CN106202666A - A kind of computational methods of marine shafting bearing adjustment of displacement - Google Patents

Abstract

The computational methods of a kind of marine shafting bearing adjustment of displacement, belong to marine propuision system technical field.The single construction that these computational methods adjust tail pipe rear bearing load for practice of construction scene needs, establish the one established based on quadratic programming with " tail pipe rear bearing load is minimum " and " bearing adjustment of displacement amount is minimum ", be the bearing adjustment of displacement optimization method of optimization aim simultaneously.Adjust the needs of multiple bearing loads for practice of construction scene, the load after conjugating using bearing is minimum as optimization aim with the absolute value of expected load difference.The computational methods optimization aim of this marine shafting bearing adjustment of displacement is clear and definite, optimizes constraints and meets practice of construction needs, simple operation and easily realizing, and when solving the adjustment of axle system, bearing displacement is difficult to the problem formulated, and improves centering of shafting efficiency.

Description

A kind of computational methods of marine shafting bearing adjustment of displacement

Technical field

The present invention relates to the computational methods of a kind of marine shafting bearing adjustment of displacement, belong to marine propuision system technology neck Territory.

Background technology

Along with the maximization day by day of shipping boats and ships, shaft alignment becomes more difficult, and centering of shafting is bad leads Causing bearing high temperature, cause tile kilning phenomenon, severe patient causes boats and ships to stop transport, and brings huge economic loss.At present, domestic and international shipyard It is difficult to once mounting axle system and i.e. realizes the reasonable distribution of bearing load, the most also need to adjust bearing displacement and make each bearing load full The requirement of foot centering of shafting.When formulating bearing adjustment of displacement scheme, common practices is work warps based on site operation personnel Testing and be adjusted bearing, this way is with the biggest blindness and higher to the competency profiling of workmen.

For the formulating method of bearing adjustment of displacement amount during centering of shafting, a lot of scholars often carry with tail pipe rear axle Lotus is minimum as optimization aim, and this optimization method with the tail pipe minimum guiding of rear bearing load does not also meet the construction of reality Need, do not consider the shadow of bearing rigidity in the bearing load impact setting up bearing adjustment of displacement optimized algorithm institute foundation simultaneously Ring, the most main frame bearing is not considered as entirety when constraints sets, does not meets practical construction process.

Summary of the invention

Present invention aims to the deficiency that prior art exists, it is provided that a kind of marine shafting bearing adjustment of displacement Computational methods, to obtaining the bearing adjustment of displacement amount meeting practical construction process, instruct Shafting Alignment of Vessels middle (center) bearing load Adjust.

The technical solution used in the present invention is: the computational methods of a kind of marine shafting bearing adjustment of displacement, including following step Rapid:

The first step: calculate and consider that the bearing load of bearing rigidity affects number

1) Propulsion Systems is reduced to the one-dimensional continuous beam system of multi-point support, and bears vertical concentrfated load, uniform Load and the effect of moment of flexure；

2) based on top act method calculation bearing rigidity

It is placed in the load of hydraulic jack near measured bearing by measurement and determines tested according to jack up factor The load of bearing；After determining measured bearing load, obtain bearing rigidity K in conjunction with bearing decrement under load effect_i, formula Subrepresentation is as follows:

$K_i=\frac{R_i}{H_i}$

In formula: R_iFor measured bearing load；H_iFor measured bearing decrement；

Wherein, measured bearing load

Measured bearing decrement

Thus, bearing rigidity K_iIt is

In formula: c is jack up factor, obtains from centering of shafting calculated description；Load Q, P and displacement Y_jLifted curve by top to obtain ?；

3) consider that the bearing load of bearing rigidity affects number based on Finite element arithmetic

In formula: R_i,0Represent the load value of the i-th bearing before bearing adjustment of displacement；ΔY_jRepresent that jth bearing displacement is adjusted Whole amount；R_i,jRepresent the jth bearing reaction influence number to i-th bearing；It is reaction influence number；

