Water work order quantity prediction method based on diffusion model

Abstract

The invention provides a water work order quantity prediction method based on a diffusion model, and belongs to the field of time sequence prediction, and the method comprises the steps: obtaining an aggregation sample through a work order detail data set; converting acceptance content fields and work order category fields in the L groups of aggregation samples into work order detail word embedding; inputting the real values of the work order quantity prediction sequences into a diffuser to obtain K noisy work order quantity prediction sequences, taking the noisy work order quantity prediction sequences as the current frame work order quantity prediction sequence to obtain noisy hidden layer prediction feature vectors, and extracting historical sequence feature hidden vectors by using an encoder of a conditional network, embedding and splicing the work order detail words, fusing the noisy hidden layer prediction feature vectors to generate a next frame of work order quantity prediction sequence, and repeating the step to obtain a final restored work order quantity prediction sequence; and calculating a mean square error loss function, updating network parameters, and obtaining the next L groups of aggregation samples and training samples. According to the method, overfitting can be avoided, and the prediction length and precision are improved.

Description

Technical Field

[0001] This invention belongs to the field of time series forecasting, specifically relating to a method for forecasting waterworks work order volume based on a diffusion model. Background Technology

[0002] With the popularization of big data application technology, water companies use various historical production and management data to train machine learning or deep learning models, and make data predictions based on them. The data prediction results are then used to guide the company's work deployment, personnel scheduling, and resource allocation, resulting in good economic benefits.

[0003] However, existing deep learning methods still face some challenges in application: 1) Most enterprises have a short digitization time and have accumulated relatively little historical data, making the model prone to overfitting; 2) In the prediction of non-stationary long sequences, it is impossible to balance the length and accuracy of the prediction. Summary of the Invention

[0004] The main objective of this invention is to propose a method for predicting waterworks work orders based on a diffusion model. This method avoids the overfitting phenomenon that is prone to occur in deep learning models under conditions of few samples, and improves the generalization ability of the model. It can still provide good prediction length and accuracy in non-stationary time series processing and emergency event response scenarios.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for predicting waterworks work order volume based on a diffusion model includes the following steps:

[0007] Step S1: Obtain the work order volume dataset and the work order details dataset. Each record in the work order volume dataset has a time period field. Based on the time period field of each record in the work order volume dataset, the work order details dataset is grouped and aggregated by hour to obtain multiple aggregated samples.

[0008] Step S2: Select L groups of aggregated samples sequentially from the work order details dataset, and input the acceptance content field and work order category field from each group of aggregated samples into the Chinese BERT module of the conditional network to convert them into work order details word embeddings;

[0009] Step S3: Obtain training samples based on the work order volume dataset. The training samples include historical work order volume sequences, actual values ​​of predicted work order volume sequences, and sequences of temperature, holiday information, and global time information. Input the actual values ​​of the predicted work order volume sequences into the diffuser and add noise in K steps until the actual values ​​of the predicted work order volume sequences become Gaussian noise. After adding noise in the kth step, a noisy predicted work order volume sequence is obtained. k=1,2,…,K This serves as a label for the current training sample.

[0010] Step S4: Add noise to the noisy work order quantity prediction sequence obtained in step k=K. The current frame work order quantity prediction sequence is input into the encoder of the diffusion denoising network to obtain the noisy hidden layer prediction feature vector. The historical sequence of work order quantity, temperature, holiday information and global time information sequence of the training sample are input into the encoder of the conditional network to extract the historical sequence feature hidden vector. The historical sequence feature hidden vector is concatenated with the work order detail word embedding. The concatenation result is fused with the noisy hidden layer prediction feature vector and input into the decoder of the diffusion denoising network. The next frame work order quantity prediction sequence is generated by weighting the current frame work order quantity prediction sequence, the decoder output and the noise random value. The next frame work order quantity prediction sequence is used as the current frame work order quantity prediction sequence and this step is repeated to obtain the final restored work order quantity prediction sequence.

[0011] Step S5: Minimize the mean squared error loss function between the final restored work order quantity prediction sequence and the actual value of the work order quantity prediction sequence, and update the parameters of the diffusion denoising network and the conditional network; proceed to step S2 to select the next L groups of aggregated samples, and obtain the next training sample in step S3, until a set number of training samples are used to obtain the trained prediction model.

