CN111753466A - Soft measurement modeling method for radial displacement of rotor of three-pole magnetic bearing - Google Patents
Soft measurement modeling method for radial displacement of rotor of three-pole magnetic bearing Download PDFInfo
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Abstract
The invention discloses a soft measurement modeling method for radial displacement of a tripolar magnetic bearing rotor, which comprises the steps of respectively forming a hidden Markov chain by taking displacement as a state value and control current as an observed value, and mutually coupling the two hidden Markov chains to form a coupling hidden Markov model; carrying out optimization training on the model parameters by adopting a genetic algorithm, a particle swarm optimization algorithm and a Baum-Welch algorithm in sequence to obtain final model parameters, establishing a coupling hidden Markov model corresponding to each group of sample databases as a sub-model by the final model parameters, obtaining a group of optimal displacement state values and output probabilities by each sub-model by utilizing a Viterbi algorithm, and calculating all the optimal displacement state values and the output probabilities by adopting a weighted average method to obtain displacement predicted values so as to form a soft measurement model; the method utilizes the interdependence relationship between the multi-channel states to establish the causal relationship and the influence between the two degrees of freedom, so that the modeling is more accurate, the advantages and disadvantages of the genetic algorithm and the particle swarm optimization algorithm are complemented, and the optimization effect of the model parameters is better.
Description
Technical Field
The invention relates to a magnetic bearing system used in the field of high-speed motor transmission, in particular to a rotor radial displacement soft measurement modeling method of a tripolar magnetic bearing based on a coupling hidden Markov model.
Background
The magnetic bearing is a non-contact high-performance bearing which suspends a rotor in an air gap between stators by utilizing magnetic field force, and a closed-loop displacement negative feedback control system needs to be established in order to realize stable suspension of the rotor of the magnetic bearing. Therefore, accurate real-time detection of the displacement of the rotor is the key of the control system. The traditional method for detecting the displacement of the rotor generally adopts a displacement sensor, and the displacement sensor cannot meet the requirement of the magnetic bearing on high-speed and high-precision development due to the problems of large occupied space, high price, low dynamic performance and the like. Therefore, a self-detection technology of the magnetic bearing is provided, wherein the soft measurement in the self-detection technology is a method for estimating an undetectable or difficultly-measured variable by using an auxiliary variable which is easy to measure online and offline analysis information, and is usually completed by taking a computer technology as a core and performing operation processing through a soft measurement model on the basis of a mature hardware sensor.
Hidden Markov Models (HMMs) are models that describe time-varying signal processes by means of probabilistic methods. It consists of two random processes of different mechanisms: one is an intrinsic finite hidden state Markov chain, and the other is a stochastic process of observation vectors associated with each state of the Markov chain, which is a double stochastic process in that not only the transitions between states are random, but the observations of each state are also random. Applying HMMs to practice requires solving three problems: the HMM has a probability calculation problem, an optimal state sequence problem, and a parameter reestimation problem, corresponding to three solution algorithms, namely, a forward-backward algorithm, a Viterbi algorithm, and a Baum-Welch algorithm. A Coupled Hidden Markov Model (CHMM) is a probabilistic model for describing the statistical properties of two or more interrelated (conditional probability dependent) stochastic processes, which can be seen as a multiple HMM chain model obtained by multiple HMMs by introducing coupling conditional probabilities between their state sequences.
The document with the Chinese patent publication number of CN107065546A discloses a soft measurement method for rotor displacement of a three-degree-of-freedom hybrid magnetic bearing, which is to respectively establish a continuous hidden Markov submodel in three directions of the rotor displacement x, y and z to form a continuous hidden Markov displacement prediction model, so that the fault tolerance rate is high, and the dynamic performance of the system is improved. However, for the asymmetry of the three-pole magnetic bearing structure, a strong displacement coupling effect exists between the radial displacement x and the radial displacement y of the rotor, and the description is not accurate enough only by using a single continuous hidden markov model, so that the error is large. The Chinese patent publication No. CN107102223A discloses an NPC photovoltaic inverter fault diagnosis method based on an improved hidden Markov model GHMM, which trains the initial value of an observed value probability matrix by using a genetic algorithm to make model parameters reach global optimization and greatly improve the fault recognition rate. However, the genetic algorithm has low convergence precision and long convergence time, and is difficult to meet the requirements of self-detection and real-time detection.
