CN113704678B - Forgetting factor least square model parameter identification method based on full rank decomposition - Google Patents
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- 238000005259 measurement Methods 0.000 claims description 10
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Abstract
The invention provides a forgetting factor least square model parameter identification method based on full rank decomposition, which enables underexcitation data to meet excitation conditions again on an identification model after dimension reduction so as to ensure convergence of tracking time-varying parameters and identification results during disturbance. The method for reducing the dimension is determined by setting a dead zone, and meanwhile, the influence of disturbance in the identification process is weakened. The real ship data under the marine environment disturbance working condition are used for identifying the course model parameters, and compared with the identification result curve and the course angular velocity forecast error curve of the ship operation model parameters identified by the FFLS and FRDLS algorithm, the full-rank decomposition least square method can be found to effectively inhibit the drift and divergence problems in the data under-excitation and parameter identification process when the marine environment disturbance exists, the parameter identification precision is improved, and meanwhile, the method has the advantages of small calculated amount, strong instantaneity, simplicity and easiness in implementation.
Description
Technical Field
The invention belongs to the field of model parameter identification, and particularly relates to a forgetting factor least square model parameter identification method based on full rank decomposition.
Background
With the continuous progress of digital and intelligent technologies, intelligent ships develop increasingly faster. At present, china is in the three-year target stage mentioned in the "intelligent ship development action plan 2019-2021", and the transition from the intelligent ship 1.0 to the intelligent ship 2.0 is being realized. The typical application scene of the intelligent ship such as automatic berthing, remote control, autonomous navigation and the like needs excellent ship course self-adaptive control algorithm. Compared with advanced products abroad, the domestic produced heading controller still has about 30% of performance indexes such as heading precision, energy consumption, steering rapidity, steering stability and the like, and the main reasons are as follows: (1) Real-time performance, convergence and identification precision of online identification of course model parameters are difficult to ensure simultaneously, and online estimation of time-varying parameters and disturbance is unsafe or inaccurate; (2) The processing of the course angular velocity signal fluctuation caused by ocean high-frequency disturbance, measurement noise and measurement pathological conditions is difficult; (3) The rudder angle control ring has insufficient self-adaptive capability for the change of the navigational speed and sea conditions; (4) The steering actuating mechanism has limited performance and has a larger gap from the foreign approach to realizing the continuous control effect.
Disclosure of Invention
The invention aims to solve the problems of linear model parameter on-line identification and disturbance real-time estimation under the data underexcitation working condition of a disturbed system, and provides a forgetting factor least square model parameter identification method based on full rank decomposition.
The purpose of the invention is realized in the following way:
a forgetting factor least square model parameter identification method based on full rank decomposition comprises the following steps:
step one: initializing an original parameter vector to be identified, an original variance matrix, a previous sampling period orthogonal change matrix, a parameter vector after full rank decomposition and a variance matrix;
step two: normalizing the measurement data of the current sampling period, and solving an orthogonal transformation matrix of the current sampling period according to the normalized data vector and the dead zone threshold value.
Step three: updating a variance matrix before full rank decomposition; if the orthogonal transformation matrix at the current moment is the same as that at the previous moment, directly updating the variance matrix and the parameter vector after full rank decomposition; otherwise, performing full rank decomposition on the pre-decomposition variance matrix to obtain a full rank decomposed variance matrix and a parameter vector, updating the full rank decomposed variance matrix and the parameter vector, and updating the pre-full rank decomposed parameter vector according to the new full rank decomposed parameter vector.
Step four: repeating the second to third steps until the identification precision meets the requirement.
Compared with the prior art, the invention has the beneficial effects that:
1. the concept of dynamic dimension reduction is introduced into a forgetting factor least square method (Forgetting Factor Least Square Algorithm, FFLS), and a least square method (Full Rank Decomposition Least Square Algorithm, FRDLS) based on full rank decomposition is provided, so that underexcitation data can meet excitation conditions again on a dimension-reduced identification model, and convergence of tracking time-varying parameters and identification results in disturbance is improved.
