CN110879528A - Method for simultaneously optimizing number and position of sensors and actuators of active vibration reduction system - Google Patents
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Abstract
The invention provides a method for simultaneously optimizing the number and the positions of a sensor and an actuator of an active vibration reduction system, which comprises the following specific processes: step 1, designing a target function; step 2, vibration measurement and system identification; step 3, iterative optimization of a genetic algorithm: and constructing a fitness function based on a target function, selecting n sensors and q actuators from a vibration system to carry out genetic algorithm iteration, calculating the fitness function corresponding to the current iteration according to the frequency domain transfer function, and taking the number and the positions of the sensors and the actuators selected by the iteration as the optimal values if the fitness functions of the current iteration and the last iteration meet set requirements. According to the method, the number and the positions of the sensor actuators in the ship active vibration reduction system are simultaneously optimized in a frequency domain, and the scale of the control system is greatly reduced under the condition that the control effect of the original system is kept as much as possible.
Description
Technical Field
The invention belongs to the technical field of ship active vibration control, and particularly relates to a method for simultaneously optimizing the number and the positions of sensors and actuators of an active vibration reduction system.
Background
The low-frequency line spectrum vibration generated by various rotating and reciprocating machines such as diesel engines and pumps on ships is very prominent. Such vibrations can produce cabin noise, which affects personnel comfort, and can also excite the hull to produce underwater radiation noise, which affects detection distance or stealth performance. Therefore, a certain measure must be adopted to control the vibration, which also becomes one of the most critical technical problems in the process of ship development.
The active vibration reduction technology has become an effective method and an important development direction for reducing vibration and noise of ships due to the advantages of strong adaptability, good control effect, low energy consumption and the like. The basic principle of the technology is to control vibration by vibration, namely, an actuator is arranged at a non-node position of a main mode of a ship body, and real-time adjustment is carried out by a controller on the basis of a feedback signal of a sensor, so that the vibration response of an active control force generated by the actuator at a key part is equal to the amplitude of the ship body vibration caused by an external disturbance excitation force and opposite in phase, and thus vibration cancellation is realized.
In the active vibration reduction system of the ship, because the vibration sources are more and distributed discretely, the number of required sensors and actuators is larger. On one hand, the use of too many sensors and actuators will cause the control system to become too complex and even affect the performance and stability of the control system; on the other hand, the sensor and the data acquisition and processing system matched with the sensor, and the actuator and the driving power supply of the actuator are high in cost. Therefore, it is desirable to reduce the number of sensors and actuators as much as possible and realize position optimization by a certain optimization method, and effectively reduce the scale of the whole control system under the condition of ensuring that the global vibration reduction effect of the system is basically unchanged.
At present, relevant documents realize the position optimization of an actuator and a sensor in an active vibration damping system through an optimization method. For example, s.j.elliott et al investigated the optimization problem of actuator (speaker) position in an active noise reduction system using genetic algorithms. In China, the optimum arrangement of actuators in an active vibration damping system is studied by using a genetic algorithm. D.e.heverly II investigated the effect of simulated annealing optimization methods in active damping systems in determining optimal position. In the above studies, the position of the actuator was optimized on the premise that the number of sensors was artificially fixed, and the sensors were not optimally arranged. The other part of research is that the position of the sensor is optimized on the premise that the number of the actuators is artificially fixed, and the actuators are not optimally configured. The land rank and the like firstly perform actuator position optimization and then perform sensor position optimization by steps, and a unified framework of multi-actuator and sensor optimization design is established, so that the purposes of optimizing the positions of the actuators in the system and reducing the number of the sensors are achieved. The research needs to be divided into two relatively independent steps to complete the optimization work, and the optimization result is difficult to ensure to be a global optimal solution due to the two steps. In summary, the existing optimal configuration method mostly gives the number of actuators and sensors, and how to determine the optimal number of actuators/sensors is still a relatively difficult problem.
Disclosure of Invention
The invention aims to provide a method for simultaneously optimizing the number and the positions of sensors and actuators in an active vibration reduction system.
The technical scheme for realizing the invention is as follows:
a method for simultaneously optimizing the number and the positions of sensors and actuators of an active vibration reduction system, wherein the active vibration system comprises m sensors and p actuators, and the specific process comprises the following steps:
step 1, designing an objective function:
establishing a mathematical model of the ship active vibration reduction system, and designing and optimizing a required objective function based on the mathematical model;
step 2, vibration measurement and system identification:
obtaining the original vibration condition of each sensor of the vibration system through measurement, and obtaining the frequency domain transfer function from each actuator to each sensor through open-loop excitation;
step 3, iterative optimization of a genetic algorithm:
constructing a fitness function based on a target function, selecting n sensors and q actuators from a vibration system to carry out genetic algorithm iteration, calculating the fitness function corresponding to the current iteration according to the frequency domain transfer function, and taking the number and the positions of the sensors and the actuators selected by the iteration as the optimal values if the fitness functions of the current iteration and the last iteration meet set requirements, wherein n is more than 0 and less than m, and q is more than 0 and less than p.