Disclosure of Invention
The purpose of the invention is: aiming at the effect of strong displacement coupling between the radial displacement x and y of the rotor of the tripolar magnetic bearing with asymmetric structure, the soft measurement modeling method for the radial displacement of the rotor of the tripolar magnetic bearing based on the coupling hidden Markov model is provided, the model can measure the displacement of the rotor of the tripolar magnetic bearing more accurately, the dynamic performance of a control system of the tripolar magnetic bearing is improved, and the fault-tolerant rate is higher.
The technical scheme adopted by the invention for realizing the purpose comprises the following steps:
step (1): taking the displacement x and y of the three-pole magnetic bearing rotor as state values and controlling current ix、iyRespectively forming a hidden Markov chain as an observed value, and mutually coupling the two hidden Markov chains to form a coupling hidden Markov model;
step (2): determining model parameters of the coupled hidden Markov model as lambda ═ { Π, A, B }, wherein Π is an initial state probability vector, A is a state transition probability matrix, and B is observed value probability distribution; solving the output probability P (O | lambda) of the corresponding state sequence generated by the coupled hidden Markov model observation sequence O and the model parameter lambda;
and (3): carrying out optimization training on the model parameter lambda ═ { Π, A, B } by adopting a genetic algorithm, a particle swarm optimization algorithm and a Baum-Welch algorithm in sequence to obtain the final model parameter lambdaB＝{ΠB,AB,BB}; collection magnetic axisCarrying n groups of rotor displacement x and y sample data and constructing an offline displacement sample database;
and (4): from the final model parameter lambdaB＝{ΠB,AB,BBAnd establishing a coupling hidden Markov model corresponding to each group of the off-line displacement sample databases as a sub-model, wherein each sub-model obtains a group of optimal displacement state values x by utilizing a Viterbi algorithmiAnd an output probability P (O | λ)Bi) For all the optimal displacement state values xiAnd an output probability P (O | λ)Bi) Calculating to obtain displacement predicted values x 'and y' by adopting a weighted average method;
and (5): and all the sub models, the Viterbi algorithm and the weighted average algorithm are built in the coupled hidden Markov displacement prediction model to form a soft measurement model.
After the technical scheme is adopted, the invention has the advantages that:
1. the strong coupling effect exists between the radial displacement x and the radial displacement y due to the asymmetry of the three-pole magnetic bearing structure, the coupling hidden Markov model is adopted on the two HMM chains of the radial displacement, the mathematical structure and the probability reasoning capability of the Hidden Markov Model (HMM) are reserved, the causal relationship and the influence between two degrees of freedom are established by utilizing the interdependency relationship between multi-channel states, the problem that the interaction behavior cannot be completely expressed by the single-chain hidden Markov model is effectively solved, and the modeling is more accurate.
2. When model parameters are optimally trained, a mixed algorithm combining a genetic algorithm, a particle swarm optimization algorithm and a Baum-Welch algorithm is used for optimizing the training, when model parameters are initialized, the characteristics of high early-stage searching capability, low later-stage searching capability, high global optimizing capability and the like are based on the genetic algorithm, the particle swarm optimization algorithm has the characteristics of low early-stage searching capability, high later-stage searching capability, easiness in falling into local optimization and the like, the genetic algorithm is used for carrying out efficient global searching on the model parameters in the early stage, and the particle swarm optimization algorithm is used for carrying out careful local searching in the later stage on the basis, so that the advantages and disadvantages of the two algorithms are complemented, the problems that the traditional Baum-Welch algorithm is sensitive to initial values and easily falls into local extreme values during parameter training can be avoided, and the.
Drawings
FIG. 1 is a schematic diagram of a coupled hidden Markov model with two chains;
FIG. 2 is a schematic diagram of a coupled hidden Markov model parameter optimization training process;
FIG. 3 is a basic flow diagram of the genetic algorithm of FIG. 2;
FIG. 4 is a schematic representation of the chromosomal coding of FIG. 3;
FIG. 5 is a basic flow diagram of the particle group optimization algorithm of FIG. 2;
FIG. 6 is a block diagram of a two-degree-of-freedom three-pole active magnetic bearing control system with displacement sensors;
FIG. 7 is a schematic diagram of the construction of a coupled hidden Markov displacement prediction model;
FIG. 8 is a block diagram of a three-pole active magnetic bearing rotor radial displacement soft measurement system based on a Coupled Hidden Markov Model (CHMM).
