Sensor arrangement and feedback control algorithm joint optimization method in structural vibration control

Abstract

The invention belongs to the technical field of vibration control, and relates to a sensor arrangement and feedback control algorithm joint optimization method in structural vibration control, which adopts a continuous time recurrent neural network CTRNN as a basic neuron, and adopts an NEAT algorithm to optimize a network structure to obtain an optimal network structure; the optimal network structure serves as a control strategy of the vibration control system, the positions of the sensors are obtained, when external excitation is applied to the structure, the optimal control force is output by the optimal network structure through state response measured by the sensors at the corresponding positions, and then an execution mechanism is controlled to generate the corresponding control force. According to the invention, the position of the sensor can be accurately optimized, a neural network architecture with the simplest structure is evolved, and the overall efficiency of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of vibration control technology, and relates to structural vibration control technology, and in particular to a joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control. Background Art

[0002] Structural vibration may cause fatigue damage to engineering structures such as buildings, bridges, and aircraft, shorten their service life, and even cause structural failure or collapse in extreme cases, endangering safety. At present, structural vibration control methods are mainly divided into three categories: passive control, active control, and semi-active control. Passive control does not require external energy input and relies on passive elastic or damping elements to achieve vibration reduction effects. It has the advantages of simple structure and high reliability. However, since the control force of passive control is passively generated with the vibration deformation of the structure, it is impossible to actively adjust the control strategy to adapt to vibrations of different frequencies, so the effect of broadband vibration suppression is relatively poor. Active control is based on modern control theory and includes sensors for collecting structural vibration information, controllers for controlling actuators based on control algorithms, and actuators for applying control forces. Active control can drive actuators through external energy to generate optimal control forces and suppress structural vibrations. Therefore, it has a vibration reduction effect that is significantly better than passive control in theory. Semi-active control adjusts its control strategy by using a small amount of energy to change the parameters of the control device (such as the damping coefficient). Although semi-active control solves the problem of high energy consumption of active control, its vibration reduction effect is between passive control and active control, and it does not achieve the vibration suppression performance of active control.

[0003] Although active control technology provides superior vibration suppression performance in theory, it has not been widely used in practical applications, mainly due to the complexity of the system. In active control systems, the linear quadratic regulation (hereinafter referred to as: LQR) algorithm is a commonly used control algorithm. However, the LQR algorithm relies on the full state feedback of the system, and in practical applications, the number of degrees of freedom of large structures is huge, and it is often impossible to install a sufficient number of sensors to achieve full state feedback. Therefore, active control methods based on output feedback have become a feasible solution to meet actual control needs. However, the existing active control technology based on output feedback has the following shortcomings: (1) Sensor placement problem: The placement of sensors usually relies on empirical design, which makes it difficult to ensure that they are in the optimal position and to ensure effective matching with the feedback control algorithm.

[0004] (2) Feedback control optimization problem: Artificial neural networks are often used as a tool for output feedback optimization, but their initial configuration (such as the number of nodes and layers) is usually based on empirical settings, which has a significant impact on the final optimization effect. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a joint optimization method for sensor arrangement and feedback control algorithm in structural vibration control, which can improve the overall control efficiency and effect of the structural vibration control system.

[0006] In a first aspect, the present invention provides a method for joint optimization of sensor arrangement and feedback control algorithm in structural vibration control, the steps of which include: S1. Establishing a simulation model of the vibration control system according to the set model parameters of the structural vibration control system, wherein the input layer of each network structure of the simulation model is the state response of the structure, the first hidden layer is the sensor, and the output layer is the control force; S2. Between the input layer and the first hidden layer of each network structure, a feedforward neural network is used as the basic neuron; between the first hidden layer and the output layer of each network structure, a continuous time recurrent neural network CTRNN is used as the basic neuron; S3, using the NEAT algorithm to optimize the first hidden layer to the output layer structure of each network structure to obtain the optimal network structure; S4. Use the optimal network structure as the control strategy of the vibration control system and obtain the position of the sensor. When the structure is subjected to external excitation, the state response measured by the corresponding position sensor is used, and the optimal control force is output by the optimal network structure, thereby controlling the actuator to generate the corresponding control force.

