CN116703003A - A Prediction Method of Residential Water Consumption - Google Patents

Abstract

The invention discloses a prediction method of residential water consumption, which comprises the following steps: s1, acquiring water consumption data of a research area in a research period through an intelligent water meter; s2, cleaning the data by adopting a Z-Score method, and removing and repairing abnormal values in the original data; s3, decomposing resident water consumption data into a plurality of subsequences with high frequency from high to low frequency through empirical mode decomposition of a time-varying filter; s4, dividing the subsequence into a high-frequency subsequence and a low-frequency subsequence according to the frequency, and reconstructing water consumption data into the high-frequency subsequence and the low-frequency subsequence; s5, respectively predicting the subsequences by using a transducer model; and S6, superposing the predicted values of the subsequences to obtain predicted water consumption of residents. According to the invention, the TVF-EMD is adopted to decompose the original data, so that the nonlinearity and the non-stationarity of the data are improved, and the prediction is easier; the transducer model increases the prediction accuracy and increases the running speed.

Description

A Prediction Method of Residential Water Consumption

technical field

The invention relates to a water quantity prediction method, in particular to a method for predicting residential water consumption.

Background technique

In recent years, energy conservation and emission reduction in the water supply industry has become a hot spot. Accurate prediction of user water volume is the basis for accurate water pumping in water delivery pump rooms, thereby reducing energy consumption in water plants and reducing carbon emissions in water supply systems. The forecast of user water volume is divided into long-term forecast, medium-term forecast and short-term forecast. The short-term forecast mainly refers to the water volume forecast on three scales of day, hour and minute. In order to scientifically regulate the water volume of users, the short-term prediction of water volume has become an urgent problem to be solved.

The traditional water quantity prediction method has the defects of low accuracy and granularity. In recent years, more and more scholars have proposed the method of using machine learning to predict the water consumption of users. When traditional machine learning predicts residential water consumption, it cannot include time-series information of water quantity, and the prediction effect is not ideal. The recurrent neural network developed in recent years considers the time-series information of data, making short-term prediction of user water consumption possible. Most of the existing water consumption prediction methods use recurrent neural networks. However, due to structural problems, recurrent neural networks cannot perform parallel operations, and the prediction efficiency is low, and it takes up a lot of memory. In addition, the existing water consumption forecasts are basically daily and hourly water consumption forecasts, lacking minute-level water consumption forecasts.

Contents of the invention

Purpose of the invention: In order to overcome the deficiencies in the prior art, the purpose of the invention is to provide a prediction method of residential water consumption with high prediction accuracy and granularity and short running time.

Technical solution: a method for predicting residential water consumption according to the present invention, comprising the following steps:

S1. Obtain the water consumption data of the research area during the research period through the smart water meter;

S2. Use the Z-Score method to clean up the data, remove and repair the abnormal values in the original data;

S3. Using the time-varying filter empirical mode decomposition to decompose the residential water consumption data into multiple subsequences with frequencies ranging from high to low;

S4. Divide the subsequences into high frequency subsequences and low frequency subsequences according to frequency, and reconstruct the water consumption data into high frequency subsequences and low frequency subsequences;

S5. Using the Transformer model to predict the two subsequences respectively;

S6. Superimpose the predicted values of the subsequences to obtain the predicted residential water consumption.

Further, step S2 specifically includes the following steps:

To calculate the Z-score of the water consumption data, the calculation method is:

In the formula, Z _i is the Z score of the i-th data, x _i is the data value of the i-th data, is the mean value of the data set, σ is the standard deviation of the data set;

Then set the critical Z score (Z _t ) of the data set. If |Z _i |>Z _t , the data is considered to be an outlier, and the random interpolation method is used to replace it, and the selection is made according to the specific situation of the data set.

Further, step S3 specifically includes the following steps:

S3-1. Calculate the local cut-off frequency, the formula is:

In the formula, Be the local cut-off frequency, η ₁ (t), η ₂ (t), a ₁ (t), a ₂ (t) are all constructed functions, and the construction method is detailed in the specific implementation;

Rearrange the local cutoff frequency to obtain the final local cutoff frequency;

S3-2. Using a time-varying filter to filter the input signal to obtain an approximation result;

After obtaining the local cutoff frequency, the signal h(t) can be obtained:

Taking the time point of the extremum value of the signal h(t) as the node m, construct a B-spline approximation time-varying filter, and set the cut-off frequency of the filter as Then B-spline approximation time-varying filtering is performed on the input signal, and the approximation result is recorded as m(t);

S3-3, judging whether m(t) satisfies the narrowband signal condition, if so, stop decomposing the input signal, if not, make x(t)=x(t)-m(t) and repeat S3- Steps 1 and S3-2, continue to decompose the input signal until the stop condition is met.

