CN117851922A - Operation monitoring method of air concentration monitoring instrument - Google Patents
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Abstract
The invention discloses an air concentration monitoring instrument operation monitoring method which comprises the steps of signal receiving, signal decomposition, parameter updating, instrument operation monitoring mixed model establishment, model parameter adjustment and instrument operation monitoring. The invention belongs to the technical field of data processing, and particularly relates to an operation monitoring method of an air concentration monitoring instrument, which is based on Hilbert transformation to obtain a unilateral spectrum, introduces constraint optimization and expands a Lagrange equation, and carries out frequency modulation according to balance constraint and punishment items so as to complete high-precision decomposition of signals; based on the alternating direction multiplier method, ADMM optimization and Hermite symmetry simplification, the calculated amount is reduced; and adopting a designed CNN layer to extract features, utilizing an LSTM layer design to capture long-term dependency of low-frequency signal data, utilizing a DBN model to predict high-frequency signals, extracting abstract features by a layered design, and finally weighting and fusing an output structure based on self-adaptive characterization learning to output a monitoring result.
Description
Technical Field
The invention belongs to the technical field of data processing, and particularly relates to an operation monitoring method of an air concentration monitoring instrument.
Background
The operation monitoring method of the air concentration monitoring instrument is to train a monitoring model by utilizing the existing signal data and label data by utilizing the data analysis and signal processing technology, and learn the characteristics of different operation states by analyzing the relation between the operation signal and the operation parameters of the instrument, so that the real-time operation state can be monitored. However, the original signal of the data source has the problems of incomplete signal and large calculation amount of parameter updating caused by coarse decomposition mode; the general monitoring model has the problems that the characteristic extraction capability is weak, and the self-adaptive learning can not be carried out on the characteristics of input data, so that the model performance is weak; the parameter searching algorithm has the problems that the searching space range is small, and the global optimum and the local optimum cannot be judged.
Disclosure of Invention
Aiming at the problems of incomplete signal and large calculation amount of parameter updating caused by coarse decomposition mode of original signals of data sources, the method obtains a unilateral spectrum based on Hilbert transformation, introduces constraint optimization, expands Lagrangian equation, carries out frequency modulation according to balance constraint and punishment items, thereby completing high-precision decomposition of signals, and reduces calculation amount based on an alternate direction multiplier method, ADMM optimization and Hermite symmetry simplification problem; aiming at the problems that the characteristic extraction capability of a general monitoring model is weak and self-adaptive learning cannot be carried out on the characteristics of input data, so that the model performance is weak, the scheme adopts a designed CNN layer to carry out characteristic extraction, utilizes an LSTM layer design to capture the long-term dependency relationship of low-frequency signal data, utilizes a DBN model to monitor high-frequency signals, adopts a layered design to extract abstract characteristics, and finally outputs a monitoring result by weighting and fusing an output structure based on self-adaptive characterization learning, so that the adaptability and generalization capability of the model are improved; aiming at the problems that the search space range is small and global optimum and local optimum cannot be judged in the parameter searching algorithm, the scheme adopts the method that the search range is enlarged by moving to the local optimum and the global optimum based on the current iteration times, and the local optimum and the global optimum are judged based on the evaluation threshold and the maximum iteration times.
The invention provides an operation monitoring method of an air concentration monitoring instrument, which comprises the following steps:
step S1: receiving signals;
step S2: signal decomposition, namely performing frequency modulation based on Hilbert transformation and an extended Lagrangian equation, so as to define an objective function and complete high-precision signal decomposition;
step S3: parameter updating, searching an optimal solution based on an alternate direction multiplier method, ADMM optimization and Hermite symmetry simplification problem;
step S4: an instrument operation monitoring mixed model is established, low-frequency signal data characteristics are extracted based on a CNN layer design, input time sequence data are initially monitored by utilizing an LSTM layer design, and monitoring results of high-frequency signal data after signal decomposition are combined with a DBN layer design to be subjected to weighted fusion, so that a final monitoring result is output;
step S5: model parameter adjustment, namely moving to local optimum and global optimum based on the current iteration times, and judging global optimum based on an evaluation threshold and the maximum iteration times;
step S6: and (5) monitoring the operation of the instrument.
