CN117572829A - Multi-mode industrial process all-condition high real-time prediction control method and equipment - Google Patents
Multi-mode industrial process all-condition high real-time prediction control method and equipment Download PDFInfo
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Abstract
The invention discloses a method and equipment for high real-time predictive control of all working conditions in a multi-mode industrial process, wherein the method is used for learning the control law of all working conditions display: firstly, an explicit control law of the current working condition is learned by using a working condition data set, namely, the parameters of a self-organizing fuzzy neural network are learned; determining whether to increase the fuzzy rule according to the data coverage rate of the learned working condition; if the working condition changes in a small range, introducing an elastic weight consolidation term mechanism on the basis of original loss, so as to ensure that a new working condition control strategy is learned and the control performance of the historical working condition is maintained; if the working condition changes in a large range, a truncated radial basis neuron growth mechanism is adopted, and a control strategy of a new working condition is learned by adding a fuzzy rule, so that the explicit control law can adapt to the working condition changes in a large range; and during on-line control, a control sequence is obtained according to the current control state by using an all-condition explicit control law. The invention solves the problem of traditional multi-model online solving optimization and realizes the accurate control effect of the whole working condition of the industrial process.
Description
Technical Field
The invention belongs to the technical field of industrial control, and particularly relates to a method and equipment for high-real-time prediction control of all working conditions of a multi-mode industrial process.
Background
With the large-scale of modern industrial systems, there is a great deal of uncertainty in the production environment, process, etc., and industrial systems exhibit complex operating characteristics, often making it difficult to build accurate mathematical models. Conventional control methods may be limited in the face of these complex systems, and it is difficult to meet the actual demands. Therefore, new computing methods and ideas need to be introduced to address challenges facing industrial systems. The fuzzy theory gives a set of systematic and effective methods for converting the knowledge described by natural language into mathematical expression form, so that the influence of uncertainty of complex systems can be overcome by expert knowledge. However, conventional fuzzy control systems typically use fuzzy reasoning and fuzzy rules to handle the relationships between inputs and outputs, with limited modeling capabilities for complex nonlinear systems. The fuzzy neural network is a nonlinear modeling tool, combines the advantages of fuzzy logic and the neural network, and can better process a nonlinear system. It can capture complex relationships between inputs and outputs through multi-layer connections and nonlinear activation functions, thereby more accurately modeling and controlling nonlinear systems.
In addition to the uncertainty of the production process, some industrial systems are actually a dynamic multi-modal process, the state of which switches between different operating conditions, due to the influence of factors such as diversification of production raw materials, complexity of the production process, etc. Thus, how to achieve precise control of complex industrial systems under varying conditions is an important and challenging problem. Model predictive control (Model Predictive Control, MPC) is an efficient industrial control method, a control algorithm currently recognized to be able to efficiently handle multivariable complex processes and take into account a variety of constraints. The basic idea of model predictive control is: based on a prediction model of the process, an optimal control sequence is obtained by solving a finite time domain open-loop optimal control problem at each control interval, and then a first control quantity of the optimal control sequence is issued to the actual process. At present, model predictive control has been widely applied to complex industrial systems such as aerospace, autopilot, robotics and nonferrous metallurgy. In the face of multi-operating industrial processes, model predictive control typically employs a multi-model or multi-controller control strategy to cope with fluctuations in the operating state of the industrial process. However, since there are a plurality of local predictive controllers operating simultaneously, the scroll optimization requires a large amount of computing resources and computing time. Especially for industrial processes with high sampling frequency or fast process variation, the above method often has difficulty in meeting the real-time requirement.
The explicit model predictive control (Explicit Model Predictive Control, EMPC) is a high-real-time control method, the method obtains an explicit control law through offline training, and the optimal control sequence can be obtained by substituting system state information at the current moment into the explicit control law for calculation during online operation, so that real-time rolling optimization solution is omitted, and rapid control is realized. The explicit model prediction control method verifies the strong capability of the explicit model prediction control method on the aspects of control instantaneity and the like, but the explicit model prediction control method still has some defects. First, as the problem size increases, such as increasing prediction horizon, increasing number of constraints, increasing system input-output dimensions, etc., the size of the explicit control laws increases exponentially. On the other hand, explicit model predictive control is initially applied to a linear time-invariant process, and although some studies have been made to apply explicit model predictive control to a nonlinear process, this inevitably results in an increase in the complexity of offline computation and an increase in the scale of explicit control laws. Compared with the piecewise affine function, the neural network has stronger parallel computing capacity and nonlinear fitting capacity, and provides a new thought for solving the large-scale multiparameter quadratic programming problem. Explicit control laws based on neural networks can provide smaller control law scales and faster computation speeds while ensuring that control performance meets requirements. However, when dealing with multi-operating industrial processes with fluctuating operating conditions, the pre-trained explicit control laws can suffer from mismatch problems, severely affecting control performance.
Disclosure of Invention
In order to solve the problem of full-working-condition real-time control of a multi-mode process, the invention provides a full-working-condition high-real-time prediction control method and equipment of the multi-mode industrial process, and provides and adopts a full-working-condition-oriented self-organizing fuzzy neural network explicit control law learning framework, all operation working conditions are adapted through self-adjusting network parameters and structures, the learned control law can eliminate the influence of control strategy mismatch in a switching stage, and the operation speed is improved.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a multi-mode industrial process full-working-condition high real-time prediction control method comprises the following steps:
offline learning:
respectively learning a corresponding output state prediction model by using a data set of each working condition of the industrial system, and learning a full-working-condition explicit control law based on a self-organizing fuzzy neural network by using data sets of all working conditions;
when learning the full-working-condition display control law, firstly, learning an explicit control law of the current working condition by using a data set of the first working condition, namely, learning parameters of a self-organizing fuzzy neural network; and then the data sets of the other working conditions are used for sequentially adjusting the current learned explicit control law: if the data coverage rate of the current learned working condition does not meet the preset condition, directly updating and learning the current network parameters; if the data coverage rate of the current learned working condition meets the preset condition, adding a fuzzy rule, namely adding neurons representing the fuzzy rule in the self-organizing fuzzy neural network, and updating and learning parameters of the self-organizing fuzzy neural network;
On-line control:
the output state at the current moment, the historical output state sequence, the control sequence and the reference track of the future output state are constructed together to serve as control state data at the current moment, and the control state data are input into the learned full-working-condition explicit control law to obtain an optimal control sequence at the current moment;
the industrial system is controlled using the first control variable of the optimal control sequence at the current time.