By ANSYS finite element software, set up axle system one-dimensional model, bearing is equivalent to Hookean spring, carry out grid and draw Divide, retrain and load applying, finally carry out solving the extraction calculated with bearing load data；By displacement in change model about Bundle, calculates and tries to achieve each bearing load after bearing conjugates 1 unit successively, finally deduct the load before each bearing does not conjugates and i.e. ask Must consider that the bearing load of bearing rigidity affects number；

Second step: definition optimization object function

1) optimization object function based on quadratic programming is defined

Set up based on quadratic programming with tail pipe rear bearing load and the most minimum optimization aim of bearing adjustment of displacement amount Object function, as follows:

$\begin{array}{cc}\min & Y^{T}HY+{\mathrm{tR}}_n^{T}Y\end{array}$

In formula: Y=(Δ Y₁,…,ΔY_j,…,ΔY_n)；H=diag_n×n(10^κ,…,10^κ,…,10^κ), κ and t is impact The factor, its purpose adjusts displacement and load proportion in optimization aim；R_n=(R_n,1,…,R_n,j,…,R_n,n)^T, subscript n acute pyogenic infection of finger tip Tail pipe rear bearing；

2) optimization object function that definition is planned based on the Special Nonlinear with absolute value number

Foundation is for the load optimal function of multiple bearings:

$\begin{array}{cc}min& \underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|\end{array}$

In formula:AndR_iLFor bearing expected load；

3rd step: definition optimizes restrictive condition

1) the load constraint after the displacement of definition bearing

Load after bearing displacement is constrained to:

R_iMin≤R′_i≤R_iMax

In formula: R '_iLoad after conjugating for bearing；R_iMinTypically take the 80% of centering of shafting calculated description set-point；R_iMaxOne As take the 120% of centering of shafting calculated description set-point；

Measurement load and load variations amount before the displacement of above-mentioned formula bearing are expressed as:

$R_{iMin}\≤R_i+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}$

2) definition main frame bearing displacement constraint

When main frame bearing is adjusted, need to increase corresponding equality constraint:

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

Above formula is explained as follows:

Assuming that tailing axle end is position starting point, from stem to stern successively to bearing number, t=1～m, m represent boss rod Hold quantity, l_tRepresent the t main frame bearing position vertically；

3) the bearing displacement constraint not being adjusted is defined

The bearing displacement constraint not being adjusted: Δ Y_i=0

4) the bearing displacement constraint being adjusted is defined

Bearing displacement is less than adjusting range, therefore increases following displacement constraint:

ΔY_iMin≤ΔY_i≤ΔY_iMax

In formula: Δ Y_iMin、ΔY_iMaxValue according to site operation personnel need set；

4th step: solve the adjustment of displacement amount of each bearing based on nonlinear optimization algorithm

The function processing constrained optimization problem in Matlab optimization toolbox is utilized to carry out the non-of bearing adjustment of displacement amount Linear optimization calculates；Before application solved function, first bearing adjustment of displacement optimization problem is converted into standard solves form；

Bearing adjustment of displacement optimized algorithm standard based on quadratic programming solves form:

$\begin{array}{cc}s.t& \begin{array}{c}{\mathrm{minY}}^{T}HY+{\mathrm{tR}}_n^{T}Y\\ \underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}-R_i\\ -\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_i-R_{iMin}\end{array}\end{array}$

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

ΔY_i=0

ΔY_iMin≤ΔY_i≤ΔY_iMax

The bearing adjustment of displacement optimized algorithm standard planned based on the Special Nonlinear with absolute value number solves form:

$\begin{array}{cc}\min & \underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|\end{array}$

S.t. with the optimization restrictive condition of above-mentioned bearing adjustment of displacement optimized algorithm based on quadratic programming；

The derivation algorithm of quadratic programming, optimizes and revises problem for bearing displacement and solves selection dynamic sequence method or sequence Quadratic programming；

When utilizing Matlab specifically to solve quadratic programming problem, use function Quadprog, solve with absolute value number Special Nonlinear planning problem time, apply function Fmincon.

