KR100765335B1 - Study on vacuum pump monitoring using mpca statistical method - Google Patents

Abstract

A method for monitoring a vacuum pump state is provided to obtain an exact state from a vacuum pump by checking main factors as references using an MPCA(Multiway Principal Component Analysis) statistical method. A first T^2 value is calculated from a normal state signal of a vacuum pump by using an MPCA based statistical method, wherein the normal state signal of the vacuum pump is obtained from a plurality of sensors. The first T^2 value is set as an UCL(Upper Control Limit), wherein the UCL is used as a reference for determining an abnormal state of the vacuum pump. A second T^2 value is calculated from an abnormal state signal of the vacuum pump by using the MPCA based statistical method. The UCL and the second T^2 value are compared with each other in order to check an exact state of the vacuum pump.

Description

Study on vacuum pump monitoring using MPCA statistical method

1 is a system configuration for informing the abnormal symptoms by analyzing the operating vacuum pump state.

2 is a flowchart showing a process of informing an abnormal symptom by analyzing a state of a working vacuum pump.

3 is a view for explaining the arrangement length adjustment.

4 is a graph showing a result of calculating an optimal path.

5 is a view for explaining a prior data processing process.

6 is a diagram illustrating a multi-principal component analysis process.

7 is a diagram illustrating a process of estimating a distribution by Kernel Smoothing.

8 is a view for explaining an abnormal point removal process.

9 is a graph for explaining an HDS period analysis process.

10 is T ² according to the operation of the vacuum pump after replacing the vacuum pump This graph shows the behavior of the diagram.

11 is a graph showing data obtained from a vacuum pump in normal operation.

12 are graphs for explaining UCL factor selection.

The present invention relates to a method for diagnosing a vacuum pump state using a statistical technique based on multi-principal component analysis. In particular, the present invention is a vacuum using a multi-principal component analysis-based statistical technique to accurately monitor the operating state of the vacuum pump to accurately predict the failure time of the vacuum pump used in the semiconductor process having harsh operating conditions and non-linear characteristics The present invention relates to a method for diagnosing a pump condition.

Various vacuum pumps used in semiconductor processes, etc., are difficult to accurately predict a failure point due to harsh operating conditions and nonlinear characteristics, resulting in problems such as mass production of defective products or unnecessary waste of resources.

Therefore, the development of a vacuum pump state diagnosis method (model) that accurately monitors the operation state of the vacuum pump and accurately recognizes the time of failure and informs the time of replacement of the vacuum pump is emerging as an urgent and serious problem.

Developing a method for diagnosing the state of the vacuum pump means establishing a vacuum pump state diagnosis system that identifies major factors that can represent the performance of the vacuum pump and determines whether the system is malfunctioning.

That is, when the vacuum pump condition diagnosis system is completed, when the operating condition of the vacuum pump is out of the normal range, an abnormal symptom of the vacuum pump is automatically detected and a warning is triggered so that the operator can react to this to stop the operation of the vacuum pump or other You can take action.

However, in order to construct a vacuum pump condition diagnosis system as described above, it is necessary to find a main factor that is a criterion for judging whether the vacuum pump has an abnormal symptom. Must be set

In order to solve the above-mentioned problems, the present invention finds a main factor that serves as a criterion for determining whether the vacuum pump has an abnormal symptom, and sets a boundary between the normal operation range and the abnormal operation range of the vacuum pump. The purpose of this is to accurately diagnose the state of the vacuum pump and to indicate whether the vacuum pump is abnormal.

Vacuum pump state diagnosis method using a multi-principal component analysis-based statistical technique according to the present invention for achieving the above object, multi-component analysis by receiving a signal for the state of the vacuum pump in the normal operating range from a plurality of sensors a first step of calculating a value of T ² by using a multivariate statistical technique based (Multiway Principal Component Analysis), and the selection of the T ² value to the UCL as a reference for determining abnormality of the vacuum pump; A second step of receiving a signal of a state of a vacuum pump after a normal operating range from the plurality of sensors and calculating a T ² value using a multivariate statistical technique based on multi-way principal component analysis; And a third step of notifying whether the vacuum pump has an abnormal symptom by comparing the UCL selected as the reference in the first step and the T ² value obtained in the second step.