Further, the self-organizing fuzzy neural network comprises an input layer, a fuzzy layer, a normalization layer and an output layer;
the input layer includes m in The neurons respectively represent m of the fuzzy neural network in Dimension input variables; the mathematical expression of the input layer is as follows:
c i (t)＝x i (t),i＝1,2,...,m in (1)
wherein x is i (t) represents the input of the ith neuron at time t, c i (t) represents the output of the ith neuron at time t;the input of the fuzzy neural network at the moment t is shown and is used for inputting control state data of the industrial system at the moment t; />The output of the input layer at the time t is represented;
the fuzzy layer is provided with P groups of neurons in total, and each group of neurons represents a fuzzy rule; each fuzzy rule adopts a radial basis function as a membership function of a fuzzy input variable, and the mathematical expression is as follows:
Wherein ζ i,j (t) represents the membership function, μ of the ith input variable corresponding to the jth fuzzy rule ij (t) and sigma ij (t) radial basis neuron centers and widths; after the membership degree of each input variable is obtained, the membership degree of each fuzzy rule is calculated, and the mathematical expression is as follows:
wherein,represents the output of the j-th radial basis neurons at time t,>represents the center of the j-th radial basis neuron group at time t,>representing the width of the j-th radial basis neuron group at the time t;
the normalization layer has P neurons, and is the same as the fuzzy rule of the fuzzy layer in number and used for normalizing the output of the fuzzy layer to obtain normalized output v (t) = [ v ] 1 (t),v 2 (t),...,v P (t)] T ；
The output layer is a linear layer, and the mathematical expression of the output is as follows:
y(t)＝W(t)v(t)
wherein,output representing self-organizing fuzzy neural network at time t for outputting control variable, < > -at time t of industrial system>Weight matrix representing output layer at time t, m o Is the number of neurons in the output layer.
Further, the data set of the first working condition is used for learning an explicit control law of the current working condition, and particularly, the optimization problem of the model predictive control strategy is converted into a loss function so as to learn the explicit control law;
Firstly, the optimization problem of the model predictive control strategy is that the objective function only considers the tracking performance of the output state of the industrial system, and the constraint condition only considers the upper and lower limiting constraints of the control variable, as follows:
wherein NN []Represents a neural network prediction model, y= [ Y (t+1), …, Y (t+n) p )] T Represents the prediction output state of the prediction model, r= [ R (t+1), …, R (t+n) p )] T Represents a reference trajectory, u= [ u (t), …, u (t+n) c -1)] T Representing the predicted control variable, u min And u max Representing upper and lower limits of the control variable, N p Representing the predicted time domain range, N c Representing the control time domain range, representing the order of the control variable u and the output state y representing the prediction model with respect to the input;
the objective function is then converted into a loss function as:
where N represents the batch size of the batch training of the self-organizing fuzzy neural network,sample index, Q, representing each batch y And Q u Weight factor representing output state and control variable, +.> And->The upper and lower limit penalty term representing the control variable is specifically as follows:
finally, the explicit control law of the first working condition is learned through the model predictive control loss function shown in the formula (7), namely, the parameter learning of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, and the parameter learning is as follows:
Wherein W (t) represents the weight of the output layer of the self-organizing fuzzy neural network, σ (t) represents the width of the fuzzy layer neurons of the self-organizing fuzzy neural network, μ (t) represents the center of the fuzzy layer neurons of the self-organizing fuzzy neural network, and η represents the learning rate.
Further, the data coverage rate calculation method comprises the following steps: firstly, adopting a truncated radial basis function as an activation function of a fuzzy layer neuron of the self-organizing fuzzy neural network, and outputting a jth fuzzy rule at the moment tExpressed as:
wherein f [ c (t)]Represents a truncated radial basis function, f ij [c i (t)]Represents the output of the ith neuron in the jth fuzzy rule at time t, a ij Represents the activation state of the ith neuron in the jth fuzzy rule at time t, excitation representing jth fuzzy ruleActive state, c ij,min (t),c ij,max (t) the upper and lower cutoff limits of the radial basis function, respectively, are set as:
wherein phi is a positive integer;
then according to the activation state alpha of all fuzzy rules j Judging the first batch of dataStatus signal of whether or not the individual data is within the range of the fuzzy rule +.>And calculating the data coverage rate DC of the current self-organizing fuzzy neural network according to the state signals of all the data, wherein the data coverage rate DC is expressed as follows:
further, the preset conditions are as follows:
Where OL represents a threshold.
Further, the adding the fuzzy rule, namely adding the neurons representing the fuzzy rule in the self-organizing fuzzy neural network, specifically, designing a newly added neuron group as follows:
wherein N is uc Data which are not covered by self-organizing fuzzy neural network in current working condition to be learnedQuantity, x j (t),j＝1,…,N uc Representing data not covered by the ad hoc fuzzy neural network,andthe new fuzzy rule at the time t is expressed to correspond to the center and the width W of the truncated radial basis neurons new (t) represents the weight, σ, of the output layer corresponding to the new fuzzy rule new And W is new And randomly initializing by the self-organizing fuzzy neural network.
Further, after adding the fuzzy rule, updating and learning parameters of the self-organizing fuzzy neural network, wherein the specifically adopted loss function is as follows:
wherein,a model predictive control loss function representing the current working condition B to be learned; θ represents the current network parameters of the ad hoc fuzzy neural network, +.>Indicate->Personal network parameters->Explicit control law learning indicating condition A is completed>Personal network parameters->Model predictive control loss function representing completed condition set AFor->λ represents the importance of the completed working condition set a; w (W) θ 、μ θ 、σ θ Representing a set of three network parameters; for the j-th fuzzy rule, < > and->Indicate->Personal network parameters->Explicit control law learning indicating condition A is completed>Personal network parameters->Model predictive control loss function representing completed condition set AFor->Second partial derivative of (2);
then, the parameter updating of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, as follows:
further, when the parameters of the self-organizing fuzzy neural network are updated and learned, the range of the width sigma of the radial basis neurons is additionally limited, as follows:
wherein sigma ij (t) the ith neuron width, σ, representing the jth fuzzy rule ij,low (t) and sigma ij,low And (t) represents upper and lower clipping, respectively.