Further, in step S1, the signal receiving is to receive an equipment operation state signal, an equipment sensor output signal, a noise sensor output signal, a vibration sensor output signal, an energy consumption monitoring signal and an equipment operation state corresponding to the data; the running state of the equipment is used as a data tag.
Further, in step S2, the signal decomposition specifically includes the following:
step S21: predefined, for each IMF, i.e. the inner pulse function, a single-sided spectrum is obtained using the Hilbert transform, the estimated bandwidth is minimized by summing, and under constraints, the accumulation of each IMF is equal to the input signal f (t), using the following formula:
；
；
where f (t) is the original signal being decomposed, delta () is the dirac distribution, t is time, x is the convolution operator, u k Is the coefficient of the kth IMF, ω k Is the center frequency of the kth IMF, K represents the total number of IMFs, ∂ t Deriving t, j1 is an imaginary unit, subscript 2 is an L2 normal form, and superscript 2 is a squaring operation;
step S22: defining an extended Lagrange equation, converting a constrained variation problem into an unconstrained optimization problem, and based on a quadratic penalty term and a Lagrange multiplier, using the following formula:
；
where λ is the Lagrangian multiplier, α is a parameter that balances the relative weights between constraint terms and penalty terms in the objective function, and 〈 〉 is the inner product;
step S23: frequency modulation, namely mixing the frequency spectrum of the IMF with a modulation index adjusted to the corresponding estimated center frequency, and transferring the frequency spectrum to a baseband region; estimating the bandwidth of each IMF, i.e., the L2 parameter of the gradient square, using gaussian smoothing of the demodulated signal;
step S24: defining an objective function, estimating the coefficient and frequency characteristic of each IMF, thereby realizing the decomposition of the original signal, wherein the objective function is expressed as follows:
。
further, in step S3, the parameter updating updates the coefficient and frequency characteristic of each IMF to achieve the decomposition of the original signal, which specifically includes the following contents:
step S31: defining a solution, using an alternating direction multiplier method to search saddle points of an augmented lagrangian function, updating u in both directions based on an ADMM optimization method k And omega k The following iterative solution is obtained:
；
；
；
where n is the number of iterations, τ is the time step, and i1 and k are both the index of the IMF;
step S32: convergence conditions are defined using the following formula:
；
where ε is the convergence threshold;
step S33: solving an optimal solution, wherein the content comprises:
step S331: updating the modality, equating the sub-problem to the following minimization problem:
；
step S332: by using the hermite symmetry of the real signal, in the reconstructed fidelity term, the form of half-space integral to non-negative frequencies is written, and the first derivative is changed to zero to find the optimal solution of the problem, and the formula is as follows:
；
in the method, in the process of the invention,、andrespectively f (omega), lambda (omega) and u i1 (ω) fourier transform, ω being a continuous frequency variable;
step S333: will omega k The optimal solution problem is equivalent to the following:
；
step S334: the optimal solution is expressed as follows:
；
step S335: the signal is finally divided into a high frequency signal and a low frequency signal based on a signal frequency threshold.
