamic force spectrum that two methods are calculated should be identical.But Nature Wind Field correlation and having differences in wind-tunnel.More reasonably running train aerodynamic force is composed in order to obtain, is needed The influence of down wind, beam wind to, vertical fluctuating wind is considered at the same time.
4) high wind effect Train topples risk analysis
Using new method identification admittance function, calculate running train unsteady aerodynamic force.The train pneumatic that will be calculated Power spectrum, track irregularity excitation spectrum load on train system as external load, can calculate windward side wheel-rail contact force sound Ying Pu.As a result of linear system, it can individually apply track irregularity excitation, fluctuating wind excitation, what is be calculated is independent Response meets SRSS principle of stackings with overall response.Pick up the car speed 70m/s, under different speed ratios, initial wind angle, track irregularity, Train response spectra under fluctuating wind independent drive is as shown in Figure 13, Figure 14.
T=120min is taken, initial 90 ° of wind angle, calculates the train capsizing probability under different speeds, wind speed, such as Figure 15 It is shown.Take capsizing probability for 5%, 10%/, 43%, further obtain the PCWC under different speeds, different wind angles, as Figure 16, Shown in Figure 17.As seen from the figure, calculated by frequency domain method, train can be quantified and issued in specific speed, wind speed, initial wind angle The raw probability to topple, obtains the PCWC under different capsizing probabilities.

Claims (1)

  1. The method for evaluating hazard 1. a kind of bullet train based on spectrum analysis topples, it is characterised in that comprise the following steps：
    Step 1：By wind tunnel test, different wind angles are testedWind angle of attack Train Wind Loads Acting aerodynamic coefficientUsing the train Wind Loads Acting aerodynamic coefficient of wind tunnel test, running train is calculated with the wind by the formula of derivation To unsteady aerodynamic force coefficient Ciu, beam wind is to unsteady aerodynamic force coefficient Civ, vertical unsteady aerodynamic force coefficient Ciw, and identify Go out admittance function χiξ0(f)；
    Wherein,For initial wind angle, VtrFor speed, U is mean wind speed,To be opposite In the mean wind speed of running train；
    According to theory deduction, ignore the influence of fluctuating wind cross-spectrum, train admittance function is identified by following formula：
    <mrow> <msub> <mi>&amp;chi;</mi> <mrow> <mi>i</mi> <mi>&amp;xi;</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <msub> <mi>F</mi> <mi>i</mi> </msub> <mi>&amp;xi;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>(</mo> <mn>0.5</mn> <msup> <mi>&amp;rho;U</mi> <mn>2</mn> </msup> <mi>H</mi> <mi>L</mi> <mo>)</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mi>&amp;xi;</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow> <mi>&amp;xi;</mi> <mi>&amp;xi;</mi> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> <msub> <mi>J</mi> <mrow> <mi>&amp;xi;</mi> <mi>&amp;xi;</mi> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> <msub> <mi>&amp;chi;</mi> <mrow> <mi>i</mi> <mi>&amp;xi;</mi> <mn>0</mn> </mrow> </msub> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mfrac> </mrow>
    Wherein,For aerodynamic force Fi(t) and pulsation wind component ξ (t) (ξ=u, v, w) cross-spectrum；χiξ0(f) to be to be identified Admittance function；ρ is atmospheric density, and H is train height, CiξFor train unsteady aerodynamic force wind load coefficient, Sξξ(f) it is wind-tunnel Middle fluctuating wind ξ (t) is composed certainly, Jξξ(f) combine for wind component ξ (t) of pulsing in wind-tunnel and receive function, for reflecting that transverse direction is not in wind-tunnel The reduction effect of perfectly correlated wind field, is calculated by following formula：
    <mrow> <msub> <mi>J</mi> <mrow> <mi>&amp;xi;</mi> <mi>&amp;xi;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>L</mi> <mo>&amp;prime;</mo> </msup> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <msup> <mi>L</mi> <mo>&amp;prime;</mo> </msup> </msubsup> <msub> <mi>coh</mi> <mrow> <mi>&amp;xi;</mi> <mi>&amp;xi;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>y</mi> </mrow>
    In above formulaL is train length；Cohξξ(y, f) is phases of the ξ to fluctuating wind in the case of wind-tunnel medium spacing is y Dry function；
    Step 2：Vehicle numerical model is established, calculates wheel-rail contact force F under train steady state0；