Further, if the data coverage rate of the current learned working condition does not meet the preset condition, directly updating and learning the current network parameter, wherein a loss function adopted by updating and learning is as follows:
wherein,a model predictive control loss function representing the current working condition B to be learned; θ represents the current network parameters of the ad hoc fuzzy neural network, +.>Represents>The personal network parameters, A represents the set of all working conditions of which explicit control learning is completed, +. >Explicit control law learning indicating the working condition set A is completed>Personal network parameters->Model predictive control loss function representing the completed set of conditions A>For->Lambda represents the importance of the completed set of conditions AA degree;
then, the parameter updating of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, as follows:
an electronic device comprising a memory and a processor, the memory having stored therein a computer program which, when executed by the processor, causes the processor to implement the method of any of the preceding claims.
Advantageous effects
The multi-mode industrial process full-working-condition high-real-time prediction control method and equipment provided by the invention adopt an explicit model prediction control strategy, a learning framework of the explicit control law consists of two modules of a fuzzy neural network explicit control law (Fuzzy neural network based explicit control law, FNNECL) and a neural network prediction model (neural network based predictive model, NNPM), the structure and parameters of the FNNECL are adjusted, so that the full-working-condition accurate control is ensured, the single network can be used for adapting to all the operating working conditions, the influence of control strategy mismatch in a switching stage can be eliminated, and meanwhile, the forward transfer calculation of the self-organizing fuzzy neural network is only needed, and the optimization solution is not needed, so that the calculation time and calculation resources are greatly saved, and the control instantaneity is greatly improved.
Drawings
FIG. 1 is an embodiment of an all-condition self-organizing fuzzy neural network explicit control law learning framework;
FIG. 2 is a diagram of network parameters θ in an embodiment of the present application 1 And theta 2 Model predictive control loss function for operating condition AIs a result of the influence of (1);
FIG. 3 is a loss function l in an embodiment of the present application MEMPC The parameter change result when the working condition changes in a large range is dealt with;
FIG. 4 is a comparison of four control effects of ETASI4PC, PWA, MMPC, FNNECL described in the examples herein;
FIG. 5 is a semi-physical simulation platform as described in an embodiment of the present application;
fig. 6 is a control effect comparison chart of the embodiment of the present application, wherein the subgraph is a control effect during the working condition switching.
Detailed Description
The following describes in detail the embodiments of the present invention, which are developed based on the technical solution of the present invention, and provide detailed embodiments and specific operation procedures, and further explain the technical solution of the present invention.
The invention provides a multi-mode industrial process full-working-condition high real-time prediction control method and equipment, which adopt an explicit model prediction control strategy, wherein a learning framework of the explicit control law consists of two modules of a fuzzy neural network explicit control law (Fuzzy neural network based explicit control law, FNNCEL) and a neural network prediction model (neural network based predictive model, NNPM), and the precise control of full working conditions is further ensured by adjusting the structure and parameters of the FNNCEL.
As shown in fig. 1, specifically, in order to ensure that the FNNECL can adapt to different working conditions, a truncated radial basis function is introduced first, a working condition change measurement index of data coverage rate is provided, and the degree of mismatch of the current working condition and the historical working condition is accurately identified. Then, aiming at the small-range working condition change, taking the inherent robustness of the neural network model into consideration, introducing an elastic weight consolidation term (Elastic Weight Consolidation, EWC) mechanism, ensuring that the FNNCEL can learn a control strategy of a new working condition, and simultaneously maintaining the control performance of a historical working condition. Finally, aiming at the large-range working condition change, considering that the expression capability of the fixed structure FNNECL to the new working condition is limited, a radial basis neuron growth mechanism based on the data coverage rate is provided, and a control strategy of the new working condition is learned by selectively adding the new neurons through calculating the data coverage rate of the fuzzy rule, so that the explicit control law can adapt to the large-range working condition change. It is worth noting that the current operation condition is not required to be known in advance in the application process of the method, the accurate control sequence is obtained rapidly based on a single FNNECL model, the problem of traditional multi-model online solving optimization is solved, the application range of the method is greatly expanded, and the accurate control effect of all the conditions is achieved.
The invention provides a multi-mode industrial process full-working-condition high real-time prediction control method, which mainly comprises two parts of off-line learning and on-line control:
1. offline learning: respectively learning a corresponding output state prediction model by using a data set of each working condition of the industrial system, and learning a full-working-condition explicit control law based on a self-organizing fuzzy neural network by using data sets of all working conditions;
when learning the full-working-condition display control law, firstly, learning an explicit control law of the current working condition by using a data set of the first working condition, namely, learning parameters of a self-organizing fuzzy neural network; and then the data sets of the other working conditions are used for sequentially adjusting the current learned explicit control law: if the data coverage rate of the current learned working condition does not meet the preset condition, directly updating and learning the current network parameters; if the data coverage rate of the current learned working condition meets the preset condition, adding a fuzzy rule, namely adding neurons representing the fuzzy rule in the self-organizing fuzzy neural network, and updating and learning parameters of the self-organizing fuzzy neural network;
for visual expression, taking working conditions A, B and C as examples, the operation characteristics of the working condition A and the working condition B are similar, and the working condition C and the other two working conditions have larger difference. Next, three parts will be specifically described respectively: the method comprises the steps of (1) constructing a self-organizing fuzzy neural network, (2) training a first working condition A, (3) adapting to small-range working condition changes of the working conditions A and B through network parameter self-adjustment, and (4) adapting to large-range working condition changes of the working conditions A, B and C through network structure self-adjustment.