[0012] Furthermore, in step S1, the work order volume dataset is divided into a work order volume training set, a work order volume validation set, and a work order volume test set. In step S3, L+H records are obtained from the work order volume training set using a sliding window method to obtain the training sample. The first L records in the training sample are used as the historical sequence of work order volume, and the last H records are used as the true values ​​of the predicted sequence of work order volume. Based on the first L records, historical L temperature, holiday information, and global time information sequences are obtained.

[0013] Furthermore, in step S3, the noise addition process is represented as follows: ,in, This is the cumulative noise attenuation coefficient. The predicted sequence of work order volume for the current sample is the true value. It is Gaussian noise.

[0014] Furthermore, in step S4, the encoder of the conditional network is based on the formula... Extracting latent vectors of historical sequence features According to the formula Hidden vectors of historical sequence features The keywords are then combined with the embedded keywords in the work order details. Indicates self-attention, This represents the historical sequence of work orders for the current training sample. This represents the sequence of temperature, holiday information, and global time information for the current training sample. This represents a linear fully connected layer. This indicates that backpropagation has stopped. Indicates splicing, This represents the conditional latent vector of the current training sample.

[0015] Furthermore, in step S4, the encoder of the diffusion denoising network is configured according to the formula... Obtain the noisy hidden layer predicted feature vector ,in, , , This represents the normalization layer of the encoder in a diffusion denoising network. For the encoder feedforward layer of the diffusion denoising network, This represents the output of the l-th sublayer of the encoder in the diffusion denoising network. This represents the output of the second sub-layer of the encoder in the diffusion denoising network.

[0016] Furthermore, in step S4, the next frame work order quantity prediction sequence According to the formula Calculate, where, This is the cumulative noise attenuation coefficient. The noise intensity is the value added at step k. , Gaussian noise is added when adding noise in step k. standard deviation This is the predicted sequence of work order volume for the current frame. The next frame prediction sequence is the decoder output of the diffusion denoising network.

[0017] Furthermore, in step S3, the global time information includes hourly, daily, weekly, and monthly codes, and the specific values ​​corresponding to the hourly, daily, weekly, and monthly codes are obtained from the L+H records truncated by the sliding window in the work order training set.

[0018] Furthermore, in step S5, the mean squared error loss function is expressed as: , This is the final predicted sequence of work order volume corresponding to the current sample. This represents the expected mean square loss of each noisy sequence prediction obtained from the current frame work order quantity prediction sequence. This indicates the data distribution that the currently predicted time series samples follow.

[0019] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0020] This invention first acquires a work order volume dataset and a work order details dataset. Each record in the work order volume dataset has a time period field. The work order details dataset is then grouped and aggregated by hour according to the time period field of each record in the work order volume dataset, resulting in multiple aggregated samples. Next, L aggregated samples are selected sequentially from the work order details dataset. The acceptance content field and work order category field from each aggregated sample are input into the Chinese BERT module of the conditional network to convert them into work order details word embeddings. Then, training samples are obtained based on the work order volume dataset. The training samples include historical work order volume sequences, actual values ​​of predicted work order volume sequences, and sequences of temperature, holiday information, and global time information. The actual values ​​of the predicted work order volume sequences are input into a diffuser, and noise is added in K steps until the actual value of the predicted work order volume sequences is Gaussian noise. After adding noise in the k-th step, a noisy predicted work order volume sequence is obtained. The noisy work order quantity prediction sequence obtained after adding noise at step k=K is... The current frame's work order quantity prediction sequence is input into the encoder of the denoising network to obtain a noisy hidden layer prediction feature vector. The historical work order quantity sequence, temperature, holiday information, and global time information sequence of the training samples are input into the encoder of the conditional network to extract historical sequence features. These historical sequence features are then concatenated with the work order detail word embeddings. The concatenated result, fused with the noisy hidden layer prediction feature vector, is input into the decoder of the diffusion denoising network. The next frame's work order quantity prediction sequence is generated by weighting the current frame's work order quantity prediction sequence, the decoder output, and random noise values. This next frame's work order quantity prediction sequence is used as the current frame's work order quantity prediction sequence, and this step is repeated to obtain the final restored work order quantity prediction sequence. Finally, the final restored work order quantity prediction sequence is constructed. The mean squared error loss function between the predicted work order quantity sequence and the actual value of the predicted work order quantity sequence is used to update the parameters of the denoising network and the conditional network to minimize the mean squared error loss function, thereby achieving the prediction of waterworks work order quantity. In the process, noise is gradually added to the actual value of the predicted work order quantity sequence to cover the entire space of historical sequence data distribution, and then the predicted sequence data distribution is fitted by reverse denoising. This enables a more accurate fit to global trends and non-stationary local drastic fluctuations under conditions with few samples, effectively reducing the risk of overfitting. Furthermore, the use of conditional constraints enhances the initiative and accuracy of the diffusion model prediction, enabling simultaneous improvement in prediction length and prediction accuracy, especially in the response to emergencies. Attached Figure Description