In the figure: 1. a displacement sensor; 3. 4, a PID controller; 5. a force/current conversion module; 6.2/3 conversion module; 7. a three-phase power inverter; 8. a current sensor; 9. a tripolar radial active magnetic bearing; clark transformation module; a CHMM displacement prediction model.
Detailed Description
The method comprises the steps of firstly establishing a coupling hidden Markov model for the three-pole magnetic bearing, determining model parameters, then optimizing and training the model parameters by using a hybrid algorithm combining a genetic algorithm, a particle swarm optimization algorithm and a Baum-Welch algorithm in sequence, building a prediction model by using the optimized and trained model parameters, and carrying out soft measurement on the radial displacement of a rotor of the three-pole magnetic bearing. The method comprises the following specific steps:
step one, for a magnetic bearing rotor displacement soft measurement system, the displacement and the control current of a rotor meet hidden Markov property, the rotor displacement is a state value, the control current is an observed value, and one degree of freedom can adopt a hidden Markov chain. Aiming at the three-pole magnetic bearing, strong coupling action exists between the radial two-degree-of-freedom x and y, and the two hidden Markov chains are mutually coupled to form a coupled hidden Markov model, so the invention adopts the magnetic bearing with the characteristics ofA coupled hidden markov model of two hidden markov chains. Fig. 1 is a schematic diagram of a coupled hidden markov model including two hidden markov chains, where x and y two radial degrees of freedom correspond to one hidden markov chain, denoted as chain 1 and chain 2, respectively, and the two chains, chain 1 and chain 2, are coupled to each other. Chain 1 and chain 2 each consist of N state values and N observations, respectively, wherein chain 1 consists of a state value of x degrees of freedom (rotor displacement x) and an observation value (control current i)x) Composition xNIs the shift of the Nth state, ixNIs the control current corresponding to the nth state shift in chain 1. The chain 2 is formed by a state value y (rotor displacement y) of y degrees of freedom and an observed value iy(control Current iy) Consisting of rotor displacement in y degrees of freedom and control current iyComposition yNIs the shift of the Nth state, iyNIs the control current corresponding to the nth state shift of the chain 2. For a three-pole magnetic bearing, the variation trend of the rotor displacement x and y is not only equal to the control current i at the previous momentx、iyThe displacement at the lower moment is also related to the displacement at the coupling chain control current at the previous moment. Therefore, for the radial displacement soft measurement of the three-pole magnetic bearing rotor, the coupling characteristic between two radial degrees of freedom can be more accurately embodied by adopting the coupling hidden Markov model.
And step two, determining parameters of the coupled hidden Markov model. The coupled hidden Markov model is composed of chains 1 and 2, and the state of the model at any moment is the combination of the states of the two chains 1 and 2. The t-th state value of the coupled hidden Markov model is st＝{st 1,st 2H, corresponding observed value is ot＝{ot 1,ot 20 < t < N, where st 1And st 2The t-th state values, o, of chain 1 and chain 2, respectivelyt 1And ot 2The observed values corresponding to the t-th state values of the chain 1 and the chain 2 respectively, and the state sequence S and the observed sequence O of the coupled hidden markov model are respectively as follows:
S＝{s1,s2,...,sN}＝{(s1 1,s1 2),(s2 1,s2 2),...,(sN 1,sN 2)}，
O＝{o1,o2,...,oN}＝{(o1 1,o1 2),(o2 1,o2 2),...,(oN 1,oN 2)}，
wherein s isNIs the Nth state value, o, in the state sequence SNIs the nth observation in observation sequence O.
