Air conditioning unit fault detection method based on non-integer order polynomial model
By introducing a network architecture of non-integer polynomial layer in air conditioner unit fault diagnosis, the existing model has solved the problem of insufficient computing efficiency and generalization capabilities in air conditioner unit fault diagnosis, and achieved high accuracy and low training time fault detection effect.
Patent Information
- Application Number
- CN202411452276.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-17
- Publication Date
- 2025-03-11
AI Technical Summary
The existing non-integer order model is difficult to effectively apply to actual fault diagnosis regression and classification problems in air conditioning unit fault diagnosis, and the training process is insufficient, especially in application scenarios with high real-time requirements, the computing efficiency and generalization capabilities are insufficient.
The air-conditioning unit fault detection method based on non-integer order polynomial model is adopted. By introducing a network architecture of non-integer order polynomial layer, the model's fitting ability to complex nonlinear data is enhanced, and overfitting is reduced while maintaining the model's accuracy. The method includes obtaining fault feature data, building a non-integer polynomial network model, performing data normalization and model training, and ultimately implementing fault detection.
It improves the accuracy and calculation efficiency of air conditioning unit fault detection, reduces overfitting, enhances the generalization ability of the model, and achieves 100% test set accuracy, which is suitable for data sets with highly nonlinear features.
Smart Images
Figure CN119598308A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of machine learning and artificial intelligence, and in particular relates to an air conditioning unit fault detection method based on a non-integer order polynomial model. Background Art
[0002] In the field of fault diagnosis of air-conditioning units, traditional machine learning and artificial intelligence technologies are often used to identify potential fault modes from a large amount of operating data. These methods include linear models, support vector machines, and neural networks, which can indeed provide effective diagnostic results in certain application scenarios. However, when it comes to high-dimensional nonlinear data analysis of complex systems such as air handling units (AHUs) in air-conditioning units, these traditional models often encounter problems of insufficient model fitting ability or overfitting. Linear models have limited ability to handle nonlinear features and are difficult to capture the complex relationships behind faults. Although neural networks can theoretically solve more nonlinear problems, they are limited by their complex network architecture, time-consuming training, and easy to fall into local optimality. In recent years, non-integer order models, as a new research direction, have provided new ideas for fault diagnosis of air-conditioning units. Unlike traditional integer order models, non-integer order polynomial models can more flexibly approximate complex nonlinear relationships by introducing non-integer power terms, so that they can theoretically better handle fault diagnosis problems of air-conditioning unit components such as AHUs. However, most of the existing non-integer order models are still in the theoretical research stage. How to effectively apply these models to actual fault diagnosis regression and classification problems and optimize their training process is still a technical problem that needs to be solved. Especially in an application scenario such as air-conditioning units, which has extremely high real-time requirements, the computational efficiency and generalization ability of the model are particularly important. Therefore, developing a model that can quickly and accurately diagnose faults and adapt to different operating conditions is of great significance to improving the reliability and energy efficiency of air-conditioning systems. Summary of the invention
[0003] Purpose of the invention: The purpose of the present invention is to provide an air conditioning unit fault detection method based on a non-integer order polynomial model. By introducing a network architecture with a non-integer order polynomial layer, the model's ability to fit complex nonlinear data is enhanced, and overfitting is reduced while maintaining model accuracy. This method can be widely used in various data regression and classification scenarios, and is particularly suitable for data sets with highly nonlinear features.
[0004] Technical solution: The present invention provides a method for detecting air conditioner unit faults based on a non-integer order polynomial model, comprising the following steps:
[0005] Step 1: Obtain fault characteristic data of the target air-conditioning unit;
[0006] Step 2: divide the fault feature data into training set and test set;
[0007] Step 3, construct a non-integer order polynomial network NIOPN model;
[0008] Step 4: Normalize the input data of the NIOPN model so that the data is within the domain of the logarithmic function;
[0009] Step 5: Train the model based on the gradient descent and Adam optimization algorithms, calculate the gradient of the loss function to the model parameters through the test set based on the back propagation algorithm, and update the model parameters to obtain the trained NIOPN model;
[0010] Step 6: Implement fault detection of the air-conditioning unit based on the trained NIOPN model.
