CN113626243B - Nonlinear system fault diagnosis method and system based on bionic optimized particle filtering - Google Patents
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Abstract
The invention provides a nonlinear system fault diagnosis method and system based on bionic optimized particle filtering, comprising the following steps: establishing a state space model of a nonlinear system to be diagnosed; generating N initial particles for each model in the state space model, and initializing the position and weight of each initial particle; based on the state space model, iteratively updating the positions of N initial particles by utilizing a sparrow algorithm and the Lewy flight variation; calculating the weights of the N initial particles after updating and normalizing; resampling particles in a state space based on the normalized weight to obtain a system state prediction value corresponding to each model in the state space model; and carrying out fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction quantity corresponding to each model in the state space model. The invention relieves the technical problem that the particle depletion is caused by adopting the standard particle filtering method in the prior art.
Description
Technical Field
The invention relates to the technical field of fault diagnosis, in particular to a nonlinear system fault diagnosis method and system based on bionic optimized particle filtering.
Background
Large electromechanical devices have been widely used in civilian production and military weaponry. These devices are very sensitive to faults due to the highly integrated, complex, time-varying and autonomous nature. Once a fault occurs, a huge economic loss and even a great deal of casualties can result. Therefore, the fault diagnosis of the complex electromechanical equipment is an indispensable part in the development of the complex electromechanical equipment, and has very important research and practical significance for guaranteeing the safe operation of the complex electromechanical equipment.
To simplify the fault diagnosis process of complex systems, a linearization system state model is generally built through a small disturbance linearization process. However, the complex system has strong nonlinearity, strong coupling and quick time-varying property, and the actual working condition environment often has serious noise interference, so that research on fault diagnosis of the nonlinear system is needed.
The fault diagnosis method can be mainly divided into a model-based method and a data-based method, and the engineering application of the methods is limited by lack of training samples under the condition that the acquisition of real data is difficult due to higher experimental cost of complex equipment although the method does not depend on a system model. Such as hypersonic cruise missiles, hypersonic aircrafts, space aircrafts and the like, the extremely high target projectile development cost makes the hypersonic cruise missiles unable to obtain mass data through multiple experiments to establish a fault model database, so that the hypersonic cruise missiles are more prone to design a diagnosis system by applying a high-precision and strong-robustness state estimation method. The method based on the model is based on an accurate analysis model, and has good diagnosis effect through deep analysis of the internal structure of the system and mechanical research of faults. As a typical representation based on models, particle filter based fault diagnosis methods aim to construct residual terms of metrology signals through accurate state estimation to achieve fault diagnosis of the system.
The particle filtering algorithm is further developed on the Monte Carlo approximate Bayesian filtering method, particle description state information with weight information is utilized, the particle mean value is used for replacing integral operation, and the probability density function of random variables in the system is approximated to realize minimum variance state estimation. The algorithm can well solve the problem of state estimation of a nonlinear and non-Gaussian system.
The standard particle filtering algorithm needs to implement the weight recursive computation step through an importance distribution function, and although the optimal choice is the true distribution of particles, the weight recursive computation is difficult to implement in an actual nonlinear system. The prior density is usually adopted as an importance distribution function in most algorithms, but the prior density is easy to realize, and the latest observation information is ignored, so that the weight of the particles is degraded. Resampling methods mitigate the degree of degradation to some extent by constantly replicating high-weight particles and discarding low-weight particles, but as iterations continue, they will lead to particle depletion.
Disclosure of Invention
Therefore, the invention aims to provide a nonlinear system fault diagnosis method and system based on bionic optimized particle filtering, so as to solve the technical problem that the particle depletion is caused by adopting a standard particle filtering method in the prior art.
In a first aspect, an embodiment of the present invention provides a method for diagnosing a nonlinear system fault based on biomimetic optimized particle filtering, including: establishing a state space model of a nonlinear system to be diagnosed; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer; generating N initial particles for each model in the state space model, and initializing the position and weight of each initial particle; the position of each initial particle corresponds to one state in the state space where the state space model is located; n is a positive integer; based on the state space model, iteratively updating the positions of the N initial particles by utilizing a sparrow algorithm and a Lewy flight variation; calculating the weights of the N initial particles after updating and normalizing; resampling the particles in the state space based on the normalized weight to obtain a system state prediction value corresponding to each model in the state space model; and carrying out fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction quantity corresponding to each model in the state space model.
Further, the state space model includes:
Further, iteratively updating the positions of the N initial particles using a sparrow algorithm and a lewy flight variation based on the state space model, including: updating the positions of the N initial particles based on the state space model; establishing an initial sparrow population based on the updated N initial particles; each particle corresponds to one sparrow; iteratively updating the position of each sparrow in the initial sparrow population through a sparrow algorithm; performing one-time Lewy flight variation on the position of each sparrow in each iterative updating process; and updating the positions of the N initial particles again based on the updated positions of each sparrow.