Similar to hidden markov models, the model parameters of a coupled hidden markov model may also be expressed as λ ═ { Π, a, B }, where Π is the initial state probability vector, and ═ Πt},ΠtIs that the model is in state s at the initial momentt＝{st 1,st 2A priori probability of. A is a state transition probability matrix, A ═ am,nIn which a ism,nIs a coupled hidden Markov model slave state sm＝{sm 1,sm 2Is transferred to state sn＝{sn 1,sn 2The probability of m is more than or equal to 0 and less than or equal to N, and N is more than or equal to 0 and less than or equal to N. B is the observation probability distribution, B ═ B (o)t) In which b (o)t) Is coupling a hidden Markov model in a state st＝{st 1,st 2Generate an observed value ot＝{ot 1,ot 2} of the probability of the error. Therefore only need to determine { Πt}、{am,nAnd { b (o) } and { b (o)t) These three sets of probability parameters allow the determination of the coupled hidden markov model parameter λ ═ Π, a, B. The output probability P (O | λ) of the observation sequence O and the model parameter λ resulting in the corresponding state sequence can be found by the conventional Viterbi algorithm.
And step three, performing optimization training on the determined model parameters. Fig. 2 shows a flowchart of the optimization training for the model parameter λ ═ { Π, a, B }. Because the Baum-Welch algorithm adopted in iterative training is sensitive to initial parameter values and is easy to fall into local optimum, and different models are trained from different initial model parameter values, the optimization training is carried out on model parameters lambda { pi, A and B } by sequentially adopting a mixed algorithm combining a genetic algorithm, a particle swarm optimization algorithm and the Baum-Welch algorithm. The method comprises the following steps:
firstly, carrying out genetic algorithm optimization training on model parameters lambda ═ { Π, A and B }, wherein the specific training process is shown in fig. 3, firstly, randomly initializing the model parameters lambda0＝{Π0,A0,B0Carrying out genetic representation of model parameters, wherein the object is an element in the model parameters, namely the coupling hidden Markov model is in a state st＝{st 1,st 2The prior probability pi oftCoupled hidden Markov model slave states sm＝{sm 1,sm 2Is transferred to state sn＝{sn 1,sn 2Probability a of }m,nAnd coupling the hidden Markov model in the state st＝{st 1,st 2Generate an observed value ot＝{ot 1,ot 2Probability b (o)t) Opposite IIt、am,nAnd b (o)t) Carrying out chromosome coding, wherein the concrete coding schematic diagram is shown in FIG. 4, and the matrix element pi in each model parametert、am,nAnd b (o)t) The rows of (a) are connected in series from top to bottom to form a chromosome. The chromosomes will be represented as an array of real numbers, all of which make up the initial population. Then, a fitness function is calculated for each chromosome, which is an evaluation mechanism for the chromosome, with higher fitness values reflecting the likelihood that the chromosome will be selected in the next generation. Considering the problem of data overflow in the probability calculation process, the logarithm of the output probability P (O | λ) is taken to be represented, and then the fitness function of an individual is represented by the logarithm probability of each training sample as:
f(λ)＝(Σuln(P(O(u)|λ0))/U，
wherein U is the total number of observation sequences, O(u)Is an initialization model parameter lambda0U is more than or equal to 1 and less than or equal to U in the U-th observation sequence.
