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284 lines
10 KiB
Python
284 lines
10 KiB
Python
15 years ago
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"""
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WAFO defintions and numenclature
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crossings :
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cycle_pairs :
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turning_points :
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wave_amplitudes :
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wave_periods :
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waves :
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"""
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def wave_amplitudes():
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r"""
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Wave amplitudes and heights definitions and nomenclature
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Definition of wave amplitudes and wave heights
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---------------------------------------------
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<----- Direction of wave propagation
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|..............c_..........|
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| /| \ |
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Hd | _/ | \ | Hu
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M | / | \ |
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/ \ | M / Ac | \_ | c_
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F \ | / \m/ | \ | / \
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------d----|---u------------------d---|---u----d------ level v
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\ | /| \ | / \L
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\_ | / | At \_|_/
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\|/..| t
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t
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Parameters
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----------
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Ac : crest amplitude
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At : trough amplitude
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Hd : wave height as defined for down crossing waves
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Hu : wave height as defined for up crossing waves
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See also
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--------
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waves, crossings, turning_points
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"""
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print(wave_amplitudes.__doc__)
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def crossings():
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r"""
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Level v crossing definitions and nomenclature
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Definition of level v crossings
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-------------------------------
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M
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. . M M
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. . . . . .
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F d . . L
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-----------------------u-------d-------o----------------- level v
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. . . . u
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. m
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m
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Let the letters 'm', 'M', 'F', 'L','d' and 'u' in the
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figure above denote local minimum, maximum, first value, last
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value, down- and up-crossing, respectively. The remaining
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sampled values are indicated with a '.'. Values that are identical
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with v, but do not cross the level is indicated with the letter 'o'.
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We have a level up-crossing at index, k, if
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x(k) < v and v < x(k+1)
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or if
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x(k) == v and v < x(k+1) and x(r) < v for some di < r <= k-1
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where di is the index to the previous downcrossing.
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Similarly there is a level down-crossing at index, k, if
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x(k) > v and v > x(k+1)
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or if
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x(k) == v and v > x(k+1) and x(r) > v for some ui < r <= k-1
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where ui is the index to the previous upcrossing.
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The first (F) value is a up crossing if x(1) = v and x(2) > v.
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Similarly, it is a down crossing if x(1) = v and x(2) < v.
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See also
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--------
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wave_periods, waves, turning_points, findcross, findtp
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"""
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print(crossings.__doc__)
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def cycle_pairs():
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r"""
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Cycle pairs definitions and numenclature
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Definition of Max2min and min2Max cycle pair
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--------------------------------------------
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A min2Max cycle pair (mM) is defined as the pair of a minimum
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and the following Maximum. Similarly a Max2min cycle pair (Mm)
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is defined as the pair of a Maximum and the following minimum.
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(all turning points possibly rainflowfiltered before pairing into cycles.)
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See also
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--------
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turning_points
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"""
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print(cycle_pairs.__doc__)
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def wave_periods():
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r"""
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Wave periods (lengths) definitions and nomenclature
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Definition of wave periods (lengths)
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------------------------------------
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<----- Direction of wave propagation
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<-------Tu--------->
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: :
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<---Tc-----> :
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: : : <------Tcc---->
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M : c : : : :
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/ \ : M / \_ : : c_ c
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F \ :/ \m/ \: :/ \ / \
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------d--------u----------d-------u----d--------u---d-------- level v
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\ / \ / :\_ _/: :\_ L
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\_ / \_t_/ : \t_/ : : \m/
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\t/ : : : :
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: : <---Tt---> :
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<--------Ttt-------> : :
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<-----Td----->
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Tu = Up crossing period
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Td = Down crossing period
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Tc = Crest period, i.e., period between up crossing and
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the next down crossing
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Tt = Trough period, i.e., period between down crossing and
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the next up crossing
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Ttt = Trough2trough period
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Tcc = Crest2crest period
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<----- Direction of wave propagation
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<--Tcf-> Tuc
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: : <-Tcb-> <->
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M : c : : : :
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/ \ : M / \_ c_ : : c
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F \ :/ \m/ \ / \___: :/ \
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------d---------u----------d---------u-------d--------u---d------ level v
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:\_ / \ __/: \_ _/ \_ L
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: \_ / \_t_/ : \t_/ \m/
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: \t/ : :
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: : : :
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<-Ttf-> <-Ttb->
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Tcf = Crest front period, i.e., period between up crossing and crest
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Tcb = Crest back period, i.e., period between crest and down crossing
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Ttf = Trough front period, i.e., period between down crossing and trough
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Ttb = Trough back period, i.e., period between trough and up crossing
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Also note that Tcf and Ttf can also be abbreviated by their crossing
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marker, e.g. Tuc (u2c) and Tdt (d2t), respectively. Similar applies
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to all the other wave periods and wave lengths.