Further, iteratively updating the location of each sparrow in the initial sparrow population by a sparrow algorithm includes: based on a preset fitness function, calculating fitness of each sparrow in the initial sparrow population, and selecting N with minimum fitness pop ·P t Only sparrows are used as discoverers, and the rest sparrows are used as followers; n (N) pop To the scale of the initial sparrow population, and N pop =N，P t Is the proportion of discoverers in sparrow algorithm; updating the position of each sparrow in the initial sparrow population based on the randomly generated warning value; generating S in the initial sparrow population d The alertors are updated and the position of each alertor is updated; s is S d Is a random integer; calculating the fitness of each sparrow in the sparrow population after the position update based on a preset fitness function; based on the fitness of each sparrow in the sparrow population after the position update, carrying out the Lewy flight variation on the sparrow population after the update, and calculating the fitness of the sparrow population after the variation; and stopping optimization if the minimum value of the fitness of the mutated sparrow population is not greater than a preset fitness threshold value or the iteration number of the sparrow algorithm is equal to the preset optimization number.
Further, the sparrow population after the updating is subjected to Lewy flight variation, Comprising the following steps: calculating an inertia weight factor based on the current iteration number; selecting M sparks to participate in the tournament each time by using the tournament selection, selecting the sparks with the smallest fitness among the M sparks to perform the Laevice flight variation, and selecting N in total pop Secondary times; wherein,
，
for the round-up function, η is the inertial weight factor.
Further, performing fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction amount corresponding to each model in the state space model, including: based on a system control quantity input vector at the previous moment, acquiring an observation vector of the nonlinear system to be diagnosed at the current moment; based on the system state prediction amount and a preset state prediction equation corresponding to each model in the state space model, calculating an observation prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector; obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value; and judging whether the nonlinear system to be diagnosed has faults at the current moment based on the residual values.
Further, based on the plurality of residual values, judging whether the nonlinear system to be diagnosed fails at the current moment, including: judging whether the absolute value of the residual value corresponding to the normal state model is larger than a preset threshold value or not; if yes, judging that the nonlinear system to be diagnosed has faults at the current moment, and determining a model corresponding to the minimum residual error value from the n fault state models to be diagnosed as the model of the nonlinear system to be diagnosed.
In a second aspect, an embodiment of the present invention further provides a nonlinear system fault diagnosis system based on biomimetic optimized particle filtering, including: the system comprises a building module, a generating module, an updating module, a calculating module, a predicting module and a diagnosing module; the system comprises a building module, a judging module and a judging module, wherein the building module is used for building a state space model of a nonlinear system to be diagnosed; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer; the generating module is used for generating N initial particles for each model in the state space model and initializing the position and weight of each initial particle; the position of each initial particle corresponds to one state in the state space where the state space model is located; n is a positive integer; the updating module is used for iteratively updating the positions of the N initial particles by utilizing a sparrow algorithm and a Lewy flight variation based on the state space model; the computing module is used for computing the weights of the N initial particles after updating and normalizing; the prediction module is used for resampling particles in the state space based on the normalized weight to obtain a system state prediction value corresponding to each model in the state space model; the diagnosis module is used for carrying out fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction quantity corresponding to each model in the state space model.
Further, the diagnostic module is further configured to: based on a system control quantity input vector at the previous moment, acquiring an observation vector of the nonlinear system to be diagnosed at the current moment; based on the system state prediction amount and a preset state prediction equation corresponding to each model in the state space model, calculating an observation prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector; obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value; and judging whether the nonlinear system to be diagnosed has faults at the current moment based on the residual values.
In a third aspect, an embodiment of the present invention further provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the processor executes the computer program to implement the steps of the method described in the first aspect.
The embodiment of the invention provides a nonlinear system fault diagnosis method and a nonlinear system fault diagnosis system based on bionic optimized particle filtering, which optimize traditional particle filtering by using a sparrow algorithm, introduce Lewy flight variation into the sparrow algorithm to perturb and mutate the sparrow position, strengthen the local escape capacity of an individual, avoid the problem that the population easily loses diversity and loses evolutionary capacity under the condition of a high-dimensional system, and relieve the technical problem that the particle depletion is caused by adopting a standard particle filtering method in the prior art.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a nonlinear system fault diagnosis method based on bionic optimized particle filtering provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of fault early warning and fault separation according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a nonlinear system fault diagnosis system based on bionic optimized particle filtering according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Embodiment one:
fig. 1 is a flowchart of a nonlinear system fault diagnosis method based on bionic optimized particle filtering according to an embodiment of the present invention. As shown in fig. 1, the method specifically includes the following steps:
step S102, a state space model of a nonlinear system to be diagnosed is established; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer.