Further, the method of judging whether m(t) satisfies the narrowband signal condition is: if θ(t)≤Δ, the signal can be considered as a narrowband signal, and the calculation formula of θ(t) is:

In the formula, B _Loughlin (t) is Loughlin instantaneous bandwidth, is the weighted average instantaneous frequency;

S3-4. The m(t) obtained through S3-1 and S3-2 is a subsequence obtained by decomposing the initial signal by the TVF-EMD method. According to the sequence of m(t), record it and name it as C1, C2...Cn, a total of n subsequences with frequency from high to low are obtained.

Further, step S4 specifically includes the following steps:

S4-1. Record C1 as index 1, C1+C2 as index 2, and so on, the sum of the previous i C sequences is index i, calculate the average value of index 1 to index n, and check whether the average is significantly different Perform t-test at 0, if the t-test is significantly different from 0 at index k, then classify C1~C(k-1) as high-frequency components, and classify Ck~Cn as low-frequency components;

S4-2. Reconstruct the subsequence according to the signal frequency to reduce the number of established models. C1～C(k-1) represent high-frequency components, and the reconstructed high-frequency component Cnew1 is:

Cnew1＝C1+C2+...+C(k-1)

Ck～Cn represent low-frequency components, and the reconstructed low-frequency component Cnew2 is:

Cnew2=Ck+C(k+1)+...+Cn.

Further, step S5 specifically includes the following steps:

S5-1. Convert the water consumption data of the input sequence into embedded vectors, and then perform position encoding on each vector;

S5-2. Add the embedding vector and position code of the water data to obtain the vector representation matrix of the input sequence, and pass the vector representation matrix of the input sequence into the encoder. The encoder is composed of multiple encoder layers, each encoder Layers include multi-head attention mechanisms, residual connections and layer normalization, feed-forward neural networks, residual connections and layer normalization;

S5-3. The decoder contains multiple decoder layers corresponding to the encoder. Each decoder layer includes masked multi-head attention mechanism, residual connection and layer normalization, multi-head attention mechanism, residual connection and Layer normalization, feed-forward neural networks, residual connections, and layer normalization;

S5-4. Using the first 80% of the data as a training set and the last 20% of the data as a test set, input the decomposed and reconstructed signal sequence of the water consumption data into the Transformer model for training and result prediction, and output the model prediction sequence.

Further, the formula of the position encoding in step S5-1 is:

In the formula, PE _2i (p) is an even-numbered position code, PE _2i+1 (p) is an odd-numbered position code, p is the position of the water consumption at this moment in n moments, and d is the dimension of PE.

Further, in step S5-2, the output of the multi-head attention mechanism is accelerated to converge through residual connection and layer normalization, and finally the final output coding information is obtained through the feed-forward neural network using multiple layers of fully connected layers.

Furthermore, in S5-3, the masked multi-head attention mechanism adds an upper triangular matrix on the basis of the multi-head attention mechanism to shield the information of the future sequence, and the Q and K of the multi-head attention mechanism in the decoder part come from the corresponding encoding The output of the decoder layer, V is derived from the input features of the decoder.

Further, the superposition formula of step S6 is:

W _pred = W _new1,p +W _new2,p

In the formula, W _pred is the predicted value of the user's water volume, W _new1,p and W _new2,p are the predicted value of the high-frequency component subsequence and the predicted value of the low-frequency component subsequence, respectively.

Beneficial effects: compared with the prior art, the present invention has the following remarkable features:

1. Use TVF-EMD to decompose the original data, which significantly improves the nonlinearity and non-stationarity of the data, making the data easier to predict;

2. Reconstruct the decomposed subsequence, reducing the number of models that need to be established, reducing equipment operation requirements and operation time;

3. Using the Transformer model for prediction, data location association operations are not limited, strong modeling capabilities, strong versatility, strong scalability, and better parallel computing;

4. The TVF-EMD-Transformer hybrid model can better predict the water volume of users at the minute level, and achieve the prediction results with high granularity and precision.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a structure diagram of the Transformer model of the present invention.