Further, in step S4, the method for creating the instrument operation monitoring hybrid model is based on the signal data obtained in step S3, which is randomly divided into a training set and a test set, and the test set is used to test the performance of the model, and the model creation specifically includes the following steps:
step S41: CNN layer design, the CNN layer is used to extract the features of low frequency data, the low frequency data after signal decomposition is input into the CNN layer with 64×1×3 convolution kernel, the convolution kernel is used as the feature extractor, the process is described as follows:
；
in the method, in the process of the invention,is the value of the feature map j at time τ1, σ in layer l+1 R Is a function of the ReLU and,is the bias value of the feature map j in the first layer, F l Is the number of feature maps in the first layer, f is the feature map index, p l Indicating the number of convolution kernels in the first layer, p is the index of the convolution kernel position,is a value generated by convolving the feature map j in the first layer with a convolution kernel f;
step S42: LSTM layer arrangementAfter the preliminary feature extraction is completed, the CNN layer inputs data into the LSTM layer as a time sequence to predict, and the system structure of the LSTM consists of four gates, namely a forgetting gate f t Update gate u t Input gate i t Output door o t And a memory cell C t By operating the gates, information is stored, written and read in the cell, the process is described as follows:
；
；
；
；
；
；
wherein W and b are respectively a weight matrix and a bias matrix related to a control gate, subscripts f, i, c and o respectively represent a forgetting gate, an input gate, a storage unit and an output gate, t and t-1 are time states, h is a hidden state, x is an input data set, and tanh is a hyperbolic tangent function;
step S43: the DBN layer design, the DBN is composed of a plurality of limited Boltzmann machines, each RBM comprises a visible unit and a hidden unit, wherein the visible unit is an input layer, the hidden unit is a characteristic detection layer, three hidden layer DBN networks are adopted to predict high-frequency signal data after signal decomposition processing, neurons among the DBN layers are independent and unconnected, and the visible unit of each RBM is connected with the hidden unit through weights, and the content comprises:
step S431: the energy function E is defined using the formula:
；
in the formula, v k1 Is the kth 1 visible unit, h m Is the mth hidden unit, ω mk1 Is v k1 And h m Weight of connection between b k1 Is the threshold of the kth 1 visible unit, c m Is the threshold of the mth hidden unit;
step S432: after the energy function is obtained, the joint probability distribution of all visible units and hidden units is calculated, and the following formula is used:
；
wherein D is all visible units and h is all hidden units; p (v, h) is the joint probability distribution of all visible and hidden units;
step S433: the activation probability of the kth 1 visible unit and the mth hidden unit of each RBM is calculated by the following formula:
；
；
in the method, in the process of the invention,is the activation probability of the kth 1 visible unit,is the activation probability of the mth hidden unit;
step S44: and carrying out weighted fusion on the LSTM layer output result and the DBN layer output result to generate a final prediction result.
Further, in step S5, the model parameter adjustment specifically includes the following:
step S51: initializing, initializing a parameter search space and n parameter positionsThe parameter adaptation degree value is based on the model monitoring accuracy established at the current position;
step S52: and updating the position, wherein if the fitness value of the new position is higher than that of the original position, the position is updated, otherwise, the position is kept unchanged, and the formula used for updating the position is as follows:
；
in the method, in the process of the invention,is the updated position, LG J Is the optimal position in the J-th dimension, WZ rJ The position of the randomly selected r parameter on the J dimension, U () is a random number generation function obeying uniform distribution, GG is a global optimal position, T1 is the current iteration number, and T is the maximum iteration number; f (f) i 、f b And f g The current fitness value, the optimal fitness value of the experience of the individual and the global optimal fitness value are respectively;
step S53: globally judging, presetting an evaluation threshold, and if parameters with fitness values higher than the evaluation threshold exist, establishing an instrument operation monitoring model based on the parameters; if the maximum iteration times are exceeded, reinitializing the parameter position to seek parameters; otherwise, continuing to search for the parameters.
Further, in step S6, the instrument operation monitoring is to set up an instrument operation monitoring hybrid model based on the best parameters of the monitoring model found in step S5, and when the monitoring accuracy of the model to the test set is higher than the accuracy threshold, the model is set up; the model receives the instrument operation signal and the operation parameter signal in real time, and based on the operation monitoring state of the output monitoring instrument, when the operation monitoring state is abnormal, early warning treatment is given.
By adopting the scheme, the beneficial effects obtained by the invention are as follows:
(1) Aiming at the problems of incomplete signal and large calculation amount of parameter updating caused by rough decomposition mode of an original signal of a data source, the scheme obtains a unilateral spectrum based on Hilbert transformation, introduces constraint optimization and expands a Lagrange equation, carries out frequency modulation according to balance constraint and punishment items, thereby completing high-precision decomposition of the signal, and reduces calculation amount based on an alternate direction multiplier method, ADMM optimization and Hermite symmetry simplification problem.