Optionally, the state space model comprises:
wherein i=0 represents a normal state model, X i(k) and Yi (k) Respectively representing the system state vector and the observation vector of the ith system at the moment k, X i (k-1) is the system state vector of the ith system at time k-1, g i(·) and hi (. Cndot.) is the state transfer function and observation function of the ith system, respectively, Θ i For the parameter set of the ith system, U i (k) The vector U is input for the system control quantity of the ith system at the moment k i (k-1) is a system control amount input vector of the ith system at the time of k-1, Q i(k) and Ri (k) State noise and observation noise variable for the ith system, and Q i(k) and Ri (k) All are noise with unknown statistical characteristics.
Step S104, generating N initial particles for each model in the state space model, and initializing the position and weight of each initial particle; the position of each initial particle corresponds to one state in the state space in which the state space model is located; n is a positive integer.
Step S106, based on the state space model, the positions of the N initial particles are iteratively updated by utilizing a sparrow algorithm and the Lewy flight variation.
Step S108, the weights of the N initial particles after updating are calculated and normalized.
Step S110, resampling the particles in the state space based on the normalized weight to obtain the system state prediction value corresponding to each model in the state space model.
And step S112, performing fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction amount corresponding to each model in the state space model.
The embodiment of the invention provides a nonlinear system fault diagnosis method based on bionic optimized particle filtering, which optimizes traditional particle filtering by using a sparrow algorithm, introduces Lewy flight variation in the sparrow algorithm to disturb variation of sparrow positions, enhances the local escape capacity of individuals, avoids the problem that the population is easy to lose diversity and lose evolutionary capacity under the high-dimensional system condition, and relieves the technical problem that the particle depletion is caused by adopting a standard particle filtering method in the prior art.
Specifically, step S106 specifically includes the following steps:
Step S1061, updating the positions of N initial particles based on the state space model;
step S1062, establishing an initial sparrow population based on the updated N initial particles; each particle corresponds to one sparrow;
step S1063, iteratively updating the position of each sparrow in the initial sparrow population by a sparrow algorithm; performing one-time Lewy flight variation on the position of each sparrow in each iterative updating process;
specifically, based on a preset fitness function, the fitness of each sparrow in the initial sparrow population is calculated, and N with the minimum fitness is selected pop ·P t Only sparrows are used as discoverers, and the rest sparrows are used as followers; n (N) pop On the scale of the initial sparrow population, and N pop =N，P t Is the proportion of discoverers in sparrow algorithm; updating the position of each sparrow in the initial sparrow population based on the randomly generated warning value; generation of S in an initial sparrow population d The alertors are updated and the position of each alertor is updated; s is S d Is a random integer; calculating the fitness of each sparrow in the sparrow population after the position update based on a preset fitness function; based on the fitness of each sparrow in the sparrow population after the position update, carrying out the Lewy flight variation on the sparrow population after the update, And calculating the adaptability of the mutated sparrow population; and stopping optimization if the minimum value of the fitness of the mutated sparrow population is not greater than a preset fitness threshold value or the iteration number of the sparrow algorithm is equal to the preset optimization number.
Wherein, carry out the variation of the Lewy flight to the sparrow population after updating, include: calculating an inertia weight factor based on the current iteration number; selecting M sparks to participate in the tournament each time by using the tournament selection, selecting the sparks with the smallest fitness among the M sparks to perform the Laevice flight variation, and selecting N in total pop Secondary times; wherein,
，/>
as a round-up function, η is an inertial weight factor. In particular, if η=0, let m=1.
In step S1064, the positions of the N initial particles are updated again based on the updated positions of each sparrow.
The sparrow algorithm is a novel heuristic optimization algorithm based on the foraging behavior simulation of the foraging behavior and the anti-predation behavior of the sparrows. Compared with other bionic algorithms such as an ant colony algorithm, a bee colony algorithm, a chicken colony algorithm, a sire algorithm and a longhorn beetle whisker algorithm, the method has better local development capability and is better in treating the optimization problem of a high-dimensional space on the basis of keeping better global exploration capability.
The individual rank and following relationship of sparrow groups are key factors in determining population migration. Sparrow groups are classified into two classes of individuals by fitness value ranking: the discoverer has more energy storage and smaller fitness, and the discoverer has less energy and larger fitness. Discoverers are dominant in the population, can obtain food preferentially, and lead individuals with great fitness. In the whole group foraging process, a small number of alertors are randomly appointed, and after a certain amount of alertors find natural enemies, the discoverers take the group to fly to other safe areas. Meanwhile, the grade and individual relation are dynamically changed, so long as a better food source can be found, each sparrow can become a finder under the condition that the population grade composition ratio is unchanged, and the requirement of searching an optimal solution by an algorithm is met. Specifically, the sparrow algorithm can be implemented by the following steps:
(1) Initializing a population: determining the proportion of discoverers, followers and alerters, randomly generating an initial population of n sparrows
An individual location initialization is performed. Wherein N is pop And d is the population size and the optimization variable dimension, respectively.