Detailed ways

As shown in Figure 1, a method for predicting residential water consumption includes the following steps:

S1. Obtain the water consumption data in the study area during the study period through the smart water meter, and the time interval of the data is 15 minutes.

S2. Use the Z-Score method to clean the data to remove and repair the abnormal values in the original data, including:

To calculate the Z-score of the water consumption data, the calculation method is:

In the formula, Z _i is the Z score of the i-th data; x _i is the data value of the i-th data; is the average value of the data set; σ is the standard deviation of the data set, and the average value and standard deviation of the data set are calculated by formulas (2)-(3) respectively.

A critical Z-score (Z _t ) for the data set is then set. If |Z _i | > Z _t , the data is considered an outlier and replaced using random interpolation. Z _t is usually 2.5, 3.0, or 3.5, and is selected according to the specific conditions of the data set.

Formula (2)-(3):

In the formula, n is the number of data in the data set, and other symbols are the same as formula (1).

S3. Considering the complexity of water consumption data, use time-varying filter empirical mode decomposition (TVF-EMD) to decompose residential water consumption data into multiple subsequences with frequencies ranging from high to low, specifically including:

S3-1. Calculating the local cutoff frequency.

Use the Hilbert transform to calculate the instantaneous amplitude and instantaneous frequency of the input signal x(t), namely:

In the formula, A(t), are the instantaneous amplitude and instantaneous frequency of the input signal, respectively; x(t) and /> Respectively represent the original input signal (time series data of residential water consumption) and the input signal after Hilbert transformation.

Then determine the maximum value sequence and minimum value sequence of the instantaneous amplitude A(t), denoted as {t _max } and {t _min }. Its analytical signal z(t) can be expressed as:

In the formula, a _i and are the magnitude and phase of the i-th order component, respectively.

After processing formula (6), we can get:

When t=t _min , it can be obtained from formula (7):

Substituting formula (9) into formula (7) and formula (8) can get:

A(t _min )＝|a ₁ (t _min )-a ₂ (t _min )| (10)

Since A(t _min ) is a local minimum, so A'(t _min )=0, then:

a′ ₁ (t _min )-a′ ₂ (t _min )=0 (12)

By solving formulas (9)-(12), a ₁ (t _min ), a ₂ (t _min ), and /> Similarly, according to formulas (13)-(16), a ₁ (t _max ), a ₂ (t _max ), /> and />

A(t _max )＝a ₁ (t _max )+a ₂ (t _max ) (14)

a' ₁ (t _max )+a' ₂ (t _max )=0 (16)

make:

β ₁ (t)=|a ₁ (t)-a ₂ (t)| (17)

β ₂ (t) = a ₁ (t) + a ₂ (t) (18)

Substitute t=t _min and t=t _max into formula (17) and formula (18) respectively to get:

β ₁ (t _min )=|a ₁ (t _min )-a ₂ (t _min )|=A(t _min ) (19)

β ₂ (t _max )=a ₁ (t _max )+a ₂ (t _max )=A(t _max ) (20)

Because a ₁ (t) and a ₂ (t) change slowly, β ₁ (t) and β ₂ (t) can be obtained by interpolating the sequences A{t _min } and A{t _max }, therefore:

Similarly, construct the following function:

Substitute t=t _min and t=t _max into formula (23) and formula (24) respectively to get:

Similarly, by solving formula (23) and formula (24):

Substitute the parameters obtained in the above steps into the local cutoff frequency The calculation formula can be obtained:

In order to solve the problem that the cutoff frequency is affected by noise, the cutoff frequency is rearranged according to the following rules:

Find the local maximum value of the signal x(t), which is recorded as u _i (i=1,2,3…), if u _i satisfies the following formula, it is recorded as e _j =u _i (j=1,2,3 ...).

In the formula, ρ is a threshold parameter, which is 0.25. if Then e _j is the rising edge, otherwise it is the falling edge. Judge each e _j , if it is on the rising edge, then /> is the bottom, if it is on the falling edge, then /> is the bottom, and the rest are peaks. Interpolate between the two peaks to get the final cutoff frequency.

S3-2. Using a time-varying filter to filter the input signal to obtain an approximation result.