[0007] In some embodiments, in step S2, the input of the feedforward neural network is the entire state response of the structure, and the feedforward neural network randomly selects a state response less than or equal to The state responses are used as the input of the first hidden layer.

[0008] In some embodiments, in step S2, for each network structure from the first hidden layer to the output layer, the weights of the nodes and connections of the structure are initialized according to Gaussian distribution. , whose mean is , and its standard deviation is , its probability density function is:

[0009] In the formula, is the probability density function, is the input variable; The initial connection of the structure part is full connection, the initial neural network type of the structure part is continuous time recurrent neural network CTRNN, the input of the structure part is the input of the first hidden layer, and the output is control force; The behavior equation of the nodes in the continuous-time recurrent neural network CTRNN is:

[0010] In the formula, It's a neuron The time constant, It's a neuron The potential, It's a neuron The activation function, It's a neuron The bias, It is to the neuron The set of indices of the neurons that provide input, It's a neuron To the neuron The connection weight of .

[0011] In some embodiments, the specific method of using the NEAT algorithm to optimize the first hidden layer to the output layer structure of each network structure to obtain the optimal network structure is: S31. All network structures are regarded as a population, and each network structure is an individual in the population; S32, using the fitness function to evaluate the individuals in the population, if the fitness of an individual in the population exceeds the fitness threshold, then stop the optimization, otherwise go to step S33; S33, selecting individuals from the parent generation to perform crossover to generate offspring, and performing mutation operations on the offspring to form a new population; S34. Divide the new population into different sub-populations according to the competition rules, and divide species within each sub-population; S35. Repeat steps S32 to S34 until a preset stop condition is reached.

[0012] In some embodiments, in step S32, the negative of the quadratic cost function is set as a fitness function, and the fitness function is expressed as:

[0013] In the formula, is the structural state response of the system, For control, The state weight matrix, Control weight matrix, is the initial time, The end time.

[0014] In some embodiments, during the optimization process, a shared fitness is set within each species. :

[0015] In the formula, is a shared function, when , its value is 0, when , its value is 1; For the Individuals, For the Individuals, is the distance threshold, The number for each species.

[0016] In some embodiments, in step S33, during the crossover process, parts with the same structure in different network structures are matched one by one, and parts with different structures are selected from parents with better fitness.

[0017] In some embodiments, in step S33, the mutation includes adding nodes and adding connections; the method of adding nodes is: adding a new node to disconnect the old connection and generate two new connections; the method of adding connections is: adding a new connection to the end of the current connection list; new node and new connection mutations are both given new genetic codes.

[0018] In some embodiments, in step S34, all individuals are divided into sub-populations according to the layout positions of the sensors, and each sub-population has an id.

[0019] In some embodiments, in step S34, when dividing species within each subpopulation, the species are divided according to the similarity distance between neural networks of different individuals; the similarity distance is expressed as:

[0020] In the formula, is the similarity distance between two individuals, For different numbers of redundant genes, For different numbers of missing genes, is the average difference in connection weights among matched genes, is the number of codes in the larger genome of the two individuals, To regulate the number of different redundant genes The coefficient of importance, To adjust the number of missing genes The coefficient of importance, The average difference in connection weights among adjusted matched genes The coefficient of importance; If the similarity distance of contemporary individuals Less than distance threshold , it means they belong to the same species. If the similarity distance of contemporary individuals is greater than or equal to the distance threshold , it means that they do not belong to the same species, and a new species is created with this individual as the representative.