[0011] Furthermore, step 1 is specifically as follows: obtaining fault characteristics to realize fault detection of the air-conditioning unit; obtaining the readings of various sensors of the cooling coil and the supply fan of the main equipment of the air-conditioning unit and the equipment parameters including: the flow rate Mchw of chilled water, the supply water temperature Tchw,sup of chilled water, the return water temperature Tchw,rn of chilled water, the mixed air flow rate Ma,mix, the supply air flow rate Ma,sup, the mixed air temperature Ta,mix, the supply air temperature Ta,sup, the power Qsf of the supply air fan, the pressure drop ΔPsf,des of the supply air fan, the set value Tsup,spt of the supply air temperature and the design value Ma,des of the supply air volume, removing missing values and constant values, and the remaining characteristics are used as fault characteristics.
[0012] Furthermore, step 3 specifically includes the following steps:
[0013] Step 3.1, constructing a non-integer order polynomial network NIOPN model, wherein the NIOPN model includes an input layer, a plurality of hidden layers and an output layer;
[0014] Step 3.2: In order to convert the outputs of the previous layers into polynomials of non-integer order, it is necessary to cancel the ln function used previously and add an exp layer;
[0015] Step 3.3. Add a fully connected layer and a softmax layer to calculate the output vector.
[0016] Further, in step 3.1, the hidden layer is composed of a non-integer order polynomial;
[0017]
[0018] in: Represents the input vector of the network at time t;
[0019]
[0020] Among them, the output vector of the ln function at time t is L(t), and then multiplied by the polynomial weight matrix Ω;
[0021]
[0022] Ω i =[ω 1,i ω 2,i … ω N,i ] T
[0023] L(t)=[l1 l2 … l N ] T
[0024] Among them, ω N,i represents the Nth weight in the i-th column of the polynomial weight matrix Ω, l N Represents the Nth element of the output vector of the ln function at time t;
[0025] Furthermore, step 3.2 is specifically as follows: the exp layer is as follows:
[0026] E(t)=exp(A(t))
[0027] e i (t) = exp(a i (t)),i=1,…,N
[0028]
[0029] Among them, A(t) represents the input vector of the exp layer at time t, a i (t) represents the i-th element of A(t), and the weight is used as the monomial coefficient to obtain a rich polynomial of different monomial combinations. Let the output E of the exp layer be multiplied by the weight matrix W j , we can get the polynomial B(t) obtained by combining different monomials; the number of monomials H is a hyperparameter; set H = c·N, where c represents an arbitrary constant and N represents the input vector dimension.
[0030] Furthermore, step 3.3 is as follows: To match two different dimensions, a fully connected layer is added, and the network output y is calculated according to the following formula:
[0031]
[0032] in
[0033] Λ k =[λ 1,k λ2,k … λ H,k ] T
[0034] B(t)=[B1(t) B2(t) … B H (t)] T
[0035] Among them, Λ k is the weight vector, the dimension of B(t) is H ≥ N, and the dimension of Y(t) is M. To further achieve classification, a softmax layer is added after the fully connected layer, that is,
[0036] P(t)=softmax(Y(t))
[0037] in
[0038] Y(t)=[y1(t) y2(t) … y M (t)] T
[0039] p(t)=[p1(t) p2(t) … p M (t)] T
[0040] Among them, the output vector is Y(t) and the output probability vector is P(t).
[0041] Furthermore, step 4 is as follows: normalize the input data so that the data is within the domain of the logarithmic function; the input X(t) of NIOPN is N-dimensional, that is, The output Y(t) is M-dimensional, that is Where M is the number of categories; the weight is used as the order, and the non-integer order of the polynomial is dynamically adjusted during model training to obtain the optimal order; using the properties of the ln function, ln(x w )=wln(x), let the input x pass through the ln function and then multiply by the weight w to obtain a non-integer order; before inputting the feature vector into NIOPN, the input X is first normalized with an offset. For the input data set {(X1,Y1),(X2,Y2),...,(X K ,Y K )}, k = 1, 2, ..., K, calculate the maximum value of all samples in each dimension max i (X) and minimum value min i (X), i = 1, 2, ..., K, and normalized by the following formula:
[0042]
[0043] Among them, the input vector of the network at time t is X(t); the normalized input vector is The normalized offset parameter is s, and the normalized input is obtained through the ln function.