After obtaining the local cutoff frequency, the signal h(t) can be obtained:

Taking the time point of the extremum value of the signal h(t) as the node m, construct a B-spline approximation time-varying filter, and set the cut-off frequency of the filter as Then B-spline approximation time-varying filtering is performed on the input signal, and the approximation result is recorded as m(t).

S3-3. Determine the stop condition.

Judge whether m(t) satisfies the narrowband signal condition, if so, stop decomposing the input signal, if not, set x(t)=x(t)-m(t) and repeat S3-1 and S3- 2 step, continue to decompose the input signal until the stop condition is reached.

The method for judging whether the signal satisfies the narrowband signal condition is: if θ(t)≤Δ, the signal can be considered as a narrowband signal. θ(t) is calculated by formula (32), where θ(t) is the criterion value; is the weighted average instantaneous frequency, calculated by formula (33); B _Loughlin (t) is the Loughlin instantaneous bandwidth, calculated by formula (34).

S3-4. Obtaining and storing the subsequence.

The m(t) obtained through S3-1 and S3-2 in each step is a subsequence obtained by decomposing the initial signal by the TVF-EMD method. According to the sequence of m(t), record and name them as C1, C2... Cn. A total of n subsequences with frequency from high to low are obtained.

S4. Divide subsequences into high-frequency subsequences and low-frequency subsequences according to frequency, and reconstruct water consumption data into high-frequency and low-frequency subsequences, specifically including:

S4-1. Determine the signal frequency of the subsequence.

Record C1 as index 1, C1+C2 as index 2, and so on, the sum of the previous i C sequences is index i, calculate the mean value from index 1 to index n, and perform t on whether the mean value is significantly different from 0 test. If the t-test is significantly different from 0 at index k, then C1-C(k-1) is classified as a high-frequency component, and Ck-Cn is classified as a low-frequency component.

S4-2. Perform component reconstruction according to the signal frequency.

Because there are multiple subsequences decomposed according to the original signal, if each subsequence is modeled, a large number of models need to be established, and the required computer memory and computing time will increase, so the subsequences are calculated according to the signal frequency Refactoring to reduce the number of models built and improve prediction efficiency.

C1-C(k-1) represents the high-frequency component, and the reconstructed high-frequency component Cnew1 is:

Cnew1＝C1+C2+...+C(k-1) (35)

Ck-Cn represents the low frequency component, then the reconstructed low frequency component Cnew2 is:

Cnew2＝Ck+C(k+1)+...+Cn (36)

S5, as shown in Figure 2, use the Transformer model to predict the two subsequences respectively, including:

S5-1. Word embedding and position encoding.

The water consumption data of the input sequence is converted into embedded vectors through Input Embedding, and then each vector is position-encoded. The position-encoding formulas are shown in equations (37)-(38). Similarly, similar word embedding and position encoding operations are performed on the water consumption data of the target sequence.

In the formula, PE _2i (p) is an even-numbered position code, PE _2i+1 (p) is an odd-numbered position code, p is the position of the water consumption at this moment in n moments; d is the dimension of PE.

S5-2. Encoder operation.

The vector representation matrix X _n×d of the input sequence is obtained by adding the embedding vector of the water data and the position code, n is the window size, that is, the n+1th time series data is predicted by n pre-order time data; d is the embedding dimension , generally take 512. The obtained sequence vector representation matrix is passed into the encoder, and the encoder is composed of multiple encoder layers, usually six encoder layers are selected, and the present invention uses six encoder layers as the encoder structure. Each encoder layer consists of four parts: multi-head attention mechanism, residual connection and layer normalization, feed-forward neural network, residual connection and layer normalization. The principle of the multi-head attention mechanism and the input and output of the encoder layer are shown below.

(1) Multi-head attention mechanism

First, on the basis of self-attention, Q, K, and V are split according to the number of heads. Q(Query), K(Key), and V(Value) all originate from the input features themselves, and are vectors generated according to the input features. Then Q, K, V (eg Q ¹ , K ¹ , V ¹ ) whose superscript second parameter is 1 are classified as Head1. Head2,..., Headn are the same. The output of each head is:

Splice the output of each Head, and then multiply the spliced output by Get the output of the multi-head attention mechanism. Here d _k =d _v =d _model /h, h is the number of heads of the multi-head attention mechanism, and the number of heads of the multi-head attention mechanism used by Transformer is 8, that is, h=8.