(2) Determining individual grades: carrying out fitness calculation on individuals in the population to obtain a population fitness matrix:
By adaptation to each individualf（x i ) And sorting, namely selecting individuals with smaller fitness as discoverers, and selecting the rest individuals as followers. Random assignment of S throughout a population d And an alerter.
(3) Foraging position updating:
during the foraging process, the discoverer is responsible for finding food for the entire sparrow population and providing foraging directions for all followers. Further, alarm value R 2 ∈[0,1]Greater than a safety value S t And when the sparrow is brought to migrate to other safety regions. In the iterative process, the location update of the discoverer is expressed as follows:
wherein it is the current iteration number, X i,j Indicating the position information of the ith sparrow in the j-th dimension. Random number gamma epsilon (0, 1), random number Q obeys normal distribution, L is the whole 1 array with dimension of 1 x d.
The follower searches for the most energetic discoverer, competing with or foraging food resources around it, and the follower's location update is described by:
wherein ,
the optimal position occupied by the position of the finder after being updated. />
Representing the current global worst position. />
Wherein A is a real number array with dimension of 1×d, and the element is randomly assigned to be + -1. i.e>At n/2, the follower of the ith hunger and intestine rumble shifts to other areas to forage because of not obtaining food so as to obtain more energy.
(4) Early warning transfer updating:
the early warning person gives an alarm after the natural enemies are found, the early warning person at the edge of the population moves rapidly like a safe region, and the early warning person in the middle of the population approaches other sparrows by walking randomly. The initial positions of these sparrows are randomly generated in the population. The location update of the precaution can be expressed in the form of:
wherein ,
for the current global optimum position, the step control parameter lambda is a random number obeying standard normal distribution, and the random number K epsilon < -1,1]，f i Is the current fitness value of the sparrow individual,f g andf w representing the current global minimum and maximum fitness values respectively, epsilon is a very small constant, and the influence that the denominator may be 0 is eliminated.
(5) And (5) updating the group level:
and forming the individuals after the position update into a next generation population, and completing the updating of discoverers, followers and alerters by calculating the sparrow fitness sequence after the position update.
The standard Particle Filter (PF) algorithm requires the step of weight recursive computation by an importance distribution function, and although the optimal choice is the true distribution of particles, it is often difficult to achieve in a practical nonlinear system. The prior density is usually adopted as an importance distribution function in most algorithms, but the prior density is easy to realize, and the latest observation information is ignored, so that the weight of the particles is degraded. The resampling method links the degradation degree to a certain extent by continuously copying high-weight particles and discarding low-weight particles, but as the iteration is continuously performed, the particles are depleted.
In the method provided by the embodiment of the invention, in the sparrow algorithm (Sparrow Search Algorithm, SSA) optimized particle filtering method, SSA is combined with the traditional PF, the sampling process of particle filtering is optimized through the improved sparrow algorithm, and the current observation information is utilized to guide the rapid optimization of particle distribution so as to increase the diversity of particles. Under the condition of a certain number of particles, the execution efficiency of the algorithm is improved, and the precision of state estimation is improved.
Sparrow algorithm optimizes particle distribution by directing sparrow groups to seek food-rich and safe areas through discoverers with higher energy reserves. The basic sparrow algorithm lacks an excellent mutation mechanism, and the random updating of the population leading layer is carried out through a follower competing mechanism, but the follower is simply and directly replaced by a finder, so that individuals are easily attracted by local optima to cause premature convergence. In order to further accelerate the convergence rate of the optimizing algorithm, the Lewy flight variation is introduced to perturb the sparrow position, so that the local escape capacity of an individual is enhanced, and the situation that the population easily loses diversity and loses the evolution capacity under the high-dimensional system condition is avoided.
A series of studies confirm that when a forager in nature searches for habitats with sufficient food sources, most short-range occasional long-distance alternate walk-through searching methods, i.e., the "lewy flight" searching strategy, are generally adopted due to the dispersion and unknowing nature of the habitat distribution. By utilizing the characteristic of Laiwei flying random walk, larger jump and direction jerk are generated in the position updating process, the sparrow individual is prevented from being bound by local extremum, meanwhile, the foraging search space is expanded, and the optimization effect of the sparrow algorithm in the high-dimensional complex space is effectively improved. In the invention, during the sparrow optimizing process, the sparrow position selected in each period is updated to perform Lewy flight searching, and the sparrow position with higher energy after flight is used for replacing the original position, so that the effectiveness of algorithm variation is endowed, and the diversity of particles is maintained.