2. The dead zone is set to determine dynamic dimension reduction, influence of disturbance in an identification process is weakened, drift and divergence problems in a parameter identification process when data are underexcited and marine environment disturbance exists are restrained, and accuracy of parameter identification is improved.
3. The method has the advantages of small calculated amount, strong real-time performance, simplicity and easiness in implementation.
Drawings
FIG. 1 is a full rank decomposition least squares flow chart of the present invention;
FIG. 2 is a data diagram of the course, the angular velocity of the course and the rudder angle of the ship according to the invention;
FIG. 3 is a graph showing the identification result of the K in the present invention;
FIG. 4 is a graph of the T recognition result of the present invention;
FIG. 5 is a diagram of the interference delta of the present invention d Identifying a result curve;
FIG. 6 is a graph of predicted angular velocity according to the present invention;
FIG. 7 is a graph of angular velocity prediction error according to the present invention;
FIG. 8 is a graph showing the time consumption of a single cycle of the algorithm of the present invention.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings.
As can be seen from fig. 3 and fig. 4, the FFLS algorithm identifies K, T parameters, and parameter divergence occurs in the vicinity of 200 seconds and 3000 seconds, and the amplitude of the disturbance identification value in fig. 3 is abnormally increased in the steering process; the FRDLS algorithm identifies K, T parameters and the disturbance process are relatively stable, and compared with the FFLS algorithm, the robustness of the parameter identification process is improved after full rank decomposition is added.
As can be seen from FIG. 7, the average error of the forecast angular velocity of the FFLS identification result is 0.0374 DEG s -1 The average error of the forecast angular velocity of the FRDLS identification result is 0.0215 DEG s -1 The FRDLS algorithm has higher comparison with the FFLS algorithmIs used for identifying the accuracy of the identification.
In fig. 8, the FFLS algorithm takes a maximum of 1.1ms for a single cycle, and an average of 0.008ms for a single cycle; the maximum single cycle time of the FRDLS algorithm is 4.48ms, and the average single cycle time is 0.027ms. Comparing the average time consumption of single cycle, the FRDLS algorithm time consumption is about three times of that of FFLS algorithm. The frequency of the ship motion control system is generally 1-5Hz, and the real-time performance of the FRDLS algorithm is within an acceptable range.
1. Acquiring data vectors
Let the given data set:wherein h is k ＝[h k1 ,h k2 ,…,h kn ] T For measuring the data vector once, let the data matrix be h= [ H ] 1 ,h 2 ,…,h N ] T ∈R N×n The output matrix is z= [ Z 1 ,z 2 ,…,z N ] T The linear regression equation can be expressed by:
Z＝Hθ+w
taking the ship course model parameter identification as an example, the ship maneuvering motion model can adopt a first-order linear Nomoto model:
wherein: r is the bow swing angular velocity of the ship body,for yaw acceleration->Is the ship bow angle, delta is the rudder angle, delta d The rudder angle is equivalent to the ocean environment disturbance moment, K, T is the ship rotation capacity and rotation inertia parameter, and is influenced by the ship load condition and the sailing speed. In preparation for recognition, the Nomoto model is sorted into a standard least squares form.
In order to accelerate the convergence speed of parameter identification, a normalization factor is introducedAnd alpha r Order-making
Selecting output z k Parameter vector θ k Data vector h k Subscript k represents the kth time
The least square measurement equation is obtained by arrangement
z k ＝h k θ k +w k
2. Solving an orthogonal matrix V k
Giving quadrature V by combining recursive least square method k Setting the k-th measurement data { h }, a solving method of (a) k ,z k The corresponding transformation matrix is V k ＝[V k1 V k2 ]
In the formula e i N-dimensional column vector, h, for the ith behavior 1, the remaining behavior 0 s Is a dead zone threshold for attenuating the effect of interference, h ki The i-th data for the kth measurement data vector, when i=1, 2, n, there is p=1, 2,..r or q=1, 2,..n-r, which is finally available
3. Full rank decomposition
Before full rank decomposition, the original system variance is calculated
Full rank decomposition of original system variance matrix and parameter vector
The forgetting factor least square method updates the parameter vector and the variance vector after full rank decomposition
4. Updating original system parameter vector
5. Judging the identification ending condition
Calculating data innovation asWhen V is k+1 Is a unit array and is new->And ending the identification when the error operation range is within, otherwise, looping the steps 2 to 4.