(2) Aiming at the problems that the characteristic extraction capability of a general monitoring model is weak and self-adaptive learning cannot be carried out on the characteristics of input data, so that the model performance is weak, the scheme adopts a designed CNN layer to carry out characteristic extraction, utilizes an LSTM layer design to capture the long-term dependency relationship of low-frequency signal data, utilizes a DBN model to monitor high-frequency signals, adopts a layered design to extract abstract characteristics, finally carries out weighted fusion on an output structure based on self-adaptive characterization learning to output a monitoring result, and improves the adaptability and generalization capability of the model.
(3) Aiming at the problems that the search space range is small and global optimum and local optimum cannot be judged in the parameter searching algorithm, the scheme adopts the method that the search range is enlarged by moving to the local optimum and the global optimum based on the current iteration times, and the local optimum and the global optimum are judged based on the evaluation threshold and the maximum iteration times.
Drawings
FIG. 1 is a schematic flow chart of an operation monitoring method of an air concentration monitoring instrument provided by the invention;
FIG. 2 is a schematic flow chart of the signal decomposition in FIG. 1;
FIG. 3 is a flow chart of parameter updating in FIG. 1;
FIG. 4 is a schematic flow chart of the method for creating the instrument operation monitoring hybrid model in FIG. 1;
fig. 5 is a flow chart of the model parameter adjustment in fig. 1.
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be understood that the terms "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," "outer," and the like indicate orientation or positional relationships based on those shown in the drawings, merely to facilitate description of the invention and simplify the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be construed as limiting the invention.
Referring to fig. 1, the operation monitoring method of the air concentration monitoring instrument provided by the present invention includes:
step S1: receiving signals;
step S2: signal decomposition;
step S3: updating parameters;
step S4: establishing an instrument operation monitoring hybrid model;
step S5: model parameter adjustment;
step S6: and (5) monitoring the operation of the instrument.
In step S1, the device operation state signal, the device sensor output signal, the noise sensor output signal, the vibration sensor output signal, the energy consumption monitoring signal, and the device operation state corresponding to the data are received; the running state of the equipment is used as a data tag.
In the third embodiment, referring to fig. 1 and 2, the signal decomposition specifically includes the following in step S2, where the embodiment is based on the above embodiment:
step S21: predefined, for each IMF, i.e. the inner pulse function, a single-sided spectrum is obtained using the Hilbert transform, the estimated bandwidth is minimized by summing, and under constraints, the accumulation of each IMF is equal to the input signal f (t), using the following formula:
；
；
where f (t) is the original signal being decomposed, delta () is the dirac distribution, t is time, x is the convolution operator, u k Is the coefficient of the kth IMF, ω k Is the center frequency of the kth IMF, K represents the total number of IMFs, ∂ t Deriving t, j1 is an imaginary unit, subscript 2 is an L2 normal form, and superscript 2 is a squaring operation;
step S22: defining an extended Lagrange equation, converting a constrained variation problem into an unconstrained optimization problem, and based on a quadratic penalty term and a Lagrange multiplier, using the following formula:
；
where λ is the Lagrangian multiplier, α is a parameter that balances the relative weights between constraint terms and penalty terms in the objective function, and 〈 〉 is the inner product;
step S23: frequency modulation, namely mixing the frequency spectrum of the IMF with a modulation index adjusted to the corresponding estimated center frequency, and transferring the frequency spectrum to a baseband region; estimating the bandwidth of each IMF, i.e., the L2 parameter of the gradient square, using gaussian smoothing of the demodulated signal;
step S24: defining an objective function, estimating the coefficient and frequency characteristic of each IMF, thereby realizing the decomposition of the original signal, wherein the objective function is expressed as follows:
。
in step S3, the parameter update is to update the coefficient and frequency characteristic of each IMF to achieve the decomposition of the original signal, and specifically includes the following steps with reference to fig. 1 and 3:
step S31: defining a solution, using an alternating direction multiplier method to search saddle points of an augmented lagrangian function, updating u in both directions based on an ADMM optimization method k And omega k The following iterative solution is obtained:
；
；
；
where n is the number of iterations, τ is the time step, and i1 and k are both the index of the IMF;
step S32: convergence conditions are defined using the following formula:
；
where ε is the convergence threshold;
step S33: solving an optimal solution, wherein the content comprises:
step S331: updating the modality, equating the sub-problem to the following minimization problem:
；
step S332: by using the hermite symmetry of the real signal, in the reconstructed fidelity term, the form of half-space integral to non-negative frequencies is written, and the first derivative is changed to zero to find the optimal solution of the problem, and the formula is as follows:
；
in the method, in the process of the invention,、andrespectively f (omega), lambda (omega) and u i1 (ω) fourier transform, ω being a continuous frequency variable;
step S333: will omega k The optimal solution problem is equivalent to the following:
；
step S334: the optimal solution is expressed as follows:
；
step S335: the signal is finally divided into a high frequency signal and a low frequency signal based on a signal frequency threshold.