1. Construction of self-organizing fuzzy neural network
First, the basic structure of the self-organizing fuzzy neural network is introduced. A fuzzy neural network is a combination of a fuzzy system and a neural network, wherein parameters of the fuzzy system can be adjusted by a neural network-based learning algorithm. The main advantage of fuzzy neural networks is to model problems using language models rather than complex mathematical models. The language model is essentially a fuzzy rule base consisting of a set of IF-THEN fuzzy rules. These rules are very intuitive and easy for human users to understand, so that the black box nature of the neural network paradigm is resolved. The number of fuzzy rules of the fuzzy neural network is an important parameter affecting the performance thereof. The self-organizing fuzzy neural network can automatically formulate the number of fuzzy rules by learning training data. In particular, when processing a multi-working-condition task, the number of fuzzy rules can change along with the change of the working condition number. Therefore, the invention adopts the self-organizing fuzzy neural network to describe the full-working-condition explicit control law. The self-organizing fuzzy neural network has four layers, namely an input layer, a fuzzy layer, a normalization layer and an output layer.
Input layer: this layer has m in total in The neurons respectively represent m of the fuzzy neural network in The dimension input variables. The mathematical expression of the input layer is as follows:
c i (t)＝x i (t),i＝1,2,...,m in (1)
wherein c i (t) represents the output of the ith neuron at time t, x i And (t) represents the input of the ith neuron at time t.And the input of the fuzzy neural network at the time t is represented. />The output of the input layer at time t is indicated.
Blur layer: this layer has P groups of neurons in total, each group representing a fuzzy rule. Wherein, the membership function for blurring the input variables is a radial basis function, and the mathematical expression is as follows:
wherein ζ i,j (t) represents the membership degree of the ith input to the jth fuzzy ruleFunction, mu ij (t) and sigma ij And (t) is the radial basis neuron center and width. After the membership degree of each input variable is obtained, the membership degree of each fuzzy rule is calculated, and the mathematical expression is as follows:
wherein,represents the output of the j-th radial basis neurons at time t,>represents the center of the j-th radial basis neuron group at time t,>the width of the j-th radial basis neuron group at time t is shown.
Normalization layer: the layer has P nerve cells, and the quantity of the nerve cells is the same as that of the fuzzy rule of the fuzzy layer, so that the nerve cells are used for defuzzifying the membership degree of the rule. Specifically, this layer will normalize the output of the blur layer, and the mathematical expression is as follows:
Wherein v is l (t) represents the normalized output of the membership of the first fuzzy rule at the time t, v (t) = [ v ] 1 (t),v 2 (t),...,v P (t)] T 。
Output layer: this layer is a linear layer and the mathematical expression of the output is as follows:
y(t)＝W(t)v(t) (5)
wherein,represents the output of the fuzzy neural network at time t, +.>And the weight matrix of the output layer at the time t is represented.
2. Training first working condition A
For ease of analysis, consider a typical model predictive control optimization problem, where the objective function only considers the tracking performance of the system output, and the constraint only considers the upper and lower clipping constraints of the manipulated variables, as follows:
wherein y= [ Y (t+1), …, Y (t+n) p )] T Represents the predicted output, r= [ R (t+1), …, R (t+n) p )] T Represents a reference trajectory, u= [ u (t), …, u (t+n) c -1)] T Representing the output of a predictive manipulated variable, i.e. a self-organizing fuzzy neural network, u min And u max Representing upper and lower limits of manipulated variables, NN [. Cndot.]The model represents a neural network prediction model, is a trained model, and the parameters of the model are frozen and not updated when the fuzzy neural network is trained. N (N) p Representing the predicted time domain range, N c Representing the control time domain range,representing the order of the predictive model with respect to the input control variable u and the output state y.
The model predictive control problem shown in equation (6) is converted into a loss function as follows:
Where N represents the batch size of the batch training of the self-organizing fuzzy neural network,sample index, Q, representing each batch y And Q u Weight factor representing output state and control variable, +.> And->The upper and lower limit penalty term representing the control variable is specifically as follows:
the explicit control law of the working condition A is learned by the model predictive control loss function shown in the formula (7). Namely, the parameter learning of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, and the parameter learning is as follows:
wherein W (t) represents the weight of the output layer of the self-organizing fuzzy neural network, σ (t) represents the width of the fuzzy layer neurons of the self-organizing fuzzy neural network, μ (t) represents the center of the fuzzy layer neurons of the self-organizing fuzzy neural network, and η represents the learning rate.
3. Network parameter self-adjustment for small range working condition change
When the training data set is switched to the working condition B, the prediction model is switched to the prediction model of the working condition B. At this time, if the explicit control law of the working condition B is still learned by using the model predictive control loss function, a catastrophic forgetting problem is caused, that is, the network parameters of the self-organizing fuzzy neural network are adjusted to a state that the control performance of the working condition B reaches the optimum, and the working condition a is ignored, so that the control performance of the working condition a is reduced. In the online control process, the explicit control law still cannot adapt to a plurality of working conditions. Therefore, the EWC loss is added on the basis of the model predictive control loss function, and the mathematical description is as follows:
Wherein,a model predictive control loss function representing the current working condition B to be learned; θ represents the current network parameters of the ad hoc fuzzy neural network, +.>Represents>The personal network parameters, A represents the set of all working conditions of which explicit control learning is completed, +.>Explicit control law learning indicating the working condition set A is completed>Personal network parameters->Model predictive control loss function representing the completed set of conditions A>For->Lambda represents the importance of the completed condition set a.
After the explicit control law finishes the control strategy learning of the working condition A, different network parameters have different convergence conditions on the model predictive control loss function of the working condition A. As shown in FIG. 2, the model predictive control loss function for operating condition AFor parameter->Is larger for the second order partial derivative of (2) and for the parameter +.>The second order bias of (2) is smaller. When the explicit control law starts the control strategy learning of the working condition B, if the parameter theta is adjusted 2 To improve the control performance of the working condition B, the model prediction control loss function of the working condition A>And tends to increase accordingly, which means that the control performance of the condition a is degraded. And if the adjustment parameter theta is selected 1 Model predictive control loss function for operating mode A >Is not substantially affected, which means that the control performance of the condition a remains unchanged. Therefore, EWC loss is used for controlling the parameter theta in the process of learning the control strategy of the working condition B 2 Variation of->Applying a larger penalty weight to the parameter θ 1 Variation of->A smaller penalty weight is applied. Therefore, the control performance of the working condition B can be improved on the premise of ensuring that the control performance of the working condition A is unchanged, so that the explicit control law can adapt to the change of the working condition in a small range.
