CN104166805B - Obtain the data processing method of petroleum casing pipe thickness - Google Patents

Abstract

The invention discloses a kind of data processing method for obtaining petroleum casing pipe thickness, specifically implement according to following steps：First, log data is gathered with logger, and using continuous every 5 log datas measured as one group, finds out the maximum a in each group of data_j；Take j=1,2,3,4,5, i.e., a₁~a₅As the 1st bag data, the average value Mean of the 1st bag data is obtained₁And replace a₁~a₅, afterwards to j ＞=6 when remainder data do average value processing；Then further according to the data a after processing_jGenerate assistance data b_j；By contrasting a_jWith b_j, find out a_jFlex point c_j；According to flex point c_j, obtain casing thickness relative value d_j；Finally, build and train neutral net, data are handled after extensive neutral net, obtain sleeve pipe actual (real) thickness value e_j.The present invention solves the problems, such as to exist in existing method that efficiency is low, precision is low.

Description

Obtain the data processing method of petroleum casing pipe thickness

Technical field

The invention belongs to information data processing technology field, is related to a kind of data information processing method, and in particular to a kind of Obtain the data processing method of petroleum casing pipe thickness.

Background technology

Oil well logging is link essential in petroleum recovery operations, and it is through whole petroleum recovery operations link In.Log data is the data on the log parameter curve by the data collecting module collected of logger.The pole of log Value point characterizes the required size for measuring downhole parameters.In order to realize the feature extraction of downhole parameters, it is necessary to extract log data Waveforms amplitude.

The method that data discrete waveforms amplitude can be used for extracting at present mainly then asks for pole by matched curve method The method being worth greatly.Most common of which is polynomial curve fitting method.But when data point is more, polynomial order is too low, Fitting precision and effect are not ideal, and to improve fitting precision and effect just needs to improve the exponent number of polynomial fitting, but exponent number It is too high and the complexity and otherwise unfavorable on calculating can be brought.Therefore, if only with a polynomial curve function It is fitted more data point, it is difficult to obtain preferable fitting precision and effect.To efficiently solve above mentioned problem, general use is divided Section curve matching.But because log data amount is big, precision prescribed is high, method of subsection simulation curve method need to could expire many sections of data point point Sufficient required precision, thus the shortcomings such as workload is big, efficiency is low be present, then ask for polynomial maximum and add data meter again Calculation amount, reduces efficiency.

The content of the invention

It is an object of the invention to provide a kind of data processing method for obtaining petroleum casing pipe thickness, using to the very big of data The average value processing method of value, solve the problems, such as there is that efficiency is low, precision is low in the method for existing extraction data waveform amplitude.

The technical solution adopted in the present invention is the data processing method of petroleum casing pipe thickness to be obtained, specifically according to following Step is implemented：

Step 1：Log data is gathered with logger；

Step 2：Using continuous every 5 log datas measured in step 1 as one group, find out in each group of data most Big value a_j(j=1,2,3 ... J)；

Step 3：Take j=1,2,3,4,5, i.e., a₁~a₅As the 1st bag data, the average value of the 1st bag data is obtained Mean₁And replace a₁~a₅；

Step 4：Remainder data during to j ＞=6 does average value processing；

Step 5：Data a after being handled according to step 4_j(j=1,2,3 ... J) generation assistance data b_j(j=1,2,3 ... J)；

Step 6：By contrasting a_jWith b_j, find out a_jFlex point c_jIf, i.e. a_j=b_j, then c_j=a_j；Otherwise, c_j=0；

Step 7：According to flex point c_j, obtain casing thickness relative value d_j；

Step 8：Build and train neutral net；

Step 9：Extensive neutral net, sample when will differ from training are input in the neutral net trained, Error ε between the output valve actual casing thickness value corresponding with sample of calculating neutral net, judges whether the error ε meets reality The requirement of border error, if meeting to require, step 10 is transferred to, otherwise goes to step 8 structures for re-starting neutral net and training；

Step 10：The neutral net for being built and being trained using step 8 is handled data, obtains sleeve pipe actual (real) thickness value e_j。

The features of the present invention also resides in,

Wherein, step 4 is specifically implemented according to following steps：

Step 4.1：By a_j~a_j+n-1Data obtain the average value Mean of the i-th bag data as the i-th bag data_i；Its In, i=2,3 ... I；N=5,3,1, and n initial value is set as 5；

Step 4.2：Obtain the bag data average value Mean of this (adjacent) two_iAnd Mean_i-1Rate of change rate_i(0<rate< 1)；The rate of change formula for seeking two bag data average values is：

Wherein, abs is takes absolute value function, Mean_iFor the average value of the i-th bag data, Mean_i-1For the flat of the i-th bag data Average；

Step 4.3：Judge rate of change rate_iWhether setting value rate is less than or equal to,

If rate_iLess than or equal to rate, then replaced with the average value of n maximum in the i-th bag data in the i-th bag data N maximum, then go to step 4.4；

If rate_iMore than setting value rate, n=n-2 is made, judges whether n is equal to 1, step 4.4 is transferred to if n is equal to 1, Step 4.1, which is transferred to, if n is more than 1 recalculates Mean_i,

Step 4.4:I=i+1 is made, judges whether i is less than I, meets that then return to step 4.1 continues to calculate this condition；If i= I is transferred to step 5.