Also, in the present invention, the plurality of sensors preferably include an intake air pressure sensor, a pressure pump acceleration sensor, three dry pump acceleration sensors, an acoustic sensor, an exhaust pressure sensor, a pressure pump current sensor, and a dry pump current sensor.

In addition, in the present invention, the T ² value, from the signals for the vacuum pump state obtained by the plurality of sensors to extract the signals obtained in the section in which the semiconductor manufacturing process actually proceeds to store as batch data (batch date) Batch creation process; A Dynamic Time Warping Algorithm process of adjusting the batch data to the same length using a Dynamic Time Warping Algorithm technique; The batch data is equally matched through a centering process for aligning the average points in a form of subtracting the average value of the batch data from the batch data and a scaling process for dividing the batch data by the standard deviation, and then the main component ( Multi-Principal Component Analysis (T _score ), P coordinate _loading and T ² ; And a purging outliers process of removing batch data showing a unique trend out of a plurality of trends among batch data by a smoothing technique technique.

In addition, in the present invention, the adjustment of the batch length, after obtaining the accumulation distance, it is preferable to select the optimal path (Optimal Path) according to the local-global constraint and to adjust the batch length equally through the averaging process based on this.

In addition, in the present invention, the T ² value for selecting the UCL as a reference for identifying the abnormal symptoms of the vacuum pump in the first step is preferably calculated every time the vacuum pump is replaced.

Hereinafter, the present invention will be described in detail.

As shown in FIG. 1, the vacuum pump state diagnosis system (module) of the present invention includes intake pressure, pressurized pump acceleration, dry pump acceleration X, dry pump acceleration Y, dry pump acceleration Z, and acoustic from nine sensors installed in the vacuum pump. It receives signals about exhaust pressure, pressurized pump current and dry pump current and uses them as basic data for vacuum pump status analysis. Based on the fact that the signals obtained by each sensor are not independent of each other and have some correlation. Rather than analyzing each signal independently, we use multivariate statistical techniques to reflect the overall trend.

In other words, using a statistical distance technique called Mahalanobis's Distance (MD) or Hotelling's T ² (hereinafter referred to as 'T ² '), a single signal called T ² is considered. Summarize information (data) with statistics. Since T ² includes not only the abnormal behavior of individual variables, but also considerations of the functional relationships among the variables, it is a statistic that includes information between variables that cannot be obtained only by observation of individual signals.

In the end, the final vacuum pump state diagnosis method (model) is implemented using a T ² is if the T ² value beyond a certain limit will be considered to exhibit a vacuum pump condition monitoring system abnormalities, wherein the limit point of the How to set the UCL (Upper Control Limit) is the main technology.

The target vacuum pump consists of a booster pump and a dry pump. The vacuum pump has two pressure sensors, four acceleration sensors, one acoustic sensor, and two current sensors. Attached.

That is, attaching the four types of sensors to the vacuum pump is appropriate because pressure is generated to create a vacuum state as current is applied to the vacuum pump, and vibration and sound are involved in this process.

Of course, there are many other factors that affect the characteristics of the vacuum pump, but once the monitoring analysis method is established, the problem of adding variables later can be easily implemented.

Figure 2 shows the process of diagnosing the state of the vacuum pump by monitoring the operating state of the vacuum pump, which can be divided into two stages. Based on this, the value of T ² to be used as a reference is calculated.

Since the vacuum pump is continuously deteriorated since the start of operation, the initial section is set to a normal operating range, which is actually used in many monitoring techniques. At this time, the data obtained in the normal operation range is called HDS (Historical Data Set).

In the next step, the actual monitoring of the vacuum pump is performed by comparing the T ² obtained after the previous step with the T ² obtained as the reference obtained in the previous step. The obtained data is called an ODS (Observed Data Set).

Hereinafter, the details of batch generation, dynamic time distortion algorithm, MPCA, and outlier elimination will be described in detail.