[0021] Compared with the prior art, the advantages and positive effects of the present invention are: (1) The joint optimization method of sensor layout and feedback control algorithm in structural vibration control provided by the present invention adopts an enhanced topology neural evolution algorithm to optimize the neural network structure, and designs an output feedback optimal controller by using the local measurement output of the structure as the input of the control algorithm to replace the traditional control method based on full-state feedback. Not only the control strategy is optimized, but also the layout position of the sensor can be optimized, and the optimal layout of the sensor and its corresponding optimal control strategy can be solved. Compared with the traditional experience-based sensor layout, the present invention can accurately optimize the position of the sensor and evolve the simplest neural network architecture at the same time, thereby improving the overall performance of the system.

[0022] (2) In traditional neural network control, the network structure needs to be defined in advance. A structure that is too simple or too complex will affect the optimization effect. The joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control provided by the present invention starts from the simplest network structure and gradually optimizes the network structure using an evolutionary algorithm, thereby solving the problem of performance degradation caused by improper initial network structure design.

[0023] (3) Traditional neural network control algorithms usually rely on experience to preset the installation position of sensors and cannot optimize the sensor layout. The joint optimization method of sensor layout and feedback control algorithm in structural vibration control provided by the present invention not only improves the control algorithm, but also optimizes the layout position of the sensor between the input layer and the first hidden layer, thereby improving the overall performance and control effect of the system.

[0024] (4) The present invention provides a joint optimization method for sensor arrangement and feedback control algorithm in structural vibration control. The evolution of the neural network structure and the search for weights greatly accelerate the speed of neural network learning complex features such as nonlinearity. The evolutionary algorithm encourages individual neural networks to compete with each other, allowing the fittest to survive. Individuals with improper structure and weight evolution are eliminated, further accelerating the speed of optimization. At the same time, local optimality is well avoided, and the algorithm has good global search capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of the joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control according to an embodiment of the present invention; Figure 2 It is a schematic diagram of a joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control according to an embodiment of the present invention; Figure 3 Add node schematic diagram for the embodiment of the present invention; Figure 4 Add a connection diagram for the embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of a three-story building according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the initial network structure of the CRNEAT algorithm for a three-story building according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the final network structure of the CRNEAT algorithm for a three-story building according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the CRNEAT algorithm evolution curve for a three-story building according to an embodiment of the present invention; Fig. 9 It is the displacement time history diagram of the first floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention; Fig.10 It is the displacement time history diagram of the second floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention; Fig.11 It is the displacement time history diagram of the third floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention; Fig.12 It is the speed time history diagram of the first floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention; Fig.13 It is the speed time history diagram of the second floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention; Fig.14 This is the speed time history diagram of the third floor under the control of the CRNEAT algorithm and the LQR algorithm of the present invention.

[0026] In the figure, 101 is a sensor, 102 is a controller, and 103 is an actuator. DETAILED DESCRIPTION

[0027] The present invention will be described in detail below by way of exemplary embodiments in conjunction with the accompanying drawings. However, it should be understood that, without further description, elements, structures and features in one embodiment may also be beneficially combined in other embodiments.

[0028] See also Figure 1 , 2 The first aspect of the present invention provides a method for joint optimization of sensor arrangement and feedback control algorithm in structural vibration control, the steps of which include: S1. A simulation model of a vibration control system is established according to set model parameters of the structural vibration control system, wherein the input layer of each network structure of the simulation model is the state response of the structure, the first hidden layer is the sensor, and the output layer is the control force.

[0029] Specifically, the vibration control system parameters include simulation time, simulation step, external excitation and system matrix.

[0030] S2. Between the input layer and the first hidden layer of each network structure, a feedforward neural network is used as the basic neuron to optimize the position of the sensor; between the first hidden layer and the output layer of each network structure, a continuous time recurrent neural network CTRNN is used as the basic neuron to optimize through network structure evolution.

[0031] Specifically, the input of the feedforward neural network is the full state response of the structure , is the number of structural state responses, and the feedforward neural network randomly selects less than or equal to from all state responses The state responses are used as the input of the first hidden layer.