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Figure 1 This is a flowchart of the present invention.

[0023] Figure 2 This is a fragment example of the work order quantity dataset of the present invention.

[0024] Figure 3 This is a fragment example of the work order details dataset of the present invention.

[0025] Figure 4 This is an example of a training sample for the present invention.

[0026] Figure 5 This is a schematic diagram of the overall structure of the present invention.

[0027] Figure 6 Figure 5 Enlarged view of section A.

[0028] Figure 7 for Figure 5 Enlarged view of section B.

[0029] Figure 8 for Figure 5 Enlarged view of section C.

[0030] Figure 9 for Figure 5 Enlarged view of section D.

[0031] Figure 10 This is a comparison chart of the prediction performance of the present invention and the Diffusion-TS method.

[0032] Figure 11 This invention compares its mean squared error (MSE) and mean absolute error (MAE) with five existing methods on four public datasets (Weather, Traffic, Electricity, and ETTh1) and the private datasets (Wqdata and Wqdata+Wddata).

[0033] Figure 12 This paper compares the invention with five existing methods on four public datasets (Weather, Traffic, Electricity, and ETTh1) and the private datasets (Wqdata and Wqdata+Wddata) in terms of context-Fréchet inception distance (Context-FID) and predictive score. Detailed Implementation

[0034] The present invention will be further described below through specific embodiments.

[0035] like Figure 1 As shown, the waterworks work order volume prediction method based on the diffusion model includes the following steps:

[0036] Step S1: Obtain the work order volume dataset and the work order details dataset. Each record in the work order volume dataset has a time period field. Based on the time period field of each record in the work order volume dataset, the work order details dataset is grouped and aggregated by hour to obtain multiple aggregated samples.

[0037] like Figure 2 The image shows a fragment example of the work order quantity dataset Wqdata. The work order quantity dataset Wqdata is divided into a training set, a validation set, and a test set in a 7:2:1 ratio. After the division, the sequence length L of the input sequence to the conditional network CN encoder and the sequence length H of the input sequence to the diffuser of the diffusion denoising network DiDeN are set according to requirements; generally, L=H. A set of training data is extracted from the work order quantity training set using a window of width L+H, and then the window slides forward one record to obtain the next set of training data. For the work order quantity data in the work order quantity training set, validation set, and test set, each batch is divided into 32 sets, with L+H records per set.

[0038] Examples of fragments of the aggregated work order details dataset Wddata Figure 3 As shown, after aggregation processing, it can meet the data format requirements of the model of this invention.

[0039] Step S2: Select L groups of aggregated samples sequentially from the work order details dataset. Input the acceptance content field and work order category field from each group of aggregated samples into the Chinese BERT module of the conditional network to convert them into work order detail term embeddings. This is to obtain work order event characteristic information, especially information on emergencies. The hidden layer dimension of the BERT module;

[0040] Step S3: Obtain training samples based on the work order volume dataset. The training samples include historical work order volume sequences, actual values ​​of predicted work order volume sequences, and sequences of temperature, holiday information, and global time information. Input the actual values ​​of the predicted work order volume sequences into the diffuser and add noise in K steps until the actual values ​​of the predicted work order volume sequences become Gaussian noise. After adding noise in the kth step, a noisy predicted work order volume sequence is obtained. k=1,2,…,K This serves as a label for the current training sample.