Finally, the parameter updating of the self-organizing fuzzy neural network is completed by the gradient of the loss function shown in a counter propagation formula (10) in the full-working condition fuzzy neural network explicit control law learning framework shown in fig. 1, and the parameter updating is as follows:
wherein W (t) represents the weight of the output layer of the self-organizing fuzzy neural network, σ (t) represents the width of the fuzzy layer neurons of the self-organizing fuzzy neural network, μ (t) represents the center of the fuzzy layer neurons of the self-organizing fuzzy neural network, and η represents the learning rate.
4. Network structure self-adjustment for changing direction and changing working condition in large range
As shown in fig. 3, the blue region represents a parameter space that allows the ad hoc fuzzy neural network to meet the control demand of the condition a, the yellow region corresponds to the condition B, and the green region corresponds to the condition C. The red trace is shown at the loss function l MEMPC Under the action of the network parameter updating condition. In the first stage, the network parameters are adjusted to the positions meeting the control requirements of the working conditions A and B at the same time, and the small-range working condition changes of the working conditions A and B can be adapted. In the second stage, the control strategy of the working condition C is larger than that of the other two working conditions, so that the loss function l MEMPC In order to learn the control strategy of the working condition C and keep the control performance of the working conditions A and B unaffected, the network parameters are finally adjusted to a middle position, so that the control performance of the full-working-condition explicit control law is drastically reduced. Therefore, the control performance of the self-organizing fuzzy neural network for three working conditions cannot meet the requirements only by adjusting network parameters. The section provides a radial basis neuron growth mechanism based on data coverage rate to adjust a network structure, a control strategy of a working condition C is learned by adding a new radial basis neuron, and the control performance of the working condition A and the working condition B is kept unchanged.
First, a novel truncated radial basis function is employed as the activation function for the blur layer neurons of the self-organizing blur neural network. Here, a one-dimensional truncated radial basis function is introduced, the curve is shown in fig. 2, and the mathematical expression is as follows:
Where μ (t) represents the center of the truncated radial basis function and σ (t) represents the width of the truncated radial basis function. When c (t) ∈ [ c ] min (t),c max (t)]When a=1, normally output; otherwise, a=0, and the output is 0. Expanding the one-dimensional truncated radial basis function to a multi-dimensional form:
/>
wherein,represents the output of the j-th fuzzy rule at time t, < >>Represents the activation state of the jth fuzzy rule, < >>Represents the center of the jth fuzzy rule at time t,the width of the jth fuzzy rule at the time t is shown. If c i (t)∈[c ij,min (t),c ij,max (t)],i＝1,2,…,m in Hold, alpha j =1 indicates that the j-th fuzzy rule is activated, outputting a corresponding value; otherwise, alpha j =0 indicates that the jth fuzzy rule is not activated, and the output is 0.c ij,max (t) and c ij,max The settings of (t) are as follows:
wherein phi is a positive integer.
The special structure of the multi-dimensional truncated radial basis activation function means that only the data is in the range [ mu ] of the jth fuzzy rule j (t)-φ·σ j (t),μ j (t)+φ·σ j (t)]The radial basis neurons will output corresponding values when in the inner time, otherwise output 0. Therefore, the data coverage index can be defined according to whether the data is within the range of the fuzzy rule, and the mathematical expression is as follows:
where DC represents the data coverage of the current ad hoc fuzzy neural network, N represents the batch size of the neural network batch training, Represents +.>Whether the data is in a state signal within the fuzzy rule range.
Then, it is determined whether or not the radial basis neurons need to be increased based on the data coverage rate DC.
Where OL represents a threshold. If the condition shown in equation (16) is satisfied, it indicates that a neuron needs to be added. The new neuron design is as follows:
wherein N is uc Representing the amount of data not covered by the self-organizing fuzzy neural network, x j (t),j＝1,…,N uc Representing data not covered by the ad hoc fuzzy neural network,represents the center of the new fuzzy rule at time t, +.>Represents the width of the new fuzzy rule at the time t, W new And (t) represents the weight of the output layer corresponding to the new fuzzy rule. Sigma (sigma) new And W is new And randomly initializing by the self-organizing fuzzy neural network.
The control strategy of the working condition C is learned by adding a new fuzzy rule, and meanwhile, whether the control performance of the self-organizing fuzzy neural network on the working condition A and the working condition B is influenced by the working condition C is considered. Considering that the EWC loss activation state should be consistent with the blur layer neurons, the activation state is added to the EWC loss, at which time the loss function is mathematically described as follows:
wherein W is θ 、μ θ 、σ θ Representing a set of three network parameters, alpha j Indicating the activation state of the j-th fuzzy rule. As shown in formulas (20) and (21), if the data x is due to the presence of the special structure of the multi-dimensional truncated radial basis activation function i Is not covered by the j-th fuzzy rule, and data x is in parameter self-adjustment process i The calculated gradient of the loss function to the neuron parameters of the jth fuzzy rule is 0. This means that the blur layer neurons will only update the parameters μ (t) and σ (t) from the data they cover. Because the range of the stable point working point of the working condition C is larger than that of the working conditions A and B, if the width sigma (t) of the radial basis neurons is proper, the data of the working condition C cannot influence the parameters of the neurons covering the data of the working conditions A and B, so that the control performance of the self-organizing fuzzy neural network on the working conditions A and B is kept unchanged. Thus, the range of the radial basis neuron width σ is additionally limited during parameter self-tuning as follows:
wherein sigma ij (t) the ith neuron width, σ, representing the jth fuzzy rule ij,low (t) and sigma ij,low And (t) represents upper and lower clipping, respectively.
Due to data x i Is not covered by the j-th fuzzy rule, alpha j =0. Therefore, the equations (20) and (21) are equivalent.
2. On-line control: the output state at the current moment, the historical output state sequence, the control sequence and the reference track of the future output state are constructed together to serve as control state data at the current moment, and the control state data are input into the learned full-working-condition explicit control law to obtain an optimal control sequence at the current moment; the industrial system is finally controlled using the first control variable of the optimal control sequence at the current moment.