[0032]

[0033] In the formula, is the desired number of sensors, is the input of the first hidden layer.

[0034] For each network structure from the first hidden layer to the output layer, the weights of the nodes and connections of the structure are initialized according to the Gaussian distribution. , whose mean is , and its standard deviation is , its probability density function is:

[0035] In the formula, is the probability density function, is the input variable; The initial connection of the structure part is full connection, the initial neural network type of the structure part is continuous time recurrent neural network CTRNN, the input of the structure part is the input of the first hidden layer, and the output is control force; The behavior equation of the nodes in the continuous-time recurrent neural network CTRNN is:

[0036] In the formula, It's a neuron The time constant, It's a neuron The potential, It's a neuron The activation function, It's a neuron The bias, It is to the neuron The set of indices of the neurons that provide input, It's a neuron To the neuron The connection weight of .

[0037] S3. Use the NEAT algorithm to optimize the first hidden layer to output layer structure of each network structure to obtain the optimal network structure.

[0038] Specifically, the specific method of using the NEAT algorithm to optimize the first hidden layer to the output layer structure of each network structure to obtain the optimal network structure is: S31. Treat all network structures as a population, and each network structure as an individual in the population.

[0039] S32. Use the fitness function to evaluate the individuals in the population. If the fitness of an individual in the population exceeds the fitness threshold, stop the optimization, otherwise go to step S33.

[0040] Specifically, in some embodiments, the negative of the quadratic cost function is set as the fitness function, and the fitness function is expressed as:

[0041] In the formula, is the structural state response of the system, For control, The state weight matrix, Control weight matrix, is the initial time, The end time.

[0042] It should be noted that the structure is in the time period [ The smaller the structural state response and control force within ], the higher the fitness. The fitness threshold is set to 0, and the evolution stops when the fitness reaches the threshold.

[0043] S33. Select individuals from the parent generation to perform crossover to generate offspring, and perform mutation operations on the offspring to form a new population.

[0044] Specifically, during the crossover process, parts with the same structure in different network structures are matched one by one, and parts with different structures are selected from parents with better fitness.

[0045] Specifically, mutation includes adding nodes and adding connections. The method of adding nodes is: adding a new node disconnects the old connection and generates two new connections. For example: see Figure 3, adding a new node 6 disconnects the old connection 3→5, and generates two new connections: connection 3→6 and connection 6→5. The method of adding a connection is to add a new connection at the end of the current connection list. For example: see Figure 4 , add a new connection 2→6 to the end of the current Connection list. Both new node and new connection mutations are given new genetic codes. It should be noted that as the network structure becomes more complex, its genetic code will gradually expand. Since new mutations do not change old genetic codes, the historical origins of network structure mutations are known throughout the evolutionary process.

[0046] S34. Divide the new population into different sub-populations according to competition rules, and divide species within each sub-population.

[0047] Specifically, all individuals are divided into subpopulations according to the layout of the sensors, and each subpopulation has an ID. For example, the subpopulation with an ID of 000011 means that all individuals in the subpopulation have sensors installed at the 5th and 6th positions. After the subpopulations are divided, species are divided within the subpopulations.

[0048] Specifically, in some embodiments, when dividing species within each subpopulation, the species are divided according to the similarity distance between neural networks of different individuals; the similarity distance is expressed as:

[0049] In the formula, is the similarity distance between two individuals, For different numbers of redundant genes, For different numbers of missing genes, is the average difference in connection weights among matched genes, is the number of codes in the larger genome of the two individuals, To regulate the number of different redundant genes The coefficient of importance, To adjust the number of missing genes The coefficient of importance, The average difference in connection weights among adjusted matched genes The coefficient of importance; If the similarity distance of contemporary individuals Less than distance threshold , it means they belong to the same species. If the similarity distance of contemporary individuals is greater than or equal to the distance threshold , it means that they do not belong to the same species, and a new species is created with this individual as the representative.