Step 5 is specifically implemented according to following steps：

Step 5.1：Seek a_r-8~a_r+8Maximum M in (r=9,10,11 ... J)_maxAnd minimum M_min；

Step 5.2：Use a_r-8~a_r+8In each data respectively with maximum M_maxAnd minimum M_minCompare, if the number According to maximum M_maxOr minimum M_minIt is equal, then b_j=a_j,；If the data neither with maximum M_maxIt is equal also not with minimum Value M_minIt is equal, then b_j=0,

Step 5.3：R=r+1 is made, judges whether r is less than or equal to J-8, meets that then return to step 5.1 continues to count this condition Calculate；If r is transferred to step 6 more than J-8.

Step 7 is specifically implemented according to following steps：

Step 7.1：Make t=2, d₁=a₁；

Step 7.2：Judge c_tWhether a is equal to_tIf c_t=a_t, then d_t=a_t；Otherwise, d_t=d_t-1；

Step 7.3：T=t+1 is made, judges whether t is less than or equal to J, meets that then return to step 7.2 continues to calculate this condition； Otherwise it is transferred to step 7.4；

Step 7.4：To d_tTake absolute value to obtain casing thickness relative value d_j。

Wherein, step 8 is specifically implemented according to following steps：

Step 8.1, neutral net is built, defines each several part variable and function in neutral net

The input vector and output vector of wherein each layer be：

Input layer input vector：X=(x₁,x₂,L,x_l)

Hidden layer input vector：Hi=(hi₁,hi₂,L,hi_p)

Hidden layer output vector：Ho=(ho₁,ho₂,L,ho_p)

Output layer input vector：Yi=(yi₁,yi₂,L,yi_q)

Output layer output vector：Yo=(yo₁,yo₂,L,yo_q)

Desired output vector：Do=(do₁,do₂,L,do_q)

Wherein,

Input layer and the connection weight in intermediate layer：W_shS=1,2, L, l h=1,2, L, p

The connection weight of hidden layer and output layer：W_hoH=1,2, L, p o=1,2, L, q

The threshold value of each neuron of hidden layer：θ_hH=1,2, L, p

The threshold value of each neuron of output layer：θ_oO=1,2, L, q

Sample data number：K=1,2, LK, wherein, K represents number of samples；

Wherein, l represents input layer number,

P represents hidden layer neuron number,

Q represents output layer neuron number；

Hidden layer is using activation primitive：f₁(net)=net (1)

Output layer is using activation primitive：

Error function：

Step 8.2, neutral net initializes,

To input layer and the connection weight W in intermediate layer_sh, hidden layer and output layer connection weight W_ho, each nerve of hidden layer The threshold θ of member_h, each neuron of output layer threshold θ_oA random number in section (- 1,1) is assigned respectively, is given and is calculated essence Angle value 0.0001, maximum frequency of training Z=1000 and learning rate η=0.8；

Step 8.3, the sample for training is inputted, calculates the output valve of output layer, the sample being trained is known The thickness relative value of the sleeve pipe of actual (real) thickness value,

Specifically implement according to following steps：

Step 8.3.1, k-th of input sample is randomly selected,

X (k)=(x₁(k),x₂(k),L,x_l(k)),

Its desired output is：

Do (k)=(do₁(k),do₂(k),L,do_q(k))；Desired output herein is that the sleeve pipe corresponding to input sample is real Border thickness value,

Step 8.3.2, the input and output of each neuron of hidden layer are calculated,

The input of each neuron of hidden layer is：

Wherein, h=1,2, L, p； (4)

The output of each neuron of hidden layer is：

ho_h(k)=f₁(hi_h(k)) h=1,2, L, p； (5)

Step 8.3.3, the input and output of each neuron of output layer are calculated,

The input of each neuron of output layer is,

The output of each neuron of output layer is：

yo_o(k)=f₂(yi_o(k)) o=1,2, L q； (7)

Step 8.4, global error is calculated, and judges whether its precision meets the requirements：

Step 8.4.1：Utilize the desired output d in step 8.3_oAnd reality output yo (k)_o(k) difference between, is obtained Global error,