And judging whether each chromosome meets the constraint condition according to the fitness function, and if not, performing genetic operations such as selection, crossing, mutation and the like to generate a new generation of population. The selection operation is to select excellent individuals from a plurality of chromosomes, a random tournament method is adopted, individuals with the tournament scale of 2 are randomly selected each time to carry out fitness size comparison, and the individuals with high fitness are inherited to the next generation group, so that the problems of premature and stagnation of the algorithm can be effectively avoided; the crossover operation is the combination of recombination parent chromosomes, a uniform crossover algorithm is selected, the crossover rate is set to be 0.5, the chromosome with the largest fitness value is selected as the parent, and the optimal parent is crossed to obtain more excellent offspring; the variation operation increases the variation of the model parameters, selects an algorithm with uniform variation, is suitable for the initial operation stage of the genetic algorithm, sets the variation probability to be 0.1, and simultaneously can avoid the premature operation of the genetic algorithm and increase the diversity of the population. Then, the optimization process is carried out on the chromosomes in the new generation population, the fitness function value of the chromosomes after optimization is determined again, whether the constraint conditions are met or not is judged in a circulating mode until the optimal solution is output, so that the overall optimal solution of the model parameters is obtained preliminarily, and the genetic algorithm optimization model parameters lambda of the overall optimal solution are obtainedG＝{ΠG,AG,BG}。
Optimizing the model parameter lambda of the genetic algorithm on the basisG＝{ΠG,AG,BGAnd performing optimization training by adopting a particle swarm optimization algorithm, wherein a specific training flow is shown in fig. 5. First, the size of the particle group is initialized, and the particle position x is initializedgAs a model parameter lambdaG＝{ΠG,AG,BGAnd (4) real number strings formed by encoding elements of each row of each matrix structure in series from top to bottom, wherein the specific encoding mode is the same as a genetic algorithm, and the specific encoding mode can be seen in a figure 4. Random initial velocity value vgAnd satisfy Vmin≤vg≤VmaxIn which V isminAnd VmaxRespectively the minimum and maximum velocity of the particle. Then, the fitness function of each particle is calculated, and the same fitness function expression as the genetic algorithm is adopted, namely f (lambda) ═ sigmauln(P(O(u)|λG) U)/U. Then updates its speed and position according to the following formula:
vg(k+1)＝w·vg(k)+c1·r1·[pbestg(k)－xg(k)]+c2·r2·[gbestg(k)－xg(k)]；
xg(k+1)＝xg(k)+vg(k+1)；
in the formula, vg(k) Is the velocity of the particle g in the kth iteration, w is the inertial weight, clAnd c2Is a positive learning factor, and can respectively adjust the maximum step length of the current particle flying to the direction of the global optimal particle and the direction of the individual optimal particle, the range is between 0 and 4, wherein 2 and r are taken1And r2Is a random number, pbest, uniformly distributed between 0 and 1gIs the position of the individual extreme point of the particle g; gbestgIs the location of the global extreme point of the entire particle swarm, xg(k) Is the current position of the particle g at the kth iteration
Judging whether the particles meet the constraint conditions according to the updated speed and position, if not, recalculating the fitness of the particles and updating the speed and position, circularly judging, outputting the optimal solution of the positions of the particles until the constraint conditions are met, namely the global optimal solution of the model parameters, and outputting the particle swarm optimization model parameters lambdaP＝{ΠP,AP,BP}。
Optimizing model parameters λ for particle swarmP＝{ΠP,AP,BPAnd performing reestimation iterative training on the data, wherein the method comprises the following steps: firstly, a control system of the tripolar radial active magnetic bearing 9 with the displacement sensor is constructed as shown in fig. 6, two displacement sensors 1 and 2 are adopted to respectively detect two radial displacements x and y of the tripolar radial active magnetic bearing 9, and the two radial displacements x and y are respectively connected with a displacement instruction signal x*And y*Subtracting the difference, and converting the difference into a corresponding levitation force command signal F through a corresponding PID controller 3, 4x *、Fy *The levitation force command signal Fx *、Fy *Then is rotated by a force/current conversion module 5Is converted into a corresponding control current signal ix *、iy *Control current signal ix *、iy *Respectively corresponding to bias current ix0、iy0After addition, the current signals pass through a 2/3 conversion module 6 with constant power to output command current signals i of all phasesa *、ib *And ic *Three-phase current signals in the coil of the tripolar radial active magnetic bearing 9 are detected by the current sensor 8 and sampled by the DSP and then are mixed with three-phase command current signals ia *、ib *And ic *The actual coil current i required is generated by a current hysteresis three-phase power inverter 7 after subtractiona、ibAnd icRadial displacement of the bearing is controlled. When the rotor displacement of the bearing changes newly, it is detected again by the displacement sensor 