(2) Input and output of the encoder layer

The output of the multi-head attention mechanism accelerates the convergence through residual connection and layer normalization, and finally obtains the final output encoding information through the feedforward neural network using multiple layers of fully connected layers.

The input and output of the encoder layer are shown in equations (39)-(40).

e ₀ ＝Embedding(inputs)+pos_Enc(inputs _position ) (39)

e _i =EncoderLayer(e _i-1 ) (40)

In the formula, e ₀ is the input of the encoder; e _i-1 and e _i are the outputs of the i-1th layer and the i-th layer of the encoder respectively; EncoderLayer( ) represents the operation of the encoder layer; i∈[1,N ], N is the number of encoder layers.

S5-3. Decoder operation.

The decoder also includes a plurality of decoder layers corresponding to the encoder, because the present invention uses six encoder layers, so six decoder layers are used to form a decoder corresponding to it. Each decoder layer consists of masked multi-head attention mechanism, residual connection and layer normalization, multi-head attention mechanism, residual connection and layer normalization, feed-forward neural network, residual connection and layer normalization6 consists of parts. The masked multi-head attention mechanism adds an upper triangular matrix to mask the information of future sequences based on the multi-head attention mechanism. The multi-head attention mechanism of the decoder part is similar to that of the encoder. The difference is that Q and K are not derived from the input features of the decoder but from the output of the corresponding encoder layer, and V is derived from the input features of the decoder. The input and output of the decoder layer are as follows:

e ₀ ＝Embedding(outputs)+pos_Enc(outputs _position ) (41)

e _i ＝DecoderLayer(e _i-1 ) (42)

e ₀ is the input of the decoder; e _i-1 and e _i are the outputs of the i-1th layer and the i-th layer of the decoder respectively; DecoderLayer( ) represents the operation of the decoder layer; i∈[1,N],N is the number of decoder layers.

S5-4. Predict the two reconstructed subsequences.

Use the first 80% of the data as the training set and the last 20% of the data as the test set. The decomposed and reconstructed signal sequence of the water consumption data is input into the Transformer model for training and result prediction, and the model prediction sequence is output.

S6. Superimpose the predicted values of the subsequences to obtain the predicted residential water consumption, specifically including:

Add the predicted values of the two subsequences in step S5 to obtain the predicted value of the user’s water volume, namely:

W _pred = W _new1,p +W _new2,p (43)

In the formula, W _pred is the predicted value of the user's water volume, W _new1,p and W _new2,p are the predicted value of the high-frequency component subsequence and the predicted value of the low-frequency component subsequence, respectively.

Claims (10)