Claims (1)
1. A forgetting factor least square model parameter identification method based on full rank decomposition is characterized by comprising the following steps: the forgetting factor least square model parameter identification method based on full rank decomposition is applied to a model parameter acquisition link in the control algorithm design process of an intelligent ship course self-adaptive controller, and specifically comprises the following steps of:
step one: initializing a parameter vector of an original ship course model to be identified, initializing an original difference variance matrix, and carrying out orthogonal change matrix in the last sampling period, wherein the parameter vector and the variance matrix are subjected to full rank decomposition;
acquiring a data vector, and setting a given data set:wherein h is k ＝[h k1 ,h k2 ,…,h kn ] T For measuring the data vector once, let the data matrix be h= [ H ] 1 ,h 2 ,…,h N ] T ∈R N×n The output matrix is z= [ Z 1 ,z 2 ,…,z N ] T The linear regression equation is expressed by:
Z＝Hθ+w
taking the parameter identification of the ship course model as an example, the ship steering motion model adopts a first-order linear Nomoto model:
wherein: r is the bow swing angular velocity of the ship body,for yaw acceleration->Is the ship bow angle, delta is the rudder angle, delta d The rudder angle is equivalent to the ocean environment disturbance moment, K, T is the ship rotation capacity and rotation inertia parameter, and is influenced by the ship load condition and the sailing speed; preparing for identification, arranging the Nomoto model into a standard least squares form;
in order to accelerate the convergence speed of parameter identification, a normalization factor is introducedAnd alpha r Order-making
Selecting output z k Parameter vector θ k Data vector h k Subscript k represents the kth time
The least square measurement equation is obtained by arrangement:
z k ＝h k θ k +w k
step two: normalizing the measurement data of the current sampling period, and solving an orthogonal transformation matrix of the current sampling period according to the normalized data vector and a dead zone threshold value;
solving an orthogonal matrix V k Giving an orthogonal V by combining a recursive least square method k Setting the k-th measurement data { h }, a solving method of (a) k ,z k The corresponding transformation matrix is V k ＝[V k1 V k2 ]
In the formula e i N-dimensional column vector, h, for the ith behavior 1, the remaining behavior 0 s Is a dead zone threshold for attenuating the effect of interference, h ki The i-th data for the kth measurement data vector, when i=1, 2, n, there is p=1, 2,..r or q=1, 2,..n-r, the end result is
Step three: updating a ship course model parameter variance matrix before full rank decomposition; if the orthogonal transformation matrix at the current moment is the same as that at the previous moment, directly updating the ship course model variance matrix and the ship course model parameter vector after full rank decomposition; otherwise, performing full rank decomposition on the pre-decomposition variance matrix to obtain a full rank decomposed ship course model variance matrix and a ship course model parameter vector, updating the full rank decomposed ship course model variance matrix and the ship course model parameter vector, and updating the ship course model parameter vector before full rank decomposition according to the new full rank decomposed ship course model parameter vector;
before full rank decomposition, the original system variance is calculated
Full rank decomposition of original system variance matrix and parameter vector
The forgetting factor least square method updates the parameter vector and the variance vector after full rank decomposition
Updating original system parameter vector
Step four: repeating the second to third steps until the accuracy of the ship course model parameter identification result meets the requirement;
judging the identification ending condition, and countingCalculating data innovation asWhen V is k+1 Is a unit array and is new->And ending the identification when the error operation range is within, otherwise, cycling the second step to the third step.
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