In the embodiment of the invention, each particle in the particle filtering is regarded as one sparrow in the sparrow population, and the position of the particle population is guided by a finder with a higher weight as a guiding layer, so that the position of the particle population is moved to a habitat with higher energy in the continuous iterative process. The particle distribution is enabled to be continuously approximate to posterior probability distribution of the real state of the system, the effectiveness of the particles is improved, and weight degradation is avoided.
It should be noted that, in the embodiment of the present invention, the following analysis is made for the correlation of both the particle filtering algorithm and the sparrow algorithm:
(1) PF randomly extracts N initial particles from prior probability distribution, LSSA randomly generates N sparrows to form initial population;
(2) The particle with the highest weight in the PF represents the most possible state of the system, and the sparrow position with the smallest adaptability in the LSSA represents the optimal value point;
(3) Particle position updating in the PF is realized through a state transition model, particle weight updating is realized through an observation model, and position updating is realized through special movements of a finder, a follower and a alerter in the LSSA;
(4) Particle diversity requires that a certain number of lower weight particles be retained in the PF, and that a follower with lower energy in the LSSA may find a farther habitat by a lewy search, and that an arm at the edge may find a better position in the process of approaching the security area.
Specifically, in the individual optimization process of the sparrow group, the latest observation value information needs to be combined, and the sparrow algorithm is considered to optimize towards the direction of smaller fitness, so that an inverse function of the particle weight is taken as a fitness function of the optimization algorithm, and the following is defined:
Wherein R is the observed noise variance, y pred and yact The current latest predicted value of the filter and the actual predicted value of the system are respectively represented, and the upper corner mark k represents the kth moment. Specifically, the positions of the N initial particles are iteratively updated by using a sparrow algorithm and a Lewy flight variation, and the steps are as follows:
step 1: initializing. Setting the iteration times it=0, and optimizing the upper limit u of the variable by using sparrow algorithm b And lower limit l b Maximum optimizing algebra it max Minimum optimization fitness thresholdf min Discoverer ratio P l Proportion S of alerter d /N pop Safety value S t Correcting the constant epsilon; the Lev search step length beta; setting the filtering step number T k Effective particle number threshold N th 。
Step 2: and (5) initial particle sampling. At initial time, N particles are sampled in a state space
As an initial particle population. Wherein the particle obeying importance distribution function is a distribution of prior probability densities:
. Initializing particle weights->
。
Step 3: each particle is regarded as a sparrow, the initial particle population is regarded as an initial sparrow population, and the sparrow population scale N pop =n. Simulating sparrow optimizing and guiding the movement of particles.
(1) And calculating the fitness of each sparrow by using the population fitness matrix. Selecting N with minimum adaptability pop ·P t Only sparrows are used as discoverers, and the rest sparrows are used as followers.
(2) Randomly generating an alert value R 2 And updating the individual position of the sparrow by using the follower position updating formula and the finder position updating formula of the sparrow algorithm.
(3) Randomly generating S d And the alerter updates the individual position of the alerter by using the position updating algorithm of the early warning person in the sparrow algorithm.
(4) And calculating the fitness value of the sparrow individual after the position is updated.
Step 4: and Levin flight variation. Calculating inertial weighting factors
With tournament selection, there is a return of the extract +.>
Individual sparrow individuals participate in tournament, the individual with the smallest fitness is selected from M sparrow individuals to carry out Lewy flight variation, and N is selected in total pop And twice.
The Levin flight variation replaces the original position by updating the position of the selected sparrow individual and by the position with better adaptability after Levin flight. The position updating formula is as follows:
in the formula,
for point-to-point multiplication, +.>
U and v are dimensions 1×d, and the elements are [0,1 ]]Random number array in the search step length 1 is more than or equal to beta is more than or equal to 3,/and is not more than or equal to>
，Γ(x)=(x-1)！。
And calculating an fitness function (namely the fitness of the sparrow population) after the Lewy flight mutation, and if the fitness is smaller, updating the position of the mutated sparrow.
Step 5: when the current global fitness (i.e. the fitness of the sparrow population) is minimum f g Not greater than a minimum optimizing fitness thresholdf min If not, stopping optimizing, otherwise, continuing to execute Step 5.
Step 6: when the iteration number it is equal to the maximum optimizing algebra it max And (3) stopping optimizing, otherwise, sequencing the fitness of each body, updating the group level, and converting into Step 3.
Step 7, calculating the weight of the particles and carrying out normalization processing. The particle weights are updated by the following formula:
, wherein />
Is the latest observation information.
Weight passing
And (5) carrying out normalization calculation.
Step 8: and (5) resampling particles and outputting a filtering result.