[0041] L+H records are obtained from the work order training set using a sliding window method to obtain training samples. The first L records in the training samples serve as the historical work order sequence, and the last H records serve as the true values ​​for the predicted work order sequence. Based on the first L records, historical L temperature, holiday information, and global time information sequences are obtained. Figure 4The image shows a training sample example. The global time information includes hourly, daily, weekly, and monthly codes. The specific values ​​corresponding to the hourly, daily, weekly, and monthly codes are obtained from the L+H records truncated by the sliding window in the work order training set. Figure 4 In this code, the sequence is filled with 0~23 to represent the hour code, 0~6 to represent the day code, 0~3 to represent the week code, and 0~11 to represent the month code. V1, V7, and V8 are defined to represent holiday codes.

[0042] The process of adding noise in step k is represented as follows: The noise addition process conforms to the Markov property, where, This is the cumulative noise attenuation coefficient, used to control the mixing ratio of the original sequence and noise. The predicted sequence of work order volume for the current sample is the true value. It is Gaussian noise.

[0043] Step S4: Add noise to the noisy work order quantity prediction sequence obtained in step k=K. The current frame work order quantity prediction sequence is input into the encoder of the diffusion denoising network to obtain the noisy hidden layer prediction feature vector. The historical sequence of work order quantity, temperature, holiday information and global time information sequence of the training sample are input into the encoder of the conditional network to extract the historical sequence feature hidden vector. The historical sequence feature hidden vector is concatenated with the work order detail word embedding. The concatenation result is fused with the noisy hidden layer prediction feature vector and input into the decoder of the diffusion denoising network. The next frame work order quantity prediction sequence is generated by weighting the current frame work order quantity prediction sequence, the decoder output and the noise random value. The next frame work order quantity prediction sequence is used as the current frame work order quantity prediction sequence and this step is repeated to obtain the final restored work order quantity prediction sequence.

[0044] like Figures 5 to 9 This is a schematic diagram of the overall structure and enlarged views of each part. The encoder of the conditional network is based on the formula... Extracting latent vectors of historical sequence features According to the formula Hidden vectors of historical sequence features The keywords are then combined with the embedded keywords in the work order details. Indicates self-attention, This represents the historical sequence of work orders for the current training sample. This represents the sequence of temperature, holiday information, and global time information for the current training sample. This represents a linear fully connected layer. This indicates that backpropagation has stopped. Indicates splicing, This represents the conditional latent vector of the current training sample.

[0045] The DiDeN diffusion denoising network's encoder uses self-attention to sample the noisy sequence to extract distribution features, specifically according to the formula... Obtain the noisy hidden layer predicted feature vector ,in, , , This represents the normalization layer of the encoder in a diffusion denoising network. For the encoder feedforward layer of the diffusion denoising network, This represents the output of the l-th sublayer of the encoder in the diffusion denoising network. This represents the output of the second sublayer of the l-th layer of the encoder in the diffusion denoising network. This represents the first training sample corresponding to the current training sample. The noisy work order quantity prediction sequence obtained after adding noise.

[0046] The decoder of the diffusion denoising network uses cross-attention to generate the prediction sequence for the next frame. According to the formula Calculate the next frame work order quantity prediction sequence ,in, Let i be the cumulative noise attenuation coefficient, i = 1, 2, ..., k. The noise intensity is the value added at step k. , Gaussian noise is added when adding noise in step k. standard deviation , For the current frame's work order quantity prediction sequence, more specifically, The input is The corresponding decoder output at that time, This represents the conditional information of the historical event sequence in the current frame, and is a known quantity.

[0047] Step S5: Minimize the mean squared error loss function between the final restored work order quantity prediction sequence and the actual value of the work order quantity prediction sequence, and update the parameters of the diffusion denoising network and the conditional network; proceed to step S2 to select the next L groups of aggregated samples, and obtain the next training sample in step S3, until a set number of training samples are used to obtain the trained prediction model.