By executing the operation, aiming at the problems of incomplete signal and large calculation amount of parameter updating caused by coarse decomposition mode of an original signal of a data source, the scheme obtains a unilateral spectrum based on Hilbert transformation, introduces constraint optimization and expands a Lagrange equation, carries out frequency modulation according to balance constraint and punishment items, thereby completing high-precision decomposition of the signal, and reduces the calculation amount based on an alternate direction multiplier method, ADMM optimization and Hermite symmetry simplification problem.
In step S4, the instrument operation monitoring hybrid model is established based on the signal data obtained in step S3, and is randomly divided into a training set and a test set, the training set is utilized to test the performance of the model, and the model establishment specifically comprises the following steps:
step S41: CNN layer design, the CNN layer is used to extract the features of low frequency data, the low frequency data after signal decomposition is input into the CNN layer with 64×1×3 convolution kernel, the convolution kernel is used as the feature extractor, the process is described as follows:
；
in the method, in the process of the invention,is the value of the feature map j at time τ1, σ in layer l+1 R Is a function of the ReLU and,is the bias value of the feature map j in the first layer, F l Is the number of feature maps in the first layer, f is the feature map index, p l Indicating the number of convolution kernels in the first layer, p is the index of the convolution kernel position,is a value generated by convolving the feature map j in the first layer with a convolution kernel f;
step S42: the LSTM layer is designed, the CNN layer inputs data as time sequence to the LSTM layer for prediction after finishing primary feature extraction, and the LSTM system structure consists of four gates, namely forgetting gate f t Update gate u t Input gate i t Output door o t And a memory cell C t By operating the gates, information is stored, written and read in the cell, the process is described as follows:
；
；
；
；
；
；
wherein W and b are respectively a weight matrix and a bias matrix related to a control gate, subscripts f, i, c and o respectively represent a forgetting gate, an input gate, a storage unit and an output gate, t and t-1 are time states, h is a hidden state, x is an input data set, and tanh is a hyperbolic tangent function;
step S43: the DBN layer design, the DBN is composed of a plurality of limited Boltzmann machines, each RBM comprises a visible unit and a hidden unit, wherein the visible unit is an input layer, the hidden unit is a characteristic detection layer, three hidden layer DBN networks are adopted to predict high-frequency signal data after signal decomposition processing, neurons among the DBN layers are independent and unconnected, and the visible unit of each RBM is connected with the hidden unit through weights, and the content comprises:
step S431: the energy function E is defined using the formula:
；
in the formula, v k1 Is the kth 1 visible unit, h m Is the mth hidden unit, ω mk1 Is v k1 And h m Weight of connection between b k1 Is the threshold of the kth 1 visible unit, c m Is the threshold of the mth hidden unit;
step S432: after the energy function is obtained, the joint probability distribution of all visible units and hidden units is calculated, and the following formula is used:
；
wherein D is all visible units and h is all hidden units; p (v, h) is the joint probability distribution of all visible and hidden units;
step S433: the activation probability of the kth 1 visible unit and the mth hidden unit of each RBM is calculated by the following formula:
；
；
in the method, in the process of the invention,is the activation probability of the kth 1 visible unit,is the activation probability of the mth hidden unit;
step S44: and carrying out weighted fusion on the LSTM layer output result and the DBN layer output result to generate a final prediction result.