1. A method for forecasting residential water consumption, comprising the following steps: S1. Obtain the water consumption data of the research area during the research period through the smart water meter; S2. Use the Z-Score method to clean up the data, remove and repair the abnormal values in the original data; S3. Using the time-varying filter empirical mode decomposition to decompose the residential water consumption data into multiple subsequences with frequencies ranging from high to low; S4. Divide the subsequences into high frequency subsequences and low frequency subsequences according to frequency, and reconstruct the water consumption data into high frequency subsequences and low frequency subsequences; S5. Using the Transformer model to predict the two subsequences respectively; S6. Superimpose the predicted values of the subsequences to obtain the predicted residential water consumption. 2. A method for predicting residential water consumption according to claim 1, wherein said step S2 specifically comprises the following steps: To calculate the Z-score of the water consumption data, the calculation method is: In the formula, Z _i is the Z score of the i-th data, x _i is the data value of the i-th data, is the mean value of the data set, σ is the standard deviation of the data set; Then set the critical Z score (Z _t ) of the data set. If |Z _i |>Z _t , the data is considered to be an outlier, and the random interpolation method is used to replace it, and the selection is made according to the specific situation of the data set. 3. A method for predicting residential water consumption according to claim 1, characterized in that: said step S3 specifically comprises the following steps: S3-1. Calculate the local cut-off frequency, the formula is: In the formula, Be local cut-off frequency, η ₁ (t), η ₂ (t), a ₁ (t), a ₂ (t) are all constructed functions; Rearrange the local cutoff frequency to obtain the final local cutoff frequency; S3-2. Using a time-varying filter to filter the input signal to obtain an approximation result; After obtaining the local cutoff frequency, the signal h(t) can be obtained: Taking the time point of the extremum value of the signal h(t) as the node m, construct a B-spline approximation time-varying filter, and set the cut-off frequency of the filter as Then B-spline approximation time-varying filtering is performed on the input signal, and the approximation result is recorded as m(t); S3-3, judging whether m(t) satisfies the narrowband signal condition, if so, stop decomposing the input signal, if not, make x(t)=x(t)-m(t) and repeat S3- Steps 1 and S3-2, continue to decompose the input signal until the stop condition is reached; S3-4. The m(t) obtained through S3-1 and S3-2 is a subsequence obtained by decomposing the initial signal by the TVF-EMD method. According to the sequence of m(t), record it and name it as C1, C2...Cn, a total of n subsequences with frequency from high to low are obtained. 4. A method for predicting residential water consumption according to claim 3, characterized in that: in said S3-3, the method for judging whether m(t) satisfies the narrowband signal condition is: if θ(t)≤Δ, Then the signal can be considered as a narrowband signal, and the calculation formula of θ(t) is: In the formula, B _Loughlin (t) is Loughlin instantaneous bandwidth, is the weighted average instantaneous frequency. 5. A method for predicting residential water consumption according to claim 1, characterized in that: said step S4 specifically comprises the following steps: S4-1. Record C1 as index 1, C1+C2 as index 2, and so on, the sum of the previous i C sequences is index i, calculate the average value of index 1 to index n, and check whether the average is significantly different Perform t-test at 0, if the t-test is significantly different from 0 at index k, then classify C1～C(k-1) as high-frequency components, and classify Ck～Cn as low-frequency components; S4-2. Reconstruct the subsequence according to the signal frequency to reduce the number of established models. C1～C(k-1) represent high-frequency components, and the reconstructed high-frequency component Cnew1 is: Cnew1＝C1+C2+...+C(k-1) Ck～Cn represent low-frequency components, and the reconstructed low-frequency component Cnew2 is: Cnew2=Ck+C(k+1)+...+Cn. 6. A method for predicting residential water consumption according to claim 1, characterized in that: said step S5 specifically comprises the following steps: S5-1. Convert the water consumption data of the input sequence into embedded vectors, and then perform position encoding on each vector; S5-2. Add the embedding vector and position code of the water data to obtain the vector representation matrix of the input sequence, and pass the vector representation matrix of the input sequence into the encoder. The encoder is composed of multiple encoder layers, each encoder Layers include multi-head attention mechanisms, residual connections and layer normalization, feed-forward neural networks, residual connections and layer normalization; S5-3. The decoder contains multiple decoder layers corresponding to the encoder. Each decoder layer includes masked multi-head attention mechanism, residual connection and layer normalization, multi-head attention mechanism, residual connection and Layer normalization, feed-forward neural networks, residual connections, and layer normalization; S5-4. Using the first 80% of the data as a training set and the last 20% of the data as a test set, input the decomposed and reconstructed signal sequence of the water consumption data into the Transformer model for training and result prediction, and output the model prediction sequence. 7. A method for predicting residential water consumption according to claim 6, characterized in that: the formula for the position coding in step S5-1 is: In the formula, PE _2i (p) is an even-numbered position code, PE _2i+1 (p) is an odd-numbered position code, p is the position of the water consumption at this moment in n moments, and d is the dimension of PE. 8. The prediction method of a kind of resident water consumption according to claim 6, it is characterized in that: in described step S5-2, the output of multi-head attention mechanism carries out accelerated convergence through residual connection and layer normalization, finally The final output encoding information is obtained by using a multi-layer fully connected layer through a feed-forward neural network. 9. The prediction method of a kind of resident water consumption according to claim 6, it is characterized in that: in described S5-3, mask multi-head attention mechanism has added upper triangular matrix on the basis of multi-head attention mechanism to shield For the information of the future sequence, Q and K of the multi-head attention mechanism in the decoder part come from the output of the corresponding encoder layer, and V comes from the input features of the decoder. 10. A method for predicting residential water consumption according to claim 1, characterized in that: the superposition formula of step S6 is: W _pred = W _new1,p +W _new2,p In the formula, W _pred is the predicted value of the user's water volume, W _new1,p and W _new2,p are the predicted value of the high-frequency component subsequence and the predicted value of the low-frequency component subsequence, respectively.