8, and the above process cycle detection is repeated. Collecting and recording sample data of n groups of rotor displacements x and y by displacement sensors 1 and 2 and constructing an off-line displacement sample database; the DSP current acquisition module records n groups of three-phase control currents ia、ib、icAnd constructing an off-line current sample database. Preprocessing the data in each sample database, and then randomly selecting half of the sample databases as training sample databases for training an initial Coupled Hidden Markov Model (CHMM) displacement prediction model, and using the other half as a test sample database for checking the prediction accuracy of the displacement prediction model and adjusting model parameters. Referring to FIG. 2 again, the training samples in the off-line training sample database are optimized to the particle swarm by Baum-Welch algorithm to obtain the model parameter λP＝{ΠP,AP,BPPerforming parameter reestimation training, and calculating the output probability P (O | lambda) by using a Viterbi algorithm after reestimation each timeP) And judging convergence, and repeating iterative calculation until the parameters converge to a set range, so as to obtain the final model parameter lambda after reestimationB＝{ΠB,AB,BB}。
Step four, performing model after model parameter optimization training is finishedAnd (3) building a system, and connecting a coupling hidden Markov Chain (CHMM) rotor displacement soft measurement module into the magnetic bearing system. FIG. 7 is a schematic diagram of a CHMM displacement prediction process based on the trained final model parameter λB＝{ΠB,AB,BBEstablishing a Coupled Hidden Markov Model (CHMM) corresponding to each group of off-line displacement sample data in the training sample database, marking as a submodel, wherein the number of the submodels is n, namely the CHMM1To CHMMn submodels, CHMM1The model parameter corresponding to the CHMMn submodel is λ1To lambdan. Taking the x direction as an example, each sub-model will obtain a set of optimal displacement state values x by using the Viterbi algorithmiAnd an output probability P (O | λ)Bi) Finally, all the optimal displacement state values x are calculatediAnd an output probability P (O | λ)Bi) Calculating a displacement predicted value x' by adopting a weighted average method:
the predicted value y' of the displacement in the y direction can be obtained in the same way.
All the submodels, Viterbi algorithm and weighted average algorithm shown in fig. 7 are built in the coupled hidden markov (CHMM) displacement pre-measurement model 11 shown in fig. 8, and a total model, namely a soft measurement model established by the present invention, is formed. Fig. 8 is a diagram of a tripolar radial active magnetic bearing rotor displacement soft measurement system based on CHMM, which is compared with fig. 6, except that two displacement sensors 1 and 2 in fig. 6 are removed on the basis of the structure of fig. 6, and a coupled hidden markov (CHMM) displacement pre-measurement model 11 is connected in series with a Clark transformation module 10. The current sensor 8 is still adopted to detect the current signal i of the current hysteresis three-phase power inverter 7a、ibAnd icThen converted into a control current i through the Clark conversion modules 10 connected in seriesx、iyAnd will control the current ix、iyAs an input of the coupled hidden markov (CHMM) displacement prediction model 11, the actual displacement prediction value x is output by the coupled hidden markov (CHMM) displacement prediction model 11yc、yycThereby realizing soft measurement of the radial displacement of the rotor of the three-pole magnetic bearing.
Claims (6)
1. A soft measurement modeling method for radial displacement of a three-pole magnetic bearing rotor is characterized by comprising the following steps:
step (1): taking the displacement x and y of the three-pole magnetic bearing rotor as state values and controlling current ix、iyRespectively forming a hidden Markov chain as an observed value, and mutually coupling the two hidden Markov chains to form a coupling hidden Markov model;
step (2): determining model parameters of the coupled hidden Markov model as lambda ═ { Π, A, B }, wherein Π is an initial state probability vector, A is a state transition probability matrix, and B is observed value probability distribution; solving the output probability P (O | lambda) of the corresponding state sequence generated by the coupled hidden Markov model observation sequence O and the model parameter lambda;
and (3): carrying out optimization training on the model parameter lambda ═ { Π, A, B } by adopting a genetic algorithm, a particle swarm optimization algorithm and a Baum-Welch algorithm in sequence to obtain the final model parameter lambdaB＝{ΠB,AB,BB}; collecting sample data of n groups of rotor displacement x and y of the magnetic bearing and constructing an offline displacement sample database;
and (4): from the final model parameter lambdaB＝{ΠB,AB,BBEstablishing a coupling hidden Markov model corresponding to each group of off-line displacement sample databases as a sub-model, and obtaining a group of optimal displacement state values x by each sub-model by utilizing a Viterbi algorithmiAnd an output probability P (O | λ)Bi) For all the optimal displacement state values xiAnd an output probability P (O | λ)Bi) Calculating to obtain displacement predicted values x 'and y' by adopting a weighted average method;
and (5): and all the sub models, the Viterbi algorithm and the weighted average algorithm are built in the coupled hidden Markov displacement prediction model to form a soft measurement model.