[0050] It should be noted that since changes in the network structure will lead to a loss of its initial fitness, measures need to be taken to protect the network structure to a certain extent so that it has time to be optimized through competition. The optimization method of the present invention divides the individuals in the population into species. The more mismatched genes in the genomes of two individuals, the lower the similarity between them. Therefore, similarity distance is used to divide species.

[0051] S35. Repeat steps S32 to S34 until a preset stop condition is reached.

[0052] Specifically, in some embodiments, during the optimization process, a shared fitness is set within each species. :

[0053] In the formula, is a shared function, when , its value is 0, when , its value is 1; For the Individuals, For the Individuals, is the distance threshold, The number for each species.

[0054] It should be noted that in order to improve the efficiency of evolution during the evolution process, it is necessary to prevent the number of individuals in a species from being too large. A shared fitness is set within each species. After each generation of training, some individuals will be eliminated according to the shared fitness, and the retained individuals will produce new individuals through crossover and mutation. If the maximum fitness of a species does not increase within several generations, this species will not produce new offspring.

[0055] S4, with the optimal network structure As a control strategy for the vibration control system and the position of the sensor, when the structure is subjected to external excitation, the state response measured by the corresponding position sensor , by the optimal network structure Output optimal control force , and then control the actuator to produce corresponding control force. Optimal network structure This is the output feedback optimal controller.

[0056]

[0057] The optimization method of the present invention adopts an enhanced topology neural evolution algorithm to optimize the neural network structure. By using the local measurement output of the structure as the input of the control algorithm, the traditional control method based on full-state feedback is replaced, and the performance degradation problem caused by improper initial network structure design is solved. Through the joint optimization of the neural network, the present invention not only improves the control algorithm, but also optimizes the layout position of the sensor between the input layer and the first hidden layer, thereby improving the overall performance and control effect of the system.

[0058] In order to verify the effectiveness of the joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control described in the above embodiment of the present invention, it is described in conjunction with the following specific embodiments.

[0059] Example: Take the structure of a three-story building as an example. See the structural diagram of the three-story building. Figure 5 , in the figure, For the quality of the first floor building, is the stiffness of the first floor building, is the displacement of the first floor building relative to the ground, For the quality of the second floor building, is the stiffness of the second-story building, is the displacement of the second-floor building relative to the ground, For the quality of the third floor building, The stiffness of the third floor building, is the displacement of the third-floor building relative to the ground, is the absolute ground displacement, is the structural control force. The motion equation of the three-story building in structural matrix form is expressed as:

[0060] in, , , They are the structural mass matrix, damping matrix and stiffness matrix respectively; , , are the relative displacement, velocity and acceleration vectors respectively; is the environmental interference position matrix; is the arrangement matrix of the actuator; For control, is the external load vector.

[0061] The equation of motion is transformed into state space form as:

[0062] in,

[0063]

[0064]

[0065]

[0066] In the formula, is the state vector, is the state matrix, is the input matrix of external loads, is the input matrix of the control force.

[0067] In structures with base isolation, external loads are used as base excitation , passive, semi-active or active dampers used in isolation systems are installed between the ground and the first mass of the structure.

[0068] In this example, the mass matrix of the three-story building , damping matrix , stiffness matrix , Environmental interference position matrix and the actuator arrangement matrix for:

[0069]

[0070]

[0071]

[0072]

[0073] In the formula, kg stands for kilogram, N stands for Newton, s stands for second, and m stands for meter.