After the network parameter self-adjustment and the network structure self-adjustment, the full-working-condition explicit control law based on the self-organizing fuzzy neural network learns the full-working-condition control strategy of the industrial process, and the mathematical description is as follows:
/>
wherein, xi FNN (. Cndot.) represents the full-condition explicit control law based on self-organizing fuzzy neural network, ζ (t) represents the control state at the current time, ζ (t) = [ y (t), …, y (t-n) y ),u(t-1),…,u(t-n u ),r(t+1),…,r(t+N p )] T Y (t) represents the output state at the current time, y (t-1), …, y (t-n) y ) Representing history n y Output state sequences at various moments, u (t-1), …, u (t-n) u ) Representing history n u Control sequence at each time instant, r (t+1), …, r (t+N) p ) Representing future N p Output state reference trajectories at each instant.
When running online, the optimal control sequence can be obtained by only constructing the control state xi (t) of the multi-mode process at the current moment and inputting the control state xi (t) into the learned full-working-condition explicit control lawThe first manipulated variable of the control sequence is then input into the actual system.
The method provided by the invention only needs forward transfer calculation of the self-organizing fuzzy neural network, and does not need optimization solution, so that the calculation time and calculation resources are greatly saved, and the control instantaneity is greatly improved. Meanwhile, compared with the traditional multi-mode predictive control method, the method omits a switching mechanism and can ensure the rapid matching of different mode control strategies. Therefore, the method can meet the all-condition control requirement of the multi-mode process by means of a single network.
In order to verify the effectiveness of the method provided by the invention, the following numerical simulation experiment and the semi-physical simulation platform experiment of the roasting process are designed for verification:
1. numerical simulation experiment
Consider a numerical simulation system as a controlled object as follows:
wherein u (t) is a manipulated variable of the system at the moment t, g (t) is an unmeasured intermediate variable of the system at the moment t, y (t) is a controlled variable of the system at the moment t, M (t) represents uncertainty interference factors changing along with time to cause the working condition of the system to change, and v (t) is Gaussian noise with the mean value of 0 and the standard deviation of 0.01. The settings for M (t) are as follows:
wherein, when t is [1,300 ]) the system operates in a working condition A, when t is [300,600 ]) the system operates in a working condition B and when t is [600,1000 ]) the system operates in a working condition C. Since the stable point working ranges of the working condition A and the working condition B have smaller differences, the change of the working condition A and the working condition B belongs to the small-range working condition change. The stable point working ranges of the working condition A and the working condition C are large, and the change of the working condition A and the working condition C belongs to the large-range working condition change.
In the offline learning stage, a random sampling data set with sufficient data quantity is adopted as a training data set, and then learning of an all-condition explicit control law based on a self-organizing fuzzy neural network is completed. To illustrate the advantages of the FNNECL method proposed by the present invention, ETASI4PC, PWA, MMPC was used as a comparative method. The parameters of the self-organizing fuzzy neural network are set as follows: the initial fuzzy rule number p=5, the radial basis neurons are centered at [0,1 ] ]Random initialization of uniform distribution, width set to 1, batch size N of batch training set to 32, parameter phi set to 3, threshold OL set to 2, learning rate η=0.01, and number of iterative steps set to 300. The control parameters were set as follows: predicting time domain range N p Set to 2, control the time domain range N c Set to 2, weight factor Q y =1 and Q u =1, upper and lower limits u of manipulated variable min =0 and u max =2, the width of radial basis neurons is limited to [0,0.8]Within a range of (2).
In the online control stage, the system is in a working condition A in a 300 th period, in a working condition B in 300 th to 600 th periods and in a working condition C in 600 th to 1000 th periods.
The set value output by the system is set as a reference track in the form of a sine function, and the performance index is selected as MSE. As can be seen from fig. 4, the ETASI4PC and PWA methods can only accommodate a small range of operating conditions, and control performance can drop dramatically when a large range of operating conditions change. The MMPC and the FNNCEL can adapt to a large-scale working condition change, and tracking control is realized in the switching process of three working conditions. As can be seen from table 1, for the multi-modal process, the overall control performance is slightly worse than FNNECL because the MMPC needs to update the prediction model through the error triggering mechanism when the wide range of operating conditions changes. Meanwhile, in the on-line control process of the FNNECL, the optimal control sequence can be obtained only by inputting the current state into the fuzzy neural network, and on-line solving of an optimization problem or row-by-row table lookup operation is not needed, so that the running time required by the FNNECL is shortest. As can be seen from the comparative experiments, the FNNECL has a faster running speed for a multi-modal process and can accommodate both large and small range of operating conditions with a single network.
Table 1 control method control performance and run time during switching of operating conditions A, B, C
2. Semi-physical simulation platform experiment in roasting process
In order to verify the full-working-condition control performance of the proposed full-working-condition explicit model predictive control based on the self-organizing fuzzy neural network in the industrial process of the running state fluctuation, a semi-physical simulation platform shown in figure 5 is built. The platform can effectively simulate an industrial field and verify engineering deployment schemes, and is used for verification of control algorithms such as multi-model predictive control and explicit model predictive control. The platform adopts a roasting furnace as a simulation object, and the roasting process is the first procedure of zinc smelting, so that zinc concentrate is converted into zinc calcine. The whole roasting furnace system is divided into a roasting furnace body, a feeding system, a blast system, an exhaust system and a zinc outlet system. In industry, the feed belt speed is generally used as a manipulated variable for the firing process and the standard temperature is used as a controlled variable. The sampling period is set to 10s and the control period is set to 30s in consideration of the communication bandwidth. To fully excite the firing process, a random signal in the range of feed belt speed set to [520,580] r/min is input to the HILS platform to generate process operating data.