The invention has the beneficial effects as follows: the computational methods optimization aim of this marine shafting bearing adjustment of displacement is clear and definite, excellent Changing constraints and meet practice of construction needs, simple operation and easily realizing, when solving the adjustment of axle system, bearing displacement is difficult to formulate Problem, improve centering of shafting efficiency.

Accompanying drawing explanation

Accompanying drawing is used for providing being best understood from the present invention, is not limited to the scope of the present invention.

Fig. 1 lifts curve synoptic diagram for top.

Fig. 2 is the calculation flow chart of the inventive method.

Detailed description of the invention

The computational methods of marine shafting bearing adjustment of displacement, comprise the following steps:

A, calculate and consider the bearing load of bearing rigidity and affect number；

B, definition optimization object function；

C, definition optimize restrictive condition；

D, solve the adjustment of displacement amount of each bearing based on nonlinear optimization algorithm；

In described step a, calculate and consider the bearing load of bearing rigidity and affect number and comprise the following steps:

1. Propulsion Systems is reduced to the one-dimensional continuous beam system of multi-point support, and bears vertical concentrfated load, uniform Load and the effect of moment of flexure；

2. the bearing rigidity computing formula calculation bearing rigidity derived based on top act method；

3. consider that the bearing load of bearing rigidity affects number by Finite element arithmetic；

In described step b, definition optimization object function comprises the following steps:

1., based on quadratic programming optimization method, establish with tail pipe rear bearing load and bearing adjustment of displacement amount the most minimum For the optimization object function of optimization aim, wherein load and each self-optimizing proportion of adjustment of displacement amount, regulated by factor of influence；

2., based on the Special Nonlinear optimization method with absolute value number, establish to adjust rear bearing load and expected load Differ the optimization object function of minimum optimization aim, the optimization proportion of the most each bearing load, regulated by weight ratio；

In described step c, definition optimizes restrictive condition and comprises the following steps:

1. the load constraint after the displacement of definition bearing；

2. definition main frame bearing displacement constraint；

3. define bearing (the not including main frame bearing) displacement constraint not being adjusted；

4. define the bearing displacement constraint being adjusted.

Specifically comprising the following steps that of the computational methods of above-mentioned marine shafting bearing adjustment of displacement

The first step: calculating considers the bearing load of bearing rigidity affects number

1) Propulsion Systems is reduced to the one-dimensional continuous beam system of multi-point support, and bears vertical concentrfated load, uniform Load and the effect of moment of flexure.

2) based on top act method calculation bearing rigidity

Top act method is to be placed in the load of hydraulic jack near measured bearing by measurement and come according to jack up factor Determine the load of measured bearing.After determining measured bearing load, the most available in conjunction with bearing decrement under load effect Bearing rigidity K_i, formula is expressed as follows:

$K_i=\frac{R_i}{H_i}$

In formula: R_iFor measured bearing load；H_iFor measured bearing decrement；

Wherein, measured bearing load

Measured bearing decrement

Thus, bearing rigidity K_iIt is

In formula: c is jack up factor, obtains from centering of shafting calculated description；Load Q, P and displacement Y_jLifted curve by top to obtain , with reference to Fig. 1.

3) consider that the bearing load of bearing rigidity affects number based on Finite element arithmetic

In formula: R_i,0Represent the load value of the i-th bearing before bearing adjustment of displacement；ΔY_jRepresent that jth bearing displacement is adjusted Whole amount；R_i,jRepresent the jth bearing reaction influence number to i-th bearing；It is reaction influence number；

By ANSYS finite element software, set up axle system one-dimensional model, bearing is equivalent to Hookean spring, carry out grid and draw Divide, retrain and load applying, finally carry out solving the extraction calculated with bearing load data, concrete calculation process such as Fig. 2.Pass through Change displacement constraint in model, it is possible to calculate and try to achieve each bearing load after bearing conjugates 1 unit successively, finally deduct each axle Hold the load before not conjugating can try to achieve consider bearing rigidity bearing load affect number.