[0044] Furthermore, step 5 is as follows: train the model using gradient descent and Adam optimization algorithms, calculate the gradient of the loss function to the model parameters through the back propagation algorithm, and update the model parameters; use the cross entropy loss function to measure the gap between the probability distribution of the model output and the target distribution. The cross entropy loss function is defined as:
[0045]
[0046] Where L(θ) is the loss function, which is a function of the model parameters θ. M is the number of classes. is the probability that the model predicts that the sample belongs to the kth category. k is the probability that the sample actually belongs to the kth category.
[0047] The AdamW optimization algorithm is used to introduce weight decay, and the model complexity is controlled through L2 regularization to avoid overfitting problems. The specific update rules are as follows:
[0048]
[0049] Among them, η is the learning rate, m t and v t They represent the first-order and second-order momentum of the gradient, ∈ is a small constant to prevent division by zero; the role of L2 regularization is to penalize excessive parameters by adding a regularization term to the loss function:
[0050]
[0051] Among them, L total represents the total loss function, α is the regularization coefficient, which controls the strength of the regularization term, and θ j Represents the jth parameter.
[0052] Furthermore, in step 5, the model parameters include the number of monomials c, the initial learning rate η, the maximum number of iterations l and the normalized offset parameter s.
[0053] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:
[0054] 1. Enhanced fitting capability: By introducing a network architecture with non-integer-order polynomial layers, the NIOPN model can more flexibly approximate complex nonlinear relationships, thereby enhancing the fitting capability of air-conditioning unit fault feature data.
[0055] 2. Reduce overfitting: While maintaining model accuracy, the NIOPN model effectively reduces overfitting and improves the generalization ability of the model through L2 regularization and the weight decay mechanism of the AdamW optimization algorithm.
[0056] 3. Improved diagnostic accuracy: The NIOPN model achieved 100% accuracy on the test set, showing high diagnostic accuracy in air conditioning unit fault detection.
[0057] 4. Training efficiency: While maintaining high accuracy, the NIOPN model only takes 5.0829 seconds on average to train, which is much shorter than the 19.9969 seconds of the Residual Multidimensional Taylor Network (ResMTN) model with the same accuracy, showing higher training efficiency.
[0058] 5. Wide applicability: This method can be widely used in various data regression and classification scenarios, especially for data sets with highly nonlinear features. It is not limited to air-conditioning unit fault detection, but can also be used for complex nonlinear problems in other fields.
[0059] 6. Dynamically adjust the polynomial order: During model training, NIOPN can dynamically adjust the non-integer order of the polynomial to obtain the optimal order, which enables the model to better adapt to the characteristics of the data. BRIEF DESCRIPTION OF THE DRAWINGS
[0060] Figure 1 Schematic diagram of the overall structure of the non-integer order polynomial network of the present invention;
[0061] Figure 2 A diagram of the framework for solving classification problems for non-integer-order polynomial networks;
[0062] Figure 3 The accuracy comparison chart of NIOPN model with random forest (RF), support vector machine (SVM), K-nearest neighbor (K-NN), and residual multidimensional Taylor network (ResMTN);
[0063] Figure 4 The training time comparison chart of the NIOPN model with random forest (RF), support vector machine (SVM), K-nearest neighbor (K-NN), and residual multidimensional Taylor network (ResMTN). DETAILED DESCRIPTION
[0064] The technical solution of the present invention is further described below in conjunction with the accompanying drawings. In order to solve the problems existing in the prior art, the present invention proposes a regression and classification method based on a non-integer order polynomial network (NIOPN). By introducing a network architecture with a non-integer order polynomial layer, the model's ability to fit complex nonlinear data is enhanced, and overfitting is reduced while maintaining the accuracy of the model. This method can be widely used in various data regression and classification scenarios, and is particularly suitable for data sets with highly nonlinear features.