TABLE 2 calcination operating condition system parameters
The change of the operation working condition in the roasting process is considered, the system parameters of the three working conditions are shown in table 2, wherein the change of the working condition A and the working condition B belongs to a small-range working condition change, and the change of the two working conditions and the working condition C belongs to a large-range working condition change. In the simulation experiment, the system of the first 400 cycles is under the working condition A, the 400 th to 800 th cycles are under the working condition B, and the 800 th to 1400 th cycles are under the working condition C. The setting of the firing process temperature was set to a step change as shown below:
considering that the roasting process control generally adopts the change amount of the rotating speed as a control variable, the original data set is subjected to differential processing and normalized to be used as a training data set. The parameters of the self-organizing fuzzy neural network are set as follows: the initial fuzzy rule number p=5, the radial basis neurons are centered at [0,1 ]]Random initialization of uniform distribution, width set to 1, batch size N of batch training set to 32, parameter phi set to 3, lambda set to 1.5, threshold OL set to 4, learning rate η=0.1, and number of iterative steps set to 100. The control parameters were set as follows: predicting time domain range N p Set to 4, control the time domain range N c Set to 2, weight factor Q y =1 and Q u =1, upper and lower limits u of manipulated variable min = -15 and u max =15, the width of radial basis neurons is limited to [0.2,0.7 ]]Within a range of (2). Training resulted in a number of fuzzy rules of 326. The performance index is selected to be MSE. The comparison method selects error-triggered multi-model predictive control, and simultaneously simplifies the optimization problem through matrix transformation so as to improve the solving speed. The control effect of both methods is shown in FIG. 6, and the quantitative results are shown in Table 3.
TABLE 3 control Performance and average run time
Experimental results show that FNNECL can stably track the temperature in the furnace to a set value in the face of the roasting process of running state fluctuation. The 800 th cycle temperature jump is caused by a wide variation in operating conditions. The FNNECL has shorter adjustment time, smaller overshoot and fluctuation, and particularly when the working conditions are changed, because the FNNECL does not need to switch a prediction model at the moment, the truncated radial basis neurons of the fuzzy layer can select a proper fuzzy rule according to the data to obtain a control sequence. Experiments prove that the FNNECL provided by the invention only needs 0.006s for each solution of the optimal control quantity, and MMPC only needs 0.513s for each solution of the optimal control quantity, which is 85.5 times of the optimal control quantity. For edge devices that need to handle multitasking, this greatly reduces the computational effort requirements, significantly improving the real-time nature of the control decisions. In summary, compared with the traditional MMPC, the FNNECL not only can adapt to all operation conditions by a single network and eliminate the control strategy mismatch influence in the switching stage, but also can meet the real-time requirement by only needing a small amount of computing resources, so that the FNNECL has more remarkable advantages.
The explicit prediction control method based on the self-organizing fuzzy neural network provided by the invention can be applied to the precise control of the multi-mode industrial process, not only can adapt to all operation conditions by means of a single network, but also can eliminate the influence of control strategy mismatch in a switching stage, simultaneously reduces the calculation force requirement, and remarkably improves the instantaneity of control decisions. Specifically, compared with the traditional MMPC algorithm which needs 0.513s for each solution, the FNNECL provided by the invention only needs 0.006s for each solution of the optimal control quantity, and the former is 85.5 times as much as the latter. Therefore, the invention is suitable for the scenes of frequent change of the running state, high sampling frequency, high real-time requirement and limited calculation resources.
The above embodiments are preferred embodiments of the present application, and various changes or modifications may be made on the basis thereof by those skilled in the art, and such changes or modifications should be included within the scope of the present application without departing from the general inventive concept.
Claims (10)
1. The method for predicting and controlling the full working condition of the multi-mode industrial process in high real time is characterized by comprising the following steps:
offline learning:
respectively learning a corresponding output state prediction model by using a data set of each working condition of the industrial system, and learning a full-working-condition explicit control law based on a self-organizing fuzzy neural network by using data sets of all working conditions;
When learning the full-working-condition display control law, firstly, learning an explicit control law of the current working condition by using a data set of the first working condition, namely, learning parameters of a self-organizing fuzzy neural network; and then the data sets of the other working conditions are used for sequentially adjusting the current learned explicit control law: if the data coverage rate of the current learned working condition does not meet the preset condition, directly updating and learning the current network parameters; if the data coverage rate of the current learned working condition meets the preset condition, adding a fuzzy rule, namely adding neurons representing the fuzzy rule in the self-organizing fuzzy neural network, and updating and learning parameters of the self-organizing fuzzy neural network;
on-line control:
the output state at the current moment, the historical output state sequence, the control sequence and the reference track of the future output state are constructed together to serve as control state data at the current moment, and the control state data are input into the learned full-working-condition explicit control law to obtain an optimal control sequence at the current moment;
the industrial system is controlled using the first control variable of the optimal control sequence at the current time.
2. The multi-modal industrial process full-condition high real-time predictive control method of claim 1, wherein the self-organizing fuzzy neural network comprises an input layer, a fuzzy layer, a normalization layer and an output layer;
The input layer includes m in The neurons respectively represent m of the fuzzy neural network in Dimension input variables; the mathematical expression of the input layer is as follows:
c i (t)＝x i (t),i＝1,2,…,m in (1)
wherein x is i (t) represents the input of the ith neuron at time t, c i (t) represents the output of the ith neuron at time t;input representing a fuzzy neural network at time tThe control state data is used for inputting the control state data of the industrial system at the moment t; />The output of the input layer at the time t is represented;
the fuzzy layer is provided with P groups of neurons in total, and each group of neurons represents a fuzzy rule; each fuzzy rule adopts a radial basis function as a membership function of a fuzzy input variable, and the mathematical expression is as follows:
wherein ζ i,j (t) represents the membership function, μ of the ith input variable corresponding to the jth fuzzy rule ij (t) and sigma ij (t) radial basis neuron centers and widths; after the membership degree of each input variable is obtained, the membership degree of each fuzzy rule is calculated, and the mathematical expression is as follows:
wherein,represents the output of the j-th radial basis neurons at time t,>represents the center of the j-th radial basis neuron group at time t,>representing the width of the j-th radial basis neuron group at the time t;
the normalization layer has P neurons, and the number of the neurons is the same as that of the fuzzy rules of the fuzzy layer, and the neurons are used for normalizing the output of the fuzzy layer to obtain normalized output Let v (t) = [ v 1 (t),v 2 (t),...,v P (t)] T ；
The output layer is a linear layer, and the mathematical expression of the output is as follows:
y(t)＝W(t)v(t)
wherein,output representing self-organizing fuzzy neural network at time t for outputting control variable, < > -at time t of industrial system>Weight matrix representing output layer at time t, m o Is the number of neurons in the output layer.