Further, the objective function of the present invention is:
Jm＝em Hem
em＝dm+Gmpup(1)
wherein e ismIs a controlled structural response signal, which is an mx 1 vector; dmIs a pre-control structure response signal, which is an mx 1 vector; u. ofpIs a controlled quantity, which is a p × 1 vector; gmpThe control channel frequency response function represents the one-to-one correspondence transfer relationship between the m sensors and the p actuators and is an m multiplied by p matrix.
Further, the establishment of the fitness function based on the objective function according to the present invention is:
Fitness＝(dm+Gmquq,opt)H(dm+Gmquq,opt)+ω1q+ω2n
wherein d ismIs a pre-control structure response signal, GmpFor controlling the channel frequency transfer function, GmqIs GmpOf a reduced set of transfer function frequency response matrices, omega1And ω2The weighting coefficients are respectively the number q of the selected sensors and the number n of the actuators.
Further, the setting conditions of the invention are as follows: and the absolute difference of the fitness function of the two adjacent iterations is smaller than a set threshold value.
Further, the invention carries out binary coding on the sensor and the actuator, sets the selected code as '1', otherwise, sets the selected code as '0', and carries out iterative optimization on the binary code by utilizing a genetic algorithm, wherein the iterative optimization mainly comprises initial population generation, fitness detection, selection, crossing and mutation operations.
Advantageous effects
(1) The existing optimization method mostly gives the number of actuators and sensors in advance; or the number of actuators and sensors is optimized in two steps, the global optimum cannot be guaranteed. The invention can simultaneously carry out global optimization design on the number and the positions of the actuators of the sensor in the active vibration reduction system of the ship in a frequency domain, greatly reduces the scale of the control system under the condition of keeping the control effect (or acceptable performance loss) of the original system as far as possible, optimizes the optimal number and the optimal positions of the actuators and the sensors and ensures global optimization.
(2) In the existing optimization method adopting binary coding, in order to avoid the genetic algorithm from selecting as many actuators and sensors as possible to improve the performance, constraint conditions need to be added in the cross and variation operations to ensure that the number of the actuators and the sensors is not changed, so that not only is the complexity of the genetic algorithm increased, but also the superiority of the genetic algorithm is difficult to embody. Because the quantity is not fixed in advance, in order to avoid optimizing the algorithm and preferably selecting as many actuators and sensors as possible, the quantity weighting term is only required to be added in the fitness function to reduce the finally selected quantity. Compared with the scheme of increasing the constraint conditions, the scheme is simpler and more effective.
Drawings
FIG. 1 is a control system gene string of the present invention comprising 10 sensors and 5 actuators;
FIG. 2 is a block diagram of the genetic algorithm of the present invention;
FIG. 3 is a value of fitness function for each generation of the genetic algorithm of the present invention;
figure 4 is a schematic view of an alternative and preferred sensor/actuator location on the base of the apparatus of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The design idea of the invention is as follows: aiming at the problem of simultaneous optimization of the number and the positions of sensors and actuators in an active vibration reduction system of a ship, firstly, a target function is designed, and then, system identification is carried out to obtain a transfer function in the target function. And then, optimizing by adopting a genetic algorithm, wherein the optimization comprises the processes of coding, initial population generation, fitness evaluation and detection, selection, crossing, mutation operation and the like, and finally obtaining the number and the positions of the sensors of the optimal actuator.
The invention discloses a method for simultaneously optimizing the number and the positions of a sensor and an actuator of an active vibration reduction system, which comprises the following specific processes:
step 1, designing an objective function.
Establishing a mathematical model of the ship active vibration reduction system, wherein for a given dynamic system, when m sensors and p actuators exist, error signals measured by the sensors can be expressed as follows:
em＝dm+Gmpup(1)
wherein e ismIs a controlled structural response signal (generally, acceleration) which is an mx 1 vector; dmIs a pre-control structure response signal, which is an mx 1 vector; u. ofpIs a controlled variable (generally, a driving voltage) which is a vector of p × 1; gmpThe control channel frequency response function represents the one-to-one correspondence transfer relationship between the m sensors and the p actuators and is an m multiplied by p matrix.