By executing the operation, the problem that the characteristic extraction capability is weak and the self-adaptive learning cannot be carried out on the characteristics of input data to cause the weak performance of the model exists in a general monitoring model is solved.
Embodiment six, referring to fig. 1 and 5, based on the above embodiment, in step S5, the model parameter adjustment specifically includes the following:
step S51: initializing, initializing a parameter search space and n parameter positionsAnd a parameter corresponding fitness value, wherein I is a parameter index, J is a parameter dimension index, and the fitness value of the parameter is a model built based on the current positionMonitoring the accuracy;
step S52: and updating the position, wherein if the fitness value of the new position is higher than that of the original position, the position is updated, otherwise, the position is kept unchanged, and the formula used for updating the position is as follows:
；
in the method, in the process of the invention,is the updated position, LG J Is the optimal position in the J-th dimension, WZ rJ The position of the randomly selected r parameter on the J dimension, U () is a random number generation function obeying uniform distribution, GG is a global optimal position, T1 is the current iteration number, and T is the maximum iteration number; f (f) i 、f b And f g The current fitness value, the optimal fitness value of the experience of the individual and the global optimal fitness value are respectively;
step S53: globally judging, presetting an evaluation threshold, and if parameters with fitness values higher than the evaluation threshold exist, establishing an instrument operation monitoring model based on the parameters; if the maximum iteration times are exceeded, reinitializing the parameter position to seek parameters; otherwise, continuing to search for the parameters.
By executing the operation, the method and the device aim at the problems that the search space range is small and the global optimum and the local optimum cannot be judged in the parameter searching algorithm, and the method and the device enlarge the search range by moving the current iteration times to the local optimum and the global optimum and judge the local optimum and the global optimum based on the evaluation threshold and the maximum iteration times.
An embodiment seven, referring to fig. 1, based on the foregoing embodiment, in step S6, the instrument operation monitoring is to set up an instrument operation monitoring hybrid model based on searching the optimal parameters of the monitoring model in step S5, and when the monitoring accuracy of the model to the test set is higher than the accuracy threshold, the model is set up; the model receives the instrument operation signal and the operation parameter signal in real time, and based on the operation monitoring state of the output monitoring instrument, when the operation monitoring state is abnormal, early warning treatment is given.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
The invention and its embodiments have been described above with no limitation, and the actual construction is not limited to the embodiments of the invention as shown in the drawings. In summary, if one of ordinary skill in the art is informed by this disclosure, a structural manner and an embodiment similar to the technical solution should not be creatively devised without departing from the gist of the present invention.
Claims (7)
1. An operation monitoring method of an air concentration monitoring instrument is characterized in that: comprising the following steps:
step S1: receiving signals;
step S2: signal decomposition, namely performing frequency modulation based on Hilbert transformation and an extended Lagrangian equation, so as to define an objective function and complete high-precision signal decomposition;
step S3: parameter updating, searching an optimal solution based on an alternate direction multiplier method, ADMM optimization and Hermite symmetry simplification problem;
step S4: an instrument operation monitoring mixed model is established, low-frequency signal data characteristics are extracted based on a CNN layer design, input time sequence data are initially monitored by utilizing an LSTM layer design, and monitoring results of high-frequency signal data after signal decomposition are combined with a DBN layer design to be subjected to weighted fusion, so that a final monitoring result is output;
step S5: model parameter adjustment, namely moving to local optimum and global optimum based on the current iteration times, and judging global optimum based on an evaluation threshold and the maximum iteration times;
step S6: and (5) monitoring the operation of the instrument.