The particle resampling process is as follows: counting the number of currently active particles
. If N eff <N th Then polynomial resampling is performed from [0,1]Is divided uniformly intoRandomly selecting the sample value U E U (0, 1) in the cloth, copying the sample value U E U to the particles E in the new particle set>
Weight of (2) is in accordance with->
. The resampling process is repeated until a new population of N equal weight particles is generated. If N eff ≥N th The state estimation is directly performed without resampling.
Estimation by least mean square error
Outputting the filtering result, i.e. x k Estimate of->
。
Optionally, step S112 further includes the steps of:
step S1121, based on the system control amount input vector of the previous moment, obtains the observation vector of the nonlinear system to be diagnosed at the current moment.
Step S1122, based on the system state prediction amount and the preset state prediction equation corresponding to each model in the state space model, calculating the observed prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector.
Step S1123, obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value.
And step S1124, judging whether the nonlinear system to be diagnosed has faults at the current moment based on the residual values.
Specifically, judging whether the absolute value of the residual value corresponding to the normal state model is larger than a preset threshold value; if yes, judging that the nonlinear system to be diagnosed has faults at the current moment, and determining a model corresponding to the minimum residual error value in n fault state models to be diagnosed as a model of the nonlinear system to be diagnosed; if not, judging that the nonlinear system to be diagnosed has no fault at the current moment.
Specifically, the fault diagnosis method based on the bionic optimized particle filtering provided by the embodiment of the invention further comprises four aspects of fault modeling, residual error generation, fault early warning and fault separation.
(1) Fault modeling:
Firstly, a fault model database to be diagnosed is established based on a particle filter structure, wherein the database comprises a normal working state model S 0 And a plurality of fault state models to be diagnosed
. And establishing a corresponding fault state model according to the nonlinear system model and the fault mechanism. In order to provide a data basis for subsequent fault separation and estimation, n+1 individual particle filters need to be configured to match different models in the database, so that all possible fault mode estimates of the system are realized.
(2) Residual error generation:
in order to generate the residual, the following assumptions need to be made: the state estimation model variable realizes error-free tracking of the actual system variable in the normal state of the system; and the model variables produce a systematic deviation containing fault information when a systematic fault occurs.
For a target nonlinear system, the state space model is built as follows:
wherein X (k) and Y (k) respectively represent a system state vector and an observation vector at the moment k, g (& gt) and h (& gt) are respectively a nonlinear system state transfer function and an observation function, Θ is a system parameter set, U (k) is a control input vector of a system at the moment k, Q (k) and R (k) are state noise and observation noise variables of the system, and both are unknown noise with statistical characteristics.
Based on the fault modeling, a database comprising 1 normal state model and n fault state models to be diagnosed is established, and then the state space model of the models in the database can be organized as follows:
the state prediction equation is:
in the formula,Xi (k|k-1) is a state prediction variable,
to observe the prediction vector.
Thus, the system residual r of the ith model at k time can be obtained i (k) Calculated by the following formula:
the physical meaning is the degree of inconsistency between the actual running state of the system and the theoretical running state of the mathematical model.
(3) Fault early warning:
after the residual error is generated, an early warning threshold r is designed based on expert experience and fault characteristics th And comparing with the normal state model residual error to judge whether a fault occurs. When |r 0 (k)|>r th And when the system is judged to have faults at the moment k, fault early warning is realized.
(4) Fault separation:
after the system sends out the early warning signal, further separating faults according to residual performances of each fault state model to be diagnosed. When r is i (k) And if so, judging that the ith fault occurs.
Fig. 2 is a schematic diagram of fault early warning and fault separation according to an embodiment of the present invention, as shown in fig. 2, a control input is first input to a nonlinear system model, then a state prediction corresponding to each model in a state space model of the system is obtained by using a particle filtering algorithm based on sparrow algorithm improvement provided by the embodiment of the present invention, and finally a residual error between an observed true value and the state prediction is calculated, and fault early warning and fault separation are performed based on the residual error.
Embodiment two:
fig. 3 is a schematic diagram of a nonlinear system fault diagnosis system based on biomimetic optimized particle filtering according to an embodiment of the present invention. As shown in fig. 3, the system includes: the system comprises a building module 10, a generating module 20, an updating module 30, a calculating module 40, a predicting module 50 and a diagnosing module 60.
Specifically, the establishing module 10 is configured to establish a state space model of the nonlinear system to be diagnosed; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer.
A generating module 20 for generating N initial particles for each of the state space models, and initializing a position and a weight of each initial particle; the position of each initial particle corresponds to one state in the state space in which the state space model is located; n is a positive integer.
The updating module 30 is configured to iteratively update the positions of the N initial particles using a sparrow algorithm and a lewy flight variation based on the state space model.