Defining the control target as the sum of the squares of the responses of the m measurement points, the objective function can be expressed as:
Jm＝em Hem(2)
according to the optimal control theory, the optimal control quantity obtained by minimizing the control target is as follows:
up,opt＝-(Gmp HGmp)-1Gmpdm(3)
the minimum value of the system-wide objective function can be expressed as:
Jm,min＝(dm+Gmpup,opt)H(dm+Gmpup,opt) (4)
when the control system has m sensors and p actuators, the channel frequency response function G is controlledmpFor an m × p matrix, that is, there are m × p one-to-one corresponding transfer relationships between actuators and points to be damped, m × p control channels need to be occupied. When the number m, p of sensors and actuators is large, the scale of control will be large, thereby causing a series of problems. Under the premise of ensuring that the overall control performance of the control system is basically unchanged, the number of the sensors and the actuators is reduced, and the position is optimized, so that the scale of the control system is greatly reduced.
With n sensors replacing the previous m sensors (0< n < m) and q actuators replacing the previous p sensors (0< q < p), the error signal vector measured at this reduced set of sensor positions can be expressed as:
en＝dn+Gnquq(5)
wherein e isnThe controlled vibration measured by a sensor reduction set is an n multiplied by 1 vector; dnThe pre-control response at the sensor reduced set is an n multiplied by 1 vector; u. ofqThe actuator reduced set control quantity is a qX 1 vector; gnqThe method is a control channel frequency response function, comprises the one-to-one corresponding transfer relations between n sensors and q actuators, and is an n multiplied by q matrix.
The reduced system objective function at this point can be expressed as:
Jn＝en Hen(6)
similarly, the actuator reduced set optimal control quantity obtained by the optimal control theory is as follows:
uq,opt＝-(Gnq HGnq)-1Gnqdn(7)
in the formula uq,optThat is, the optimal control amount when controlling the n sensors with the q actuators.
And (3) bringing the actuator reduced set optimal control quantity (7) into the formula (2), the minimum value of the whole system objective function can be expressed as:
in the formula (d)mStill m multiplied by 1 vectors, corresponding to the vibration of each original point to be damped; gmqIs GmpA reduced set of transfer function frequency response matrices. Compared with the formula (4), the formula (8) is the minimum value of the whole system objective function obtained by reducing the optimal control quantity of the actuator after reducing the number of the sensors and the actuators and optimizing the positions.
Theoretically, there are
But when
And Jm,minWith little difference (e.g. of
) In time, it is considered that the control effect of the original system is maintained as much as possible under the condition of reducing the control scale, thereby obtaining an engineering acceptable solution.
In practical engineering, the output of the actuator cannot be unlimited, and the actuator often has a maximum limit input, namely a target function needs to be added with a limiting condition, namely upC is less than or equal to C, wherein C is a constant vector; or the formula (2) is designed to be Jm＝em Hem+βup HupIn the equation β, a control amount weighting coefficient is used to reduce the probability of selecting a maximum actuator drive voltage solution.
And 2, vibration measurement and system identification.
Obtaining pre-control response d at each sensor of vibration system through measurementm(ii) a Obtaining the frequency domain transfer function G from each actuator to each sensor through open loop excitationmpInputs may be provided for solving the optimal control quantity equations (3) and (7) and the objective function minimum equations (4) and (8).
And 3, iterative optimization of the genetic algorithm.
First, the sensors and actuators are binary coded.
All sensors and actuators are coded separately using the simplest binary numbers, selected as "1" and "0" otherwise, i.e. the simplest binary numbers
For example, as shown in FIG. 1, for a control system comprising 10 sensors and 5 actuators, b in a gene string1-b10Bit represents a sensor, wherein b2,b5,b9And b10Genes at (a) represent selected sensors (4 in total); b11-b15Position indicating actuator, wherein b12、b13And b15Genes at (a) indicate the selected actuators (3 in total).
And then, constructing a fitness function required by the genetic algorithm through the objective function. The system-wide objective function minimum (8) can be used directly as the fitness function. Since the number of actuators selected in two offspring will change after the binary codes are crossed, and the genetic algorithm will select as many sensors and actuators as possible to improve the performance without any constraint, a weighting term for the number of sensors and actuators needs to be added to the fitness function, for example:
Fitness＝(dm+Gmquq,opt)H(dm+Gmquq,opt)+ω1q+ω2n (10)
in the formula, ω1And ω2The weighting coefficients are respectively the number q of the selected sensors and the number n of the actuators.
Further, as shown in fig. 2, iterative optimization of a genetic algorithm is performed, which mainly includes operations such as initial population generation, fitness detection, selection, crossing, variation and the like, and finally, the number and the positions of the sensors of the optimal actuators are obtained. To eliminate the uncertainty factor as much as possible, the final Fitness function may take the average of multiple Fitness values.