Second step: definition optimization object function

1) optimization object function based on quadratic programming is defined

When reality measures marine propulsion shafting load, it sometimes appear that the situation that tail pipe rear bearing load is excessive, due to Tail pipe rear bearing stressing conditions is complicated, the most impaired, belongs to and pays close attention to object, it is also contemplated that during actual adjustment bearing displacement, Adjustment amount is difficult to excessive, thus establish based on quadratic programming with tail pipe rear bearing load and bearing adjustment of displacement amount The little object function for optimization aim, as follows:

$\begin{array}{cc}min& Y^{T}HY+{\mathrm{tR}}_n^{T}Y\end{array}$

In formula: Y=(Δ Y₁,…,ΔY_j,…,ΔY_n)；H=diag_n×n(10^κ,…,10^κ,…,10^κ), κ and t is impact The factor, its purpose adjusts displacement and load proportion in optimization aim；R_n=(R_n,1,…,R_n,j,…,R_n,n)^T, subscript n acute pyogenic infection of finger tip Tail pipe rear bearing；

2) optimization object function that definition is planned based on the Special Nonlinear with absolute value number

The bearing adjustment of displacement optimization object function based on quadratic programming of above-mentioned foundation, is only for tail pipe rear bearing The load optimal of the single bearing carried out, and field condition majority to be the most multiple bearing load be all unsatisfactory for that centering of shafting is wanted Ask, establish the load optimal function for multiple bearings for this:

$\begin{array}{cc}\min & \underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|\end{array}$

In formula:AndR_iLFor bearing expected load, (centering of shafting calculated description is given Theoretical value).

3rd step: definition optimizes restrictive condition

1) the load constraint after the displacement of definition bearing

When, after shafting installation, when bearing load is unsatisfactory for centering of shafting calculated description requirement, bearing being carried out adjustment of displacement, adjust At bearing load needs after whole within limits, the load after i.e. bearing conjugates is constrained to:

R_iMin≤R′_i≤R_iMax

In formula: R '_iLoad after conjugating for bearing；R_iMinTypically take the 80% of centering of shafting calculated description set-point；R_iMaxOne As take 120% (R of centering of shafting calculated description set-point_iMinAnd R_iMaxValue set also dependent on the needs of site operation personnel Fixed).

Measurement load and load variations amount before the displacement of above-mentioned formula bearing are expressed as:

$R_{iMin}\≤R_i+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}$

2) definition main frame bearing displacement constraint

Owing to main frame bearing is attached on main engine foundation, when main frame bearing is adjusted, All hosts axle often Make and move up and down for overall structure, therefore need to increase corresponding equality constraint:

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

Above formula is explained as follows:

Assuming that tailing axle end is position starting point, from stem to stern successively to bearing number, t=1～m, m represent boss rod Hold quantity, l_tRepresent the t main frame bearing position vertically；

3) bearing (the not including main frame bearing) displacement constraint not being adjusted is defined

In view of the needs of site technique, not all bearings are all carried out adjustment of displacement, such as tail tube bearing due to knot Structure limits can not carry out adjustment of displacement, thus increases corresponding equality constraint:

ΔY_i=0

4) the bearing displacement constraint being adjusted is defined

Considering actual condition, bearing displacement not can exceed that certain adjusting range, therefore increases following displacement constraint:

ΔY_iMin≤ΔY_i≤ΔY_iMax

In formula: Δ Y_iMin、ΔY_iMaxValue according to site operation personnel need set；

4th step: solve the adjustment of displacement amount of each bearing based on nonlinear optimization algorithm

Utilize the function processing constrained optimization problem in Matlab (Optimization Toolbox) optimization toolbox The nonlinear optimization carrying out bearing adjustment of displacement amount calculates.First bearing adjustment of displacement optimization was asked before application solved function Topic is converted into standard and solves form.