Batch Generation

Since signals obtained by the sensors as shown in FIG. 1 also include information on sections in which the semiconductor fabrication process is not performed, only the sections in which the process is actually performed are separately extracted and stored as batch data.

In other words, a batch means one process unit. During the process, the inlet pressure is maintained at a high value, but until the end of the process and the next process starts, the inlet pressure drops to almost zero, so if the signal waveform of the intake pressure sensor is observed, the process progresses. It is possible to determine, and the remaining variables are also selected as the data of the process in the same section and stored as batch data.

Dynamic Time Warping Algorithm

The duration of the semiconductor process varies depending on the situation, so the batch length will vary from one person to another. If the analysis is performed as it is, the inverse matrix may diverge in the process of obtaining the covariance matrix, so the batch length should be set in advance. In this case, it is important to keep the initial input trend as it is in the process of adjusting the length of the batch.

As described above, the DTW technique used to adjust the batch length is widely used in the speech recognition field, and Kassidas et al. Has applied it to the batch process.

As shown in Figure 3, in order to adjust the length of the sample batch (Reference Batch) equal to the length of the reference batch (Reference Batch), the optimal path (Optimal Path) is selected as follows in accordance with the specified regulatory conditions and algorithms. .

와 축적 거리(Accumulated Distance)

를 구하는 것이 주된 알고리즘인데 이때 가가중치(Weighting) W가 수렴할 때까지 반복수행한다. 10번 정도의 반복수행으로 W가 수렴하는 것을 확인할 수 있다.Local distance as shown in Equations 1, 2, and 3 above

And Accumulated Distance

The main algorithm is to find the algorithm and iterate until the weighting W converges. You can see that W converges in about 10 iterations.

가 구해지고 나면 로컬-글로벌 제약(Local-global Constraint)에 따라 최적경로(Optimal Path)를 선정하고 이를 기반한 평균화과정을 통해 배치 길이를 동일하게 맞춘다.

Once found, the optimal paths are selected according to local-global constraints and the batch lengths are equalized through averaging.

를 구한 후 최적경로(Optimal Path)를 산출한 결과를 보인 것이다.4 is as above

After finding, we calculate the Optimal Path.

Multiway Principal Component Analysis

In the above dynamic time distortion algorithm step, the basic condition for performing multi-principal component analysis (MPCA) was satisfied by adjusting the batch length uniformly, but the preliminary work of centering and scaling should be performed before the full-scale analysis. do.

Since the multi principal component analysis (MPCA) is intended to identify the behavior characteristics of a representative batch, each batch should be compared under the same conditions. Each batch will have a different average value. This problem is solved by centering the average points to zero in a batch that subtracts the average value from the data.

In addition, nine variables have their own system of units, which needs to be considered. Even if the value is the same, the weight varies depending on which unit is used. If this value is not corrected, excessive weight is given to the data of a specific variable, which may cause an error in the overall analysis. This can be solved by a scaling process that divides each data by its standard deviation.

As shown in FIG. 5, the existing three-dimensional matrix is developed in two dimensions, and then the average and standard deviation are obtained to perform the centering and scaling process on each data.

After the above data preprocessing, all conditions for performing multiple principal components analysis are satisfied.

Rearranging the matrix in a form suitable for multiple principal component analysis is as shown in FIG.

The principal component analysis is a technique of extracting data components having a high contribution by rotating a coordinate axis. In this case, the eigenvector is used as the transformed main coordinate, and the eigenroot means data distribution in each main coordinate direction. This is simply implemented using the SVD (Singular Value Decomposition) technique in Matlab (Matrix Laboratory) internal functions. Then, if the orthogonal data is orthogonal to each eigenvector, the principal components can be obtained, and each principal component has a variance corresponding to the eigen root. However, if the redundant data is included in the existing data, the principal components with very small roots appear. If left unchanged, an error that an abnormal value increases in the subsequent T ² calculation occurs. If the principal component is called t _score and the principal coordinate vector is named P _loading , T ² is calculated as shown in Equation 4 below.