A calculating module 40, configured to calculate weights of the N initial particles after updating and normalize the weights.
The prediction module 50 is configured to resample the particles in the state space based on the normalized weights, so as to obtain a system state prediction value corresponding to each of the state space models.
The diagnosing module 60 is configured to perform fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction amount corresponding to each of the state space models.
The embodiment of the invention provides a nonlinear system fault diagnosis system based on bionic optimized particle filtering, which optimizes traditional particle filtering by utilizing a sparrow algorithm, introduces Lewy flight variation in the sparrow algorithm to disturb variation on the sparrow position, enhances the local escape capacity of individuals, avoids the problem that the population is easy to lose diversity and lose evolutionary capacity under the high-dimensional system condition, and relieves the technical problem that the particle depletion is caused by adopting a standard particle filtering method in the prior art.
Optionally, the updating module 30 is further configured to:
updating the positions of the N initial particles based on the state space model;
establishing an initial sparrow population based on the updated N initial particles; each particle corresponds to one sparrow;
iteratively updating the position of each sparrow in the initial sparrow population through a sparrow algorithm; performing one-time Lewy flight variation on the position of each sparrow in each iterative updating process;
specifically, based on a preset fitness function, the fitness of each sparrow in the initial sparrow population is calculated, and N with the minimum fitness is selected pop ·P t Only sparrows are used as discoverers, and the rest sparrows are used as followers; n (N) pop On the scale of the initial sparrow population, and N pop =N，P t Is the proportion of discoverers in sparrow algorithm; updating the position of each sparrow in the initial sparrow population based on the randomly generated warning value; generation of S in an initial sparrow population d The alertors are updated and the position of each alertor is updated; s is S d Is a random integer; calculating the fitness of each sparrow in the sparrow population after the position update based on a preset fitness function; carrying out Lewy flight mutation on the updated sparrow population, and calculating the adaptability of the mutated sparrow population; and stopping optimization if the minimum value of the fitness of the mutated sparrow population is not greater than a preset fitness threshold value or the iteration number of the sparrow algorithm is equal to the preset optimization number.
Wherein, carry out the variation of the Lewy flight to the sparrow population after updating, include: calculating an inertia weight factor based on the current iteration number; with tournament selection, each time there is a playExtracting M sparrows back to participate in the tournament, selecting the sparrow with the smallest fitness among the M sparrows to carry out Laevice flight variation, and selecting N altogether pop Secondary times; wherein,
，/>
as a round-up function, η is an inertial weight factor. In particular, if η=0, let m=1.
Based on the position of each sparrow after the update, the positions of the N initial particles are updated again.
Optionally, the diagnostic module 60 is further configured to: based on a system control quantity input vector at the previous moment, acquiring an observation vector of a nonlinear system to be diagnosed at the current moment; based on the system state prediction amount and the preset state prediction equation corresponding to each model in the state space model, calculating the observation prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector; obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value; based on the residual values, judging whether the nonlinear system to be diagnosed has faults at the current moment.
The embodiment of the invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the steps of the method in the first embodiment.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (9)
1. A nonlinear system fault diagnosis method based on bionic optimized particle filtering is characterized by comprising the following steps:
establishing a state space model of a nonlinear system to be diagnosed; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer;
generating N initial particles for each model in the state space model, and initializing the position and weight of each initial particle; the position of each initial particle corresponds to one state in the state space where the state space model is located; n is a positive integer;
based on the state space model, iteratively updating the positions of the N initial particles by utilizing a sparrow algorithm and a Lewy flight variation;
calculating the weights of the N initial particles after updating and normalizing;
resampling the particles in the state space based on the normalized weight to obtain a system state prediction value corresponding to each model in the state space model;
performing fault diagnosis on the nonlinear system to be diagnosed based on the system state prediction amount corresponding to each model in the state space model;
based on the state space model, iteratively updating the positions of the N initial particles using a sparrow algorithm and a lewy flight variation, comprising:
Updating the positions of the N initial particles based on the state space model;
establishing an initial sparrow population based on the updated N initial particles; each particle corresponds to one sparrow;
iteratively updating the position of each sparrow in the initial sparrow population through a sparrow algorithm; performing one-time Lewy flight variation on the position of each sparrow in each iterative updating process;
and updating the positions of the N initial particles again based on the updated positions of each sparrow.
2. The method of claim 1, wherein the state space model comprises:
wherein i=0 represents a normal state model, X i(k) and Yi (k) Respectively representing the system state vector and the observation vector of the ith system at the moment k, X i (k-1) is the system state vector of the ith system at time k-1, g i(·) and hi (. Cndot.) is the state transfer function and observation function of the ith system, respectively, Θ i For the parameter set of the ith system, U i (k) The vector U is input for the system control quantity of the ith system at the moment k i (k-1) is a system control amount input vector of the ith system at the time of k-1, Q i(k) and Ri (k) State noise and observation noise variable for the ith system, and Q i(k) and Ri (k) All are noise with unknown statistical characteristics.