Whether the global error of the neutral net calculated in step 8.4.2, judgment step 8.4.1 meets to require, if entirely Office's error is not up to default precision 0.0001 and frequency of training is less than the maximum times 1000 of setting, then goes to step 8.5 and repaiied Just, if global error reaches default precision 0.0001 or learns the maximum times 1000 that number is more than setting, 9 are gone to step；

Step 8.5, calculated according to network desired output do (k) and reality output yo (k), to input layer and intermediate layer Connection weight W_sh, hidden layer and output layer connection weight W_ho, each neuron of hidden layer threshold θ_h, each neuron of output layer Threshold θ_oIt is modified,

Specifically implement according to following steps：

Step 8.5.1, using error function e, output layer is calculated to the connection weight adjustment amount Δ w of hidden layer_ho；

Because

If willIt is defined as-δ_o(k), i.e.,

Then (9) formula abbreviation is

Δw_ho=η δ_o(k)ho_h(k) (12)

Step 8.5.2, using error function e, hidden layer is calculated to the connection weight adjustment amount Δ w of input layer_lh；

Because

If willIt is defined as-δ_h(k), i.e.,

Then formula (13) abbreviation is

Δw_sh=η δ_h(k)x_s(k) (16)

Step 8.5.3, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of output layer_o；

Step 8.5.4, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of hidden layer_h；

Step 8.5.4, utilize the δ of each neuron of output layer_o(k) and each neuron of hidden layer output ho_h(k) correct Connection weight w_ho(k)；

After then correcting,

Wherein z (z=1,2,3 ..., Z) it is frequency of training；

Step 8.5.5：Utilize the δ of each neuron of hidden layer_h(k) and each neuron of input layer input x_s(k) amendment connection Weight w_sh(k)；

After then correcting,

Step 8.5.6：Correct the threshold θ of each neuron of hidden layer_hWith the threshold θ of each neuron of output layer_o；

After then correcting,

θ_h ^z+1=θ_h+Δθ_h (21)

θ_o ^z+1=θ_o+Δθ_o (22)

Using revisedθ_h ^z+1And θ_o ^z+1Return to step 8.3 is trained again, wherein revisedWith θ_o ^z+1WithWith θ_h ^z+1The w corresponded respectively in the formula in step 8.3 (6)_hoWith and θ_oW in formula (4)_shWith θ_h。

Step 10 is specifically implemented according to following steps：

Step 10.1, casing thickness relative value d step 7 drawn_jAs input value be input to step 9 carry out it is extensive after In obtained neutral net, hidden layer input vector hi is obtained using formula (4)_h(j)；

Step 10.2：By the input vector hi of the hidden layer obtained in step 10.1_h(j) it is public to substitute into hidden layer output vector Formula (5) ho_h(j)=f₁(hi_h(j) in) h=1,2, L, p,

Obtain hidden layer output vector ho_h(j)；

Step 10.3：By ho_h(j) the input vector formula (6) of output layer is substituted into：

Obtain the input vector yi of output layer_o(j)；

Step 10.4：By yi_o(j) output layer output vector formula is substituted into：

yo_o(j)=f₂(yi_o(j)) o=1,2, L q,

Obtain output layer output vector yo_o(j), i.e. sleeve pipe actual (real) thickness value e_j。

The invention has the advantages that data point need not be fitted to multinomial by the inventive method then tries to achieve extreme value Point, data waveform amplitude is directly extracted by initial data, not only execution efficiency is high, and is not influenceed by data amount check；According to Data variation rate replaces the processing method of maximum with average value, and flash removed can be gone to disturb, and improves precision.Therefore present invention side Method has that processing data is more efficient, precision is higher, the simpler advantage of Project Realization.

Brief description of the drawings

Fig. 1 is the flow chart for the data processing method that the present invention obtains petroleum casing pipe thickness；

Fig. 2 is the ripple that log data connects into step 1 in the data processing method of the invention for obtaining petroleum casing pipe thickness Shape detail view；

Fig. 3 is that the present invention obtains dispersion number in the step 3 and step 4 obtained in the data processing method of petroleum casing pipe thickness According to the discrete envelope figure of the most value of waveforms amplitude；

Fig. 4 is the thickness log at the coupling of petroleum casing pipe measured in practice；

Fig. 5 is that the petroleum casing pipe obtained in the data processing method of present invention acquisition petroleum casing pipe thickness by step 7 connects Thickness is with respect to change curve at hoop；

Fig. 6 is to utilize neutral net to carry out data processing in the data processing method of present invention acquisition petroleum casing pipe thickness Flow chart

Fig. 7 is that the extensive output of BP neural network and expectation are defeated in the data processing method of the invention for obtaining petroleum casing pipe thickness Go out data line chart；

Fig. 8 is that the extensive output of BP neural network and expectation are defeated in the data processing method of the invention for obtaining petroleum casing pipe thickness The error amount line chart gone out；

Fig. 9 is that the present invention obtains in the data processing method of petroleum casing pipe thickness casing wall thickness schematic diagram at box cupling.