2. An air concentration monitoring instrument operation monitoring method according to claim 1, wherein: in step S3, the parameter updating updates the coefficient and frequency characteristic of each IMF to achieve the decomposition of the original signal, which specifically includes the following contents:
step S31: defining a solution, using an alternating direction multiplier method to search saddle points of an augmented lagrangian function, updating u in both directions based on an ADMM optimization method k And omega k The following iterative solution is obtained:
；
；
；
where n is the number of iterations, τ is the time step, and i1 and k are both the index of the IMF;
step S32: convergence conditions are defined using the following formula:
；
where ε is the convergence threshold;
step S33: solving an optimal solution, wherein the content comprises:
step S331: updating the modality, equating the sub-problem to the following minimization problem:
；
step S332: by using the hermite symmetry of the real signal, in the reconstructed fidelity term, the form of half-space integral to non-negative frequencies is written, and the first derivative is changed to zero to find the optimal solution of the problem, and the formula is as follows:
；
in the method, in the process of the invention,、/>and->Respectively f (omega), lambda (omega) and u i1 (ω) fourier transform, ω being a continuous frequency variable;
step S333: will omega k The optimal solution problem is equivalent to the following:
；
step S334: the optimal solution is expressed as follows:
；
step S335: the signal is finally divided into a high frequency signal and a low frequency signal based on a signal frequency threshold.
3. An air concentration monitoring instrument operation monitoring method according to claim 1, wherein: in step S2, the signal decomposition specifically includes the following:
step S21: predefined, for each IMF, i.e. the inner pulse function, a single-sided spectrum is obtained using the Hilbert transform, the estimated bandwidth is minimized by summing, and under constraints, the accumulation of each IMF is equal to the input signal f (t), using the following formula:
；
；
where f (t) is the original signal being decomposed, delta () is the dirac distribution, t is time, x is the convolution operator, u k Is the coefficient of the kth IMF, ω k Is the center frequency of the kth IMF, K represents the total number of IMFs, ∂ t Deriving t, j1 is an imaginary unit, subscript 2 is an L2 normal form, and superscript 2 is a squaring operation;
step S22: defining an extended Lagrange equation, converting a constrained variation problem into an unconstrained optimization problem, and based on a quadratic penalty term and a Lagrange multiplier, using the following formula:
；
where λ is the Lagrangian multiplier, α is a parameter that balances the relative weights between constraint terms and penalty terms in the objective function, and 〈 〉 is the inner product;
step S23: frequency modulation, namely mixing the frequency spectrum of the IMF with a modulation index adjusted to the corresponding estimated center frequency, and transferring the frequency spectrum to a baseband region; estimating the bandwidth of each IMF, i.e., the L2 parameter of the gradient square, using gaussian smoothing of the demodulated signal;
step S24: defining an objective function, estimating the coefficient and frequency characteristic of each IMF, thereby realizing the decomposition of the original signal, wherein the objective function is expressed as follows:
。
4. an air concentration monitoring instrument operation monitoring method according to claim 1, wherein:
in step S4, the instrument operation monitoring hybrid model is established by randomly dividing the signal data obtained in step S3 into a training set and a test set, and using the training set to train the model, the test set is used to test the performance of the model, and the model establishment specifically comprises the following steps:
step S41: CNN layer design, the CNN layer is used to extract the features of low frequency data, the low frequency data after signal decomposition is input into the CNN layer with 64×1×3 convolution kernel, the convolution kernel is used as the feature extractor, the process is described as follows:
；
in the method, in the process of the invention,is the value of the feature map j at time τ1, σ in layer l+1 R Is a ReLU function, +.>Is the bias value of the feature map j in the first layer, F l Is the number of feature maps in the first layer, f is the feature map index, p l Indicating the number of convolution kernels in layer i, p being the index of the convolution kernel position, +.>Is a value generated by convolving the feature map j in the first layer with a convolution kernel f;