    <mrow> <msub> <mi>M</mi> <mi>V</mi> </msub> <msub> <mover> <mi>Y</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>C</mi> <mi>V</mi> </msub> <msub> <mover> <mi>Y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mi>V</mi> </msub> <msub> <mi>Y</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mi>W</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>F</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
    Wherein, YD(t) motion vector is responded for Train Dynamic；For YD(t) first derivative；For YD(t) second dervative； MV、CV、KVRespectively train system quality, damping, stiffness matrix；FW(t)、FT(t) it is respectively wind loads, track irregularity Load vector；
    Step 3：Determine Surface Winds Over characteristic, including：Mean wind speed U, down wind turbulence intensity Iu, beam wind is to turbulence intensity IvWith Vertical turbulence intensity Iw, down wind turbulence integral scale Lu, beam wind is to turbulence integral scale Lv, vertical turbulence integral scale Lw, ground Face down wind fluctuating wind composes S certainlyu(f), ground beam wind composes S certainly to fluctuating windv(f), the vertical fluctuating wind in ground composes S certainlyw(f), and Ground pulse wind coherent function Cohu(Δy,f)；
    Step 4：Calculate vehicle velocity VtrWith initial wind angleUnder running train down wind fluctuating wind from composing Su′u′(f), mobile row Car beam wind composes S certainly to fluctuating windv′v′(f), the vertical fluctuating wind of running train composes S certainlyw′w′(f), further calculate on running train Fluctuating wind combine and receive function Jξ′ξ′(f)；
    <mrow> <msub> <mi>R</mi> <mrow> <mi>u</mi> <mi>u</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>u</mi> <mi>u</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>
    Suu(Δ y, f)=Cohu(Δy,f)Su(f)
    <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;tau;</mi> </mrow>
    Wherein, Ruu(Δ y, τ+τ ') represents ground pulse wind down wind correlation function, Suu(Δ y, f) represents the pulsation of ground down wind Wind cross-spectrum, f are frequency, and τ is time interval, and τ ' is fluctuating wind freeze-off time, and Δ y is ground point beam wind to spacing；Ru′u′(Δη, τ) represent train fluctuating wind correlation function, Δ η is to put spacing on train；Su(f) composed certainly for ground down wind fluctuating wind, Cohu(Δ Y, f) it is ground pulse wind coherent function；Su′u′(Δ η, f) is running train down wind fluctuating wind cross-spectrum；Using same side Method, obtains on running train beam wind to fluctuating wind cross-spectrum Sv′v′(Δ η, f), vertical fluctuating wind cross-spectrum Sw′w′(Δη,f)；
    <mrow> <msub> <mi>R</mi> <mrow> <mi>v</mi> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>v</mi> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>
    Svv(Δ y, f)=Cohu(Δy,f)Sv(f)
    <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>v</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>v</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>v</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>v</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;tau;</mi> </mrow>
    Wherein, Rvv(Δ y, τ+τ ') represents ground pulse wind beam wind to correlation function, Svv(Δ y, f) represents ground beam wind to pulsation Wind cross-spectrum；
    <mrow> <msub> <mi>R</mi> <mrow> <mi>w</mi> <mi>w</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>S</mi> <mrow> <mi>w</mi> <mi>w</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>y</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>+</mo> <msup> <mi>&amp;tau;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mi>d</mi> <mi>f</mi> </mrow>
    Sww(Δ y, f)=Cohu(Δy,f)Sw(f)
    <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>w</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>w</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </msubsup> <msub> <mi>R</mi> <mrow> <msup> <mi>w</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>w</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mi>f</mi> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>&amp;tau;</mi> </mrow>
    Wherein, Rvv(Δ y, τ+τ ') represents the vertical correlation function of ground pulse wind, Svv(Δ y, f) represents that the vertical fluctuating wind in ground is mutual Spectrum；
    Further calculate the fluctuating wind on running train and combine and receive function Jξ′ξ′(f)；
    <mrow> <msub> <mi>J</mi> <mrow> <msup> <mi>&amp;xi;</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>&amp;xi;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mi>L</mi> <mo>&amp;prime;</mo> </msup> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <msup> <mi>L</mi> <mo>&amp;prime;</mo> </msup> </msubsup> <mfrac> <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>&amp;eta;</mi> <mo>,</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>S</mi> <mrow> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>d</mi> <mi>y</mi> </mrow>