In this case, the covariance matrix S _D becomes a diagonal matrix having the unique root as a diagonal element after the coordinate transformation, so T ² is the sum of squares of t _scores weighted by the inverse of the natural roots. Therefore, when the high root has a small value close to 0, the value of T ² is greatly increased. In fact, a component having no specific gravity increases the value of T ² , which is difficult to reflect the original trend.

For this reason, the principal component should be reduced in dimension, which is achieved through observation of the high root.

In other words, the cumulative variance is calculated using Equation 5 above, and the number of variables until the value exceeds 95% is defined as a reduced dimension.

Applying the principal component analysis process to HDS, t _score , P _loading , and T ² are obtained, and afterwards, ODS does not calculate P _loading , but instead calculates the t _score , by orthogonally plotting the data on P _{loading which} is already obtained. T ² is obtained.

-Purging Outliers

Outlier is a term used to refer to some data that shows unusual trends out of the trend of the majority of data. If left unchecked, severe distortion may occur in estimating the overall trend. It must be preserved correctly.

Outlier elimination first estimates the distribution curve of the data, removes some data at the end, and then iterates the distribution curve of the reconstructed data again and performs iteration until the estimated distribution is stabilized. Is done.

The method of estimating the distribution uses the kernel smoothing technique as shown in Equation 6 below.

Here, ø is the normal distribution function of mean 0, variance 1, and when the h value of each normal function is determined using the constraint that the sum of probability distributions is 1 from the distribution of T ² values, the waveform of the normal function is determined and their linear combination The final distribution is determined.

Once the distribution is determined, as shown in FIG. 7, the T ² point of the ratio corresponding to α (%) is found in the right tail portion and selected as UCL, and the T ² value exceeding this value is excluded from the data. If the ratio of outliers is not very high, the distribution is stabilized even if only one of these operations is performed, but if there are many outliers, the removal of the outliers should be repeated and the work continued until the estimated distribution no longer changes and converges. do.

In FIG. 8, the actual abnormal point removal process is shown, and the UCL and the number of abnormal points removed at each step are shown.

The above-mentioned historical data set (HDS) is a data of a normal operating range, and provides a reference for monitoring the subsequent ODS (Oserved Data Set). HDS should have enough length to represent the behavior of normal operation, but if it is chosen too long, the period for actual monitoring can be shortened, so an appropriate level of compromise must be found.

9 is a result of analyzing the data while changing the HDS period from 1 to 8 days using the vacuum pump operation data. The abscissa number (No.) is a batch of batches and is the time sequence of the process.

As can be seen from this result, if the HDS is too small, it can be seen that the T ² value easily diverges due to lack of representativeness. As the HDS increases, the T ² distribution gradually stabilizes and converges at a certain level. In other words, it can be seen from FIG. 9 that the trend has converged to some extent since HDS-5. As a result of investigating all six cases, the same phenomenon was observed, it is considered that 5 days is appropriate for HDS.

HDS is the standard of normal operating range and consists of data for the first 5 days after vacuum pump replacement. However, if all pumps assume the same performance under normal operation, we can think of the situation where the existing HDS can be used even if the pump is replaced. Extracting the reference data from the HDS takes a lot of time by itself, so if it is possible to set up and use the HDS only once, it can help speed up the computation. This situation can be confirmed by direct data analysis.

10 is a T ² diagram according to the vacuum pump operation, in which the vacuum pump is replaced at the end. Although the vacuum pump was replaced, in order to compare the characteristics with the existing vacuum pump, the initial data of the replaced vacuum pump was intentionally used as ODS without resetting to HDS. As can be seen from the figure, immediately after the vacuum pump is replaced, the T ² value increases rapidly. If the normal operation performance of the replaced vacuum pump and the conventional vacuum pump are the same, the T ² value after the vacuum pump is replaced will be similar to the distribution of T ^{2 in} the beginning of FIG.

Currently, we have six cases of vacuum pump data. In the other five cases, the result of analyzing the results shows that the T ² value increases after the vacuum pump is replaced. Normal operation characteristics are different so HDS should be reset when vacuum pump is replaced.