2. The modeling method for the radial displacement soft measurement of the rotor of the three-pole magnetic bearing as set forth in claim 1, wherein the modeling method comprises the following steps:
in step (2), the initial state probability vector Π is { Π ═ Πt},ΠtIs the initial moment coupled hidden Markov model in the state st＝{st 1,st 2A priori probability of st＝{st 1,st 2Is the t-th state value of the coupled hidden Markov model, and the corresponding observed value is ot＝{ot 1,ot 2Two hidden Markov chains each consisting of N state values and N observations, st 1And st 2T is the t state value of two hidden Markov chains, and t is more than or equal to 0 and less than or equal to N;
state transition probability matrix a ═ am,n}，am,nIs a coupled hidden Markov model slave state sm＝{sm 1,sm 2Is transferred to state sn＝{sn 1,sn 2The probability of m is more than or equal to 0 and less than or equal to N, and N is more than or equal to 0 and less than or equal to N;
observed value probability distribution B ═ B (o)t)}，b(ot) Is that the model is in state st＝{st 1,st 2Generate an observed value ot＝{ot 1,ot 2-probability of the next step; ot 1And ot 2The observation values corresponding to the t-th state values of the two hidden Markov chains, and the observation sequence O { (O) of the coupled hidden Markov model1 1,o1 2),(o2 1,o2 2),...,(oN 1,oN 2)}，oNIs the nth observation in observation sequence O.
3. The modeling method for the radial displacement soft measurement of the rotor of the three-pole magnetic bearing as set forth in claim 2, wherein the modeling method comprises the following steps: in the genetic algorithm described in step (3), a model parameter λ is randomly initialized0＝{Π0,A0,B0Get each model parameter λ ═ toMatrix element Π in { Π, A, B }, e.g. Xt、am,nAnd b (o)t) The rows of (a) are connected in series from top to bottom to form a chromosome, and the fitness function f (lambda) ═ sigma of each chromosome is calculateduln(P(O(u)|λ0) U, U is the total number of observation sequences, O(u)Is an initialization model parameter lambda0U is more than or equal to 1 and less than or equal to U, judging whether each chromosome meets the constraint condition according to the fitness function, if not, carrying out selection, crossing and variation operations until the constraint condition is met to obtain the genetic algorithm optimization model parameter lambdaG＝{ΠG,AG,BG}。
4. The modeling method for the radial displacement soft measurement of the rotor of the three-pole magnetic bearing as set forth in claim 3, wherein the modeling method comprises the following steps: initializing a particle position x in the particle swarm optimization algorithm in the step (3)gOptimizing model parameters λ for genetic algorithmsG＝{ΠG,AG,BGCalculating a fitness function f (lambda) of each particle, updating the speed and the position, and outputting a particle swarm optimization model parameter lambda (lambda) by using a real number string formed by encoding each row of elements of each matrix structure from top to bottom in seriesP＝{ΠP,AP,BP}。
5. The modeling method for the radial displacement soft measurement of the rotor of the three-pole magnetic bearing as set forth in claim 4, wherein the modeling method comprises the following steps: in the Baum-Welch algorithm in the step (3), for the constructed offline displacement sample databases, randomly selecting half of each sample database as a training sample database and the other half as a test sample database, and performing the Baum-Welch algorithm on the training samples to optimize the model parameter lambda of the particle swarmP＝{ΠP,AP,BPPerforming parameter reestimation training, and calculating the output probability P (O | lambda) by using a Viterbi algorithm after reestimation each timeP) And judging convergence, and repeatedly performing iterative calculation until the parameters converge to a set range to obtain the final reestimated model parameter lambdaB＝{ΠB,AB,BB}。
6. The modeling method for the radial displacement soft measurement of the rotor of the three-pole magnetic bearing as set forth in claim 5, wherein the modeling method comprises the following steps: the weighted average method adopted in the step (4) is a formula
And calculating to obtain a displacement predicted value x 'in the x direction and a displacement predicted value y' in the y direction.
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