Embodiment

The present invention is described in detail with reference to the accompanying drawings and detailed description.

The present invention obtains the data processing method of petroleum casing pipe thickness, as shown in figure 1, specifically implementing according to following steps：

Step 1：Log data is gathered with logger；

Step 2：Using continuous every 5 log datas measured in step 1 as one group, find out in each group of data most Big value a_j(j=1,2,3 ... J)；

Step 3：Take j=1,2,3,4,5, i.e., a₁~a₅As the 1st bag data, the average value of the 1st bag data is obtained Mean₁And replace a₁~a₅；

Step 4：Remainder data during to j ＞=6 does average value processing：

Step 4.1：By a_j~a_j+n-1(n=5,3,1) data obtain the i-th bag as i-th (i=2,3 ... I) bag data The average value Mean of data_i；If n initial value is 5；

Step 4.2：Obtain the bag data average value Mean of this (adjacent) two_iAnd Mean_i-1Rate of change rate_i(0<rate< 1)；The rate of change formula for seeking two bag data average values is：

Wherein, abs is takes absolute value function, Mean_iFor the average value of the i-th bag data, Mean_i-1For the flat of the i-th bag data Average；

Step 4.3：Judge rate of change rate_iWhether setting value rate is less than or equal to,

If rate_iLess than or equal to rate, then replaced with the average value of n maximum in the i-th bag data in the i-th bag data N maximum, then go to step 4.4；

If rate_iMore than setting value rate, n=n-2 is made, judges whether n is equal to 1, step 4.4 is transferred to if n is equal to 1, Step 4.1, which is transferred to, if n is more than 1 recalculates Mean_i。

Step 4.4：I=i+1 is made, judges whether i is less than I, meets that then return to step 4.1 continues to calculate this condition；If i= I is transferred to step 5.

Step 5：Data a after being handled according to step 4_j(j=1,2,3 ... J) generation assistance data b_j(j=1,2,3 ... J),

Specifically implement according to following steps：

Step 5.1：Seek a_r-8~a_r+8Maximum M in (r=9,10,11 ... J)_maxAnd minimum M_min。

Step 5.2：Use a_r-8~a_r+8In each data respectively with maximum M_maxAnd minimum M_minCompare, if the number According to maximum M_maxOr minimum M_minIt is equal, then b_j=a_j,；If the data neither with maximum M_maxIt is equal also not with minimum Value M_minIt is equal, then b_j=0.

Step 5.3：R=r+1 is made, judges whether r is less than or equal to J-8, meets that then return to step 5.1 continues to count this condition Calculate；If r is transferred to step 6 more than J-8.

Step 6：Find out a_jFlex point c_j.If a_j=b_j, then c_j=a_j；Otherwise, c_j=0.

Step 7：According to flex point c_j, obtain casing thickness relative value d_j。

Specifically implement according to following steps：

Step 7.1：Make t=2, d₁=a₁；

Step 7.2：Judge c_tWhether a is equal to_tIf c_t=a_t, then d_t=a_t；Otherwise, d_t=d_t-1。

Step 7.3：T=t+1 is made, judges whether t is less than or equal to J, meets that then return to step 7.2 continues to calculate this condition； Otherwise it is transferred to step 7.4.

Step 7.4：To d_tTake absolute value to obtain casing thickness relative value d_j。

Step 8：Build and train neutral net, as shown in fig. 6, specifically implementing according to following steps：

Step 8.1, neutral net is built, defines each several part variable and function in neutral net

The input vector and output vector of wherein each layer be：

Input layer input vector：X=(x₁,x₂,L,x_l)

Hidden layer input vector：Hi=(hi₁,hi₂,L,hi_p)

Hidden layer output vector：Ho=(ho₁,ho₂,L,ho_p)

Output layer input vector：Yi=(yi₁,yi₂,L,yi_q)

Output layer output vector：Yo=(yo₁,yo₂,L,yo_q)

Desired output vector：Do=(do₁,do₂,L,do_q)

Wherein,

Input layer and the connection weight in intermediate layer：W_shS=1,2, L, l h=1,2, L, p

The connection weight of hidden layer and output layer：W_hoH=1,2, L, p o=1,2, L, q

The threshold value of each neuron of hidden layer：θ_hH=1,2, L, p

The threshold value of each neuron of output layer：θ_oO=1,2, L, q

Sample data number：K=1,2, L K, wherein, K represents number of samples；

Wherein, l represents input layer number,

P represents hidden layer neuron number,

Q represents output layer neuron number.