3. The method of claim 1, wherein iteratively updating the location of each sparrow in the initial sparrow population by a sparrow algorithm comprises:
based on a preset fitness function, calculating fitness of each sparrow in the initial sparrow population, and selecting N with minimum fitness pop ·P t Only sparrows are used as discoverers, and the rest sparrows are used as followers; n (N) pop To the scale of the initial sparrow population, and N pop =N，P t Is the proportion of discoverers in sparrow algorithm;
updating the position of each sparrow in the initial sparrow population based on the randomly generated warning value;
generating S in the initial sparrow population d The alertors are updated and the position of each alertor is updated; s is S d Is a random integer;
calculating the fitness of each sparrow in the sparrow population after the position update based on a preset fitness function;
based on the fitness of each sparrow in the sparrow population after the position update, carrying out the Lewy flight variation on the sparrow population after the update, and calculating the fitness of the sparrow population after the variation;
and stopping optimization if the minimum value of the fitness of the mutated sparrow population is not greater than a preset fitness threshold value or the iteration number of the sparrow algorithm is equal to the preset optimization number.
4. A method according to claim 3, wherein the subjecting the updated sparrow population to lewy flight variation comprises:
calculating an inertia weight factor based on the current iteration number;
selecting M sparks to participate in the tournament each time by using the tournament selection, selecting the sparks with the smallest fitness among the M sparks to perform the Laevice flight variation, and selecting N in total pop Secondary times; wherein,
，/>
for the round-up function, η is the inertial weight factor.
5. The method of claim 1, wherein diagnosing the nonlinear system to be diagnosed based on the system state predictions corresponding to each of the state space models, comprises:
based on a system control quantity input vector at the previous moment, acquiring an observation vector of the nonlinear system to be diagnosed at the current moment;
based on the system state prediction amount and a preset state prediction equation corresponding to each model in the state space model, calculating an observation prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector;
obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value;
And judging whether the nonlinear system to be diagnosed has faults at the current moment based on the residual values.
6. The method of claim 5, wherein determining whether the nonlinear system to be diagnosed is malfunctioning at a current time based on the plurality of residual values comprises:
judging whether the absolute value of the residual value corresponding to the normal state model is larger than a preset threshold value or not;
if yes, judging that the nonlinear system to be diagnosed has faults at the current moment, and determining a model corresponding to the minimum residual error value from the n fault state models to be diagnosed as the model of the nonlinear system to be diagnosed.
7. A nonlinear system fault diagnosis system based on biomimetic optimized particle filtering, comprising: the system comprises a building module, a generating module, an updating module, a calculating module, a predicting module and a diagnosing module; wherein,
the building module is used for building a state space model of the nonlinear system to be diagnosed; the state space model comprises a normal state model and n fault state models to be diagnosed, wherein n is a positive integer;
the generating module is used for generating N initial particles for each model in the state space model and initializing the position and weight of each initial particle; the position of each initial particle corresponds to one state in the state space where the state space model is located; n is a positive integer;
The updating module is used for iteratively updating the positions of the N initial particles by utilizing a sparrow algorithm and a Lewy flight variation based on the state space model;
the computing module is used for computing the weights of the N initial particles after updating and normalizing;
the prediction module is used for resampling particles in the state space based on the normalized weight to obtain a system state prediction value corresponding to each model in the state space model;
the diagnosis module is used for carrying out fault diagnosis on the nonlinear system to be diagnosed based on the system state pre-measurement corresponding to each model in the state space model;
the updating module is further configured to:
updating the positions of the N initial particles based on the state space model;
establishing an initial sparrow population based on the updated N initial particles; each particle corresponds to one sparrow;
iteratively updating the position of each sparrow in the initial sparrow population through a sparrow algorithm; performing one-time Lewy flight variation on the position of each sparrow in each iterative updating process;
and updating the positions of the N initial particles again based on the updated positions of each sparrow.
8. The system of claim 7, wherein the diagnostic module is further configured to:
based on a system control quantity input vector at the previous moment, acquiring an observation vector of the nonlinear system to be diagnosed at the current moment;
based on the system state prediction amount and a preset state prediction equation corresponding to each model in the state space model, calculating an observation prediction vector of each model in the state space model at the current moment; one model corresponds to one observation prediction vector;
obtaining a plurality of residual values based on the observation vector and the observation prediction vector; one model corresponds to one residual value;
and judging whether the nonlinear system to be diagnosed has faults at the current moment based on the residual values.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method of any of the preceding claims 1 to 6 when the computer program is executed.
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