[0074] Set the fitness function of CRNEAT to:

[0075] in,

[0076] In the formula, is the identity matrix The sensor arrangement and feedback control algorithm joint optimization method in structural vibration control of the present invention (hereinafter referred to as: CRNEAT algorithm) is used to As the input of the neural network, and the number of sensors installed is set to no more than 2, the initial neural network is as follows Figure 6 As shown, the final neural network is Figure 7As shown, in Figure 7 In1, In2, In3, In4, In5, and In6 are the displacements and velocities of the 1st to 3rd layers, respectively. Act1 is the final control force. 256, 1429, and 1397 are the evolved hidden layer nodes. The results show that the sensor should be a velocity sensor and installed on the 1st and 3rd layers. Figure 8 The optimal individual evolution curve in the subpopulation of the CRNEAT algorithm of the present invention is shown in the figure. The optimal subpopulation adopts the configuration that the speed sensor is installed on the 1st and 3rd layers, while the speed sensor is only installed on the 3rd layer in subpopulation 1; subpopulation 2 chooses to install the displacement sensor on the 1st layer and the speed sensor on the 2nd layer; the configuration of subpopulation 3 is to install the displacement sensor on the 3rd layer and the speed sensor on the 1st layer. As can be seen from the figure, the fitness values ​​of each subpopulation are generally low in the early stage, but with the increase of evolutionary generations, the fitness of the optimal individuals in different subpopulations gradually increases. In particular, subpopulation 1 and subpopulation 2 become extinct after reaching the maximum stagnation generation, while subpopulation 3 and the optimal subpopulation continue to evolve and eventually converge to the local optimal solution of their respective solution space domains. The results show that the CRNEAT algorithm using the species partitioning strategy significantly improves the solution efficiency. Through the parallel evolution of neural networks in different solution space domains, the algorithm can effectively avoid the local optimal solution and improve the global search capability, thereby accelerating the optimization process.

[0077] The optimization method proposed in this invention has excellent vibration control effect on earthquakes. In order to better illustrate the performance of this method, the optimal control LQR algorithm is introduced for comparison. The optimal control LQR algorithm is the most widely used control in the field of structural control, and its expression is:

[0078] In the formula, is the optimal feedback gain matrix, is the parameter matrix of the optimal controller.

[0079] In order to compare the superiority of the CRNEAT algorithm of the present invention, the displacement and velocity time histories of different floors under the control of the CRNEAT algorithm of the present invention and the LQR algorithm are compared, as shown in FIG. Figures 9 to 14 Combining the root mean square values ​​and peak values ​​of displacement, velocity and acceleration of the LQR and CRNEAT algorithms shown in Table 1, it can be seen that the control performance of the CRNEAT algorithm of the present invention is basically consistent with that of the LQR control.

[0080] Table 1

[0081] In summary, the optimization method of the present invention can optimize the sensor layout while optimizing the control strategy, solving the problem of model performance degradation that may be caused by traditional experience-based sensor installation. And through the evolutionary algorithm, the neural network individuals are naturally selected in the competition, the survival of the fittest, and the individuals with improper structure and weight evolution are eliminated, which accelerates the optimization process and effectively avoids local optimality. In addition, the optimization method of the present invention can also evolve the simplest neural network structure, further improving the efficiency and performance of the system, and showing a strong global search capability.

[0082] The above embodiments are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A joint optimization method for sensor placement and feedback control algorithm in structural vibration control, characterized in that: The steps include: S1. Establishing a simulation model of the vibration control system according to the set model parameters of the structural vibration control system, wherein the input layer of each network structure of the simulation model is the state response of the structure, the first hidden layer is the sensor, and the output layer is the control force; S2. Between the input layer and the first hidden layer of each network structure, a feedforward neural network is used as the basic neuron; between the first hidden layer and the output layer of each network structure, a continuous time recurrent neural network CTRNN is used as the basic neuron; S3, using the NEAT algorithm to optimize the first hidden layer to the output layer structure of each network structure to obtain the optimal network structure; S4. Use the optimal network structure as the control strategy of the vibration control system and obtain the position of the sensor. When the structure is subjected to external excitation, the state response measured by the corresponding position sensor is used, and the optimal control force is output by the optimal network structure, thereby controlling the actuator to generate the corresponding control force.

2. The joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control according to claim 1, characterized in that: In step S2, the input of the feedforward neural network is the total state response of the structure, and the feedforward neural network randomly selects a state response less than or equal to The state responses are used as the input of the first hidden layer.