Hidden layer is using activation primitive：f₁(net)=net (1)

Output layer is using activation primitive：

Error function：

Step 8.2, neutral net initializes,

To input layer and the connection weight W in intermediate layer_sh, hidden layer and output layer connection weight W_ho, each nerve of hidden layer The threshold θ of member_h, each neuron of output layer threshold θ_oA random number in section (- 1,1) is assigned respectively, is given and is calculated essence Angle value 0.0001, maximum frequency of training Z=1000 and learning rate η=0.8；

Step 8.3, the sample for training is inputted, calculates the output valve of output layer, the sample being trained is known The thickness relative value of the sleeve pipe of actual (real) thickness value,

Specifically implement according to following steps：

Step 8.3.1, k-th of input sample is randomly selected,

X (k)=(x₁(k),x₂(k),L,x_l(k)),

Its desired output is：

Do (k)=(do₁(k),do₂(k),L,do_q(k))；Desired output herein is that the sleeve pipe corresponding to input sample is real Border thickness value,

Step 8.3.2, the input and output of each neuron of hidden layer are calculated,

The input of each neuron of hidden layer is：

Wherein, h=1,2, L, p； (4)

The output of each neuron of hidden layer is：

ho_h(k)=f₁(hi_h(k)) h=1,2, L, p； (5)

Step 8.3.3, the input and output of each neuron of output layer are calculated,

The input of each neuron of output layer is,

The output of each neuron of output layer is：

yo_o(k)=f₂(yi_o(k)) o=1,2, L q； (7)

Step 8.4, global error is calculated, and judges whether its precision meets the requirements：

Step 8.4.1：Utilize the desired output d in step 8.3_oAnd reality output yo (k)_o(k) difference between, is obtained Global error,

Whether the global error of the neutral net calculated in step 8.4.2, judgment step 8.4.1 meets to require, if entirely Office's error is not up to default precision 0.0001 and frequency of training is less than the maximum times 1000 of setting, then goes to step 8.5 and repaiied Just, if global error reaches default precision 0.0001 or learns the maximum times 1000 that number is more than setting, 9 are gone to step.

Step 8.5, calculated according to network desired output do (k) and reality output yo (k), to input layer and intermediate layer Connection weight W_sh, hidden layer and output layer connection weight W_ho, each neuron of hidden layer threshold θ_h, each neuron of output layer Threshold θ_oIt is modified,

Specifically implement according to following steps：

Step 8.5.1, using error function e, output layer is calculated to the connection weight adjustment amount Δ w of hidden layer_ho。

Because

If willIt is defined as-δ_o(k), i.e.,

Then formula (9) abbreviation is

Δw_ho=η δ_o(k)ho_h(k) (12)

Step 8.5.2, using error function e, hidden layer is calculated to the connection weight adjustment amount Δ w of input layer_lh。

Because

If willIt is defined as-δ_h(k), i.e.,

Then formula (13) abbreviation is

Δw_sh=η δ_h(k)x_s(k) (16)

Step 8.5.3, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of output layer_o。

Step 8.5.4, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of hidden layer_h。

Step 8.5.4, utilize the δ of each neuron of output layer_o(k) and each neuron of hidden layer output ho_h(k) correct Connection weight w_ho(k)；

After then correcting,

Wherein z (z=1,2,3 ..., Z) it is frequency of training；

Step 8.5.5：Utilize the δ of each neuron of hidden layer_h(k) and each neuron of input layer input x_s(k) amendment connection Weight w_sh(k)；

After then correcting,

Step 8.5.6：Correct the threshold θ of each neuron of hidden layer_hWith the threshold θ of each neuron of output layer_o。

After then correcting,

θ_h ^z+1=θ_h+Δθ_h (21)

θ_o ^z+1=θ_o+Δθ_o (22)

Using revisedθ_h ^z+1And θ_o ^z+1Return to step 8.3 is trained again, wherein revisedWith θ_o ^z+1WithWith θ_h ^z+1The w corresponded respectively in the formula in step 8.3 (6)_hoWith and θ_oW in formula (4)_shWith θ_h。

Step 9：Extensive neutral net, sample when will differ from training are input in the neutral net trained, Error ε between the output valve actual casing thickness value corresponding with sample of calculating neutral net, judges whether the error ε meets reality Border error requirement (0.75mm, ε be less than casing thickness 10%), if meet require, be transferred to step 10, otherwise go to step 8 Re-start structure and the training of neutral net.