[0065] The core of the present invention is to propose a regression and classification method based on a non-integer order polynomial network, which is characterized by comprising the following steps:
[0066] Step A: construct a non-integer order polynomial network (NIOPN) model, wherein the NIOPN model includes an input layer, a plurality of hidden layers and an output layer, wherein the hidden layer is composed of a non-integer order polynomial, and the ln function is as follows;
[0067]
[0068] in
[0069]
[0070] The output vector of the ln function at time t is L(t). Then, it is multiplied by the polynomial weight matrix Ω;
[0071]
[0072] with
[0073] Ω i =[ω 1,i ω 2,i … ω N,i ] T
[0074] L(t)=[l1 l2 … l N ] T
[0075] In order to convert the outputs of the previous layers into polynomials of non-integer order, it is necessary to cancel out the ln function used previously. Therefore, it is necessary to add an exp layer, as shown below:
[0076] E(t)=exp(A(t))
[0077] with
[0078] e i (t) = exp(a i (t)),i=1,…,N
[0079] After that, in order to obtain a rich polynomial with different monomial combinations, the weights need to be used as monomial coefficients, and the output E of the exp layer is multiplied by the weight matrix W j , we can get the polynomial B(t) obtained by combining different monomials. The number of monomials H is a hyperparameter. When H is small, the fitting accuracy may be low. However, if H is too large, it will lead to overfitting. Here we set H = c·N. Among them, c is set to 3 according to the experimental results. That is:
[0080] B(t)=[B1(t),B2(t),…,B H (t)], H=c·N
[0081] with
[0082]
[0083] with
[0084]
[0085] E(t)=[e1 e2 … e N ] T
[0086] Among them, W j is the weight matrix corresponding to the jth monomial, the dimension of E(t) is N, and the dimension of Y(t) is H. Because the output dimension of the polynomial layer is H, and the number of categories is M.
[0087] In order to match these two different dimensions, a fully connected layer needs to be added. The network output y is calculated according to the following formula:
[0088]
[0089] in
[0090] Λ k =[λ 1,k λ 2,k … λ H,k ] T
[0091] B(t)=[B1(t) B2(t) … B H (t)] T
[0092] Among them, Λ k is the weight vector, the dimension of B(t) is H ≥ N, and the dimension of Y(t) is M. In order to further achieve classification, a softmax layer is added after the fully connected layer, that is,
[0093] P(t)=softmax(Y(t))
[0094] in
[0095] Y(t)=[y1(t) y2(t) …y M (t)] T
[0096] P(t)=[p1(t) p2(t) … P M (t)] T
[0097] Among them, the output vector is Y(t), and the output probability vector is P(t). Finally, the purpose of fault classification is achieved.
[0098] Step B: Normalize the input data to ensure that the data is within the domain of the logarithmic function;
[0099] The input X(t) of NIOPN is N-dimensional, that is, The output Y(t) is M-dimensional, that is Where M is the number of categories. In order to dynamically adjust the non-integer order of the polynomial during model training and obtain the optimal order, the weight needs to be used as the order. To achieve this goal, using the properties of the ln function, ln(x w )=wln(x), let the input x pass through the ln function and then multiply it by the weight w to get a non-integer order. Since the ln function is calculated for the input X, when the input X is negative or close to 0, it will make it impossible to take the logarithm or cause the gradient to disappear. To solve this problem, before inputting the feature vector into NIOPN, the input X is first normalized with an offset. For the input data set {(X1,Y1),(X2,Y2),...,(X K ,Y K )}, k = 1, 2, ..., K, calculate the maximum value of all samples in each dimension max i (X) and minimum value min i (X), i = 1, 2, ..., K. And normalized by the following formula:
[0100]
[0101] Among them, the input vector of the network at time t is X(t); the normalized input vector is The normalized offset parameter is s. The normalized input is obtained by the ln function.
[0102] Step C: Use gradient descent and AdamW optimization algorithms to train the model, calculate the gradient of the loss function to the model parameters through the back propagation algorithm, and update the model parameters;
[0103] The core task of NIOPN is to approximate complex nonlinear functions and is suitable for classification tasks. Its parameters mainly include: Polynomial coefficients: the weight of each polynomial term, which is used to control the contribution of the polynomial in different dimensions. In addition, compared with traditional integer-order polynomials, NIOPN enhances the expressiveness of the model by introducing non-integer orders, which need to be optimized through learning. For classification tasks, the loss function uses the cross-entropy loss function to minimize the difference between the category distribution predicted by the model and the true category distribution. The cross-entropy loss function is a commonly used loss function in classification problems. It can measure the gap between the probability distribution output by the model and the target distribution. The cross-entropy loss function is defined as:
[0104]
[0105] By minimizing the cross entropy loss function, the model is able to learn better category prediction probabilities, thereby improving the accuracy of classification tasks.