    Step 5：Pass through the mean wind speed relative to running trainRunning train down wind fluctuating wind composes S certainlyu′u′(f), it is mobile Train beam wind composes S certainly to fluctuating windv′v′(f), the vertical fluctuating wind of running train composes S certainlyw′w′(f), admittance function χiξ0(f), it is mobile Train down wind unsteady aerodynamic force coefficient Ciu, beam wind is to unsteady aerodynamic force coefficient Civ, vertical unsteady aerodynamic force coefficient Ciw, calculate running train Wind Loads ActingAnd calculate wind loads on running train and composeTrack irregularity Traffic spectra
    <mrow> <msub> <mi>S</mi> <msub> <mi>F</mi> <mi>W</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>W</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msub> <mi>S</mi> <mi>W</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>W</mi> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>S</mi> <msub> <mi>F</mi> <mi>T</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>H</mi> <msub> <mi>F</mi> <mi>T</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msub> <mi>S</mi> <mi>X</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msubsup> <mi>H</mi> <msub> <mi>F</mi> <mi>T</mi> </msub> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow>
    Wherein,For running train Wind Loads Acting, AW(f) matrix to be made of aerodynamic coefficient, admittance；For arteries and veins Dynamic wind load matrix,For track irregularity load matrix；SW(f) it is pulsating wind spectrum matrix, SX(f) for track not Smooth out spectral power matrix；
    Step 6：By Wind Loads ActingWind loads are composedTrack irregularity traffic spectraIt is loaded into train On numerical model, mean wind load Train static displacement vector Y is calculatedS, Train Dynamic response spectraFurther calculate Go out to calculate the wheel under the effect of windward side mean wind load to off-loadWheel composes off-load dynamic response
    KVYS=FS
    <mrow> <msub> <mi>S</mi> <msub> <mi>Y</mi> <mi>D</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>H</mi> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <msub> <mi>S</mi> <msub> <mi>F</mi> <mi>T</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>S</mi> <msub> <mi>F</mi> <mi>W</mi> </msub> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mi>H</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> </mrow>
    Wherein, KVFor train system stiffness matrix, YSFor mean wind load Train static displacement vector；FSFor mean wind load vector； AW(f) matrix to be made of aerodynamic coefficient, admittance；For wind loads matrix,For track irregularity Load matrix；SW(f) it is pulsating wind spectrum matrix, SX(f) it is track irregularity spectral power matrix；For Train Dynamic Response spectra；H (f) responds transmission function, H for train system*(f) associate matrix for being H (f)；
    Step 7：Extreme value type I Geng Bell distribution is obeyed according to the extreme value of Gaussian process, calculates corresponding mean wind speed U, initial Wind angleThe probability that Train topples
    Wherein,For mean wind speed U and initial wind angleCapsizing probability under operating mode；Moved for wheel-rail contact force State off-load extreme value；klTo take turns to off-load rate limit value；F0For wheel-rail contact force under train steady state；Under being acted on for mean wind load Wheel to off-load；FD(t) for fluctuating wind, track irregularity effect under wheel to off-load；v0It is stationary Gaussian process in zero-mean Crossing-over rate；It is poor for wheel-rail contact force extreme value response criteria；
    Step 8：Adjust initial wind angleScope is in [0,2 π], mean wind speed, and scope is [0, Umax], UmaxFor train restricted driving wind Speed, is recalculated from step 3, until initial wind angle reaches 2 π, mean wind speed reaches Umax, obtain different mean wind speed U, Initial wind angleTrain runs capsizing probability curve；
    Step 9：Consider corresponding initial wind angleLower mean wind speed U probability of happeningInitial wind angleOccur general RateCalculate mean wind speed U and initial wind angleTrain capsizing probability under composite conditionFinally Calculate the capsizing probability run along fixed vehicle speed Train
    Step 10：It is fixed value p to take failure probabilityf, vehicle velocity V is selected from the capsizing probability curve that step 8 obtainstr, initial wind To angleUnder wind velocity U of topplingc, train probability characteristics wind speed curve is obtained, for as guarantee high wind effect Train safety The reference frame of operation.
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