Step 10：The neutral net for being built and being trained using step 8 is handled data, obtains sleeve pipe actual (real) thickness value e_j, specifically implement according to following steps：

Step 10.1, casing thickness relative value d step 7 drawn_jAs input value be input to step 9 carry out it is extensive after In obtained neutral net, hidden layer input vector hi is obtained using formula (4)_h(j)；

Step 10.2：By the input vector hi of the hidden layer obtained in step 10.1_h(j) it is public to substitute into hidden layer output vector Formula (5) ho_h(j)=f₁(hi_h(j) in) h=1,2, L, p,

Obtain hidden layer output vector ho_h(j)；

Step 10.3：By ho_h(j) the input vector formula (6) of output layer is substituted into：

Obtain the input vector yi of output layer_o(j)；

Step 10.4：By yi_o(j) output layer output vector formula is substituted into：

yo_o(j)=f₂(yi_o(j)) o=1,2, L q

Obtain output layer output vector yo_o(j), i.e. sleeve pipe actual (real) thickness value e_j。

During step 1 gathered data, new double far-field electromagnetic focusing thickness meters, the data measured such as Fig. 2 well loggings are used Shown in the waveform detail view that data connect into, data point therein is exactly the data used in the inventive method in step 1.Well logging Data are the data on the log parameter curve by the data collecting module collected of logger.Due to the remote biography of data It is defeated, it is desirable to describing the information data transmission of each physical parameter in underground should as quickly as possible, it is few, and accurately.This experimental data is to use The log data of the 5 data points composition sampled on the thickness curve at coupling of petroleum casing pipe in a measurement period, it is each The amplitude of point represents the casing thickness inscribed when this.

Fig. 3 is the discrete envelope figure of most value for the discrete data waveforms amplitude that step 3 and step 4 obtain, wherein index point * Represent data point；Fig. 4 is the thickness log at coupling of petroleum casing pipe, log be by logger in depth under The curve of each physical parameter in underground is measured during upper km；By comparison diagram 3 and Fig. 4, two figures have identical amplitude Profile, show that the inventive method being capable of the accurate amplitude extracted on thickness log.

Fig. 5 be at coupling of petroleum casing pipe that step 7 obtains thickness with respect to change curve.

Fig. 7 is the extensive output of BP neural network and desired output.The extensive output of BP neural network and desired output in figure Error is as shown in Figure 8.Know from figure, its worst error is 0.3368mm, fully meets engineering demand.

Fig. 9 is casing wall thickness schematic diagram at box cupling.At box cupling actual casing wall thickness be followed successively by from left to right 7.5mm, 17.75mm、10.25mm、17.75mm、7.5mm.Alphabetical A, B, C, D, E meaning curve thickness characterizes successively in Fig. 5 figures connects Actual casing wall thickness 7.5mm, 17.75mm, 10.25mm, 17.75mm, 7.5mm at hoop.Pass through result figure and schematic diagram Contrast knows that the result of the inventive method processing meets casing wall actual (real) thickness change curve.

The inventive method, it is not necessary to data point is fitted to multinomial and then tries to achieve extreme point, is directly carried by initial data According to waveforms amplitude, not only execution efficiency is high, precision is high, and is not influenceed by data amount check for access.Therefore, can be quick and precisely Ground obtains petroleum casing pipe thickness from a large amount of log datas.

Claims (3)

1. obtain the data processing method of petroleum casing pipe thickness, it is characterised in that specifically implement according to following steps：

Step 1：Log data is gathered with logger；

Step 2：Using continuous every 5 log datas measured in step 1 as one group, the maximum in each group of data is found out a_j, wherein, j=1,2,3 ... J；

Step 3：Take j=1,2,3,4,5, i.e., a₁~a₅As the 1st bag data, the average value Mean of the 1st bag data is obtained₁And Instead of a₁~a₅；

Step 4：Remainder data during to j ＞=6 does average value processing, specifically implements according to following steps：

Step 4.1：By a_j~a_j+n-1Data obtain the average value Mean of the i-th bag data as the i-th bag data_i；Wherein, i= 2,3…I；N=5,3,1, and n initial value is set as 5；

Step 4.2：Obtain this adjacent two bag datas average value Mean_iAnd Mean_i-1Rate of change rate_i, wherein, 0<rate_i<1； The rate of change formula for seeking two bag data average values is：

<mrow> <msub> <mi>rate</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>a</mi> <mi>b</mi> <mi>s</mi> <mfrac> <mrow> <msub> <mi>Mean</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>Mean</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>Mean</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow>

Wherein, abs is takes absolute value function, Mean_iFor the average value of the i-th bag data, Mean_i-1For being averaged for the i-th -1 bag data Value；

Step 4.3：Judge rate of change rate_iWhether setting value rate is less than or equal to,

If rate_iLess than or equal to rate, then n in the i-th bag data are replaced with the average value of n maximum in the i-th bag data Maximum, then go to step 4.4；

If rate_iMore than setting value rate, n=n-2 is made, judges whether n is equal to 1, step 4.4 is transferred to if n is equal to 1, if n is big Step 4.1, which is transferred to, in 1 recalculates Mean_i,