step S42: the LSTM layer is designed, and the CNN layer inputs data as time sequence into the LSTM layer for carrying out after the preliminary feature extraction is completedThe architecture of the LSTM is predicted to consist of four gates, respectively the forget gate f t Update gate u t Input gate i t Output door o t And a memory cell C t By operating the gates, information is stored, written and read in the cell, the process is described as follows:
；
；
；
；
；
；
wherein W and b are respectively a weight matrix and a bias matrix related to a control gate, subscripts f, i, c and o respectively represent a forgetting gate, an input gate, a storage unit and an output gate, t and t-1 are time states, h is a hidden state, x is an input data set, and tanh is a hyperbolic tangent function;
step S43: the DBN layer design, the DBN is composed of a plurality of limited Boltzmann machines, each RBM comprises a visible unit and a hidden unit, wherein the visible unit is an input layer, the hidden unit is a characteristic detection layer, three hidden layer DBN networks are adopted to predict high-frequency signal data after signal decomposition processing, neurons among the DBN layers are independent and unconnected, and the visible unit of each RBM is connected with the hidden unit through weights, and the content comprises:
step S431: the energy function E is defined using the formula:
；
in the formula, v k1 Is the kth 1 visible unit, h m Is the mth hidden unit, ω mk1 Is v k1 And h m Weight of connection between b k1 Is the threshold of the kth 1 visible unit, c m Is the threshold of the mth hidden unit;
step S432: after the energy function is obtained, the joint probability distribution of all visible units and hidden units is calculated, and the following formula is used:
；
wherein D is all visible units and h is all hidden units; p (v, h) is the joint probability distribution of all visible and hidden units;
step S433: the activation probability of the kth 1 visible unit and the mth hidden unit of each RBM is calculated by the following formula:
；
；
in the method, in the process of the invention,is the activation probability of the kth 1 visible unit,/->Is the activation probability of the mth hidden unit;
step S44: and carrying out weighted fusion on the LSTM layer output result and the DBN layer output result to generate a final prediction result.
5. An air concentration monitoring instrument operation monitoring method according to claim 1, wherein: in step S5, the model parameter adjustment specifically includes the following:
step S51: initializing, initializing a parameter search space and n parameter positionsThe parameter corresponding fitness value is a model prediction accuracy established based on the current position;
step S52: and updating the position, wherein if the fitness value of the new position is higher than that of the original position, the position is updated, otherwise, the position is kept unchanged, and the formula used for updating the position is as follows:
；
in the method, in the process of the invention,is the updated position, LG J Is the optimal position in the J-th dimension, WZ rJ The position of the randomly selected r parameter on the J dimension, U () is a random number generation function obeying uniform distribution, GG is a global optimal position, T1 is the current iteration number, and T is the maximum iteration number; f (f) i 、f b And f g The current fitness value, the optimal fitness value of the experience of the individual and the global optimal fitness value are respectively;
step S53: globally judging, presetting an evaluation threshold, and if parameters with the fitness value higher than the evaluation threshold exist, establishing a fire grate vibration prediction model based on the parameters; if the maximum iteration times are exceeded, reinitializing the parameter position to seek parameters; otherwise, continuing to search for the parameters.
6. An air concentration monitoring instrument operation monitoring method according to claim 1, wherein: in step S1, the signal receiving is to receive an equipment operation state signal, an equipment sensor output signal, a noise sensor output signal, a vibration sensor output signal, an energy consumption monitoring signal and an equipment operation state corresponding to data; the running state of the equipment is used as a data tag.
7. An air concentration monitoring instrument operation monitoring method according to claim 1, wherein: in step S6, the instrument operation monitoring is to establish an instrument operation monitoring hybrid model based on the best parameters of the monitoring model found in step S5, and when the monitoring accuracy of the model to the test set is higher than the accuracy threshold, the model establishment is completed; the model receives the instrument operation signal and the operation parameter signal in real time, and based on the operation monitoring state of the output monitoring instrument, when the operation monitoring state is abnormal, early warning treatment is given.
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