3. The joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control according to claim 1, characterized in that: In step S2, for each network structure from the first hidden layer to the output layer, the weights of the nodes and connections of the structure are initialized according to the Gaussian distribution. , whose mean is , and its standard deviation is , its probability density function is: In the formula, is the probability density function, is the input variable; The initial connection of the structure part is full connection, the initial neural network type of the structure part is continuous time recurrent neural network CTRNN, the input of the structure part is the input of the first hidden layer, and the output is control force; The behavior equation of the nodes in the continuous-time recurrent neural network CTRNN is: In the formula, It's a neuron The time constant, It's a neuron The potential, It's a neuron The activation function, It's a neuron The bias of It is to the neuron The set of indices of the neurons that provide input, It's a neuron To the neuron The connection weight of .

4. The joint optimization method of sensor arrangement and feedback control algorithm in structural vibration control according to claim 1, characterized in that: The specific method of using the NEAT algorithm to optimize the first hidden layer to the output layer structure of each network structure to obtain the optimal network structure is: S31. All network structures are regarded as a population, and each network structure is an individual in the population; S32, using the fitness function to evaluate the individuals in the population, if the fitness of an individual in the population exceeds the fitness threshold, then stop the optimization, otherwise go to step S33; S33, selecting individuals from the parent generation to perform crossover to generate offspring, and performing mutation operations on the offspring to form a new population; S34. Divide the new population into different sub-populations according to the competition rules, and divide species within each sub-population; S35. Repeat steps S32 to S34 until a preset stop condition is reached.

5. The method for joint optimization of sensor arrangement and feedback control algorithm in structural vibration control according to claim 4, characterized in that: In step S32, the negative number of the quadratic cost function is set as the fitness function, and the fitness function is expressed as: In the formula, is the structural state response of the system, For control, The state weight matrix, Control weight matrix, is the initial time, The end time.

6. The method for joint optimization of sensor arrangement and feedback control algorithm in structural vibration control according to claim 5, characterized in that: During the optimization process, a shared fitness is set within each species. : In the formula, is a shared function, when , its value is 0, when , its value is 1; For the Individuals, For the Individuals, is the distance threshold, The number for each species.

7. The method for joint optimization of sensor placement and feedback control algorithm in structural vibration control according to claim 4, characterized in that: In step S33, during the crossover process, parts with the same structure in different network structures are matched one by one, and parts with different structures are selected from parents with better fitness.

8. The method for joint optimization of sensor placement and feedback control algorithm in structural vibration control according to claim 4, characterized in that: In step S33, mutations include adding nodes and adding connections; the method for adding nodes is: adding a new node to disconnect the old connection and generate two new connections; the method for adding connections is: adding a new connection at the end of the current connection list; new node and new connection mutations are both given new genetic codes.

9. The method for joint optimization of sensor placement and feedback control algorithm in structural vibration control according to claim 4, characterized in that: In step S34, all individuals are divided into sub-populations according to the layout positions of the sensors, and each sub-population has an id.

10. The method for joint optimization of sensor placement and feedback control algorithm in structural vibration control according to claim 4, characterized in that: In step S34, when dividing species within each subpopulation, the species are divided according to the similarity distance between the neural networks of different individuals; the similarity distance is expressed as: In the formula, is the similarity distance between two individuals, For different numbers of redundant genes, For different numbers of missing genes, is the average difference in connection weights among matched genes, is the number of codes in the larger genome of the two individuals, To regulate the number of different redundant genes The coefficient of importance, To adjust the number of missing genes The coefficient of importance, The average difference in connection weights among adjusted matched genes The coefficient of importance; If the similarity distance of contemporary individuals Less than distance threshold , it means they belong to the same species. If the similarity distance of contemporary individuals is greater than or equal to the distance threshold , it means that they do not belong to the same species, and a new species is created with this individual as the representative.

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