[0048] Specifically, the mean squared error loss function is expressed as: After calculating the mean squared error loss function, backpropagation is performed using the Adam optimizer to minimize the mean squared error loss function and update the network parameters. This is the final predicted sequence of work order volume corresponding to the current sample. This represents the expected mean square loss of each noisy sequence prediction obtained from the current frame work order quantity prediction sequence. This indicates the data distribution that the currently predicted time series samples follow.

[0049] Step S6: Validate the prediction model using the work order quantity validation set to obtain the mean squared error loss based on the validation set. Repeat steps S2 to S5 until the mean squared error based on the validation set no longer decreases. The training process ends. Input the input sequence given by the prediction task into the trained prediction model to obtain the prediction sequence.

[0050] from Figure 10 It can be seen that the present invention (Wo-Diff) can predict the trend of work order volume changes throughout the entire process in the early stage of an emergency. The comparison scheme (Diffusion-TS) relies on historical statistical patterns. Due to the sparsity of emergencies, the predicted value can only passively follow the original trend and cannot accurately predict the overall trend of work order volume changes.

[0051] Figure 11 In the diagram, the experimental results of the best-performing scheme under each experimental condition are shown in bold, while the experimental results of the second-best-performing scheme are shown in underline. It can be seen that the performance of the present invention is superior to the other five comparative schemes. For example, compared with Diffusion-TS, the present invention reduces the mean squared error (MSE) by 71.68%, 51.54%, 58.18%, 9.44%, 62.24%, and 65.99% on the six datasets, respectively, with an average reduction of 53.20%.

[0052] Figure 12 The results show the experimental performance of six schemes—this invention, Diffusion-TS, TimeDiff, TTS-GAN, Dlinear, and FEDformer—on six datasets—Weather, Traffic, Electricity, ETTh1, Wqdata, and Wqdata+Wddata—under the same experimental conditions. The metrics used are Context-FID (Context Fréchet inception distance) and Predictive Score. Context-FID measures not only the distributional similarity between the generated sequence and the real sequence but also considers the degree of matching of conditional information; a low Context-FID value indicates high-quality predicted sequences that meet the conditions. The Predictive Score evaluates whether the model retains the statistical characteristics and semantic information of the real data; a low value indicates better performance. Compared to the suboptimal scheme, this invention shows an average improvement of 11.06% in Context-FID and an average improvement of 38.60% in Predictive Score.

[0053] In summary, compared to methods that rely solely on the statistical characteristics of historical data and cannot proactively adapt to the nonlinear effects of sudden events, this invention can effectively handle non-stationary data with the assistance of background conditions. Furthermore, this invention explicitly models the impact of sudden events through a conditional mechanism, allowing for adjustments to the generated trajectory in the early stages, thus achieving predictions that are more closely aligned with real-world scenarios.

[0054] In this invention, the terms "first," "second," and "third," etc., are used only to distinguish similar objects and are not necessarily used to describe a specific order or sequence, nor should they be construed as indicating or implying relative importance. The use of terms such as "upper," "lower," "left," "right," "front," and "rear" to indicate orientation or positional relationships is based on the orientation or positional relationships shown in the accompanying drawings and is only for the convenience of describing the invention, not to indicate or imply that the device referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation on the scope of protection of this invention. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0055] Furthermore, in the description of this application, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0056] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A method for predicting waterworks work order volume based on a diffusion model, characterized in that: Includes the following steps: Step S1: Obtain the work order volume dataset and the work order details dataset. Each record in the work order volume dataset has a time period field. Based on the time period field of each record in the work order volume dataset, the work order details dataset is grouped and aggregated by hour to obtain multiple aggregated samples. Step S2: Select L groups of aggregated samples sequentially from the work order details dataset, and input the acceptance content field and work order category field from each group of aggregated samples into the Chinese BERT module of the conditional network to convert them into work order details word embeddings; Step S3: Obtain training samples based on the work order volume dataset. The training samples include historical work order volume sequences, actual values ​​of predicted work order volume sequences, and sequences of temperature, holiday information, and global time information. Input the actual values ​​of the predicted work order volume sequences into the diffuser and add noise in K steps until the actual values ​​of the predicted work order volume sequences become Gaussian noise. After adding noise in the kth step, a noisy predicted work order volume sequence is obtained. k=1,2,…,K This serves as a label for the current training sample. Step S4: Add noise to the noisy work order quantity prediction sequence obtained in step k=K. The current frame work order quantity prediction sequence is input into the encoder of the diffusion denoising network to obtain the noisy hidden layer prediction feature vector. The historical sequence of work order quantity, temperature, holiday information and global time information sequence of the training sample are input into the encoder of the conditional network to extract the historical sequence feature hidden vector. The historical sequence feature hidden vector is concatenated with the work order detail word embedding. The concatenation result is fused with the noisy hidden layer prediction feature vector and input into the decoder of the diffusion denoising network. The next frame work order quantity prediction sequence is generated by weighting the current frame work order quantity prediction sequence, the decoder output and the noise random value. The next frame work order quantity prediction sequence is used as the current frame work order quantity prediction sequence and this step is repeated to obtain the final restored work order quantity prediction sequence. Step S5: Minimize the mean squared error loss function between the final restored work order quantity prediction sequence and the actual value of the work order quantity prediction sequence, and update the parameters of the diffusion denoising network and the conditional network; proceed to step S2 to select the next L groups of aggregated samples, and obtain the next training sample in step S3, until a set number of training samples are used to obtain the trained prediction model.