[0106] The parameters of non-integer order polynomial networks, including the coefficients and orders of each term, can be learned and adjusted through optimization algorithms. In order to efficiently update the model parameters, the back propagation algorithm combined with the AdamW optimization algorithm is used to adjust the weights and order of the network. The basic principle of back propagation is to calculate the gradient of the loss function to the parameters of each layer through the chain rule, and update the parameters layer by layer from the output layer to the input layer. For a multi-layer structure such as NIOPN, the back propagation algorithm can adjust the weights and polynomial order of the model by calculating the derivative of the error to the parameters at each layer. The AdamW optimization algorithm is a gradient-based adaptive learning rate optimization method. Its core idea is to adjust the learning rate by combining the first-order and second-order momentum estimates when each parameter is updated. The characteristic of AdamW is the introduction of weight decay, which can effectively control the complexity of the model through L2 regularization, thereby avoiding the problem of overfitting. The specific update rules are as follows:
[0107]
[0108] Among them, η is the learning rate, m t and v t denote the first-order and second-order momentum of the gradient, respectively, and ∈ is a small constant to prevent division by zero. In addition, the L2 regularization term is introduced to ensure that the model parameters are not too large and cause overfitting. The role of L2 regularization is to penalize excessive parameters by adding a regularization term to the loss function:
[0109]
[0110] Among them, α is the regularization coefficient, which controls the strength of the regularization term.
[0111] The hyperparameters in model training include the number of monomials c, the initial learning rate η, the maximum number of iterations l, and the normalization offset parameter s. Among them, the number of polynomial terms c in the NIOPN model is an important hyperparameter that determines the complexity and expressiveness of the model. Choosing a suitable c value can strike a balance between the complexity of the model and the difficulty of training. The learning rate η determines the step size of each parameter update. A learning rate that is too large may cause the model to fail to converge, while a learning rate that is too small may cause the model to train too slowly or even fall into a local optimum. We determined the appropriate initial learning rate η through experiments, and combined it with the adaptive adjustment mechanism of the AdamW optimization algorithm to further improve the convergence speed of the model. The number of iterations determines the number of training rounds. Usually, too many iterations will lead to overfitting, while insufficient iterations may cause the model to fail to learn fully. The appropriate maximum number of iterations l was determined through cross-validation to ensure that the model can achieve the best performance. In the process of normalizing the training data, the normalization offset parameter s is used to scale the features to a uniform range. Reasonable normalization can make the contribution of different features to the model more balanced, thereby improving the training effect. Appropriate hyperparameters can be determined through experiments.
[0112] like Figure 3 As shown in the figure, the accuracy of the NIOPN model is compared with that of Random Forest (RF), Support Vector Machine (SVM), K-Nearest Neighbor (K-NN), and Residual Multidimensional Taylor Network (ResMTN). The accuracy of the NIOPN model reached 100% on the test set, which is the same as ResMTN and better than other models.
[0113] like Figure 4 As shown in the figure, the training time of the NIOPN model is compared with that of the random forest (RF), support vector machine (SVM), K-nearest neighbor (K-NN), and residual multidimensional Taylor network (ResMTN). While maintaining high accuracy, the NIOPN model only takes 5.0829 seconds on average to train, which is much shorter than the 19.9969 seconds of the ResMTN model with the same accuracy.
Claims
1. A method for detecting air conditioner unit faults based on a non-integer order polynomial model, characterized in that: The steps include: Step 1: Obtain fault characteristic data of the target air-conditioning unit; Step 2: divide the fault feature data into training set and test set; Step 3, construct a non-integer order polynomial network NIOPN model; Step 4: Normalize the input data of the NIOPN model so that the data is within the domain of the logarithmic function; Step 5: Train the model based on the gradient descent and Adam optimization algorithms, calculate the gradient of the loss function to the model parameters through the test set based on the back propagation algorithm, and update the model parameters to obtain the trained NIOPN model; Step 6: Implement fault detection of the air-conditioning unit based on the trained NIOPN model.
2. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 1, characterized in that: Step 1 is specifically as follows: obtaining fault features to realize fault detection of the air-conditioning unit; obtaining the readings of various sensors of the main equipment cooling coil and supply fan of the air-conditioning unit and the equipment parameters including: chilled water flow Mchw, chilled water supply temperature Tchw,sup, chilled water return temperature Tchw,rn, mixed air flow Ma,mix, supply air flow Ma,sup, mixed air temperature Ta,mix, supply air temperature Ta,sup, supply air fan power Qsf, supply air fan pressure drop ΔPsf,des, supply air temperature set value Tsup,spt and supply air volume design value Ma,des, removing missing values and constant values, and the remaining features are used as fault features.
3. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1, constructing a non-integer order polynomial network NIOPN model, wherein the NIOPN model includes an input layer, a plurality of hidden layers and an output layer; Step 3.2: In order to convert the outputs of the previous layers into polynomials of non-integer order, it is necessary to cancel the ln function used previously and add an exp layer; Step 3.
3. Add a fully connected layer and a softmax layer to calculate the output vector.
4. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 3, characterized in that: In step 3.1, the hidden layer is composed of a non-integer order polynomial; in: Represents the input vector of the network at time t; Among them, the output vector of the ln function at time t is L(t), and then multiplied by the polynomial weight matrix Ω; Oh i =[ω 1，i oh 2，i … oh N，i ] T L(t)=[l1 l2 … l N ] T Among them, ω N，i represents the Nth weight in the i-th column of the polynomial weight matrix Ω, l N Represents the Nth element of the output vector of the ln function at time t.
5. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 3, characterized in that: Step 3.2 is as follows: the exp layer is as follows: E(t)=exp(A(t)) e i (t)=exp(a i (t)),i=1,...,N Among them, A(t) represents the input vector of the exp layer at time t, a i (t) represents the i-th element of A(t), and the weight is used as the monomial coefficient to obtain the polynomial of different monomial combinations, so that the output E of the exp layer is multiplied by the weight matrix W j , we can get the polynomial B(t) obtained by combining different monomials; the number of monomials H is a hyperparameter; set H = c·N, where c represents an arbitrary constant and N represents the dimension of the network input vector.
6. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 3, characterized in that: Step 3.4 is as follows: To match two different dimensions, add a fully connected layer, and the network output y is calculated according to the following formula: in L k =[λ 1，k l 2，k … l H，k ] T B(t)=[B1(t) B2(t) … B H (t)] T Among them, Λ k is the weight vector, the dimension of B(t) is H ≥ N, and the dimension of Y(t) is M. To further achieve classification, a softmax layer is added after the fully connected layer, that is, P(t)=softmax(Y(t)) in Y(t)=[y1(t) y2(t) … y M (t)] T P(t)=[p1(t) p2(t) … p M (t)] T Among them, the output vector is Y(t) and the output probability vector is P(t).
7. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 1, characterized in that: Step 4 is as follows: normalize the input data so that the data is within the domain of the logarithmic function; the input X(t) of NIOPN is N-dimensional, that is, The output Y(t) is M-dimensional, that is Where M is the number of categories; the weight is used as the order, and the non-integer order of the polynomial is dynamically adjusted during model training to obtain the optimal order; using the properties of the ln function, ln(x w )=wln(x), let the input x pass through the ln function and then multiply by the weight w to obtain a non-integer order; before inputting the feature vector into NIOPN, the input X is first normalized with an offset. For the input data set {(X1, Y1), (X2, Y2), ..., (X K ,Y K )}, k = 1, 2, ..., K, calculate the maximum value of all samples in each dimension max i (X) and minimum value min i (X), i = 1, 2, ..., K, and normalized by the following formula: Among them, the input vector of the network at time t is X(t); the normalized input vector is The normalized offset parameter is s, and the normalized input is obtained through the ln function.
8. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 1, characterized in that: Step 5 is as follows: use the gradient descent and Adam optimization algorithms to train the model, calculate the gradient of the loss function to the model parameters through the back propagation algorithm, and update the model parameters; use the cross entropy loss function to measure the gap between the probability distribution of the model output and the target distribution. The cross entropy loss function is defined as: Where L(θ) is the loss function, which is a function of the model parameters θ, M is the number of categories, is the probability that the model predicts that the sample belongs to the kth category, p k is the probability that the sample actually belongs to the kth category; The AdamW optimization algorithm is used to introduce weight decay, and the model complexity is controlled through L2 regularization to avoid overfitting problems. The specific update rules are as follows: Among them, η is the learning rate, m t and v t They represent the first-order and second-order momentum of the gradient, ∈ is a small constant to prevent division by zero; the role of L2 regularization is to penalize excessive parameters by adding a regularization term to the loss function: Among them, L total represents the total loss function, α is the regularization coefficient, which controls the strength of the regularization term, and θ j Represents the jth parameter.
9. The method for detecting air conditioner unit faults based on a non-integer order polynomial model according to claim 1, characterized in that: In step 5, the model parameters include the number of monomials c, the initial learning rate η, the maximum number of iterations l and the normalized offset parameter s.