In order to verify the effectiveness of the method, example verification is performed, which specifically comprises the following steps:
the equipment base inside a certain ship is supported on the ship body through 27 vibration isolators, and the vibration of the large-scale motor on the base excites the vibration of the base and is transmitted to the ship body through the 27 vibration isolators so as to radiate noise outwards. The vibration is greatly reduced after passing through the vibration isolator, but in order to further reduce the low-frequency line spectrum radiation noise of the whole platform, an active vibration reduction technology is adopted. In view of the critical effect of vibration isolators on vibration transmission, actuators are to be installed in their vicinity to isolate the transmission of forces to the hull. The system then contains 27 alternative sensors (m 27) and 27 alternative actuator positions (p 27). Due to the large scale of the control system, the number and the positions of the sensors and the actuators need to be optimized.
Firstly, measuring a vibration signal d at the position of an alternative sensor under the operation condition of a motorm(ii) a Then, measuring the frequency response function G from the alternative actuator to the alternative sensor under the condition that the motor is not operatedmp. Based on the above measurement results and fitness function formula (8), optimization work is carried out. FIG. 3 shows ω1＝ω2＝1×10-7The optimization results in this case, fig. 4 is a schematic diagram of alternative and preferred sensor/actuator positions on the base of the device.
The optimization results show that 12 sensor positions and 8 actuator positions are optimized by genetic algorithms. The fitness function values before and after control are respectively 1.27 multiplied by 10-5And 1.08X 10-5. According to the formula (2), the minimum value of the target function of the whole system before control is 8.21 multiplied by 10-3(ii) a From equation (4), if all 27 candidate sensors and 27 candidate actuators are selected, the minimum value of the system-wide objective function is 0.83 × 10-3(ii) a According to the formula (8), after the optimized actuators are adopted to reduce the set optimal control quantity, the minimum value of the whole system objective function is 0.96 multiplied by 10-3. Therefore, the 27-in 27-out full system can reduce the global vibration by 89.9%, and the optimized 12-in 8-out reduction control system can reduce the vibration by 88.3%, which is not much different from the effect of the full system. So that the system performance is only reduced by 1.6%Under the circumstances, the scale of the active control system is greatly reduced. At the same time, actuator power consumption is reduced by 47%, i.e., almost the same control performance is obtained with less power consumption. In fact, as the system scale decreases, the stability of the control system will be greatly improved.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A method for simultaneously optimizing the number and the positions of sensors and actuators of an active vibration reduction system, wherein the active vibration system comprises m sensors and p actuators, is characterized by comprising the following specific processes:
step 1, designing an objective function:
establishing a mathematical model of the ship active vibration reduction system, and designing and optimizing a required objective function based on the mathematical model;
step 2, vibration measurement and system identification:
obtaining the original vibration condition of each sensor of the vibration system through measurement, and obtaining the frequency domain transfer function from each actuator to each sensor through open-loop excitation;
step 3, iterative optimization of a genetic algorithm:
constructing a fitness function based on a target function, selecting n sensors and q actuators from a vibration system to carry out genetic algorithm iteration, calculating the fitness function corresponding to the current iteration according to the frequency domain transfer function, and taking the number and the positions of the sensors and the actuators selected by the iteration as the optimal values if the fitness functions of the current iteration and the last iteration meet set requirements, wherein n is more than 0 and less than m, and q is more than 0 and less than p.
2. The method for simultaneous optimization of the number of positions of the sensors and actuators of the active damping system according to claim 1, wherein the objective function is:
Jm＝em Hem
em＝dm+Gmpup(1)
wherein e ismIs a controlled structural response signal, which is an mx 1 vector; dmIs a pre-control structure response signal, which is an mx 1 vector; u. ofpIs a controlled quantity, which is a p × 1 vector; gmpThe control channel frequency response function represents the one-to-one correspondence transfer relationship between the m sensors and the p actuators and is an m multiplied by p matrix.
3. The method for simultaneous optimization of the number and the positions of the sensors and the actuators of the active damping system according to claim 2, wherein the objective function-based construction of the fitness function is:
Fitness＝(dm+Gmquq,opt)H(dm+Gmquq,opt)+ω1q+ω2n
wherein d ismIs a pre-control structure response signal, GmpFor controlling the channel frequency transfer function, GmqIs GmpOf a reduced set of transfer function frequency response matrices, omega1And ω2The weighting coefficients are respectively the number q of the selected sensors and the number n of the actuators.
4. The method for simultaneous optimization of the number of positions of the sensors and actuators of the active damping system according to claim 1, characterized in that the set conditions are: and the absolute difference of the fitness function of the two adjacent iterations is smaller than a set threshold value.
5. The method for simultaneously optimizing the number and the positions of the sensors and the actuators of the active vibration reduction system according to claim 1, wherein the sensors and the actuators are binary-coded, a selected code is set to be '1', otherwise, the selected code is '0', and iterative optimization is performed on the binary codes by using a genetic algorithm, wherein the iterative optimization mainly comprises initial population generation, fitness detection, selection, crossing and mutation operations.
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