After checking the characteristics (definition) of the HDS, the UCL (Upper Control Limit) is selected. Since the UCL is the limit line of the normal operating range, the basis can be found in the HDS. That is, the UCL is determined from the T ² distribution of the HDS. The method of determining the UCL varies depending on the technique. In the present invention, the technique using the mean and standard deviation of HDS T ² is selected (Equation 7).

It is commonly used in terms of 3-sigma, 6-sigma, etc., but it cannot simply be used unconditionally, but a factor must be obtained through practical analysis.

The vacuum pump data used in the present invention is data of a total of six sections, one of which is data consisting of only normal operation. That is, it holds data for six sections obtained from a plurality of sensors when the vacuum pump is installed and operated, the operation is stopped, and the new vacuum pump is replaced. Therefore, the approximate factor can be detected first from the data consisting of normal operation only, and then the specific values can be defined from the remaining five data.

First of all, we look at the data of vacuum pump which is composed only of normal operation. At this time, in order to show the clarity of the trend, the abnormalities are removed from ODS as well as HDS, and the same work is performed in all cases discussed later.

Fig. 11 shows data obtained from a vacuum pump in normal operation, and UCLs with factors of 5, 10, and 20 are shown, and HDS is up to Observation Number 7691. The UCL should be located above the T ² data to avoid sending false alarms despite normal operation. From this it can be thought that UCL will be determined approximately between factors 10-20.

Hereinafter, a process of determining the UCL factor based on the remaining five cases will be described.

In the various graphs of Figure 12, the lower horizontal line represents the UCL point with factor = 10 and the upper horizontal line with factor = 20. In addition, the first 5 days of each graph are used as HDS and the vacuum pump is replaced at the end.

12, it can be seen that the change pattern of the T ² value is divided into two cases.

That is, in cases 1, 3, and 5, the value of T ² has already increased significantly before the replacement of the vacuum pump, whereas in cases 2 and 4, the value of T ² remains relatively small and only after the vacuum pump is replaced It is rising to a value.

Currently, the semiconductor production site decides when to replace the vacuum pump with its own evaluation criteria. This is done by observing only a few external phenomena, which is a comprehensive consideration of the overall characteristics of the system including the vacuum pump. Since it is not possible to see the replacement point of the vacuum pump, it cannot be considered absolute.

In this sense, in case 1, 3 and 5, the replacement timing of the vacuum pump can be considered to be later than the optimum time. In case 2 and 4, the vacuum pump is too prematurely replaced. In this case, if the vacuum pump is continuously replaced without replacing the T ² value increases as in Cases 1, 3, and 5.

Therefore, in cases 2 and 4, it can not be assumed that the normal operation is performed, but at least the value of T ² may not be considerably out of the UCL, which provides a clue to the UCL factor determination. In other words, considering the T ² distribution of cases 2 and 4 together with the previous result that the UCL factor should be determined between 10 and 20, the UCL factor may be selected as 20.

Since the UCL factor is set to 20, the graphs of FIG. 12 are analyzed based on the UCL factor.

In cases 2 and 4, there is a section where the T ² value exceeds UCL for a while before the vacuum pump is replaced, but the trend does not last long and is restored to the normal range. It is called the UCL should focus on how you transformed the basis of the absolute value is not in itself just one indicator rather than to pay attention to changes in the local T ² of the overall T ² trend UCL, which suggested the possibility of failure do.

On the other hand, in case 1, case 3 and case 5, signs of failure have already appeared before the replacement time of the vacuum pump. In particular, it is necessary to pay attention to cases 1 and 5. In Case 1, the value of T ² gradually increases beyond the UCL at some point, while in Case 5, the value of T ² increases abruptly and keeps increasing. In other words, in case 1, it is easy to catch the signs of gradual deterioration before the vacuum pump is completely out of order, which causes trouble in the operation, while in case 5, the failure occurs in a moment. There is no time to grasp. In Case 3, these two situations are compounded.