2. The waterworks work order volume prediction method based on a diffusion model according to claim 1, characterized in that: In step S1, the work order volume dataset is divided into a work order volume training set, a work order volume validation set, and a work order volume test set. In step S3, L+H records are obtained from the work order volume training set using a sliding window method to obtain the training sample. The first L records in the training sample are used as the historical sequence of work order volume, and the last H records are used as the true values ​​of the predicted sequence of work order volume. Based on the first L records, historical L temperature, holiday information, and global time information sequences are obtained.

3. The waterworks work order volume prediction method based on a diffusion model according to claim 2, characterized in that: In step S3, the noise addition process is represented as follows: ,in, This is the cumulative noise attenuation coefficient. The predicted sequence of work order volume for the current sample is the true value. It is Gaussian noise.

4. A method for predicting waterworks work volume based on a diffusion model according to claim 1, 2, or 3, characterized in that: In step S4, the encoder of the conditional network is based on the formula Extracting latent vectors of historical sequence features According to the formula Hidden vectors of historical sequence features The keywords are then combined with the embedded keywords in the work order details. Indicates self-attention, This represents the historical sequence of work orders for the current training sample. This represents the sequence of temperature, holiday information, and global time information for the current training sample. This represents a linear fully connected layer. This indicates that backpropagation has stopped. Indicates splicing, This represents the conditional latent vector of the current training sample.

5. A method for predicting waterworks work volume based on a diffusion model according to claim 1, 2, or 3, characterized in that: In step S4, the encoder of the diffusion denoising network is based on the formula... Obtain the noisy hidden layer predicted feature vector ,in, , , This represents the normalization layer of the encoder in a diffusion denoising network. For the encoder feedforward layer of the diffusion denoising network, This represents the output of the l-th sublayer of the encoder in the diffusion denoising network. This represents the output of the second sub-layer of the encoder in the diffusion denoising network.

6. A method for predicting waterworks work volume based on a diffusion model according to claim 1, 2, or 3, characterized in that: In step S4, the next frame work order quantity prediction sequence According to the formula Calculate, where, This is the cumulative noise attenuation coefficient. The noise intensity is the value added at step k. , Gaussian noise is added when adding noise in step k. standard deviation This is the predicted sequence of work order volume for the current frame. The next frame prediction sequence is the decoder output of the diffusion denoising network.

7. A method for predicting waterworks work volume based on a diffusion model according to claim 2 or 3, characterized in that: In step S3, the global time information includes hour code, day code, week code, and month code. The specific values ​​corresponding to the hour code, day code, week code, and month code are obtained from the L+H records that are truncated by the sliding window in the work order training set.

8. A method for predicting waterworks work volume based on a diffusion model according to claim 2 or 3, characterized in that: In step S5, the mean square error loss function is expressed as: , This is the final predicted sequence of work order volume corresponding to the current sample. This represents the expected mean square loss of each noisy sequence prediction obtained from the current frame work order quantity prediction sequence. This indicates the data distribution that the currently predicted time series samples follow.

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