Step 4.4:I=i+1 is made, judges whether i is less than I, meets that then return to step 4.1 continues to calculate this condition；If i=I turns Enter step 5；

Step 5：Data a after being handled according to step 4_jGenerate assistance data b_j；Specifically implement according to following steps：

Step 5.1：For r=9,10,11 ... J, a is sought respectively_r-8~a_r+8In maximum M_maxAnd minimum M_min；

Step 5.2：Use a_r-8~a_r+8In each data respectively with maximum M_maxAnd minimum M_minCompare, if the data with Maximum M_maxOr minimum M_minIt is equal, then b_j=a_j；If the data neither with maximum M_maxIt is equal also not with minimum M_min It is equal, then b_j=0,

Step 5.3：R=r+1 is made, judges whether r is less than or equal to J-8, meets that then return to step 5.1 continues to calculate this condition；If r Step 6 is transferred to more than J-8；

Step 6：By contrasting a_jWith b_j, find out a_jFlex point c_jIf, i.e. a_j=b_j, then c_j=a_j；Otherwise, c_j=0；

Step 7：According to flex point c_j, obtain casing thickness relative value d_j；Specifically implement according to following steps：

Step 7.1：Make t=2, d₁=a₁；

Step 7.2：Judge c_tWhether a is equal to_tIf c_t=a_t, then d_t=a_t；Otherwise, d_t=d_t-1；

Step 7.3：T=t+1 is made, judges whether t is less than or equal to J, meets that then return to step 7.2 continues to calculate this condition；Otherwise It is transferred to step 7.4；

Step 7.4：To d_tTake absolute value to obtain casing thickness relative value d_j；

Step 8：Build and train neutral net；

Step 9：Extensive neutral net, sample when will differ from training are input in the neutral net trained, are calculated Error ε between the output valve of neutral net actual casing thickness value corresponding with sample, judges whether the error ε meets actual mistake The requirement of difference, if meeting to require, step 10 is transferred to, otherwise goes to step 8 structures for re-starting neutral net and training；

Step 10：The neutral net for being built and being trained using step 8 is handled data, obtains sleeve pipe actual (real) thickness value e_j。

2. the data processing method according to claim 1 for obtaining petroleum casing pipe thickness, it is characterised in that described step 8 specifically implement according to following steps：

Step 8.1, neutral net is built, defines each several part variable and function in neutral net

The input vector and output vector of wherein each layer be：

Input layer input vector：X=(x₁,x₂,…,x_l)

Hidden layer input vector：Hi=(hi₁,hi₂,…,hi_p)

Hidden layer output vector：Ho=(ho₁,ho₂,…,ho_p)

Output layer input vector：Yi=(yi₁,yi₂,…,yi_q)

Output layer output vector：Yo=(yo₁,yo₂,…,yo_q)

Desired output vector：Do=(do₁,do₂,…,do_q)

Wherein,

The connection weight in input layer and intermediate layer is W_sh, wherein, s=1,2 ..., l, h=1,2 ..., p,

The connection weight of hidden layer and output layer is W_ho, wherein, o=1,2 ..., q,

The threshold value of each neuron of hidden layer is θ_h,

The threshold value of each neuron of output layer is θ_o,

Sample data number：K=1,2 ... K, wherein, K represents number of samples；

Wherein, l represents input layer number,

P represents hidden layer neuron number,

Q represents output layer neuron number；

Hidden layer is using activation primitive：f₁(net)=net (1)

Output layer is using activation primitive：

Error function：

Step 8.2, neutral net initializes,

To input layer and the connection weight W in intermediate layer_sh, hidden layer and output layer connection weight W_ho, hidden layer each neuron Threshold θ_h, each neuron of output layer threshold θ_oA random number in section (- 1,1) is assigned respectively, gives computational accuracy value 0.0001, maximum frequency of training Z=1000 and learning rate η=0.8；

Step 8.3, the sample for training is inputted, calculates the output valve of output layer, the sample being trained is known reality The thickness relative value of the sleeve pipe of thickness value,

Specifically implement according to following steps：

Step 8.3.1, k-th of input sample is randomly selected,

X (k)=(x₁(k),x₂(k),…,x_l(k)),

Its desired output is：

Do (k)=(do₁(k),do₂(k),…,do_q(k))；Desired output herein is that the sleeve pipe corresponding to input sample is actual Thickness value,

Step 8.3.2, the input and output of each neuron of hidden layer are calculated,

The input of each neuron of hidden layer is：

Wherein, h=1,2 ..., p；(4)

The output of each neuron of hidden layer is：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>ho</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>p</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

Step 8.3.3, the input and output of each neuron of output layer are calculated,

The input of each neuron of output layer is,

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <msub> <mi>ho</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>o</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