When combined with the failure factors of the vacuum pump, two patterns are clearly revealed. That is, there will be a failure factor that gradually degrades the performance of the vacuum pump and a failure factor that rapidly drops in performance at a moment. The former is easy to predict, while the latter is difficult to detect.

Therefore, the present invention uses the MPCA technique, which is a multivariate statistical technique, to diagnose the state of the vacuum pump and to indicate whether there is an abnormal symptom by expressing the characteristics of the entire system as one representative factor of T ² and selecting UCL to determine normal operation. By selecting as a reference, abnormal symptoms of the vacuum pump in the semiconductor manufacturing process and the like can be detected and coped with in a timely manner.

In other words, by developing an algorithm that selects batch data based on the intake pressure variable and applies outlier elimination to ODS as well as HDS, it is possible to clearly determine the distribution trend of T ² .

In addition, the optimized length of HDS can be obtained from the data set obtained from the vacuum pump for about 5 days, and each vacuum pump is clearly different from each other and every vacuum is confirmed by rapidly increasing the T ² value after replacing the vacuum pump. You will find that you need to reset the HDS every time you replace the pump.

Also, even if T ² temporarily leaves the UCL, if the trend returns to the normal range, the UCL criterion can be obtained from the mean and standard deviation of HDS T ² .

Therefore, according to the present invention, a method for diagnosing a state of a vacuum pump for a semiconductor process operating under harsh operating conditions based on the use of multivariate statistical analysis techniques based on the correlation of signals obtained from a vacuum pump by a plurality of sensors is proposed. By using the signals obtained from the vacuum pump, it is possible to predict the abnormal condition of the vacuum pump. Based on this, if a lot of data is accumulated in the field such as semiconductor manufacturing process and attempted to be combined with actual physical factors or failure factors, more practical and sophisticated condition diagnosis method can be provided.

Claims (5)

The T ² value calculating T ² values, and using a multivariate statistical technique based on multi-component analysis (Multiway Principal Component Analysis) receives a signal about the condition of the vacuum pump in a normal operating range from a plurality of sensors of the vacuum pump A first step of selecting UCL as a standard for determining abnormal symptoms; A second step of receiving a signal of a state of a vacuum pump after a normal operating range from the plurality of sensors and calculating a T ² value using a multivariate statistical technique based on multi-way principal component analysis; And A third step of notifying whether the vacuum pump has an abnormal symptom by comparing the UCL selected as the reference in the first step and the T ² value obtained in the second step; Vacuum pump state diagnostic method using a multi-principal component analysis-based statistical technique comprising a. The method of claim 1, The plurality of sensors include an intake pressure sensor, a pressure pump acceleration sensor, three dry pump acceleration sensors, an acoustic sensor, an exhaust pressure sensor, a pressure pump current sensor, and a dry pump current sensor. Vacuum pump condition diagnosis method using. The method of claim 1, The T ² value may include: a batch generation process of extracting signals obtained in a section in which a semiconductor manufacturing process is actually performed among signals for a vacuum pump state obtained by the plurality of sensors and storing the extracted signals as batch data; A Dynamic Time Warping Algorithm process of adjusting the batch data to the same length using a Dynamic Time Warping Algorithm technique; The batch data is equally matched through a centering process for aligning the average points in a form of subtracting the average value of the batch data from the batch data and a scaling process for dividing the batch data by the standard deviation, and then the main component ( Multi-Principal Component Analysis (T _score ), P coordinate _loading and T ² ; And Purging Outliers process of removing batch data showing unusual trends out of many trends among batch data by a Smoothing Technique technique; Vacuum pump status diagnosis method using a multi-principal component analysis-based statistical technique, characterized in that obtained through. The method of claim 3, The control of the batch length, after obtaining the accumulation distance, selects the optimal path (Optimal Path) according to the local-global constraints and based on the averaging process based on the multi-component analysis based statistics, characterized in that Vacuum Pump Condition Diagnosis Method. The method of claim 1, In the first step, the T ² value for selecting the UCL, which is a reference for identifying the abnormal symptom of the vacuum pump, is calculated every time the vacuum pump is replaced. How to diagnose the condition.

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