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(The nomenclature for wave length is similar, just substitute T and
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period with L and length, respectively)
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<----- Direction of wave propagation
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<--TMm-->
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<-TmM-> : :
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M : : M :
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/ \ : M /:\_ : M_ M
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F \ : / \m/ : \ : /: \ / \
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\ : / : \ : / : \ / \
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\ : / : \ : / : \_ _/ \_ L
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\_ : / : \_m_/ : \m_/ \m/
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\m/ : : : :
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<-----TMM-----> <----Tmm----->
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TmM = Period between minimum and the following Maximum
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TMm = Period between Maximum and the following minimum
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TMM = Period between Maximum and the following Maximum
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Tmm = Period between minimum and the following minimum
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See also
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--------
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waves,
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wave_amplitudes,
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crossings,
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turning_points
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"""
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print(wave_periods.__doc__)
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def turning_points():
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r"""
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Turning points definitions and numenclature
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Definition of turningpoints
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---------------------------
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<----- Direction of wave propagation
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M M
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/ \ .... M /:\_ M_ M
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F \ | / \m/ : \ /: \ / \
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\ h | / : \ / : \ / \
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\ | / : \ / : \_ _/ \_ L
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\_ | / : \_m_/ : \m_/ \m/
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\m/ : : : :
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<------Mw-----> <-----mw----->
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Local minimum or maximum are indicated with the
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letters 'm' or 'M'. Turning points in this connection are all
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local max (M) and min (m) and the last (L) value and the
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first (F) value if the first local extremum is a max.
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(This choice is made in order to get the exact up-crossing intensity
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from rfc by mm2lc(tp2mm(rfc)) )
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See also
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--------
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waves,
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crossings,
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cycle_pairs
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findtp
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"""
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print(turning_points.__doc__)
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def waves():
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r"""
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Wave definitions and nomenclature
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Definition of trough and crest
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------------------------------
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A trough (t) is defined as the global minimum between a
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level v down-crossing (d) and the next up-crossing (u)
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and a crest (c) is defined as the global maximum between a
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level v up-crossing and the following down-crossing.
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Definition of down- and up -crossing waves
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------------------------------------------
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A level v-down-crossing wave (dw) is a wave from a
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down-crossing to the following down-crossing.
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Similarly, a level v-up-crossing wave (uw) is a wave from an up-crossing
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to the next up-crossing.
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Definition of trough and crest waves
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------------------------------------
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A trough-to-trough wave (tw) is a wave from a trough (t) to the
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following trough. The crest-to-crest wave (cw) is defined similarly.
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Definition of min2min and Max2Max wave
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--------------------------------------
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A min2min wave (mw) is defined starting from a minimum (m) and
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ending in the following minimum.
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Similarly a Max2Max wave (Mw) is thus a wave from a maximum (M)
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to the next maximum (all waves optionally rainflow filtered).
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<----- Direction of wave propagation
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<------Mw-----> <----mw---->
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M : : c :
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/ \ M : / \_ : c_ c
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F \ / \m/ \ : /: \ /:\
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------d--------u----------d-------u----d--------u---d------ level v
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\ /: \ : /: : :\_ _/ : :\_ L
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\_ / : \_t_/ : : : \t_/ : : \m/
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\t/ <-------uw---------> : <-----dw----->
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: : : :
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<--------tw--------> <------cw----->
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(F=first value and L=last value).
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See also
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--------
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turning_points,
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crossings,
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wave_periods
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findtc,
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findcross
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"""
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print(waves.__doc__)
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