The output of each neuron of output layer is：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>yo</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>o</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Step 8.4, global error is calculated, and judges whether its precision meets the requirements：

Step 8.4.1：Utilize the desired output do (k) in step 8.3 and reality output yo_o(k) difference between, obtains the overall situation Error,

Whether the global error of the neutral net calculated in step 8.4.2, judgment step 8.4.1 meets to require, if global miss The not up to default precision 0.0001 of difference and frequency of training are less than the maximum times 1000 of setting, then go to step 8.5 and be modified, if Global error reaches default precision 0.0001 or learns the maximum times 1000 that number is more than setting, then goes to step 9；

Step 8.5, according to network desired output do (k) and reality output yo_o(k) calculated, to input layer and the company in intermediate layer Meet weights W_sh, hidden layer and output layer connection weight W_ho, each neuron of hidden layer threshold θ_h, each neuron of output layer threshold Value θ_oIt is modified,

Specifically implement according to following steps：

Step 8.5.1, using error function e, output layer is calculated to the connection weight adjustment amount Δ w of hidden layer_ho；

<mrow> <msub> <mi>&amp;Delta;w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

Because

<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <msub> <mi>ho</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>ho</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

If willIt is defined as-δ_o(k), i.e.,

Then (9) formula abbreviation is

Δw_ho=η δ_o(k)ho_h(k) (12)

Step 8.5.2, using error function e, hidden layer is calculated to the connection weight adjustment amount Δ w of input layer_sh；

<mrow> <msub> <mi>&amp;Delta;w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

Because

<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>s</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>1</mn> </munderover> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>h</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

If willIt is defined as-δ_h(k), i.e.,

Then formula (13) abbreviation is

Δw_sh=η δ_h(k)x_s(k) (16)

Step 8.5.3, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of output layer_o；

<mrow> <msub> <mi>&amp;Delta;&amp;theta;</mi> <mi>o</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

Step 8.5.4, utilize error function e, the adjusting thresholds amount Δ θ of calculating each neuron of hidden layer_h；

<mrow> <msub> <mi>&amp;Delta;&amp;theta;</mi> <mi>h</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;theta;</mi> <mi>h</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>&amp;eta;</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>e</mi> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>hi</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;theta;</mi> <mi>h</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

Step 8.5.4, utilize the δ of each neuron of output layer_o(k) and each neuron of hidden layer output ho_h(k) connected to correct Weight w_ho(k)；

After then correcting,

<mrow> <msubsup> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> <mrow> <mi>z</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>

Wherein z is frequency of training, 1≤z≤Z；

Step 8.5.5：Utilize the δ of each neuron of hidden layer_h(k) and each neuron of input layer input x_s(k) connection weight is corrected w_sh(k)；

After then correcting,

<mrow> <msubsup> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> <mrow> <mi>z</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msub> <mi>w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;w</mi> <mrow> <mi>s</mi> <mi>h</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>

Step 8.5.6：Correct the threshold θ of each neuron of hidden layer_hWith the threshold θ of each neuron of output layer_o；

After then correcting,

θ_h ^z+1=θ_h+Δθ_h (21)

θ_o ^z+1=θ_o+Δθ_o (22)

Using revisedθ_h ^z+1And θ_o ^z+1Return to step 8.3 is trained again, wherein revisedWith θ_o ^z+1WithWith θ_h ^z+1The w corresponded respectively in the formula in step 8.3 (6)_hoWith and θ_oW in formula (4)_shWith θ_h。

3. the data processing method according to claim 2 for obtaining petroleum casing pipe thickness, it is characterised in that described step 10 specifically implement according to following steps：

Step 10.1, casing thickness relative value d step 7 drawn_jAs input value be input to step 9 carry out it is extensive after obtain Neutral net in, obtain hidden layer input vector hi using formula (4)_h(j)；

Step 10.2：By the input vector hi of the hidden layer obtained in step 10.1_h(j) hidden layer output vector formula is substituted into (5)：

In,

Obtain hidden layer output vector ho_h(j)；

Step 10.3：By ho_h(j) the input vector formula (6) of output layer is substituted into：

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>p</mi> </munderover> <msub> <mi>w</mi> <mrow> <mi>h</mi> <mi>o</mi> </mrow> </msub> <msub> <mi>ho</mi> <mi>h</mi> </msub> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>o</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>

Obtain the input vector yi of output layer_o(j)；

Step 10.4：By yi_o(j) output layer output vector formula is substituted into：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>yo</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>yi</mi> <mi>o</mi> </msub> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>o</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mi>q</mi> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> </mrow>

Obtain output layer output vector yo_o(j), i.e. sleeve pipe actual (real) thickness value e_j。