3. The multi-modal industrial process full-condition high real-time predictive control method according to claim 1, wherein the learning of the explicit control law of the current condition using the data set of the first condition specifically converts the optimization problem of the model predictive control strategy into a loss function to learn the explicit control law;
firstly, the optimization problem of the model predictive control strategy is that the objective function only considers the tracking performance of the output state of the industrial system, and the constraint condition only considers the upper and lower limiting constraints of the control variable, as follows:
wherein NN []Represents a neural network prediction model, y= [ Y (t+1), …, Y (t+n) p )] T Represents the prediction output state of the prediction model, r= [ R (t+1), …, R (t+n) p )] T Represents a reference trajectory, u= [ u (t), …, u (t+n) c -1)] T Representing the predicted control variable, u min And u max Representing upper and lower limits of the control variable, N p Representing the predicted time domain range, N c Representing the control time domain range, Representing the order of the control variable u and the output state y representing the prediction model with respect to the input;
the objective function is then converted into a loss function as:
where N represents the batch size of the batch training of the self-organizing fuzzy neural network,sample index, Q, representing each batch y And Q u Weight factor representing output state and control variable, +.> And->The upper and lower limit penalty term representing the control variable is specifically as follows:
finally, the explicit control law of the first working condition is learned through the model predictive control loss function shown in the formula (7), namely, the parameter learning of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, and the parameter learning is as follows:
wherein W (t) represents the weight of the output layer of the self-organizing fuzzy neural network, σ (t) represents the width of the fuzzy layer neurons of the self-organizing fuzzy neural network, μ (t) represents the center of the fuzzy layer neurons of the self-organizing fuzzy neural network, and η represents the learning rate.
4. The multi-modal industrial process all-condition high real-time predictive control method of claim 3, wherein the data coverage calculation method is as follows: firstly, adopting a truncated radial basis function as an activation function of a fuzzy layer neuron of the self-organizing fuzzy neural network, and outputting a jth fuzzy rule at the moment t Expressed as:
wherein f [ c (t)]Represents a truncated radial basis function, f ij [c i (t)]Represents the output of the ith neuron in the jth fuzzy rule at time t, a ij Represents the activation state of the ith neuron in the jth fuzzy rule at time t, representing the activation state of the jth fuzzy rule, c ij,min (t),c ij,max (t) the upper and lower cutoff limits of the radial basis function, respectively, are set as:
wherein phi is a positive integer;
then according to the activation state alpha of all fuzzy rules j Judging the first batch of dataStatus signal of whether or not the individual data is within the range of the fuzzy rule +.>And calculating the data coverage rate DC of the current self-organizing fuzzy neural network according to the state signals of all the data, wherein the data coverage rate DC is expressed as follows:
5. the method for high real-time predictive control of full operating mode in a multi-modal industrial process according to claim 4, wherein the preset conditions are:
where OL represents a threshold.
6. The method for high real-time predictive control of full operating mode in a multi-modal industrial process according to claim 4, wherein the adding of the fuzzy rule is to add neurons representing the fuzzy rule in the ad hoc fuzzy neural network, and the specific newly added neuron group is designed as follows:
wherein N is uc Representing the data quantity which is not covered by the self-organizing fuzzy neural network in the current working condition to be learned, x j (t),j＝1,…,N uc Representing data not covered by the ad hoc fuzzy neural network,andthe new fuzzy rule at the time t is expressed to correspond to the center and the width W of the truncated radial basis neurons new (t) represents the weight, σ, of the output layer corresponding to the new fuzzy rule new And W is new And randomly initializing by the self-organizing fuzzy neural network.
7. The method for high real-time predictive control of full operating mode in multi-modal industrial process according to claim 6, wherein the parameters of the self-organizing fuzzy neural network are updated and learned after adding the fuzzy rule, and the loss function is specifically:
wherein,a model predictive control loss function representing the current working condition B to be learned; θ represents the current network parameters of the ad hoc fuzzy neural network, +.>Indicate->Personal network parameters->Explicit control law learning indicating condition A is completed>Personal network parameters->Model predictive control loss function representing the completed set of conditions A>For a pair ofλ represents the importance of the completed working condition set a; w (W) θ 、μ θ 、σ θ Representing a set of three network parameters; for the j-th fuzzy rule, < > and->Indicate->Personal network parameters->Explicit control law learning indicating condition A is completed >Personal network parameters->Model predictive control loss function representing the completed set of conditions A>For a pair ofSecond partial derivative of (2);
then, the parameter updating of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, as follows:
8. the method for high real-time predictive control of full operating mode in a multi-modal industrial process according to claim 7, wherein the range of the width σ of the radial basis neurons is additionally limited when the parameters of the self-organizing fuzzy neural network are updated and learned as follows:
wherein sigma ij (t) the ith neuron width, σ, representing the jth fuzzy rule ij,low (t) and sigma ij,low And (t) represents upper and lower clipping, respectively.
9. The method for high real-time predictive control of full operating mode in multi-modal industrial process according to claim 3, wherein if the data coverage rate of the current learned operating mode does not meet the preset condition, the current network parameters are directly updated and learned, and the loss function adopted by the updated and learned is:
wherein,a model predictive control loss function representing the current working condition B to be learned; θ represents the current network parameters of the ad hoc fuzzy neural network, +.>Represents >The personal network parameters, A represents the set of all working conditions of which explicit control learning is completed, +.>Explicit control law learning indicating the working condition set A is completed>Personal network parameters->Model predictive control loss function representing the completed set of conditions A>For->λ represents the importance of the completed working condition set a;
then, the parameter updating of the self-organizing fuzzy neural network is completed through the gradient of the loss function shown in the following back propagation formula, as follows:
10. an electronic device comprising a memory and a processor, the memory having stored therein a computer program which, when executed by the processor, causes the processor to implement the method of any of claims 1-9.
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