Bearing adjustment of displacement optimized algorithm standard based on quadratic programming solves form:

$\begin{array}{cc}s.t& \begin{array}{c}{\mathrm{minY}}^{T}HY+{\mathrm{tR}}_n^{T}Y\\ \underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}-R_i\\ -\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_i-R_{iMin}\end{array}\end{array}$

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

ΔY_i=0

ΔY_iMin≤ΔY_i≤ΔY_iMax

The bearing adjustment of displacement optimized algorithm standard planned based on the Special Nonlinear with absolute value number solves form:

$\begin{array}{cc}min& \underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|\end{array}$

S.t. with the optimization restrictive condition of above-mentioned bearing adjustment of displacement optimized algorithm based on quadratic programming；

Quadratic programming has the derivation algorithm of maturation, and particularly when H-matrix positive definite or positive semidefinite, quadratic programming problem is convex QP problem, its any locally optimal solution, is also globally optimal solution.Its general derivation algorithm includes: trusted zones bounce technique (Trust-region-reflective), dynamic sequence method (Active-set), interior point method (Interior-point- convex)。

For also wrapping in addition to above-mentioned three kinds of algorithms with the derivation algorithm of the Special Nonlinear criterion problem of absolute value number Containing Sequential Quadratic Programming method (Sequential Quadratic Programming).

Trusted zones bounce technique and interior point method belong to large-scale optimization algorithm, and dynamic sequence method and Sequential Quadratic Programming method belong to Medium-sized optimized algorithm.Large-scale optimization algorithm applies in general to only bound constraint or the situation of linear equality constraints, and medium-sized The optimized algorithm suitability is relatively wide, optimizes and revises solving of problem thus for bearing displacement and select dynamic sequence method or sequence Quadratic programming.

When utilizing Matlab specifically to solve quadratic programming problem, function Quadprog can be used, solve with definitely Value number Special Nonlinear planning problem time, function Fmincon can be applied.

Claims (1)

1. the computational methods of a marine shafting bearing adjustment of displacement, it is characterised in that: comprise the following steps:

The first step: calculate and consider that the bearing load of bearing rigidity affects number

1) Propulsion Systems is reduced to the one-dimensional continuous beam system of multi-point support, and bears vertical concentrfated load, uniform load Effect with moment of flexure；

2) based on top act method calculation bearing rigidity

It is placed in the load of hydraulic jack near measured bearing by measurement and determines measured bearing according to jack up factor Load；After determining measured bearing load, obtain bearing rigidity K in conjunction with bearing decrement under load effect_i, formula table Show as follows:

$K_i=\frac{R_i}{H_i}$

In formula: R_iFor measured bearing load；H_iFor measured bearing decrement；

Wherein, measured bearing load

Measured bearing decrement

Thus, bearing rigidity K_iIt is

In formula: c is jack up factor, obtains from centering of shafting calculated description；Load Q, P and displacement Y_jLifted curve by top to obtain；

3) consider that the bearing load of bearing rigidity affects number based on Finite element arithmetic

In formula: R_i,0Represent the load value of the i-th bearing before bearing adjustment of displacement；ΔY_jRepresent jth bearing adjustment of displacement amount； R_i,jRepresent the jth bearing reaction influence number to i-th bearing；It is reaction influence number；

By ANSYS finite element software, set up axle system one-dimensional model, bearing is equivalent to Hookean spring, carry out stress and strain model, about Bundle and load apply, and finally carry out solving the extraction calculated with bearing load data；By changing displacement constraint in model, calculate Try to achieve each bearing load after bearing conjugates 1 unit successively, finally deduct the load before each bearing does not conjugates and i.e. try to achieve consideration The bearing load of bearing rigidity affects number；

Second step: definition optimization object function

1) optimization object function based on quadratic programming is defined

Set up based on quadratic programming with tail pipe rear bearing load and the mesh of the most minimum optimization aim of bearing adjustment of displacement amount Scalar functions, as follows:

$min{Y}^{T}HY+{\mathrm{tR}}_n^{T}Y$

In formula: Y=(Δ Y₁,…,ΔY_j,…,ΔY_n)；H=diag_n×n(10^κ,…,10^κ,…,10^κ), κ and t is factor of influence, Its purpose adjusts displacement and load proportion in optimization aim；R_n=(R_n,1,…,R_n,j,…,R_n,n)^T, subscript n acute pyogenic infection of finger tip tail pipe Rear bearing；

2) optimization object function that definition is planned based on the Special Nonlinear with absolute value number

Foundation is for the load optimal function of multiple bearings:

$min\underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|$

In formula:AndR_iLFor bearing expected load；

3rd step: definition optimizes restrictive condition

1) the load constraint after the displacement of definition bearing

Load after bearing displacement is constrained to:

R_iMin≤R′_i≤R_iMax

In formula: R '_iLoad after conjugating for bearing；R_iMinTypically take the 80% of centering of shafting calculated description set-point；R_iMaxTypically take The 120% of centering of shafting calculated description set-point；

Measurement load and load variations amount before the displacement of above-mentioned formula bearing are expressed as:

$R_{iMin}\≤R_i+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}$

2) definition main frame bearing displacement constraint

When main frame bearing is adjusted, need to increase corresponding equality constraint:

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

Above formula is explained as follows:

Assuming that tailing axle end is position starting point, from stem to stern successively to bearing number, t=1～m, m represent main frame bearing number Amount, l_tRepresent the t main frame bearing position vertically；

3) the bearing displacement constraint not being adjusted is defined

The bearing displacement constraint not being adjusted: Δ Y_i=0

4) the bearing displacement constraint being adjusted is defined

Bearing displacement is less than adjusting range, therefore increases following displacement constraint:

ΔY_iMin≤ΔY_i≤ΔY_iMax

In formula: Δ Y_iMin、ΔY_iMaxValue according to site operation personnel need set；

4th step: solve the adjustment of displacement amount of each bearing based on nonlinear optimization algorithm

The function processing constrained optimization problem in Matlab optimization toolbox is utilized to carry out the non-linear of bearing adjustment of displacement amount Optimize and calculate；Before application solved function, first bearing adjustment of displacement optimization problem is converted into standard solves form；

Bearing adjustment of displacement optimized algorithm standard based on quadratic programming solves form:

$min{Y}^{T}HY+{\mathrm{tR}}_n^{T}Y$

$\begin{array}{cc}s.t.& \underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_{iMax}-R_i\\ & -\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j\≤R_i-R_{iMin}\end{array}$

[1-(l_t-l_m)/(l₁-l_m)]ΔY_m-ΔY_t+(l_t-l_m)/(l₁-l_m)ΔY₁=0

ΔY_i=0

ΔY_iMin≤ΔY_i≤ΔY_iMax

The bearing adjustment of displacement optimized algorithm standard planned based on the Special Nonlinear with absolute value number solves form:

$\begin{array}{cc}min& \underset{i=1}{\overset{n}{\Σ}}{w}_i|R_i-R_{iL}+\underset{j=1}{\overset{n}{\Σ}}{R}_{i,j}{\mathrm{\ΔY}}_j|\end{array}$

S.t. with the optimization restrictive condition of above-mentioned bearing adjustment of displacement optimized algorithm based on quadratic programming；

The derivation algorithm of quadratic programming, optimizes and revises problem for bearing displacement and solves selection dynamic sequence method or sequence secondary Law of planning；

When utilizing Matlab specifically to solve quadratic programming problem, use function Quadprog, solve the spy with absolute value number During different nonlinear programming problem, apply function Fmincon.